Breaking of isospin symmetry in compound-nucleus reactions

Abstract

The authors present an analysis of all extant data on isospin mixing in statistical compound-nucleus reactions. The analysis is based on a generalization of the Hauser-Feshbach formula allowing for isospin mixing. The strength of the mixing is described by a single parameter $z$. The theory is applicable when all compound-nucleus resonances overlap strongly. It is derived from a statistical theory of nuclear reactions allowing for the mixing of two classes of states. The parameter $z$ comprises both internal mixing (via the Coulomb interaction) and external mixing (via the channels). The theory contains both the static criterion (Coulomb matrix elements compared with spacings) and the dynamical criterion (spreading widths compared with decay widths) for isospin symmetry breaking. The theory yields the dependence on $z$ of observables like average cross sections, and auto- and cross-correlation functions. The data show that isospin symmetry breaking is neither so weak as to be altogether negligible, nor so strong as to reduce our theory to a Hauser-Feshbach formalism without any reference to the isospin quantum number. The authors argue in favor of a parametrization of isospin symmetry breaking in the data in terms of a spreading width rather than a Coulomb matrix element. They find that internal mixing dominates, and that the associated spreading width is nearly independent of mass number and excitation energy.