The microscopic Interacting Boson Model for nondegenerate orbits

The microscopic Interacting Boson Model formalism is outlined and a general procedure is described for deriving the parameters of the model when the valence orbits are nondegenerate. This latter technique involves expanding pair creation operators for J = 0 (or J = 2) correlated pairs in terms of J = 0 (or J = 2) pair creation operators for individual orbits. This expansion enables us to relate matrix elements for the multi-orbit problem to matrix elements for individual orbits for which the well-known Racah-seniority reduction formulae apply. Our calculated results for the parameters of the boson-boson quadrupole-quadrupole interaction show a definite relationship to the underlying subshell structure of each major shell, in agreement with the phenomenological results. It is also discovered that the results obtained using particle states are not the same as those obtained using hole states, due to the truncation scheme used to extablish the correlated J = 0 and J = 2 pairs.