Determination of a pairing residual interaction from Bohr quadrupole collective dynamics

It is shown that an efficient yet very simple way of adjusting the intensity of a T z = 1 zero-range (δ) pairing residual interaction in a given region of the nuclear chart is to perform a fit of the moments of inertia of the first 2+ states of carefully chosen deformed nuclei. These nuclei must be well-deformed and rigid with respect to quantal shape fluctuations around their classical equilibrium solution. This qualification is assessed quantitatively a posteriori by producing the results of a full 5D quadrupole dynamical calculations à la Bohr. The seven scalar functions of the relevant collective Hamiltonian are obtained from a set of static solutions spanning a (β, γ) sextant obtained within the Highly Truncated Diagonalization Approach (HTDA) using the fitted residual interaction. The particle-hole part of the Hamiltonian includes the SIII Skyrme interaction the quality of which for deformation properties has been well established for a very long time. The adiabatic parameters in use, are derived from a non-self-consistent Adiabatic Time-Dependent Hartree-Fock-Bogolyubov Approach (ATDHFB) crudely corrected for the so-called Thouless-Valatin time-odd consistency effects. The quality of this approach is exemplified here for nuclei in and around the rare-earth nuclear region.