Effective-Interaction Theory of Nuclear Spectral Relations. I. Particle-Hole Relations

Abstract

A theory of the relation between particle-particle (pp) and particle-hole (ph) spectra is developed using the effective interaction of the Brueckner-Goldstone many-body theory. The shell-model relation of Pandya, Goldstein, and Talmi is shown to be an approximation to a more general many-particle relation. The main terms omitted by the shell-model pp-ph transformation are found to be of an effective three-body nature. The new theory is applied to the case of ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$(pp) and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$(ph), and gives considerably better agreement with experiment than does the standard shell-model relation. For example, the root-mean-square deviation between the predicted and experimental levels of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ is 310 keV for the new theory, as compared to 580 keV for the shell-model relation.