Exactly solvable configuration mixing scheme in the vibrational limit of the interacting boson model

Abstract

An intruder configuration mixing scheme with $2n$-particle and $2n$-hole configurations from $n=0$ up to $n\ensuremath{\rightarrow}\ensuremath{\infty}$ in the U(5) (vibrational) limit of the interacting boson model is proposed. A simple Hamiltonian suitable to describe the intruder and normal configuration mixing is found to be exactly solvable, and its eigenstates can be expressed as the SU(1,1) coherent states built on the U(5) basis vectors of the interacting boson model. It is shown that the configuration mixing scheme keeps lower part of the vibrational spectrum unchanged and generates the intruder states due to the mixing. Some low-lying level energies and experimentally known $B(E2)$ ratios of $^{108,110}\mathrm{Cd}$ are fitted and compared with the experimental results.