Odd-even mass differences of well and rigidly deformed nuclei in the rare earth region: Test of a newly proposed fit for average pairing matrix elements*

Abstract We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle (sp) states around the Fermi level, denoted as λ. This method, known as the uniform gap method (UGM), highlights the critical importance of the averaged sp level density . The pairing matrix elements within the UGM approach are deduced from microscopically calculated values of and gaps obtained from analytical formulae of a semi-classical nature. Two effects generally ignored in similar fits are addressed: (a) a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions, as discussed by Möller and Nix [Nucl. Phys. A 476, 1 (1992)], and (b) a correction for a systematic spurious enhancement of for protons in the vicinity of λ , caused by the local Slater approximation commonly employed in treating Coulomb exchange terms ( e.g., [Phys. Rev. C 84, 014310 (2011)]). This approach has demonstrated significant efficiency when applied to Hartree-Fock + Bardeen-Cooper-Schrieffer (BCS) calculations (including the seniority force and self-consistent blocking for odd nuclei) of a large sample of well and rigidly deformed even-even rare-earth nuclei. The experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data [Phys. Rev. C 99, 064306 (2019)]. In this study, we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd- N or odd- Z nuclei in the same region. The agreement with experimental data was found to be comparable to that obtained through direct fitting, as reported in [Phys. Rev. C 99, 064306 (2019)].