Effective-interaction theory of nuclear spectral relations. II

A theory of particle-hole relations among spectra, presented in Part I, is extended to include hole-hole (hh) spectra as well as the particle-particle (pp) and particle-hole (ph) cases previously treated. This theory, which incorporates configuration mixing into many-body effective interactions, goes beyond the simple shell-model particle-hole relations of Pandya, Goldstein, and Talmi. A new shell-model relation involving all three partners (the triptych: pp, ph, and hh) is derived. We apply the many-body theory and the triptych relation to the nuclei Sc42, Sc48, and Co54, which are partners in the f72 shell. We find that we can then relate the spectra of these three nuclei to considerably greater accuracy than do the standard shell-model relations.