Benchmarking rotational correction energies in odd-mass nuclei

TL;DR

This paper benchmarks the rotational correction energies in odd-mass nuclei calculated via the cranking approximation against exact angular-momentum projection within a covariant DFT framework, highlighting their agreement and addressing divergence issues.

Contribution

It provides a detailed comparison between cranking approximation and exact AMP for RCE in odd-mass nuclei, introducing a regulator for divergence issues.

Findings

Cranking approximation closely matches exact AMP for RCE in most nuclei.

Discrepancies occur near-spherical even-even nuclei.

A regulator improves RCE calculations for odd-mass nuclei.

Abstract

Nuclear energy density functional theory (DFT) provides a microscopic approach to describing nuclear masses. By incorporating pairing correlations and deformation within DFT, nuclear masses can be predicted with sub-MeV accuracy. A crucial factor in achieving this precision is the dynamical correlation energy associated with restoring rotational symmetry, known as rotational correction energy (RCE). This correction is typically estimated using the cranking approximation in perturbation theory. In this work, we benchmark the results of these calculations against exact angular-momentum projection (AMP) for both even-even and odd-mass nuclei from light to heavy mass region, utilizing a covariant DFT framework. We find that the RCE, computed using the full moment of inertia (MoI) in the cranking approximation, closely matches the results from exact AMP for both even-even and odd-mass nuclei, with the exception of near-spherical even-even nuclei. For certain configurations in odd-mass nuclei, however, the RCEs can become abnormally small, a phenomenon linked to the divergence of the MoI. To address this, a regulator is introduced for the MoI of an odd-mass nucleus, the validity of which is examined through exact AMP calculations.