Microscopic study of low energy collective states in even-even nuclei: A prospective analysis of dynamical corrections to vibrational mass parameters

A systematic study of low energy nuclear structure at normal deformation has been carried out using the Generator Coordinate Method mapped onto a 5-Dimensional Collective quadrupole Hamiltonian (5DCH) by using the Gaussian Overlap Approximation (GCM-GOA). The collective space is spanned by Hartree Fock Bogoliubov (HFB) states under axial and triaxial quadrupole constraints deduced with the D1S Gogny force. In addition, our 5DCH includes the Thouless-Valatin dynamical corrections to its rotational kinetic terms. The work is described in detail elsewhere together with the corresponding comparisons with experimental data when it is available. Many properties show a satisfactory agreement with experiment, but there is an almost systematic overestimation of vibrational band head energies, which is the subject of the present paper. We show here the performance of the theory on related observables, and propose improvements of the theory to address the problem of the vibrational band heads. An important reason for the deficient is the treatment of vibrational inertial parameters. In particular, the theory needs to include the dynamical Thouless-Valatin corrections to the vibrational terms in the 5DCH. In present work, on the aim of a simple formula grounded by known symmetry rules within the 5DCH, these dynamical TV corrections are roughly estimated, allowing us to handle their possible effects in term of spectroscopic properties, to present a guess of the next model improvment, and to isolate some areas in the chart where states I_n^π = 0⁺₂, 2⁺₂ or 2⁺₃ seem to have important components out of the scope of a pure collective quadrupole approach.