Band structure of odd-Arubidium isotopes in the interacting boson fermion model

Abstract

Energy spectra and $E2\mathrm{}$ matrix elements have been calculated by means of the interacting boson fermion model for ${}_{}{}^{79,81,83}{}_{}{}^{}\mathrm{Rb}$. A more schematic description obtained by assuming that the extra proton which is coupled to an even-even Kr core is in a pure $g_{\frac{9}{2}}$ particle state has been compared with calculations within a larger model space including the $d_{\frac{5}{2}}$ and $g_{\frac{7}{2}}$ particle states. We find that it is possible to achieve excellent agreement for both the schematic and the more detailed calculation as far as only level energies are concerned. However, the choice of the model space turns out to have a strong influence on the model parameters. Moreover, we find that $B\left(E2\mathrm{}\right)\mathrm{}$ values differ considerably in both descriptions. We conclude that even if there is a large separation between shells, the mixing due to the strong core-particle quadrupole force does not allow for restricting the model space to a single $j$ shell.