Lowest eigenvalue of the nuclear shell model Hamiltonian

TL;DR

This paper identifies regular patterns in the nuclear shell model Hamiltonian's matrix elements and introduces a simple formula to accurately predict its lowest eigenvalue.

Contribution

The paper presents a novel, straightforward formula for predicting the lowest eigenvalue of the nuclear shell model Hamiltonian based on observed matrix element patterns.

Findings

The proposed formula predicts the lowest eigenvalue with remarkable accuracy.

Regular patterns in matrix elements are identified and utilized.

The approach simplifies understanding of the Hamiltonian's spectral properties.

Abstract

In this paper we investigate regular patterns of matrix elements of the nuclear shell model Hamiltonian $H$, by sorting the diagonal matrix elements from the smaller to larger values. By using simple plots of non-zero matrix elements and lowest eigenvalues of artificially constructed "sub-matrices" $h$ of $H$, we propose a new and simple formula which predicts the lowest eigenvalue with remarkable precisions.