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

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 lambda. 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 M & ouml;ller and Nix [Nucl. Phys. A 476, 1 (1992)], and (b) a correction for a systematic spurious enhancement of rho(e)for protons in the vicinity of lambda, 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)].