Spontaneous symmetry breaking and the energy of nuclear isobaric analog states

The asymmetry between proton and neutron numbers in a nucleus is viewed as a consequence of the spontaneous symmetry breaking of the isospin symmetry. The signatures of this effect, as it was suggested by Danchev, Khanna, and Umezawa and co-workers, may have been seen already in the energetics of the nuclear isobaric analog resonance state and in the systematic of double-odd double-even mass differences. In order to account for finite size effects, not included in Umezawa's approach, we have calculated the mean field term of the Hamiltonian in a realistic nuclear single-particle basis. The nonvanishing value of the I-3 current in the nonperturbative vacuum is explained in terms of rho meson exchange.