Pairing gaps in the Hartree-Fock-Bogoliubov theory with the Gogny D1S interaction

Abstract

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z = 8, 50 and 82 spherical chains and the Z = 62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by 100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings.

Tables of E2 transition probabilities from the first 2+ states in even–even nuclei

“…The 32 Ar measurement, taken together with previously existing Coulomb excitation data for 32 Si [1998Ib01], yields the isoscalar and isovector multipole matrix elements for the transition between T =2 states in the A=32 system. Complementary Coulex and RDM measurements of 44,46 Ar were conducted at GANIL, France and Legnaro, Italy facilities [2009Zi01, 2010Me07], respectively. These experiments addressed the development of deformation and shape coexistence in the vicinity of the doubly magic 48 Ca, related to the weakening of the N =28 shell closure.…”

Spin constraints on nuclear energy density functionals

“…We have developed new code to find the Hartree-Fock-Bogoliubov minima of the Gogny functional in axially symmetric nuclei, treating for the first time time-odd fields including the spin-dependent ones [8]. Applying the code to spin splittings in deformed nuclei, we found that the predicted splittings violated the GM rule more often than not.…”

Competition between pairing correlations and deformation from the odd-even mass staggering of francium and radium isotopes

“…The description of the properties of odd nuclides has received considerable interest during recent years in the framework of mean-field theory [1,[6][7][8][9][10][11][12], where the OES of binding energies is the main constraint for the pairing interaction. As such, efforts have been devoted to understanding the different contributions to the OES and designing precise estimators for the pairing gap.…”