Sensitivity analysis of random two-body interactions

TL;DR

This paper demonstrates that low-lying spectra in the shell model are highly sensitive to only a few linear combinations of two-body matrix elements, whether from random ensembles or empirical fits, revealing underlying similarities.

Contribution

It shows that random two-body interactions exhibit sensitivity patterns similar to empirical interactions, highlighting fundamental features of nuclear spectra.

Findings

Low-lying spectra are sensitive to few linear combinations of matrix elements.

Random and empirical interactions share similar sensitivity patterns.

Spectral sensitivity analyzed using monopole and contact interactions.

Abstract

The input to the configuration-interaction shell model includes many dozens or hundreds of independent two-body matrix elements. Previous studies have shown that when fitting to experimental low-lying spectra, the greatest sensitivity is to only a few linear combinations of matrix elements. Here we consider interactions drawn from the two-body random ensemble, or TBRE, and find that the low-lying spectra are also most sensitive to only a few linear combinations of two-body matrix elements, in a fashion nearly indistinguishable from an interaction empirically fit to data. We find in particular the spectra for both the random and empirical interactions are sensitive to similar matrix elements, which we analyze using monopole and contact interactions.