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 22Na (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 (approx.7th order) are required to achieve reasonable accuracy for states lying below the lowest eigenvalue of the interaction in the excluded space. For higher-lying states the Brillouin-Wigner self-consistent results diverge