Hiroharu Bando

Three-particle one-hole multiple scattering contribution to the nuclear effective interaction in mass-18 nuclei

Abstract Within the systematic framework of the double partition approach, the three-particle one-hole multiple scattering andQ-☐ formalisms are combined to give the valence-linked and connected energy-independent effective interaction. All low-lying [2p + 3p1h] contributions to the mass-18 effective interaction are evaluated using an essentially exact energy-dependent reaction matrix based on the Reid SC potential. The low-lying one-body field of the core nucleus is treated consistently with the underlying reaction matrix G through particle- and hole-line self-energy insertions. Center-of-mass motion, folded diagrams and starting energy dependence are properly taken into account throughout. The low-lying [2p + 3p1h] correlations are stongly damped by self-energy insertions. By incorporating only the folded diagram contributions with origins in the low-lying space, the net effect of all low-lying [2p + 3p1h] correlations is to give back the bare-G plus second-order core-polarization spectra which are found to be in respectable agreement with the experimental spectra. However, including the full folded diagram contribution, which has additional contributions from the high-lying space through the energy dependence of G , leads to final spectra which deviate sizably from experiment. The present results are conclusive in the sense that the treatment is essentially exact for low-lying [2p + 3p1h] correlations which originate from the high-lying two-particle correlations through the reaction matrix G

On the Renormalization Effect due to the Ground State Correlation on the Nuclear Vibrational Motion

A method is given which takes into account the renormalization effects due to the ground state correlation in the nuclear vibrational motion of medium and heavy nuclei. The collective eigenmode is taken as a two-quasi-particle mode; this means that Bogoliubov bound pairs break up in a coherent manner. Self-consistent equations are derived which determine the vibrational eigenmodes and the Bogoliubov quasi-particles, both renormalized owing to the effects of the ground state correlations. Calculations are made for the simple case of a single j-shell with the aim of seeing the physical features of the effect, especially the dependence of the effects on the properties of the nuclear interaction, ~y changing the ratio of the magnitude of the particle-particle and particle-hole matrix elements of the interaction. According as the particle-particle or the particle-hole matrix elements of the nuclear interaction is dominant, we get different results for the renormalization effects on the quasi-particle energy and the E2 transition probability from the vibrational state to the ground state. In either case the renormalization effects reduce the ground state correlation by reducing the difference of the magnitude of the particle-particle and particle-hole matrix elements.