Nucleon-pair truncation of the shell model for medium-heavy nuclei

TL;DR

This paper introduces an efficient shell model truncation method based on nucleon pairs, enabling accurate predictions of low-lying nuclear states in medium-heavy nuclei with deformation and shape coexistence.

Contribution

The authors develop a novel truncation scheme combining Hartree-Fock, NBCS, and angular momentum projection, improving computational efficiency for complex nuclei.

Findings

Good agreement with full shell model calculations for various nuclei

Predictions for nuclei difficult to compute with large-scale models

Highlights the importance of pairing and configuration mixing in nuclear collectivity

Abstract

Background: Computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations. Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum. Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast. Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: $^{44,46,48}$Ti, $^{48,50}$Cr, $^{52}$Fe, $^{60,62,64}$Zn, $^{66,68}$Ge, $^{68}$Se, and $^{108,110}$Xe. We predict low-lying states of $^{112-114}\textrm{Ba}$ and $^{116-120}\textrm{Ce}$, nuclei difficult to reach by large-scale SM calculations. Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.