Effect of Fine Structure on Nucleon Transfer to Analog States

We extend our previous distorted-wave Born-approximation treatment of reactions of the form $A(d,p)B$ (in which $B$ is an unbound state) to include the case where $B$ is (a) dissolved into a fine structure of resonances that may overlap strongly, and (b) unstable against emission of other particles in addition to the transferred particle $n$. We assume that the reaction is strongly peripheral and goes through the $n+A$ channel of $B$ via the $\mathrm{np}$ interaction. We discuss the cross section for an experiment in which only particle $p$ is detected, while the decay products of $B$ are not observed or identified. For an isobaric-analog resonance we find that the cross section is proportional to ${\Gamma }_{n}cos2({\delta }_N+\phi )$, where ${\Gamma }_n$ is the $n$ escape width, ${\delta }_N$ is the nuclear background phase shift, and $\phi$ is the asymmetry phase. The cross section is entirely determined by the gross-structure parameters of the resonance, and does not depend on the nature of the fine structure. For the reaction ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}\mathrm{}(d,n)\mathrm{}$ to $d_{\frac{5}{2}}$ (8.40-MeV), $s_{\frac{1}{2}}$ (9.33-MeV), and $d_{\frac{3}{2}}$ (9.91-MeV) analog states, we find that the effect of ${\delta }_N+\phi$ is negligible.