Fermi operator expansion method for nuclei and inhomogeneous matter with nuclear energy density functional

TL;DR

This paper evaluates the Fermi operator expansion method as an efficient alternative to traditional diagonalization techniques for finite nuclei and inhomogeneous nuclear matter at finite temperature, demonstrating its effectiveness and scalability.

Contribution

It introduces and tests the Fermi operator expansion method for nuclear density functional calculations, avoiding diagonalization and orthonormalization, suitable for large-scale parallel computing.

Findings

Effective for high-temperature nuclear matter simulations

Reduces computational costs compared to traditional methods

Suitable for massively parallel and large-scale calculations

Abstract

The nuclear energy density functional method at finite temperature is a useful tool for studies of nuclear structure at high excitation, and also for researches of nuclear matter involved in explosive stellar phenomena and neutron stars. However, its unrestricted calculation requires large computational costs for the three-dimensional coordinate-space solvers, especially for the Hamiltonian matrix diagonalization and (or) the Gram-Schmidt orthonormalization of the single-particle wave functions. We test numerical performance of the Fermi operator expansion method, that requires neither the diagonalization nor the Gram-Schmidt orthonormalization, for finite nuclei and inhomogeneous nuclear matter. The method is applied to isolated finite N=Z nuclei and to non-uniform symmetric nuclear matter at finite temperature, which turns out be very effective with the three-dimensional coordinate-space representation, especially at high temperature. The Fermi operator expansion method is a useful tool for studies of various nuclear phases at finite temperature with the energy density functional calculations. The method is suitable for massively parallel computing with distributed memory. Furthermore, when the space size is large, the calculation may benefit from its order-N scaling property.