Shape phase transitions in the interacting boson model: Phenomenological versus microscopic descriptions

Abstract

We investigate the shape phase transition in even-even ${}_{64}$Gd and ${}_{66}$Dy isotopes within the proton-neutron interacting boson model (IBM-2). The parameters of the IBM-2 Hamiltonian are fixed in two different ways: the usual phenomenological fitting calculation and the mapping of the constrained self-consistent mean-field calculation with a Skyrme energy density functional onto the appropriate boson system. Notable differences are found between the energy surfaces for the phenomenological and the mapped IBM-2. Key quantities for the collective structural evolution, including level energies, $B(\mathrm{E}2)$ values, quadrupole moments, and the two-neutron separation energies, are analyzed in comparison to the experimental data. We show that the transition in these quantities occurs rapidly with the neutron number in the IBM-2 phenomenology but is somewhat smeared out in the mapped IBM-2. The differences in the measurable quantities are consistent with what is suggested by the energy-surface analysis.