Program in C for studying characteristic properties of two-body interactions in the framework of spectral distribution theory

TL;DR

This paper introduces a C program that uses spectral distribution theory to analyze two-body nuclear interactions, providing tools to measure similarity, strength, and key features like monopole parts and density dependence in complex nuclear systems.

Contribution

The program offers novel capabilities to identify monopole components, density-dependent parts, and compare interactions within large model spaces, advancing nuclear interaction analysis.

Findings

Calculates correlation coefficients and Hilbert-Schmidt norms for interactions.

Identifies monopole parts and density-dependent components of interactions.

Facilitates large-scale nuclear interaction studies beyond valence shells.

Abstract

We present a program in C that employs spectral distribution theory for studies of characteristic properties of a many-particle quantum-mechanical system and the underlying few-body interaction. In particular, the program focuses on two-body nuclear interactions given in a JT-coupled harmonic oscillator basis and calculates correlation coefficients, a measure of similarity of any two interactions, as well as Hilbert-Schmidt norms specifying interaction strengths. An important feature of the program is its ability to identify the monopole part (centroid) of a 2-body interaction, as well as its 'density-dependent' one-body and two-body part, thereby providing key information on the evolution of shell gaps and binding energies for larger nuclear systems. As additional features, we provide statistical measures for 'density-dependent' interactions, as well as a mechanism to express an interaction in terms of two other interactions. This, in turn, allows one to identify, e.g., established features of the nuclear interaction (such as pairing correlations) within a general Hamiltonian. The program handles the radial degeneracy for 'density-dependent' one-body interactions and together with an efficient linked list data structure, facilitates studies of nuclear interactions in large model spaces that go beyond valence-shell applications.