Towards accurate nuclear mass tables in covariant density functional theory

TL;DR

This paper analyzes and compares optimization protocols in covariant density functional theory, investigates basis truncation errors in nuclear binding energy calculations, and proposes methods to improve accuracy and convergence in nuclear mass tables.

Contribution

It introduces a new optimization approach (ABOA), studies basis truncation errors globally, and proposes a novel procedure for better error control in covariant density functional theory.

Findings

ABOA achieves similar results to other methods with less computational time.

Truncating the bosonic basis at N_B=28 reduces errors below 10 keV for most nuclei.

Convergence speed of binding energies depends on the type of energy density functional.

Abstract

The current investigation focuses on detailed analysis of the anchor based optimization approach (ABOA), its comparison with alternative global fitting protocols and on the global analysis of the truncation of basis effects in the calculation of binding energies. It is shown that ABOA provides a solution which is close to that obtained in alternative approaches but at small portion of their computational time. The application of softer correction function after few initial iterations of ABOA stabilizes and speeds up its convergence. For the first time, the numerical errors in the calculation of binding energies related to the truncation of bosonic and fermionic bases have been globally investigated with respect of asymptotic values corresponding to the infinite basis in the framework of covariant density functional theory (CDFT). These errors typically grow up with the increase of the mass and deformation of the nuclei. To reduce such errors in bosonic sector below 10 keV for almost all nuclei with proton number $Z<120$ one should truncate the bosonic basis at $N_B=28$ instead of presently used $N_B=20$. The reduction of the errors in binding energies due to the truncation of the fermionic basis in CDFT is significantly more numerically costly. For the first time it is shown that the pattern and the speed of the convergence of binding energies as a function of the size of fermionic basis given by $N_F$ depend on the type of covariant energy density functional. The use of explicit density dependence of the meson-nucleon coupling constants or point couplings slows down substantially the speed of convergence of binding energies as a function of $N_F$. A new procedure for finding the asymptotic values of binding energies is suggested in the present paper: it allows better control of numerical errors.