Sensitivity analysis of random shell-model interactions

The input to the configuration-interaction shell model includes many dozens or even 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. Following Brown and Richter [1], here we consider general two-body interactions in the 1s-0d shell and find that the low-lying spectra are also only sensitive to a few linear combinations of two-body matrix elements. We find out in particular the ground state energies for both the random and non-random (here given by the USDB) interaction are dominated by similar matrix elements, which we try to interpret in terms of monopole and contact interactions, while the excitation energies have completely different character. \\[4pt] [1] B. Alex Brown and W. A. Richter, Phys. Rev. C 74, 034315 (2006)