Random interactions, isospin, and the ground states of odd-Aand odd-odd nuclei

Abstract

It was recently shown that the ground state quantum numbers of even-even nuclei have a high probability to be reproduced by an ensemble of random but rotationally invariant two-body interactions. In the present work we extend these investigations to odd-$A$ and odd-odd nuclei, considering in particular the isospin effects. Studying the realistic shell model as well as the single-$j$ model, we show that random interactions have a tendency to assign the lowest possible total angular momentum and isospin to the ground state. In the $\mathrm{sd}$ shell model this reproduces correctly the isospin but not the spin quantum numbers of actual odd-odd nuclei. An odd-even staggering effect in probability of various ground state quantum numbers is present for even-even and odd-odd nuclei, while it is smeared out for odd-$A$ nuclei. The observed regularities suggest the underlying mechanism of bosonlike pairing of fermionic pairs in $T=0$ and $T=1$ states generated by the off-diagonal matrix elements of random interactions. The relation to the models of random spin interactions is briefly discussed.