Effect of Fine Structure on Nucleon Transfer to Analog States

Abstract

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 ${\ensuremath{\Gamma}}_{n}cos2({\ensuremath{\delta}}_{N}+\ensuremath{\varphi})$, where ${\ensuremath{\Gamma}}_{n}$ is the $n$ escape width, ${\ensuremath{\delta}}_{N}$ is the nuclear background phase shift, and $\ensuremath{\varphi}$ 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 $^{92}\mathrm{Mo}(d,n)$ 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 ${\ensuremath{\delta}}_{N}+\ensuremath{\varphi}$ is negligible.