Random matrix structure of nuclear shell model Hamiltonian matrices and comparison with an atomic example

Abstract

We present a comprehensive analysis of the structure of Hamiltonian matrices based on visualization of the matrices in three dimensions as well as in terms of measures for GOE, banded and two-body random matrix ensembles (TBRE). We have considered two nuclear shell model examples, 22Na with \(\ensuremath J^{\pi} T = 2^+0\) and 24Mg with \(\ensuremath J^{\pi} T = 0^+0\) and, for comparison we have also considered the SmI atomic example. It is clearly established that the matrices are neither GOE nor banded. For the TBRE structure we have examined the correlations between diagonal elements and eigenvalues, fluctuations in the basis states variances and structure of the two-body part of the Hamiltonian in the eigenvalue basis. Unlike the atomic example, nuclear examples show that the nuclear shell model Hamiltonians can be well represented by TBRE.