Influence of the g boson on the interacting boson approximation Hamiltonian

The interacting boson approximation Hamiltonian for s and d bosons is renormalized in lowest order for the effects of the g boson using second-order perturbation theory in a single j shell approximation. In this paper only the correction term which renormalizes the single-boson energy is investigated in detail, with a specific application to the Ba isotopes. In the evaluation of this correction, the general form of the matrix elements of two-body quadrupole operators, taken between paired-fermion states, is obtained. Our numerical results for Ba indicate that the effects of the g boson on the single-boson energy are of the correct sign and magnitude and that a perturbative approach to including these effects appears to be appropriate. NUCLEAR STRUCTURE Interacting boson approximation, perturbation theory of g boson, calculated 2+ - 0+ splittings in Ba.