Publications Related to the Project

1. Axially Deformed Solution of the Skyrme-Hartree-Fock-Bogoliubov Equations Using the Transformed Harmonic Oscillator Basis. The program HFBTHO (v1.66p)
   M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, and P. Ring,
   Comp. Phys. Commun. 167, 43­63 (2005)
   In this work, we describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogoliubov calculations with Skyrme-forces and a zero-range pairing interaction using Harmonic-Oscillator and/or Transformed Harmonic-Oscillator states. The particle-number symmetry is approximately restored using the Lipkin-Nogami prescription, followed by an exact particle number projection after the variation. The program can be used in a variety of applications, including systematic studies of wide ranges of nuclei, both spherical and axially deformed.

2. Systematic Study of Deformed Nuclei at the Drip Lines and Beyond
   M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, and D. J. Dean
   Phys. Rev. C 68, 054312 (2003)
   This work contains the first large-scale application of the code HFBTHO (v1.66p) described above. The HFB+THO framework that follows accurately reproduces the results of coordinate-space HFB calculations for spherical nuclei, including those that are weakly bound. Furthermore, it is fully automated, facilitating its use in systematic investigations of large sets of nuclei throughout the periodic table. As a first application, we have carried out calculations using the Skyrme Force SLy4 and volume pairing, with exact particle number projection following application of the Lipkin-Nogami prescription. Calculations were performed for all even-even nuclei from the proton drip line to the neutron drip line having proton numbers Z=2,4,...,108 and neutron numbers N=2,4,...,188.

3. Local Density Approximation for Proton-Neutron Pairing Correlations. Formalism
   E. Perlińska, S. G. Rohoziński, J. Dobaczewski, and W. Nazarewicz
   Phys. Rev. C 69, 014316 (2004)
   In this study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The complete list of expressions required to calculate total energy is presented.

4. Particle-Number-Projected HFB method with Skyrme Forces and Delta Pairing
   M. Stoitsov, J. Dobaczewski, and W. Nazarewicz Proc. 8th International Sping Seminar on Nuclear Physics, Key Topics in Nuclear Structure, Paestum, Italy, 23-27 May 2004. Ed. by Aldo Covello (World Scientific, Singapore); pp. 167-176.
   Particle-number restoration before variation is implemented in the HFB method employing the Skyrme force and zero-range delta pairing. Results are compared with those obtained within the Lipkin-Nogami method, with or without the particle-number projection after variation. Shift invariance property is proven to be valid also in the case of density functional calculations which allows the well known singularity in PNP HFB calculations to be safely avoided.

5. Shell Energy in the Heaviest Nuclei Using the Green's Function Oscillator Expansion Method
   S. Ćwiok, W. Dudek, P. Kaszyński, and W. Nazarewicz
   Eur. Phys. J. A 23, 387-393 (2005)
   In this work, the Green's function oscillator expansion method and the generalized Strutinsky smoothing procedure are applied to shell corrections in the heaviest elements. A microscopic-macroscopic method with a finite, deformed Woods-Saxon potential is used. The stability condition for the shell correction is discussed in detail and the parameters defining the smoothing procedure are carefully determined. It is demonstrated that the spurious contribution to the total binding energy due to the unphysical particle gas that appears in the standard method can be as large as 1.5 MeV for weakly bound neutron-rich superheavy nuclei, but the effect on energy differences (e.g., alpha decay values) is fairly small.

6. Skyrme Hartree Fock Calculations of Fission Barriers of The Heaviest and Superheavy Nuclei
   A. Staszczak, J. Dobaczewski, and W. Nazarewicz
   Int. J. Mod. Phys. E 14 (2005) 395-402
   In this work, self-consistent Skyrme-Hartree-Fock (SHF) calculations of static fission barriers are presented for even-even Fermium isotopes as well as for superheavy even-even N=184 isotones. In the particle-hole channel, we use the SLy4 Skyrme parametrization, while in the particle-particle channel we take a T=1 seniority pairing force treated in the BCS approximation. The influence of reflection-asymmetric and triaxial degrees of freedom on the static fission paths are investigated.

7. Self-Consistent Study of Fission Barriers of Even-Even Superheavy Nuclei
   A. Staszczak, J. Dobaczewski, and W. Nazarewicz
   Proc. "3rd International Workshop on Nuclear Fission and Fission-Product Spectroscopy", 11-14 May 2005 Cadarache, France, AIP Conf. Proc. 798, 93 (2005).
   In this work, static fission barriers of even-even nuclei with 100≤Z≤110 are investigated using the Skyrme-Hartree-Fock model with particular attention paid to symmetry-breaking effects along the fission path. Effects of reflection-asymmetric and triaxial degrees of freedom on the fission barriers are discussed.

8. Shape coexistence and triaxiality in the superheavy nuclei
   S. Ćwiok, P.-H. Heenen, and W. Nazarewicz
   Nature 433, 705-709 (2005).
   Superheavy nuclei represent the limit of nuclear mass and charge; they inhabit the remote corner of the nuclear landscape, whose extent is unknown. The discovery of new elements with atomic numbers Z≥110 has brought much excitement to the atomic and nuclear physics communities. The existence of such heavy nuclei hangs on a subtle balance between the attractive nuclear force and the disruptive Coulomb repulsion between protons that favours fission. Here we model the interplay between these forces using self-consistent energy density functional theory; our approach accounts for spontaneous breaking of spherical symmetry through the nuclear Jahn­Teller effect. We predict that the long-lived superheavy elements can exist in a variety of shapes, including spherical, axial and triaxial configurations. In some cases, we anticipate the existence of metastable states and shape isomers that can affect decay properties and hence nuclear half-lives.

9. Large-Scale HFB Calculations for Deformed Nuclei with the Exact Particle-Number Projection
   M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, and J. Terasaki
   Eur. Phys. J. A 25, s1.567-s1.568 (2005).
   Recent theoretical advances in the large-scale HFBTHO calculations of nuclear ground-state properties are presented with the emphasis on the exact particle number projection. The applicability of the widely used Lipkin-Nogami procedure is discussed together with the analysis of the particle number projection after variation.

10. On the non-Unitarity of the Bogoliubov Transformation due to the Quasiparticle Space Truncation
    J. Dobaczewski, P.J. Borycki, W. Nazarewicz, and M. Stoitsov
    Eur. Phys. J. A 25, s1.541-s1.542 (2005).
    We show that due to the energy cutoff in the Hartree-Fock-Bogoliubov quasiparticle space, the Bogoliubov transformation becomes non-unitary. We propose a method of restoring the unitarity by introducing a truncated single-particle Hilbert space, in which the HFB equations are to be solved.

11. Nuclear Fission with Mean-Field Instantons
    J. Skalski
    Proc. Int. Workshop on "New Developments in Nuclear Self-Consistent Mean-Field Theories", Yukawa Institute for Theoretical Physics, Kyoto, Japan May 30 - June 1, 2005; YITP-W-05-01 (Soryushi-ron Kenkyu) p. B62.
    Quantum tunneling process in spontaneous nuclear fission may be analyzed in terms of imaginary-time solutions to selfconsistent mean-field theory. An advantage of such formulation is that it identifies a unique semiclassical prediction for the dominant (exponential) part of the fission half-life as instanton action, and that this prediction is based solely on the underlying mean-field theory (there is no arbitrariness in the selection of mass parameters). We try to advance a variational approach to finding instanton action, hoping that a good estimate of action may be easier to find than that of the instanton itself.

12. From Finite Nuclei to the Nuclear Liquid Drop: Leptodermous Expansion Based on the Self-consistent Mean-Field Theory
    P.-G. Reinhard, M. Bender, W. Nazarewicz, and T. Vertse
    Phys. Rev. C 73, 014309 (2006)
    The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of inverse nuclear radius and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons. The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.

13. Fission Barriers of Superheavy Nuclei in the Skyrme-Hartree-Fock Model
    A. Staszczak, J. Dobaczewski, and W. Nazarewicz
    Int. J. Mod. Phys. E15, 302 (2006)
    Constrained Skyrme-Hartree-Fock calculations of static fission barriers are performed for even-even elements with Z=100-110 as well as for superheavy N=184 isotones. In our study we use the Skyrme parametrization SLy4 and a seniority pairing force treated in the BCS approximation. The computations are carried out applying a code that makes it possible to break all self-consistent symmetries of the nuclear mean field, including axial symmetry and reflection symmetry. The influence of reflection-asymmetric and triaxial degrees of freedom on fission barriers are discussed.

14. Large-Scale Self-Consistent Nuclear Mass Calculations
    M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz and P. Borycki
    Int.J. Mass Spectrometry 251, 243 (2006).
    The program of systematic large-scale self-consistent nuclear mass calculations that is based on the nuclear density functional theory represents a rich scientific agenda that is closely aligned with the main research directions in modern nuclear structure and astrophysics, especially the radioactive nuclear beam physics. The quest for the microscopic understanding of the phenomenon of nuclear binding represents, in fact, a number of fundamental and crucial questions of the quantum many-body problem, including the proper treatment of correlations and dynamics in the presence of symmetry breaking. Recent advances and open problems in the field of nuclear mass calculations are presented and discussed.

15. Relative kinetic energy correction to self-consistent fission barriers
    J. Skalski
    Phys. Rev. C 74, 051601(R) (2006)
    The effect of spurious relative kinetic energy removal on the fission barriers is discussed within the Skyrme Hartree-Fock method. Calculations for medium-heavy nuclei show that this correction is large and in the right direction.

16. Pairing renormalization and regularization within the local density approximation
    P.J. Borycki, J. Dobaczewski, W. Nazarewicz and M. V. Stoitsov
    Phys. Rev. C73, 044319 (2006)
    We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure makes it a method of choice for future applications.

17. Collective inertia and fission barriers within the Skyrme-Hartree-Fock theory
    A. Baran, A. Staszczak, J. Dobaczewski, and W. Nazarewicz
    Int. J. Mod. Phys. E16, 443 (2007)
    Spontaneous fission barriers, quadrupole inertia, and zero-point quadrupole-energy corrections are calculated for 252,256,258Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing dynamical inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.

18. Pairing properties of superheavy nuclei
    A. Staszczak, J. Dobaczewski, and W. Nazarewicz
    Int. J. Mod. Phys. E 16, 310 (2007)
    Pairing properties of even-even superheavy N=184 isotones are studied within the Skyrme-Hartree-Fock+BCS approach. In the particle-hole channel we take the Skyrme energy density functional SLy4, while in the particle-particle channel we employ the seniority pairing force and zero-range delta-interactions with different forms of density dependence. We conclude that the calculated static fission trajectories weakly depend on the specific form of the delta-pairing interaction. We also investigate the impact of triaxiality on the inner fission barrier and find a rather strong Z dependence of the effect.

19. Bimodal fission in the Skyrme-Hartree-Fock approach
    A. Staszczak, J. Dobaczewski, and W. Nazarewicz
    Acta. Phys. Pol. B, 38, 1589 (2007)
    Spontaneous-fission properties of 256Fm, 258Fm, and 260Fm isotopes are studied within the Skyrme-Hartree-Fock+BCS framework. In the particle-hole channel we take the Skyrme SkM* effective force, while in the particle-particle channel we employ the seniority pairing interaction. Three static fission paths for all investigated heavy fermium isotopes are found. The analysis of these fission modes allows to describe observed asymmetric fission of 256Fm, as well as bimodal fission of 258Fm and symmetric fission in 260Fm.

20. Variation after particle-number projection for the Hartree-Fock-Bogoliubov method with the Skyrme energy density functional
    M. V. Stoitsov, J. Dobaczewski, R. Kirchner, W. Nazarewicz, and J. Terasaki
    Phys. Rev. C 76, 014308 (2007)
    Variation after particle-number restoration was incorporated for the first time into the Hartree-Fock-Bogoliubov framework employing the Skyrme energy density functional with zero-range pairing. The resulting projected HFB equations can be expressed in terms of the local gauge-angle-dependent densities. Results of projected calculations are compared with those obtained within the Lipkin-Nogami method in the standard version and with the Lipkin-Nogami method followed by exact particle-number projection

21. Particle-Number Projection and the Density Functional Theory
    J. Dobaczewski, M. V. Stoitsov, W. Nazarewicz, and P. -G. Reinhard
    Phys. Rev. C 76, 054315 (2007)
    In the framework of the Density Functional Theory for superconductors, we studied the restoration of the particle number symmetry by means of the projection technique. Conceptual problems were outlined and numerical difficulties discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the Density Functional Theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.

22. Adiabatic fusion barriers from selfconsistent calculations
    J. Skalski
    Phys. Rev. C 76, 044603 (2007)
    We studied adiabatic fusion barriers within the static Hartree-Fock method with the effective Skyrme interactions SkM* and SLy6. We discussed the problem of kinetic energy of the relative motion becoming spurious for separate fragments, relevant for fusion and fission barriers. We also discussed specific assumptions necessary to compensate for the non-uniqueness of the static method. Barriers obtained with two forces agree to within 2 MeV and seem nearly decoupled from errors in binding energies, specific to each force. For a number of reactions, comparisons are made with experimental estimates of barriers and barriers calculated with the frozen densities. The adiabatic barriers are generally lower than the experimental estimates. The offset amounts to less than 3 MeV in lighter systems and varies between zero and ~10 MeV in heavy ones. We also calculated HF energy surfaces for three heavy systems looking for a relation between adiabatic potential and the fusion hindrance at large ZTZP. One can see a link between quasi-fission and the force opposing fusion, acting inside the Coulomb barrier. One surface illustrates the identity of the adiabatic fusion barrier with the fission saddle of a compound nucleus.

23. Empirical proton-neutron interactions and nuclear density functional theory: global, regional, and local comparisons
    M. Stoitsov, R.B. Cakirli, R.F. Casten, W. Nazarewicz, and W. Satula
    Phys. Rev. Lett. 98, 132502 (2007)
    Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.

24. Universal Nuclear Energy Density Functional: Computing Atomic Nuclei
    G.F. Bertsch, D.J. Dean, and W. Nazarewicz
    SciDAC Review, Issue 6, 42 (2007)
    A popular article for the SciDAC Review that also features our fission research.

25. Nuclear fission with mean-field instantons
    J. Skalski
    Phys. Rev. C 77, 064610 (2008)
    We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons - periodic imaginary-time solutions to time-dependent mean-field equations - that allows for a comparison with more familiar and used generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfils the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions of energy conservation and the velocity-momentum relations. In the adiabatic limit the instanton method reduces to the time-odd ATDHF equation, with collective mass including the time-odd Thouless-Valatin term, while the GCM mass completely ignores velocity-momentum relations. This implies that GCM inertia generally overestimates instanton-related decay rate. The very existence of the minimum principle offers a hope for a variational search for instantons, and sharply contrasts with absence of a suitable functional for real-time mean-field dynamics. After the inclusion of pairing, the instanton equations and the variational principle can be expressed in terms of the imaginary-time-dependent Hartree-Fock- Bogolyubov (TDHFB) theory. The adiabatic limit of this theory reproduces ATDHFB inertia.

26. Relative motion correction to fission barriers
    J. Skalski
    Int. J. Mod. Phys. E 17, 151 (2008).
    We discuss the effect of kinetic energy of the relative motion becoming spurious for separate fragments on the selfconsistent mean-field fission barriers. The treatment of the relative motion in the cluster model is contrasted with the necessity of a simpler and approximate approach in the mean-field theory. A scheme of the energy correction to the Hartree-Fock is proposed. The results obtained with the effective Skyrme interaction SLy6 show that the correction, previously estimated as ~8 MeV in A=70-100 nuclei, amounts to 4 MeV in the medium heavy nucleus 198Hg and to null in 238U. However, the corrected barrier implies a shorter fission half-life of the latter nucleus. The same effect is expected to lower barriers for multipartition (i.e. ternary fission, etc) and make hyperdeformed minima less stable.

27. Broyden's Method in Nuclear Structure Calculations
    A. Baran, A. Bulgac, M.M. Forbes, G. Hagen, W. Nazarewicz, N. Schunck and M.V. Stoitsov
    Phys. Rev. C 78, 014318 (2008).
    Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broyden's method a tool of choice for large-scale nuclear structure calculations.

28. Deformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations
    J.C. Pei, M.V. Stoitsov, G.I. Fann, W. Nazarewicz, N. Schunck and F.R. Xu
    Phys. Rev. C 78, 064306 (2008).
    The coordinate space formulation of the Hartree-Fock-Bogoliubov (HFB) method enables self-consistent treatment of mean-field and pairing in weakly bound systems whose properties are affected by the particle continuum space. Of particular interest are neutron-rich, deformed drip-line nuclei which can exhibit novel properties associated with neutron skin. To describe such systems theoretically, we developed an accurate 2D lattice Skyrme-HFB solver HFB-AX based on B-splines. Compared to previous implementations, we made a number of improvements aimed at boosting the solver's performance. These include: explicit imposition of axiality and space inversion, use of the modified Broyden's method to solve self-consistent equations, and a partial parallelization of the code. {hfbax} has been benchmarked against other HFB solvers, both spherical and deformed, and the accuracy of the B-spline expansion was tested by employing the multiresolution wavelet method. Illustrative calculations are carried out for stable and weakly bound nuclei at spherical and very deformed shapes, including constrained fission pathways. In addition to providing new physics insights, {hfbax} can serve as a useful tool to assess the reliability and applicability of coordinate-space and configuration-space HFB solvers, both existing and in development.

29. Adiabatic Mass Parameters for Spontaneous Fission
    A. Baran, J.A. Sheikh, and W. Nazarewicz
    Int. J. Mod. Phys. E 18, 1054 (2009).
    The collective mass tensor derived from the adiabatic time-dependent Hartree-Fock-Bogoliubov theory, perturbative cranking approximation, and the Gaussian overlap approximation to the generator coordinate method is discussed. Illustrative calculations are carried out for 252-Fm using the nuclear density functional theory with Skyrme interaction SkM* and seniority pairing.

30. Fission Quadrupole Mass Parameters in HF+BCS and HFB Methods
    A. Baran, J.A. Sheikh, A. Staszczak, and W. Nazarewicz
    Int. J. Mod. Phys. E 18, 1049 (2009).
    The self-consistent Hartree-Fock+BCS and Hartree-Fock-Bogoliubov methods are compared at large nuclear deformations. The calculations are carried out for the fission pathway and quadrupole mass parameter of 252Fm.

31. Fission barriers of compound superheavy nuclei
    J.C. Pei, W. Nazarewicz, J.A. Sheikh, and A.K. Kerman, Phys. Rev. Lett. 102, 192501 (2009)
    Phys. Rev. Lett. 102, 192501 (2009).
    The dependence of fission barriers on the excitation energy of the compound nucleus impacts the survival probability of superheavy nuclei synthesized in heavy-ion fusion reactions. In this work, we investigated the isentropic fission barriers with nuclear DFT. For nuclei around 278-112 produced in Òcold fusionÓ reactions, we predicted a more rapid decrease of fission barriers with excitation energy as compared to the nuclei around 292-114 synthesized in "hot fusion". The relationship between isothermal and isentropic descriptions has been demonstrated. The effect of the particle gas is found to be negligible in the range of temperatures studied.

32. Systematic study of fission barriers of excited superheavy nuclei
    J.A. Sheikh, W. Nazarewicz, and J.C. Pei
    Phys. Rev. C 80, 011302(R) (2009)
    In this paper, we performed systematic study of fission-barrier dependence on excitation energy using the self-consistent finite-temperature Hartree-Fock+BCS (FT-HF+BCS) formalism. The calculations have been carried out for even-even superheavy nuclei with Z ranging between 110 and 124. For an accurate description of fission pathways, the effects of triaxial and reflection-asymmetric degrees of freedom have been fully incorporated. Our survey demonstrates that the dependence of isentropic fission barriers on excitation energy changes rapidly with particle number, pointing to the importance of shell effects even at large excitation energies characteristic of compound nuclei. The fastest decrease of fission barriers with excitation energy is predicted for deformed nuclei around N=164 and spherical nuclei around N=184 that are strongly stabilized by ground-state shell effects. For nuclei 240Pu and 256Fm, which exhibit asymmetric spontaneous fission, our calculations predict a transition to symmetric fission at high excitation energies due to the thermal quenching of static reflection asymmetric deformations.

33. Microscopic description of complex nuclear decay: Multimodal fission
    A. Staszczak, A. Baran, J. Dobaczewski, and W. Nazarewicz
    Phys. Rev. C 80, 014309 (2009).
    In this paper, we described a study of spontaneous fission using the symmetry-unrestricted nuclear density functional theory. Our results show that the observed bimodal fission can be explained in terms of pathways in multidimensional collective space corresponding to different geometries of fission products. We also predict a new phenomenon of trimodal spontaneous fission for some rutherfordium, seaborgium, and hassium isotopes.

34. Toroidal super-heavy nuclei in Skyrme-Hartree-Fock approach
    A. Staszczak and C. Y. Wong
    Acta Phys. Polonica B 40, 753 (2009).
    Within the self-consistent constraint SkyrmeÐHartreeÐFock+BCS model, we found equilibrium toroidal nuclear density distributions in the region of superheavy elements. For nuclei with a sufficient oblate deformation, it becomes energetically favourable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus = 1) SHF+BCS solution relative to the compact (genus = 0) ground state energy is strongly dependent both on the atomic number Z and the mass num- ber A. We discuss the region of Z and A where the toroidal SHF+BCS total energy begins to be a global minimum.

35. Thermal Fission Pathways in 232-Th
    J.D. McDonnell, W. Nazarewicz, J.A. Sheikh
    Proc. 4th International Workshop on Fission and Fission Product Spectroscopy, AIP Conference Proceedings 1175, 371, (2009)
    Two-dimensional thermal potential energy surfaces have been investigated for 232-Th using the finite temperature HF+BCS approach with Skyrme energy density functional SkM*. At low excitation energy, the calculated static fission path goes through families of triaxial and reflection-asymmetric shapes. With increasing excitation energy, the shallow third minimum associated with a nonzero octupole moment becomes washed out, and the static fission valley moves towards the axial and reflection-symmetric limit.

36. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.: (VI) hfodd (v2.40h): A new version of the program
    J. Dobaczewski, W. Satula, B. G. Carlsson, J. Engel, P. Olbratowski, P. Powalowski, M. Sadziak, J. Sarich, N. Schunck, A. Staszczak, M. V. Stoitsov, M. Zalewski, and H. Zdunczuk
    Comput. Phys. Comm. 180, 2361 (2009).
    We describe the new version of the code hfodd which solves the nuclear Skyrme- Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state- dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected two insignificant errors.

37. Fission barriers and neutron gas in compound superheavy nuclei
    J.C. Pei, W. Nazarewicz, J.A. Sheikh, and A.K. Kerman
    Nucl. Phys. A 834, 381c (2010).
    Fission and neutron emission are the principal cooling mechanisms of the compound superheavy nuclei. In the framework of the Finite-Temperature Hartree-Fock-Bogoliubov method, the fission barriers and neutron gas have been studied in the excited superheavy systems. Very different energy dependence of fission barriers has been found for 278112 and 292114. On the other hand, the energy dependence of thermal neutron gas has been found to be almost identical for both systems.

38. Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
    A. Staszczak, M.Stoitsov, A. Baran, and W. Nazarewicz
    Eur. Phys. J. A 46, 85 (2010).
    The augmented Lagrangiam method, widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov variant. The ALM allows precise calculations of multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.

39. Computing Heavy Elements
    N. Schunck, A. Baran, M. Kortelainen, J. McDonnell, J. More, W. Nazarewicz, J. Pei, J. Sarich, J. Sheikh, A. Staszczak, M. Stoitsov, and S.M. Wild
    Proceedings, SciDAC 2011 conference, Jul. 10-15, 2011, Denver, CO
    Reliable calculations of the structure of heavy elements are crucial to address fundamental science questions. Applications relevant for energy production, medicine, or national security also rely on theoretical predictions of basic properties of atomic nuclei. Heavy elements are best described within the nuclear density functional theory (DFT) and its various extensions. While relatively mature, DFT has never been implemented in its full power, as it relies on a very large number of expensive calculations. The advents of leadership-class computers, as well as dedicated large-scale collaborative efforts, have dramatically changed the field. This article gives an overview of the various computational challenges related to the nuclear DFT, as well as some of the recent achievements.

40. Towards a Predictive Theory of Fission
    W. Nazarewicz and J. McDonnell
    Stewardship Science Academic Alliances Annual 2011 DOE/NA-0016, p.18 (2011).

41. Surface Symmetry Energy of Nuclear Energy Density Functionals
    N. Nikolov, N. Schunck, W. Nazarewicz, M. Bender, and J. Pei
    Phys. Rev. C 83, 034305 (2011)
    We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron- rich matter and description of fission rates for r-process nucleosynthesis.

42. Fission half lives of fermium isotopes within Skyrme Hartree-Fock-Bogoliubov theory
    A. Baran, A. Staszczak, and W. Nazarewicz
    Int. J. Mod. Phys. E 20, 557 (2011)
    Nuclear fission barriers, mass parameters and spontaneous fission half lives of fermium isotopes calculated in a framework of the Skyrme Hartree-Fock-Bogoliubov model with the SkM* force are discussed. Zero-point energy corrections in the ground state are determined for each nucleus using the Gaussian overlap approximation of the generator coordinate method and in the cranking formalism. Results of spontaneous fission half lives are compared to experimental data.

43. Breaking of axial and reflection symmetries in spontaneous fission of fermium isotopes
    A. Staszczak, A. Baran, and W. Nazarewicz
    Int. J. Mod. Phys. E 20, 552 (2011)
    The nuclear fission phenomenon is a magnificent example of a quantal collective motion during which the nucleus evolves in a multidimensional space representing shapes with different geometries. The triaxial degrees of freedom are usually important around the inner fission barrier, and reduce the fission barrier height by several MeV. Beyond the inner barrier, reflection-asymmetric shapes corresponding to asymmetric elongated fragments come into play. We discuss the interplay between different symmetry breaking mechanisms in the case of even-even fermium isotopes using the Skyrme HFB formalism.

44. Quadrupole collective inertia in nuclear fission: cranking approximation
    A. Baran, J. A. Sheikh, J. Dobaczewski and W. Nazarewicz
    Phys. Rev. C 84, 054321 (2011)
    A collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian overlap approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256-Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

45. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): a new version of the program
    N. Schunck, J. Dobaczewski, J. McDonnell, W. Satula, J.A. Sheikh, A. Staszczak, M. Stoitsov, and P. Toivanen
    Comput. Phys. Commun. 183, 166 (2012) Catalogue identifier: ADFL_v3_0
    We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.

46. Fission modes of mercury isotopes
    M. Warda, A. Staszczak, and W. Nazarewicz.
    Phys. Rev. C 86, 024601 (2013)
    Recent experiments on beta-delayed fission in the mercury-lead region and the discovery of asymmetric fission in 180-Hg have stimulated theoretical interest in the mechanism of fission in heavy nuclei. In this work, we studied fission modes and fusion valleys in 180-Hg and 198-Hg to reveal the role of shell effects in pre-scission region and explain the experimentally observed fragment mass asymmetry and its variation with A. We used the self-consistent nuclear density functional theory employing Skyrme and Gogny energy density functionals. The potential energy surfaces in multi-dimensional space of collective coordinates, including elongation, triaxiality, reflection-asymmetry, and necking, were calculated. The asymmetric fission valleys - well separated from fusion valleys associated with nearly spherical fragments - were found in in both cases considered. The density distributions at scission configurations were studied and related to the experimentally observed mass splits. We predicted a transition from asymmetric fission in 180-Hg towards more symmetric distribution of fission fragments in 198-Hg - consistent with experiment.

47. Nuclear energy density optimization: Large deformations
    M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, and M.V. Stoitsov.
    Phys. Rev. C 85, 024304 (2012)
    A new Skyrme-like energy density suitable for studies of strongly elongated nuclei has been determined in the framework of the Hartree-Fock-Bogoliubov theory using the recently developed model-based, derivative-free optimization algorithm. A sensitivity analysis at the optimal solution has revealed the importance of states at large deformations in driving the parameterization of the functional. The good agreement with experimental data on masses and separation energies, achieved with the previous parameterization, is largely preserved. In addition, the new energy density gives a much improved description of the fission barriers in 240-Pu and neighboring nuclei.

48. Quality Input for Microscopic Fission Theory
    W. Nazarewicz, N. Schunck, and S. Wild
    Stockpile Stewardship Quarterly, 2(1), 2012, p. 6.

49. Spontaneous fission modes and lifetimes of superheavy elements in the nuclear density functional theory
    A. Staszczak, A. Baran, and W. Nazarewicz
    Phys. Rev. C 87, 024320 (2013)
    The reactions with the neutron-rich 48-Ca beam and actinide targets resulted in the detection of new superheavy (SH) nuclides with Z=104-118. The unambiguous identification of the new isotopes, however, still poses a problem because their alpha-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between alpha-decay and SF channels in SH nuclei is, therefore, of crucial importance for our ability to map the SH region and to assess its extent. In this work, we performed self-consistent calculations of the competing decay modes of even-even SH isotopes. We used the state-of-the-art computational framework based on self-consistent symmetry-unrestricted nuclear density functional theory capable of describing the competition between nuclear attraction and electrostatic repulsion. The collective mass tensor of the fissioning superfluid nucleus was computed by means of the cranking approximation to the adiabatic time-dependent HFB approach. Breaking axial symmetry and parity turned out to be crucial for a realistic estimate of collective action; it results in lowering SF lifetimes by more than 7 orders of magnitude in some cases. We predicted two competing SF modes: reflection symmetric modes and reflection asymmetric modes. The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by 280-Hs, 284-Fl, and 284-Uuo that separates the regions of SH nuclei synthesized in cold-fusion and hot-fusion reactions. The region of long-lived SH nuclei is expected to be centered on 294-Ds with a total half-life of about 1.5 days. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.

50. Third minima in thorium and uranium isotopes in a self-consistent theory
    J. D. McDonnell, W. Nazarewicz, and J. A. Sheikh
    Phys. Rev. C 87, 054327 (2013)
    Well-developed third minima, corresponding to strongly elongated and reflection-asymmetric shapes associated with dimolecular configurations, have been predicted in some non-self-consistent models to impact fission pathways of thorium and uranium isotopes. These predictions have guided the interpretation of resonances seen experimentally. On the other hand, self-consistent calculations consistently predict very shallow potential-energy surfaces in the third minimum region. In this work, we investigated the interpretation of third-minimum configurations in terms of dinuclear (cluster) states. We studied the isentropic potential-energy surfaces of selected even-even thorium and uranium isotopes at several excitation energies. In order to understand the driving effects behind the presence of third minima, we investigated the interplay between pairing and shell effects. We predicted very shallow or no third minima in the potential-energy surfaces of 232-Th and 232-U. In the lighter Th and U isotopes with N=136 and 138, the third minima seem to be better developed. We showed that the reflection-asymmetric configurations around the third minimum can be associated with dinuclear states involving the spherical doubly magic 132-Sn and a lighter deformed Zr or Mo fragment. We also studied isotopic chains to demonstrate the evolution of the depth of the third minimum with neutron number. We showed that the neutron shell effect that governs the existence of the dinuclear states around the third minimum is consistent with the spherical-to-deformed shape transition in the Zr and Mo isotopes around N=58. The thermal reduction of pairing, and related enhancement of shell effects, at small excitation energies help to develop deeper third minima. At large excitation energies, shell effects are washed out and third minima disappear altogether.

51. Microscopic Description of Nuclear Fission: Fission Barrier Heights of Even-Even Actinides
    J. McDonnell, N. Schunck, and W. Nazarewicz
    Fission and Properties of Neutron-Rich Nuclei, edited by: J H Hamilton and A V Ramayya (World Scientific, 2013), p. 597 LLNL-PROC-612272
    We evaluated the performance of modern nuclear energy density functionals for predicting inner and outer fission barrier heights and energies of fission isomers of even-even actinides. For isomer energies and outer barrier heights, we find that the self-consistent theory at the HFB level is capable of providing quantitative agreement with empirical data. In particular, the recently developed UNEDF1 energy density functional yields predictions that agree well with experimental values and are on a par with, or better, than predictions of other self-consistent or macroscopic-microscopic models. While the inner barrier heights are systematically overestimated, one also needs to bear in mind that empirical values are subject to error that is at least 0.3MeV. As fit-observables are selected for future optimizations, it will be valuable to consider if additional data such as one-neutron separation energy may help to better constrain fission barrier heights.

52. Systematic study of fission fragment mass distribution using 2-dimensional Langevin dynamics
    J. Sadhukhan and S. Pal
    Fission and Properties of Neutron-Rich Nuclei, edited by: J H Hamilton and A V Ramayya (World Scientific, 2013), p. 564
    The fragment mass distribution from fission of hot nuclei is studied in the framework of two-dimensional Langevin equations. First, the finite-range liquid drop model potential, collective inertia and one-body dissipation strength are calculated for different compound nuclei over a wide range of fissility parameter. Then, the mass asymmetry coordinate distribution is obtained from the dynamical calculation both at the saddle and the scission regions to explain the role of saddle-to-scission dynamics. Specifically, the competition between dissipative and conservative forces in determining the fragment mass distribution is investigated.

53. Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new version of the program
    M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild
    Comput. Phys. Commun. 184, 1592-1604 (2013)
    We published the new version 2.00d of the code HFBTHO that solves the nuclear HF or HFB problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas.

54. Spontaneous fission lifetimes from the minimization of self-consistent collective action
    Jhilam Sadhukhan, K. Mazurek, A. Baran, J. Dobaczewski, W. Nazarewicz, and J.A Sheikh
    Phys. Rev. C 88, 064314 (2013)
    The spontaneous fission lifetime of 264-Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the non-perturbative mass parameters, the dynamic fission pathway becomes strongly triaxial and it approaches the static fission valley. On the other hand, when the standard perturbative cranking inertia tensor is used, axial symmetry is restored along the path to fission; an effect that is an artifact of the approximation used. The calculation of the full ATDHFB inertia is in progress, also developments are initiated in the context of dynamical effects due to the competition between triaxial and reflection asymmetric degrees of freedom, and pairing.

55. Theoretical Description of the Fission Process
    W. Nazarewicz
    Stewardship Science Academic Alliances Annual 2013 DOE/NA-0019, p.11 (2013).

56. Nuclear energy density optimization: Shell structure
    M. Kortelainen, J. McDonnell, W. Nazarewicz, E. Olsen, P.-G. Reinhard, J. Sarich, N. Schunck, S.M. Wild, D. Davesne, J. Erler, and A. Pastore
    Phys. Rev. C 89, 054314 (2014).
    In this work, we propose a new parameterization UNEDF2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDerS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parameterization UNEDF1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting UNEDF2 parameterization is comparable with UNEDF1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous UNEDF parameterizations, the parameter confidence interval for UNEDF2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits and significant changes to the form of the functional are needed.

57. Error Estimates of Theoretical Models: a Guide
    J. Dobaczewski, W. Nazarewicz, and P.-G. Reinhard
    J. Phys. G 41, 074001 (2014).
    This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover inter-dependencies by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.

58. Excitation-energy dependence of fission in the mercury region
    J. D. McDonnell, W. Nazarewicz, J. A. Sheikh, A. Staszczak, and M. Warda
    Phys. Rev. C. 90, 021302(R) (2014).
    To elucidate the roles of proton and neutron numbers and excitation energy in determining symmetric- and asymmetric-fission yields, we compute and analyze the isentropic potential energy surfaces of Hg and Po nuclei. Our self-consistent theory suggests that excitation energy weakly affects the fission pattern of the nuclei considered. The transition from the asymmetric fission in the proton-rich nuclei to a more symmetric fission in the heavier isotopes is governed by the shell structure of pre-scission configurations.

59. Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure
    J. C. Pei, G. I. Fann, R. J. Harrison, W. Nazarewicz, Yue Shi, and S. Thornton
    Phys. Rev. C. 90, 024317 (2014).
    To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. The proposed MADNESS-HFB framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are strongly elongated and dinuclear configurations such as those present in fission and heavy-ion fusion.

60. Focus Issue on Enhancing the interaction between nuclear experiment and theory through information and statistics
    edited by D.G. Ireland and W. Nazarewicz
    J. Phys. G 42, 030301 (2015).
    As a follow-up to a recently published guide, J. Phys. G 41, 074001 (2014), we have edited the Focus Issue of Journal of Physics G on Enhancing the interaction between nuclear experiment and theory through information and statistics, which will contain many excellent examples of uncertainty quantification in nuclear modeling, and in fission modeling in particular.

61. Pairing-induced speedup of nuclear spontaneous fission
    J. Sadhukhan, J. Dobaczewski, W. Nazarewicz, J. A. Sheikh, and A. Baran
    Phys. Rev. C 90, 061304(R) (2014).
    Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of 264Fm and 240Pu using the state-of-the-art self-consistent framework. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates. Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of 264Fm, where the effect of triaxiality on the fission barrier is large, the geometry of fission pathway in the space of shape degrees of freedom is weakly impacted by pairing. This is not the case for 240Pu, where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory. The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom.

62. Multidimensional Skyrme-Density-Functional Study of the Spontaneous Fission of 238U
    J. Sadhukhan, K. Mazurek, J. Dobaczewski, W. Nazarewicz, J.A. Sheikh, and A. Baran
    Acta. Phys. Pol. 46, 575 (2015).
    We determined the spontaneous fission lifetime of 238U by a minimization of the action integral in a three-dimensional space of collective variables. Apart from the mass-distribution multipole moments Q20 and Q30, we also considered the pairing-fluctuation parameter as a collective coordinate. The inertia tensor was obtained within the nonperturbative cranking approximation to the adiabatic time-dependent HartreeÐFockÐ Bogoliubov approach. The pairing-fluctuation parameter allowed us to control the pairing gap along the fission path, which significantly changed the spontaneous fission lifetime.

63. Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
    J.D. McDonnell, N. Schunck, D. Higdon, J. Sarich, S.M. Wild, and W. Nazarewicz
    Phys. Rev. Lett. 114, 122501 (2015).
    Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models; to estimate model errors and thereby improve predictive capability; to extrapolate beyond the regions reached by experiment; and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

64. Benchmarking Nuclear Fission Theory
    G.F. Bertsch, W. Loveland, W. Nazarewicz, and P. Talou
    J. Phys. G 42, 077001 (2015).
    We suggest a small set of fission observables to be used as test cases for validation of theoretical calculations. The purpose is to provide common data to facilitate the comparison of different fission theories and models. The proposed observables are chosen from fission barriers, spontaneous fission lifetimes, fission yield characteristics, and fission isomer excitation energies. Obviously the fission process is very complex and rich, and many more data exist beyond this very small sample. One should view these notes as a living document, which will need to be updated as more useful information becomes available, and as fidelity of fission theory improves.

65. Complex-energy approach to sum rules within nuclear density functional theory
    N. Hinohara, M. Kortelainen, W. Nazarewicz, and E. Olsen
    Phys. Rev. C 91, 044323 (2015).
    The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. The FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.

66. Twist-averaged boundary conditions for nuclear pasta Hartree-Fock calculations
    B. Schuetrumpf and W. Nazarewicz
    Phys. Rev. C 92, 045806 (2015) [Editor's Suggestion].
    Nuclear pasta phases, present in the inner crust of neutron stars, are associated with nucleonic matter at subsaturation densities arranged in regular shapes. Those complex phases, residing in a layer which is approximately 100-m thick, impact many features of neutron stars. Theoretical quantum-mechanical simulations of nuclear pasta are usually carried out in finite three-dimensional boxes assuming periodic boundary conditions. The resulting solutions are affected by spurious finite-size effects. To remove spurious finite-size effects, it is convenient to employ twist-averaged boundary conditions (TABC) used in condensed matter, nuclear matter, and lattice quantum chromodynamics applications. In this work, we study the effectiveness of TABC in the context of pasta phase simulations within nuclear density functional theory. We demonstrated that by applying TABC reliable results can be obtained from calculations performed in relatively small volumes. By studying various contributions to the total energy, we gain insights into pasta phases in mid-density range. Future applications will include the TABC extension of the adaptive multiresolution 3D Hartree-Fock solver and Hartree-Fock-Bogoliubov TABC applications to superfluid pasta phases and complex nucleonic topologies as in fission.

67. Special Issue on Superheavy Elements
    Edited by Ch. E. Duellmann, R.-D. Herzberg, W. Nazarewicz and Y. Oganessian
    Nucl. Phys. A 944, 1-690 (2015).
    Reflecting the breadth of research opportunities in the field of superheavy element research, this special issue covers the range of topics in a comprehensive way, including synthesis of superheavy isotopes, nuclear structure, atomic shell structure, and chemical properties. The contributions detail the status of the field and lay out perspectives for the future. The prospects are bright: new isotopes are awaiting discovery, completing the landscape of superheavy nuclei and bridging the currently existing gap between nuclei synthesized in cold fusion reactions and those from 48Ca induced fusion reactions. The possibility that the limits of nuclear structure studies can be pushed even further in mass and charge has greatly motivated a number of new facilities. Advances in experimental techniques will allow studies on isotopes produced significantly be-low the 1pb level. Chemical studies progressing to elements never studied to date are already being prepared. Ultra-fast chemistry setups are under development and it will be fascinating to see them at work, elucidating the influence of relativistic effects on superheavy elements. The richness of chemical systems available for transactinides will expand further, giving access to new chemical systems, giving more information on the architecture of the periodic table.

68. Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals
    J. Dobaczewski, A.V. Afanasjev, M. Bender, L.M. Robledo and Yue Shi
    Nucl. Phys. A 944, 388 (2015).
    We calculated properties of the ground and excited states of nuclei in the nobelium region for proton and neutron numbers of 92²Z²104 and 144²N²156, respectively. We used three different energy-density-functional (EDF) approaches, based on covariant, Skyrme, and Gogny functionals, each with two different parameter sets. A comparative analysis of the results obtained for quasiparticle spectra, oddÐeven and two-particle mass staggering, and moments of inertia allows us to identify single-particle and shell effects that are characteristic to these different models and to illustrate possible systematic uncertainties related to using the EDF modeling.

69. Microscopic modeling of mass and charge distributions in the spontaneous fission of 240Pu
    J. Sadhukhan, W. Nazarewicz, and N. Schunck
    Phys. Rev. C 93 011304 (R) (2016).
    In this paper, we outlined a methodology to calculate microscopically mass and charge distributions of spontaneous fission yields. We combined the multi-dimensional minimization of collective action for fission with stochastic Langevin dynamics to track the relevant fission paths from the ground-state configuration up to scission. The nuclear potential energy and collective inertia governing the tunneling motion were obtained with nuclear density functional theory in the collective space of shape deformations and pairing. We obtained a quantitative agreement with experimental data and find that both the charge and mass distributions in the spontaneous fission of 240Pu are sensitive both to the dissipation in collective motion and to adiabatic characteristics.

70. Impact of nuclear mass uncertainties on the r process
    D. Martin, A. Arcones, W. Nazarewicz, and E. Olsen
    Phys. Rev. Lett. 116, 121101 (2016).
    Nuclear masses play a fundamental role in understanding how the heaviest elements in the Universe are created in the r-process. In this work, we predicted r-process nucleosynthesis yields using neutron capture and photodissociation rates that are based on the nuclear density functional theory. Using six Skyrme energy density functionals based on different optimization protocols, we determined for the first time systematic uncertainty bands - related to mass modeling - for r-process abundances in realistic astrophysical scenarios. We found that features of the underlying microphysics make an imprint on abundances especially in the vicinity of neutron shell closures: Abundance peaks and troughs are reflected in trends of neutron separation energy.

71. Time-dependent density functional theory with twist-averaged boundary conditions
    B. Schuetrumpf, W. Nazarewicz, and P.-G. Reinhard
    Phys. Rev. C. 93, 054304 (2016)
    Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, 3D coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a box. For finite quantum systems (atoms, molecules, nuclei), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. These artifacts can be practically cured by introducing absorbing boundary conditions (ABC) through an absorbing potential in a certain boundary region sufficiently far from the described system. But also the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust) suffer artifacts from a finite computational box. In this regime, twist- averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extended TABC to time-dependent framework and applied it to resolve the box artifacts for finite quantum systems using as test case small- and large-amplitude nuclear vibrations. We demonstrated that by using such a method, one can reduce finite volume effects drastically without adding any additional parameters. While they are almost equivalent in the linear regime, TABC and ABC differ in the nonlinear regime in their treatment of evaporated particles.

72. Recoil-alpha-fission and recoil-alpha-alpha-fission events observed in the reaction 48Ca + 243Am
    U. Forsberg et al.
    Nucl. Phys. A 953, 117 (2016).
    A recent high-resolution alpha, X-ray, and gamma-ray coincidence-spectroscopy experiment at GSI offered the first glimpse of excitation schemes of isotopes along alpha-decay chains of Z=115. To understand these observations and to make predictions about shell structure of superheavy nuclei below 288Mc, we employed nuclear DFT. We find that the presence and nature of low-energy E1 transitions in well-deformed nuclei around Z=110, N=168 strongly depends on the strength of the spin-orbit coupling; hence, it provides an excellent constraint on theoretical models of superheavy nuclei.

73. Nucleon localization and fragment formation in nuclear fission
    C.L. Zhang, B. Schuetrumpf, and W. Nazarewicz
    Phys. Rev. C 94, 064323 (2016)
    An electron localization measure was originally introduced to characterize chemical bond structures in molecules. Recently, a nucleon localization based on Hartree-Fock densities has been introduced to investigate alpha-cluster structures in light nuclei. Compared to the local nucleonic densities, the nucleon localization function has been shown to be an excellent indicator of shell effects and cluster correlations. In this work, using the spatial nucleon localization measure, we investigated the emergence of fragments in fissioning heavy nuclei using the self-consistent energy density functional method with a quantified energy density functional optimized for fission studies. We studied the particle densities and spatial nucleon localization distributions along the fission pathways of 264Fm, 232Th, and 240Pu. We demonstrated that the fission fragments were formed fairly early in the evolution, well before scission. To illustrate the usefulness of the localization measure, we showed how the hyperdeformed state of 232Th could be understood in terms of a quasimolecular state made of 132Sn and 100Zr fragments. Compared to nucleonic distributions, the nucleon localization function more effectively quantifies nucleonic clustering: its characteristic oscillating pattern, traced back to shell effects, is a clear fingerprint of cluster/fragment configurations. This is of particular interest for studies of fragment formation and fragment identification in fissioning nuclei.

74. Charge Radii of Neutron-Deficient 52,53Fe Produced by Projectile Fragmentation
    K. Minamisono et al.
    Phys. Rev. Lett. 117, 252501 (2016)
    To interpret charge radii in 52,53Fe measured with bunched-beam collinear laser spectroscopy, we employed nuclear density functional theory with Fayans and Skyrme energy density functionals. We demonstrated that the trend of charge radii along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects. This work employed results of our systematic DFT calculations stored in the massexplorer database.

75. Clustering and pasta phases in nuclear density functional theory
    B. Schuetrumpf, C.L. Zhang, and W. Nazarewicz
    in: Nuclear Particle Correlations and Cluster Physics, Ch. 5, p. 135 (2017)
    Nuclear density functional theory is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we use the concept of nucleon localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.

76. Central depression in nucleonic densities: Trend analysis in the nuclear density functional theory approach
    B. Schuetrumpf, W. Nazarewicz, and P.-G. Reinhard
    Phys. Rev. C 96, 024306 (2017)
    In this work, we revealed mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. To this end, we introduced several measures of the internal nucleonic density. Through the statistical analysis, we studied the information content of these measures with respect to nuclear matter properties. We demonstrate that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for superheavy systems it is firmly driven by the electrostatic repulsion. An appreciable semibubble structure in proton density is predicted for 294Og, which is currently the heaviest nucleus known experimentally.

77. Cluster formation in pre-compound nuclei in the time-dependent framework
    B. Schuetrumpf and W. Nazarewicz
    Phys. Rev. C 96, 064608 (2017). Editors' Suggestion. Featured in Physics.
    Modern applications of nuclear time-dependent density functional theory (TDDFT) are often capable of providing quantitative description of heavy ion reactions. However, the structures of precompound (preequilibrium, prefission) states produced in heavy ion reactions are difficult to assess theoretically in TDDFT as the single-particle density alone is a weak indicator of shell structure and cluster states. In this work, we employed the time-dependent nucleon localization function (NLF) to reveal the structure of precompound states in nuclear reactions involving light and medium-mass ions. We utilized the symmetry-free TDDFT approach with the Skyrme energy density functional UNEDF1 and computed the time-dependent NLFs to describe 16O+16O, 40Ca+16O, 40Ca+40Ca, and 16,18O+12C collisions at energies above the Coulomb barrier. We demonstrated that NLFs reveal a variety of time-dependent modes involving cluster structures. Our result supports the experimental findings that the presence of cluster structures in the projectile and target nuclei gives rise to strong entrance channel effects and enhanced alpha emission.

78. Formation and distribution of fragments in the spontaneous ssion of 240Pu
    J. Sadhukhan, C.L. Zhang, W. Nazarewicz, and N. Schunck
    Phys. Rev. C 96, 061301((R) (2017)
    We studied the characteristics of the tails of yield distributions, which correspond to very asymmetric fission into a very heavy and a very light fragment. We used the stochastic Langevin framework to simulate the nuclear evolution after the system tunnels through the multidimensional potential barrier. For a representative sample of different initial configurations along the outer turning-point line, we define effective fission paths by computing a large number of Langevin trajectories. We extracted the relative contribution of each such path to the fragment distribution. We then used nucleon localization functions along effective fission pathways to analyze the characteristics of prefragments at prescission configurations. We found that non-Newtonian Langevin trajectories, strongly impacted by the random force, produce the tails of the fission fragment distribution of 240Pu. The prefragments deduced from nucleon localizations are formed early and change little as the nucleus evolves towards scission. On the other hand, the system contains many nucleons that are not localized in the prefragments even near the scission point. Such nucleons are distributed rapidly at scission to form the final fragments. Fission prefragments extracted from direct integration of the density and from the localization functions typically differ by more than 30 nucleons even near scission.

79. Scalable nuclear density functional theory with Sky3D
    M. Afibuzzaman, B. Schuetrumpf, and H.M. Aktulga
    Comput. Phys. Comm. 223, 34 (2018)
    In this paper, we describe techniques for an efficient and scalable parallel implementation of Sky3D, a nuclear density functional theory solver that operates on an equidistant grid. Presented techniques allow Sky3D to achieve good scaling and high performance on a large number of cores, as demonstrated through detailed performance analysis on a Cray XC40 supercomputer.

80. Electron and nucleon localization functions of oganesson: Approaching the Thomas-Fermi limit
    P. Jerabek, B. Schuetrumpf, P. Schwerdtfeger, and W. Nazarewicz
    Phys. Rev. Lett. 120, 053001 (2018) Editors' Suggestion. Featured in Physics. and major news outlets.
    Fermion localization functions are used to discuss electronic and nucleonic shell structure effects in the superheavy element oganesson, the heaviest element discovered to date. Spin-orbit splitting in the 7p electronic shell becomes so large that Og (Z=118) is expected to show uniform-gas-like behavior in the valence region with a rather large dipole polarizability compared to the lighter rare gas elements. The nucleon localization in Og is also predicted to undergo a transition to the Thomas-Fermi gas behavior in the valence region. This effect, particularly strong for neutrons, is due to the high density of single-particle orbitals.

81. The limits of nuclear mass and charge
    W. Nazarewicz
    Nature Phys. 14, 537 (2018). Featured in Science Alert and major news outlets.
    Four new elements with atomic numbers Z=113, 115, 117 and 118 have recently been added to the periodic table. The questions pertaining to these superheavy systems are at the forefront of research in nuclear and atomic physics, and chemistry. This Perspective offers a high-level view of the field and outlines future challenges.

82. Probing sizes and shapes of nobelium isotopes by laser spectroscopy
    S. Raeder, D. Ackermann, H. Backe, R. Beerwerth, J. C. Berengut, M. Block, A. Borschevsky, B. Cheal, P. Chhetri, Ch.E. Dullmann, V.A. Dzuba, E. Eliav, J. Even, R. Ferrer, V.V. Flambaum, S. Fritzsche, F. Giacoppo, S. Gotz, F.P. Hessberger, M. Huyse, U. Kaldor, O. Kaleja, J. Khuyagbaatar, P. Kunz, M. Laatiaoui, F. Lautenschlager, W. Lauth, A.K. Mistry, E. Minaya Ramirez, W. Nazarewicz, S.G. Porsev, M.S. Safronova, U.I. Safronova, B. Schuetrumpf, P. Van Duppen, T. Walther, C. Wraith, and A. Yakushev
    Phys. Rev. Lett. 120, 232503 (2018). Editors' Suggestion. Featured in Physics. and major news outlets.
    Until recently, ground-state nuclear moments of the heaviest nuclei could only be inferred from nuclear spectroscopy, where model assumptions are required. Laser spectroscopy in combination with modern atomic structure calculations is now able to probe these moments directly, in a comprehensive and nuclear- model-independent way. In this work, we reported on unique access to the differential mean-square charge radii of 252;253;254No, and therefore to changes in nuclear size and shape. State-of-the-art nuclear density functional calculations describe well the changes in nuclear charge radii in the region of the heavy actinides, indicating an appreciable central depression in the deformed proton density distribution in 252,254No isotopes.

83. Non-perturbative collective inertias for fission: a comparative study
    S. A. Giuliani, L. M. Robledo
    Phys. Lett. B 787, 134 (2018)
    The non-perturbative method to compute Adiabatic Time Dependent Hartree Fock Bogoliubov (ATDHFB) collective inertias is extended to the Generator Coordinate Method (GCM) in the Gaussian overlap approximation (GOA) including the case of density dependent forces. The two inertias schemes are computed along the fission path of the 234U and compared with the perturbative results. We find that the non-perturbative schemes predict very similar collective inertias with a much richer structure than the one predicted by perturbative calculations. Moreover, the non-perturbative inertias show an extraordinary similitude with the exact GCM inertias computed numerically from the energy overlap. These results indicate that the non-perturbative inertias provide the right structure as a function of the collective variable and only a phenomenological factor is required to mock up the exact GCM inertia, bringing new soundness to the microscopic description of fission.

84. Bayesian approach to model-based extrapolation of nuclear observables
    L. Neufcourt, Y. Cao, W. Nazarewicz, and F. Viens
    Phys. Rev. C 98, 034318 (2018) Editors' Suggestion.
    We considered 10 global models based on nuclear density functional theory with realistic energy density functionals as well as two more phenomenological mass models. The emulators of two-neutron separation energy residuals and Bayesian confidence intervals defining theoretical error bars were constructed using Bayesian Gaussian processes and Bayesian neural networks. By establishing statistical methodology and parameters, we carried out extrapolations toward the two-neutron dripline. While both Gaussian processes (GP) and Bayesian neural networks reduce the root-mean-square (rms) deviation from experiment significantly, GP offers a better and much more stable performance. The increase in the predictive power of microscopic models aided by the statistical treatment is quite astonishing: The resulting rms deviations from experiment on the testing dataset are similar to those of more phenomenological models. The estimated credibility intervals on predictions make it possible to evaluate predictive power of individual models and also make quantified predictions using groups of models. The proposed robust statistical approach to extrapolation of nuclear model results can be useful for assessing the impact of current and future experiments in the context of model developments. The new Bayesian capability to evaluate residuals is also expected to impact research in the domains where experiments are currently impossible, for instance, in simulations of the astrophysical r process.

85. Colloquium: Superheavy elements: Oganesson and beyond
    S.A. Giuliani, Z. Matheson, W. Nazarewicz, E. Olsen, P.-G. Reinhard, J. Sadhukhan, B. Schuetrumpf, N. Schunck, and P. Schwerdtfeger
    Rev. Mod. Phys. 91, 011001 (2019)
    During the last decade, six new superheavy elements were added into the seventh period of the periodic table, with the approval of their names and symbols. This milestone was followed by proclaiming 2019 the International Year of the Periodic Table of Chemical Elements by the United Nations General Assembly. According to theory, due to their large atomic numbers, the new arrivals are expected to be qualitatively and quantitatively different from lighter species. The questions pertaining to superheavy atoms and nuclei are in the forefront of research in nuclear and atomic physics and chemistry. This Colloquium offers a broad perspective on the field and outlines future challenges.

86. Competing fission modes in 178Pt
    I. Tsekhanovich, A.N. Andreyev, K. Nishio, D. Denis-Petit, K. Hirose, H. Makii, Z. Matheson, K. Morimoto, K. Morita, W. Nazarewicz, R. Orlandi, J. Sadhukhan, T. Tanaka, M. Vermeulen, and M. Warda
    Phys. Lett. B 790, 583 (2019)
    Fragment mass distributions from fission of the excited compound nucleus 178Pt have been deduced from the measured fragment velocities. The data are indicative of a mixture of the mass-asymmetric and mass-symmetric fission modes associated with higher and lower total kinetic energies of the fragments, respectively. Most probable experimental fragment-mass split of the asymmetric mode, AL/AH=79/99, is well reproduced by nuclear density functional theory using the UNEDF1-HFB and D1S density functionals. The symmetric mode is associated by theory with very elongated fission fragments, which is consistent with the observed total kinetic energy/fragment mass correlation.

87. Cluster radioactivity of 294Og
    Z. Matheson, S.A. Giuliani, W. Nazarewicz, J. Sadhukhan, and N. Schunck
    Phys. Rev. C 99, 041304(R) (2019)
    According to theory, cluster radioactivity becomes an important decay mode in superheavy nuclei. In this work, we predict that the strongly asymmetric fission, or cluster emission, is in fact the dominant fission channel for 194Og, which is currently the heaviest synthetic isotope known. Our theoretical approach incorporates important features of fission dynamics, including quantum tunneling and stochastic dynamics up to scission. We show that despite appreciable differences in static fission properties such as fission barriers and spontaneous fission lifetimes, the prediction of cluster radioactivity in 194Og is robust with respect to the details of calculations, including the choice of energy density functional, collective inertia, and strength of the dissipation term.

88. r-Process Nucleosynthesis: Connecting Rare-Isotope Beam Facilities with the Cosmos
    C. J. Horowitz, A. Arcones, B. Cote, I. Dillmann, W. Nazarewicz, I. Roederer, H. Schatz, A. Aprahamian, D. Atanasov, A. Bauswein, J. Bliss, M. Brodeur, J. A. Clark, A. Frebel, F. Foucart, C. J. Hansen, O. Just, A. Kankainen, G. C. McLaughlin, J. M. Kelly, S. N. Liddick, D. M. Lee, J. Lippuner, D. Martin, J. Mendoza-Temis, B. D. Metzger, M. R. Mumpower, G. Perdikakis, J. Pereira, B. W. O'Shea, R. Reifarth, A. M. Rogers, D. M. Siegel, A.Spyrou, R. Surman, X. Tang, T. Uesaka, and M. Wang
    J. Phys. G 46, 083001 (2019)
    This is an exciting time for the study of r-process nucleosynthesis. Recently, a neutron star merger GW170817 was observed in extraordinary detail with gravitational waves and electromagnetic radiation from radio to gamma rays. FRIB and other rare-isotope beam facilities will soon have dramatic new capabilities to synthesize many neutron-rich nuclei that are involved in the r-process. The new capabilities can significantly improve our understanding of the r-process and likely resolve one of the main outstanding problems in classical nuclear astrophysics. However, to make best use of the new experimental capabilities and to fully interpret the results, a great deal of infrastructure is needed in many related areas of astrophysics, astronomy, and nuclear theory. In this review, we placed these experiments in context by discussing astrophysical simulations and observations of r-process sites, observations of stellar abundances, galactic chemical evolution, and nuclear theory for the structure and reactions of very neutron-rich nuclei.

89. alpha-decay energies of superheavy nuclei: Systematic trends
    E. Olsen and W. Nazarewicz
    Phys. Rev. C 99, 014317 (2019)
    Known superheavy nuclei primarily decay through alpha emission and spontaneous fission. In this paper, we evaluated the Q-alpha values for even-even nuclei from Fm to Z=120. For well-deformed nuclei between Fm and Ds, we find excellent consistency between different model predictions, and a good agreement with experimental results. For transitional nuclei beyond Ds, intermodel differences grow, resulting in an appreciable systematic error. The robustness of DFT predictions for well-deformed superheavy nuclei supports the idea of using experimental Q-alpha values, together with theoretical predictions, as reasonable (Z,A) indicators. Unfortunately, this identification method is not expected to work well in the region of deformed-to-spherical shape transition as one approaches N=184.

90. Neutron Drip Line in the Ca Region from Bayesian Model Averaging
    L. Neufcourt, Y. Cao, W. Nazarewicz, E. Olsen, and F. Viens
    Phys. Rev. Lett. 122, 062502 (2019)
    We used a Bayesian model averaging analysis based on GP-based extrapolations we introduced the posterior probability for each nucleus to be bound to neutron emission. We found that extrapolations for drip-line locations, at which the nuclear binding ends, are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular, considering the current experimental information and current global mass models, we predicted that 68Ca has an average posterior probability of 76% to be bound to two-neutron emission. This pilot study of the Bayesian Model Averaging will be extended to fission observables.

91. Role of dynamic pairing correlations in fission dynamics
    R. Bernard, S.A. Giuliani, and L.M. Robledo
    Phys. Rev. C 99, 064301 (2019)
    We studied the role of dynamic pairing correlations in fission dynamics by considering intrinsic HFB wave functions that are obtained by minimizing the particle number projected energy. For the restricted variational space, the set of self-consistent wave functions with different values of proton and neutron number particle fluctuations are considered. The particle number projected energy is used to define potential energy surface for fission whereas collective inertias are computed within the traditional formulas for the intrinsic states. The results show that the effect of the restricted variation after particle number projection in the potential energy surface is small while collective inertias substantially decrease. On the other hand, we showed that this quenching is strongly mitigated when Coulomb antipairing is considered.

92. Spallation-altered Accreted Compositions for X-Ray Bursts: Impact on Ignition Conditions and Burst Ashes
    J. S. Randhawa, Z. Meisel, S. A. Giuliani, H. Schatz, B. S. Meyer, K. Ebinger, A. A. Hood, and R. Kanungo
    Astrophys. J. 887, 100 (2019)
    Model predictions of X-ray burst ashes and light curves depend on the composition of the material accreted from the companion star, in particular the abundance of CNO elements. It has previously been pointed out that spallation in the atmosphere of the accreting neutron star can destroy heavy elements efficiently. In this work we studied this spallation using a realistic reaction network that follows the complete spallation cascade and takes into account not only destruction, but also production of elements by the spallation of heavier species. We find an increased survival probability of heavier elements compared to previous studies, resulting in significantly higher CNO abundances. We provide resulting compositions as a function of accretion rate and explore their impact on 1D multi-zone X-ray burst models.

93. Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei
    L. Neufcourt, Y. Cao, S. Giuliani, W. Nazarewicz, E. Olsen, and O. B. Tarasov
    Phys. Rev. C 101, 014319 (2020)
    Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements. We studied the impact of such model mixing in the proton-rich region of the nuclear chart. Separation energies were computed within nuclear density functional theory using several Skyrme and Gogny energy density functionals. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one- and two-proton separation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two-proton decay studies have been identified,

94. Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei
    L. Neufcourt, Y. Cao, S. A. Giuliani, W. Nazarewicz, E. Olsen, and O. B. Tarasov
    Phys. Rev. C 101, 044307 (2020)
    Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. In this work, we used microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. To account for uncertainties, Bayesian Gaussian processes were trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allowed to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. According to our Bayesian model averaging analysis, 7759 nuclei with Z<120 have a probability of existence ³0.5. The extrapolations obtained in this study will be put through stringent tests when new experimental information on exotic nuclei becomes available.

95. Efficient method for estimation of fission fragment yields of r-process nuclei
    J. Sadhukhan, S. A. Giuliani, Z. Matheson, and W. Nazarewicz
    Phys. Rev. C 101, 065803 (2020)
    The knowledge of fission fragment yields of hundreds of nuclei inhabiting very neutron-rich regions of the nuclear landscape is crucial for the modeling of heavy-element nucleosynthesis. In this study, we proposed a novel model for a fast calculation of fission fragment yields based on the concept of shell-stabilized prefragments calculated within realistic nuclear density functional theory. The new approach has been benchmarked against experimental data and advanced calculations reaffirming the dominant role of shell effects in the pre-scission region for forming fission yields.

96. Fission and the r-process nucleosynthesis of translead nuclei
    S. A. Giuliani, G. Martinez-Pinedo, Meng-Ru Wu, and L. M. Robledo
    Phys. Rev. C 102, 045804 (2020)
    We studied the impact of fission on the production and destruction of translead nuclei during the r-process nucleosynthesis occurring in neutron star mergers. Abundance patterns and rates of nuclear energy production are obtained for different ejecta conditions using two sets of stellar reaction rates, one of which is based on microscopic and consistent calculations of nuclear masses, fission barriers and collective inertias. We show that the accumulation of fissioning material during the r process can strongly affect the free neutron abundance after the r-process freeze-out. This leads to a significant impact on the abundances of heavy nuclei that undergo alpha decay or spontaneous fission, affecting the radioactive energy production by the ejecta at timescales relevant for kilonova emission.

97. Future of Nuclear Fission Theory
    M. Bender, R. Bernard, G. Bertsch, S. Chiba, J. Dobaczewski, N. Dubray, S. A. Giuliani, K. Hagino, D. Lacroix, Z. Li, P. Magierski, J. Maruhn, W. Nazarewicz, J. Pei, S. Peru, N. Pillet, J. Randrup, D. Regnier, P.-G. Reinhard, L. M. Robledo, W. Ryssens, J. Sadhukhan, G. Scamps, N. Schunck, C. Simenel, J. Skalski, I. Stetcu, P. Stevenson, S. Umar, M. Verriere, D. Vretenar, M. Warda, and S. Aberg
    J. Phys. G 47, 113002 (2020)
    There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarizes its findings and recommendations.

98. Landscape of pear-shaped even-even nuclei
    Y. Cao, S. E. Agbemava, A.V. Afanasjev, W. Nazarewicz, and E. Olsen
    Phys. Rev. C 102, 024311 (2020)
    We carried out global analysis of ground-state octupole deformations for particle-bound even-even nuclei with Z < 110 and N < 210 using nuclear density functional theory with several non-relativistic and covariant energy density functionals. We identified several regions of ground-state octupole deformation. In addition to the traditional regions of neutron-deficient actinide nuclei around 224Ra and neutron-rich lanthanides around 146Ba, we identified vast regions of reflecion-asymmetric shapes in very neutron-rich nuclei around 200Gd and 288Pu, as well as in several nuclei around 112Ba. Our analysis suggests several promising candidates with stable ground-state octupole deformation, primarily in the neutron-deficient actinide region, that can be reached experimentally. Octupole shapes predicted in this study are consistent with the current experimental information. This work can serve as a starting point of a systematic search for parity doublets in odd-mass and odd-odd nuclei, which can be of interest in the context of new physics searches.

99. Quantified limits of the nuclear landscape
    L. Neufcourt, Y. Cao, S. A. Giuliani, W. Nazarewicz, E. Olsen, and O. B. Tarasov
    Phys. Rev. C 101, 044307 (2020)
    Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a variety of applications, including the modeling of stellar nucleosynthesis. In this work, we used microscopic nuclear mass models and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines. To account for uncertainties, Bayesian Gaussian processes were trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allowed to account for systematic and statistical uncertainties and propagate them to extrapolative predictions. According to our Bayesian model averaging analysis, 7759 nuclei with Z<120 have a probability of existence >0.5. The extrapolations obtained in this study will be put through stringent tests when new experimental information on exotic nuclei becomes available.

100. Comparison of fission and quasi-fission modes
     C. Simenel, P. McGlynn, A.S. Umar, and K. Godbey
     Phys. Lett. B 822, 136648 (2021)
     Quantum shell effects are known to affect the formation of fragments in nuclear fission. Shell effects also affect quasi-fission reactions occurring in heavy-ion collisions. Systematic time-dependent Hartree-Fock simulations of 50Ca+176Yb collisions show that the mass equilibration between the fragments in quasi-fission is stopped when they reach similar properties to those in the asymmetric fission mode of the 226Th compound nucleus. Similar shell effects are then expected to determine the final repartition of nucleons between the nascent fragments in both mechanisms. Future experimental studies that could test these observations are discussed.

101. Fragment Intrinsic Spins and FragmentsÕ Relative Orbital Angular Momentum in Nuclear Fission
     A. Bulgac, I. Abdurrahman, K. Godbey, and I. Stetcu
     Phys. Rev. Lett. 128, 022501 (2022)
     This is the first fully unrestricted microscopic calculations of the primary fission fragment intrinsic spins and of the fission fragmentsÕ relative orbital angular momentum using the time-dependent density functional theory framework. Within this microscopic approach, we evaluate the triple distribution of the fission fragment intrinsic spins and of their fission fragmentsÕ relative orbital angular momentum and show that their dynamics is dominated by their bending collective modes in contradistinction to the predictions of the existing phenomenological models and some interpretations of experimental data.

102. Theoretical description of fission yields: Toward a fast and efficient global model
     J. Sadhukhan, S.A. Giuliani, and W. Nazarewicz
     Phys. Rev. C 105, 014619 (2022)
     Fission trajectories on two-dimensional potential energy surfaces were obtained within the density functional theory framework, allowing for a microscopic determination of the most probable fission fragment configurations. Mass and charge yield distributions were constructed by means of a statistical approach rooted in a microcanonical ensemble. We show that the proposed hybrid model can reproduce experimental mass and charge fragment yields for a wide range of fissioning nuclei as well as the observed odd-even staggering. Furthermore, experimental isotopic yields can be accurately described with a simple neutron evaporation scheme. Finally, we explored fission fragment distributions of exotic neutron-rich and superheavy systems, and compare our predictions with other state-of-the art global calculations. Our study suggests that microscopic rearrangements of nucleons into a fissioning nucleus occur well before the scission, and the subsequent dynamics is mainly driven by the thermal excitations and bulk features of the nuclear binding.

103. Nudged elastic band approach to nuclear fission pathways
     E. Flynn, D. Lay, S. Agbemava, P. Giuliani, K. Godbey, W. Nazarewicz, and J. Sadhukhan
     Phys. Rev. C105, 054302 (2022)
     The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential-energy surfaces obtained with the Skyrme-Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The nudged elastic band (NEB) method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential-energy surface of the fissioning nucleus that determine the static fission path. The dynamic programming method also performs quite well and it can be used in many-dimensional cases to provide initial conditions for the NEB calculations.

104. Training and projecting: A reduced basis method emulator for many-body physics
     Edgard Bonilla, Pablo Giuliani, Kyle Godbey, and Dean Lee
     Phys. Rev. C 106, 054322 (2022)
     We present the reduced basis method as a tool for developing emulators for equations with tunable parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few values of the model parameters and then projects the equations over a well-chosen low-dimensional subspace. We connect some of the results in the eigenvector continuation literature to the formalism of reduced basis methods and show how these methods can be applied to a broad set of problems. As we illustrate, the possible success of the formalism on such problems can be diagnosed beforehand by a principal component analysis. The outstanding performance of the approach, together with its straightforward implementation, show promise for its application to the emulation of computationally demanding calculations, including uncertainty quantification.

105. Theoretical uncertainty quantification for heavy-ion fusion
     K. Godbey, A. S. Umar, and C. Simenel
     Phys. Rev. C 106, L051602 (2022) (Editors' Suggestion)
     Despite recent advances and focus on rigorous uncertainty quantification for microscopic models of quantum many-body systems, the uncertainty on the dynamics of those systems has been underexplored. To address this, we have used time-dependent Hartree-Fock to examine the model uncertainty for a collection of low-energy, heavy-ion fusion reactions. Fusion reactions at near-barrier energies represent a rich test-bed for the dynamics of quantum many-body systems owing to the complex interplay of collective excitation, transfer, and static effects that determine the fusion probability of a given system. The model uncertainty is sizable for many of the systems studied and the primary contribution arises from static properties that are ill-constrained, such as the neutron radius of neutron-rich nuclei. These large uncertainties motivate the use of information from reactions to better constrain existing models and to infer static properties from reaction data.

106. Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method
     P. Giuliani, K. Godbey, E. Bonilla, F. Viens, and J. Piekarewicz
     Front. Phys. 10, 1054524 (2023)
     A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the calibration is enabled by the emulation of the high-fidelity model through the implementation of a reduced basis method - a set of dimensionality reduction techniques that can speed up demanding calculations involving partial differential equations by several orders of magnitude. The RBM emulator we build - using only 100 evaluations of the high-fidelity model - is able to accurately reproduce the model calculations in tens of milliseconds on a personal computer, an increase in speed of nearly a factor of 3,300 when compared to the original solver.

107. Hexadecapole strength in the rare isotopes 74,76Kr
     M. Spieker, S.E. Agbemava, D. Bazin, S. Biswas, P.D. Cottle, P.J. Farris, A. Gade, T. Ginter, S. Giraud, K.W. Kemper, J. Li, W. Nazarewicz, S. Noji, J. Pereira, L.A. Riley, M. Smith, D. Weisshaar, and R.G.T. Zegers
     Phys. Lett. B 841, 137932 (2023)
     In the Ge-Sr mass region, isotopes with neutron number N<40 are known to feature rapid shape changes with both nucleon number and angular momentum. By performing coupled-channels calculations, hexadecapole deformation parameters were determined for the J=4 states of 74,76Kr from inelastic proton scattering cross sections. Two possible coupled-channels solutions were found. A comparison to predictions from nuclear energy density functional theory, employing both non-relativistic and relativistic functionals, clearly favors the large, positive beta4 solutions. These values are unambiguously linked to the well-deformed prolate configuration.

108. Cluster model of 12C in the density functional theory framework
     A.S. Umar, K. Godbey, and C. Simenel
     Phys. Rev. C 107, 064605 (2023)
     We employ the constrained density functional theory to investigate cluster phenomena for the 12C nucleus. The proton and neutron densities are generated from the placement of three 4He nuclei (alpha particles) geometrically. These densities are then used in a density constrained Hartree-Fock calculation that produces an antisymmetrized state with the same densities through energy minimization. In the calculations no a priori analytic form for the single-particle states is assumed and the full energy density functional is utilized. The geometrical scan of the energy landscape provides the ground state of 12C as an equilateral triangular configuration of three alphas with molecular bond like structures. The use of the nucleon localization function provides further insight to these configurations. One can conclude that these configurations are a hybrid between a pure mean-field and a pure alpha particle condensate. This development could facilitate DFT based fusion calculations with a more realistic 12C ground state.

109. The quest for superheavy elements and the limit of the periodic table
     O. Smits, C. E. Duellmann, P. Indelicato, W. Nazarewicz, and P. Schwerdtfeger
     Nat. Rev. Phys. 6, 86 (2024)
     The borders of the periodic table of the elements and of the chart of nuclides are not set in stone. The desire to explore the properties of atoms and their nuclei in a regime of very large numbers of electrons, protons and neutrons has motivated new experimental facilities to create new elements and nuclides at the limits of atomic number and mass. But the small production rates and short lifetimes of superheavy nuclei and their atoms mean that atom-at-a-time studies are the only experimental way to probe them. The physical and chemical data obtained so far, augmented by theoretical calculations, indicate significant deviations from extrapolations from lighter elements and isotopes. This situation raises the following question: how much further can one push the limits of the periodic table? In this Review, we describe the major challenges in the field of the superheavy elements and speculate about future directions.

110. Pushing the Limits of the Periodic Table Ð A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements
     O. R. Smits,, P. Indelicato, W. Nazarewicz, M. Piibeleht, and P. Schwerdtfeger
     Phys. Rep. 1035, 1 (2023)
     We review the progress in atomic structure theory with a focus on superheavy elements and their predicted ground state configurations important for an element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is essential to correctly solve the Dirac equation in strong Coulomb fields, and to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge, where electronic levels dive into the negative energy continuum.

111. Shell effects in fission and quasi-fission reactions
     C. Simenel, K. Godbey, H. Lee, P. McGlynn and A.S. Umar
     J. Phys.: Conf. Ser. 2586 012063 (2023)
     Quantum shell effects are responsible for asymmetric fission. They are also expected to affect the formation of fission fragments in quasi-fission reactions occurring in heavy-ion collisions. Systematic time-dependent Hartree-Fock simulations of 40Ð56Ca+176Yb collisions show that quasi-fission fragment properties share strong similarities with fragments formed in fission of the compound nuclei. This is an indication that similar shell effects are responsible for the final asymmetry in both mechanisms.

112. Global properties of nuclei at finite-temperature within the covariant energy density functional theory
     A. Ravlic, E. Yuksel, T. Niksic, and N. Paar
     Phys. Rev. C 109, 014318 (2024)
     In stellar environments nuclei appear at finite temperatures, becoming extremely hot in core-collapse supernovae and neutron-star mergers. However, due to theoretical and computational complexity, most model calculations of nuclear properties are performed at zero temperature, while those existing at finite temperatures are limited only to selected regions of the nuclide chart. In this study we perform the global calculation of nuclear properties for even-even nuclei at temperatures below 2 MeV. Calculations are based on the finite-temperature relativistic Hartree-Bogoliubov model supplemented by the Bonche-Levit-Vautherin vapor subtraction procedure.

113. Influence of the symmetry energy on the nuclear binding energies and the neutron drip line position
     A. Ravlic, E. Yuksel, T. Niksic, and N. Paar
     Phys. Rev. C 108, 054305 (2023)
     A clear connection can be established between properties of nuclear matter and finite-nuclei observables, such as the correlation between the slope of the symmetry energy and the dipole polarizability, or between compressibility and the isoscalar monopole giant resonance excitation energy. Establishing a connection between realistic atomic nuclei and an idealized infinite nuclear matter leads to a better understanding of underlying physical mechanisms that govern nuclear dynamics. In this work, we aim to study the dependence of the binding energies and related quantities (e.g., location of drip lines, the total number of bound even-even nuclei) on the symmetry energy.

114. Search for beyond-mean-field signatures in heavy-ion fusion reactions
     R. T. deSouza, K. Godbey, S. Hudan, and W. Nazarewicz
     Phys. Rev. C 109, L041601 (2024); Editors' Suggestion
     Examination of high-resolution, experimental fusion excitation functions for 16-18O+12C reveals a remarkable irregular behavior that is rooted in the structure of both the colliding nuclei and the quasimolecular composite system. The impact of the angular-momentum--dependent fusion barriers is assessed using a time-dependent Hartree-Fock model, viewed as a mean-field reference. Barrier penetrabilities, taken directly from a density-constrained calculation, provide a significantly improved description of the experimental data as compared to the standard Hill-Wheeler approach. The remaining deviations between the parameter-free theoretical mean-field predictions and experimental fusion cross sections are exposed and discussed.

115. Neural Network Emulation of Spontaneous Fission
     D. Lay, E. Flynn, S. A. Giuliani, W. Nazarewicz, and L. Neufcourt
     Phys. Rev. C 109, 044305 (2024).
     We explore the use of neural networks (NNs) to construct DFT emulators capable of predicting potential energy surfaces and collective inertia tensors across the whole nuclear chart, starting from a minimal set of DFT calculations. The potential energy predicted by NNs agrees with the DFT value to within a root-mean-square error of 500 keV, and the collective inertia components agree to within an order of magnitude. These results are largely independent of the NN architecture.

116. Multimodal fission from self-consistent calculations
     D. Lay, E. Flynn, S. Agbemava, K. Godbey, W. Nazarewicz, S. A. Giuliani, and J. Sadhukhan
     Phys. Rev. C 109, 044306 (2024).
     We generalize the previously proposed hybrid model for fission-fragment yield distributions to predict competing fission modes and estimate the resulting yield distributions. Our framework allows for a comprehensive large-scale calculation of fission-fragment yields suited for r-process nuclear network studies.