Importance-Truncated Large-Scale Shell Model

TL;DR

This paper introduces an importance-truncation scheme for the nuclear shell model that enables calculations in larger valence spaces by selectively including significant basis states, improving computational efficiency while maintaining accuracy.

Contribution

The authors develop a perturbative importance-truncation method that extends shell-model calculations to larger spaces and nuclei, with a posteriori extrapolation techniques to recover full results.

Findings

Efficiently handles larger valence spaces in shell-model calculations.

Accurately reproduces full shell-model results through extrapolation.

Demonstrates applicability to medium-mass nuclei like 56-Ni, 60-Zn, and 64-Ge.

Abstract

We propose an importance-truncation scheme for the large-scale nuclear shell model that extends its range of applicability to larger valence spaces and mid-shell nuclei. It is based on a perturbative measure for the importance of individual basis states that acts as an additional truncation for the many-body model space in which the eigenvalue problem of the Hamiltonian is solved numerically. Through a posteriori extrapolations of all observables to vanishing importance threshold, the full shell-model results can be recovered. In addition to simple threshold extrapolations, we explore extrapolations based on the energy variance. We apply the importance-truncated shell model for the study of 56-Ni in the pf valence space and of 60-Zn and 64-Ge in the pfg9/2 space. We demonstrate the efficiency and accuracy of the approach, which pave the way for future shell-model calculations in larger valence spaces with valence-space interactions derived in ab initio approaches.