The moment of inertia in the interacting boson model

Abstract

We perform a self-consistent cranking calculation of intrinsic states of IBM-1 and IBM-2 for three reasons: (a) to study the effect of Coriolis and centrifugal forces in the IBM; (b) to derive approximate analytic formulae for the energy in some cases where the IBM hamiltonian does not have dynamical symmetry; (c) to study the dependence of the moments of inertia on the variables of the intrinsic IBM states. Choosing a coordinate system where the quadrupole tensor is diagonal reduces the number of variables considerably. Among other applications of our formalism we study the transition between the symmetries SU(3) and SU ∗(3) in the IBM-2 hamiltonian H = −( Q π + Q ν ) · ( Q π + Q ν ). We find that the moments of inertia and the asymmetry variables show a kind of phase transition, as a function of the parameter χ ν occurring in Q ν .