Mirror nuclei are those with the same atomic number but with the numbers of protons and neutrons interchanged. The figure shows an example for A=52 that compares 52Cr with Z=24 protons and N=28 neutrons with 52Ni with Z=28 protons and N=24 neutrons. Due to the isospin symmetry of the nuclear forces, the properties of these two nuclei are nearly identical except that the protons (red) and neutrons (blue) are interchanged.

The difference between the root-mean-square radii of neutrons and protons in a neutron-rich nuclei such as 52Cr is called the neutron skin. A measurement of the neutron skin is important since it determines the derivative of the neutron equation of state (EOS) [1]. The neutron EOS is the energy per neutron for a large number of neutrons as a function of their density. The balance between the positive neutron EOS and the attractive gravitation energy determines the mass and radius of neutron stars. The value of the neutron EOS near nuclear saturation density of 0.16 nucleons per fermi3 can be inferred from an extrapolation of the nuclear binding energies. This value together with its derivative helps one to extrapolate the EOS to the lower and higher densities required to model neutron star formation and properties [2].

The proton rms radius can be determined very precisely by the electromagnetic interaction of electrons with the protons in the nucleus. Parity-violating electron scattering experiments can determined the neutron rms radius (via the exchange of a Z boson), but the error from these experiments at Jefferson Laboratory is at present very large [3].

When there is exact mirror symmetry, the proton rms radius in the mirror nucleus 52Ni is equal to the neutron rms radius in 52Cr. This together with the previously measured proton radius of 52Cr determines its neutron skin. However, the mirror symmetry is partly destroyed by the Coulomb interaction between protons in the nucleus and other isospin-breaking effects. A recent paper [4]. has pointed out that the Coulomb interaction distorts the neutron skin with the addition of a term that depends on the value of the neutron EOS. This extra term becomes important when the difference in the number of neutrons and protons (N-Z) becomes small. But the difference in the mirror proton rms radii remains a robust measure of the derivative. The paper points out several possibilities for new measurements at the NSCL and FRIB that can be made by the laser spectroscopy group.


[1] B. A. Brown, Phys. Rev. Lett. {\bf 85}, 5296 (2000). [link to paper].

[2] A. W. Steiner, J. M. Lattimer, and E. F. Brown, Astrophys. J. {\bf 765}, L5 (2013).

[3] C. J. Horowitz et al.,Phys. Rev. C {\bf 85}, 032501 (2012).

[4] B. A. Brown, Phys. Rev. Lett. ??, ???? (2017). [link to paper].