Parameter adjustment of nuclear leading-order local pairing energy density functionals

Abstract

(See paper for full abstract) This study reports on the benchmarking of a protocol for the adjustment of the parameters of a local leading-order (LO) T=1 (like-particle) pairing EDF that consists in adjusting the density-dependence of the 1S0 pairing gap at the chemical potential in infinite nuclear matter (INM). When using a suitably chosen reference calculation, this protocol leads to consistent results for the odd-even staggering of masses of spherical and heavy deformed nuclei and also for the rotational moments of inertia calculated in a time-reversal-breaking cranked HFB approach. The implementation of the HFB solver for infinite matter at arbitrary isospin asymmetry used for this study is sketched in appendices. Additional points that are discussed concern (i) the illustration that the gaps at the chemical potential are not necessarily sufficient to completely characterise the pairing interaction in infinite matter, and that adjusting LO pairing EDF to reproduce gaps obtained from finite-range pairing interactions in HFB or from more microscopic calculations can lead to unrealistic predictions for finite nuclei; (ii) the finding that some regions of the parameter space for the density dependence of the T=1 LO pairing EDF lead to a spurious transition to a Bose-Einstein condensate of di-nucleons in spite of producing realistic pairing correlations for well-bound nuclei; (iii) the correlation between effective mass and the parameters of the LO pairing EDF that control the form factor of the density dependence when reproducing pairing gaps in infinite matter, (iv) the significant impact on the odd-even staggering of masses made by either including or not the spin-gradient terms in the particle-hole part of the Skyrme EDF; (v) the sizeable impact of keeping or not the contribution from the density-dependent LO pairing EDF to the mean fields on the odd-even staggering of radii.

Figures (25)

• Figure 1: Total energies $\Delta E$ of 1qp configurations in odd-mass Sn, Pb, and Yb isotopes relative to the ground state extracted from NuDatESNDF (upper row) compared with calculations with 1T2T(0.80) (also known as SLy7*) (middle row) for states with $K = \langle \hat{J}_z \rangle$ and parity as indicated. Following the convention of Ref. Dobaczewski15a, the sign indicates if the dominant single-particle component of the blocked qp is above (positive) or below (negative) the chemical potential (see text). Solid (dotted) lines indicate configurations of positive (negative) parity, whereas colour indicates angular momentum. The lower row displays the difference between the eigenvalues of the single-particle Hamiltonian $\varepsilon_i$ and the chemical potential of neutrons $\lambda_n$ in the even-even isotopes in between. For Yb isotopes, several deformed neutron shell closures predicted by 1T2T(0.80) are indicated.
• Figure 2: Gap $\Delta_q(k_{\lambda,q})$ of protons and neutrons at the respective $k_{\lambda,q}$ in paired INM calculated with SLy4+ULB at asymmetries between $I = 0$ (symmetric matter) and $I=1$ (neutron matter) in steps of 0.1 as a function of the total density $\rho$.
• Figure 3: Same as Fig. \ref{['fig:Delta:rho:SLy4+ULB']}, but as a function of the $k_{\lambda,q}$ of the respective nucleon species.
• Figure 4: Difference between $k_{\text{F},q}$ and $k_{\lambda,q}$ in symmetric INM calculated with SLy4+ULB.
• Figure 5: Product of occupation amplitudes $u_k v_k$ (panel a) and matrix elements $\Delta_k$ (panel b) and as a function of $k$ in a calculation with SLy4+ULB in symmetric INM at the densities as indicated.