Double-step truncation procedure for large-scale shell-model calculations

TL;DR

This paper introduces a double-step truncation method for large-scale shell-model calculations that reduces computational complexity while effectively preserving the influence of excluded degrees of freedom, validated on isotopic chains around 88Sr.

Contribution

The paper presents a novel two-step truncation procedure combining effective single-particle energy analysis and unitary transformation to create smaller, accurate shell-model spaces.

Findings

The method effectively reduces model space size while maintaining accuracy.

Shell-model results are reliable across various isotopic chains.

The approach preserves the role of excluded orbitals in the effective Hamiltonian.

Abstract

We present a procedure that is helpful to reduce the computational complexity of large-scale shell-model calculations, by preserving as much as possible the role of the rejected degrees of freedom in an effective approach. Our truncation is driven first by the analysis of the effective single-particle energies of the original large-scale shell-model hamiltonian, so to locate the relevant degrees of freedom to describe a class of isotopes or isotones, namely the single-particle orbitals that will constitute a new truncated model space. The second step is to perform an unitary transformation of the original hamiltonian from its model space into the truncated one. This transformation generates a new shell-model hamiltonian, defined in a smaller model space, that retains effectively the role of the excluded single-particle orbitals. As an application of this procedure, we have chosen a realistic shell-model hamiltonian defined in a large model space, set up by seven and five proton and neutron single-particle orbitals outside 88Sr, respectively. We study the dependence of shell-model results upon different truncations of the original model space for the Zr, Mo, Ru, Pd, Cd, and Sn isotopic chains, showing the reliability of this truncation procedure.