Isotopic-Spin Mixing in Direct and Compound-Nuclear Reactions

The semidirect mechanism of isospin violation in deuteron-induced nuclear reactions, which was presented in an earlier article, is recapitulated. A number of reactions involving the same basic mechanism are discussed and the available data on them are briefly reviewed. This mechanism also leads to much stronger isospin mixing in certain levels in light nuclei than is predicted by the usual perturbative treatment of Coulomb interactions. Such mixing is discussed in terms of a simple two-level model. A suggestion by Levinson has led to a reexamination of the Wilkinson hypothesis that isospin-violating reactions proceed via formation of isotopically impure compound-nuclear levels at "intermediate" excitation energies. It is shown that the most important factor in determining the contribution of these levels is not their degree of isospin mixing, but rather the experimental energy resolution. If the resolution $I$ is poor compared to the average spacing $〈D_J〉$ of levels of given $J^P$, then in general the contribution of these levels is reduced by the ratio $\frac{〈D_J〉}{I}$. When compound levels are so correlated as to give rise to intermediate structure, or a giant resonance, or an isobaric analog state, their contribution to the isospin-nonconserving amplitude need not be small. This implies that isospin-violating reactions are ideally suited to the study of intermediate structure. Because the actual level density in light nuclei at intermediate excitation is not well known, it is not clear whether Levinson's suggestion is relevant to the studies so far conducted on (a) ${\mathrm{C}}^{12}(d,\alpha ){\mathrm{B}}^{10*}\mathrm{}(1.74,T=1)\mathrm{}$, and (b) ${\mathrm{O}}^{16}(d,\alpha ){\mathrm{N}}^{14*}\mathrm{}(2.31,T=1)\mathrm{}$. It is surely relevant to heavier compound nuclei, however, and estimates based on a statistical level-density formula suggest that Levinson's idea is even relevant for the ${\mathrm{N}}^{14}$ and ${\mathrm{F}}^{18}$ compound nuclei entering reactions (a) and (b) above. Finally, the data of Meyer-Schützmeister et al. are analyzed for evidence of compound-direct interference. It is conjectured on the basis of a crude but suggestive calculation that the broad $3^{-}$ (with some possible $1^{-}$ admixture) resonance seen by them in ${\mathrm{N}}^{14}$ at $E_x\sim 18$ MeV is actually an intermediate-structure resonance whose "doorway state" is a "single-particle cluster resonance" in either the entrance or exit channels, or in both. A brief theoretical discussion of compound-direct interference is included for completeness.