EFFECTIVE INTERACTIONS FOR DOMINANT SHELL-MODEL CONFIGURATIONS - DS-SHELL EXAMPLE

Starting from the ds-shell interaction of Kuo, orthogonal polynomial and Brillouin-Wigner expansions for effective interactions in the dominant configuration space for low-lying states of Na22 (J=2, T=0) have been calculated. Although the states represented have no more than 27% of their strength in the model space, the orthogonal polynomial series converges in low order and good predictions can be obtained with only a third order theory, especially if self consistency is required. For the Brillouin-Wigner expansion, however, we find that higher-order approximations (∼7th order) are required to achieve reasonable accuracy for states lying below the lowest eigenvalue of the interaction in the excluded space. For higherlying states the Brillouin-Wigner self-consistent results diverge. NUCLEAR STRUCTURE Effective interaction; statistical spectroscopy; orthogonal polynomial expansion; Brillouin-Wigner expansion; renormalization; selfconsistency: Na22. © 1979 The American Physical Society.