Consequences of Isospin and Other Conserved Quantum Numbers for Compound-Nucleus Reactions

Abstract

Consequences of the conserved isospin quantum number $T$ are developed for compound-nucleus reactions with particular emphasis on statistical cross-section fluctuations. The formalism is based on the Hauser-Feshbach and Ericson theories. The appropriate autocorrelation function in case of levels of two different isospin values in the compound nucleus contains an interference term between two Lorentzian functions that are associated with the two isospins. The formalism is applied to the statistical reactions ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}(p,p)$ and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}(p,\alpha )$, where the coherence widths in the proton and $\alpha$ channels are markedly different. This is attributed to the decay properties of states with different isospin in the compound nucleus ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$. The formalism developed for the isospin quantum number $T$ can be extended to other quantum numbers. For the case of angular momentum and parity $J\pi$ interesting consequences with respect to heavy-ion reactions are discussed.