Coulomb effects and isospin symmetry

An important observation that follows from a comparison of Figs. 1 and 2 is that the neutron and proton routhian spectra are almost identical, apart from a nearly constant shift in energy that amounts to about 6MeV. Such a constant shift expresses the fact that despite a possibly non-trivial evolution of the individual-nucleonic wave functions in terms of the rotational frequency, the corresponding Coulomb interactions average out to nearly a constant, and correspond to the Coulomb energy of a rotating but otherwise $\hbar\omega$-independent charge distribution.

On the one hand, degeneracy of neutron and proton routhians is a manifestation of a charge-independence of the forces used. On the other hand, however, the pairs of nearly degenerate proton and neutron wave-functions may be used to introduce an alternative representation in terms of the isoscalar- and isovector-coupled wave-functions. In such a case any arbitrary isospin-symmetric residual interaction is likely to introduce systematic differences in the spectra of the T=0 and T=1 states. This would allow to test that particular component of the forces against experiment - or, conversely, from an existence of systematic discrepancies between experiment and mean-field calculations - it would allow to optimize the residual interactions. The observed near-degeneracy of the corresponding proton and neutron levels is in fact a prerequisite indication that in this mass region the isospin-symmetry effects could be very important. We will use the above observation as a guideline in further analysis of the neutron/proton configurations in ³²S and neighboring nuclei.