Microscopic calculations of nuclear level densities with the Lanczos method

TL;DR

This paper introduces an extrapolated Lanczos method to accurately compute nuclear level densities, enabling predictions near neutron separation energies with fewer iterations, validated against experimental data for specific isotopes.

Contribution

The paper presents a novel extrapolated Lanczos matrix approach that predicts nuclear level densities efficiently from limited iterations, improving computational accuracy.

Findings

Accurately predicts level densities near neutron separation energy.

Shows good agreement with experimental data for selected nuclei.

Provides insights into J-dependence of nuclear moments.

Abstract

A new method for computing the density of states in nuclei making use of an extrapolated form of the tri-diagonal matrix obtained from the Lanczos method is presented. It will be shown that the global, average properties of the entire Lanczos matrix can be predicted from just four Lanczos iterations. The extrapolated Lanczos matrix (ELM) approach provides for an accurate computation of the density of states described within the configuration space, which, in some cases, is sufficient to accurately calculate the density of states at, or near, the neutron separation energy. Comparisons between theory and experiment are shown for $^{57}$Fe, $^{74}$Ge, and $^{76}$Ge. In addition, we show results for the $J$-dependence of moments and the level density for these three nuclei.