Alignment and decay of isobaric analog states formed by ($p,n$) reactions

Calculations are presented here for the angular correlation between the neutron and proton in ($p,np$) reactions, where the ($p,n$) reaction excites the isobaric analog state of the target ground state, which then decays by proton emission. The ($p,n$) reaction is treated as a charge-exchange direct reaction and calculations are done in the plane wave Born approximation, with a microscopic proton-nucleus interaction taken as a sum of two-body interactions. While the commonly used macroscopic charge-exchange interaction $V_0\mathrm{}\left(r\right)\mathrm{}\overrightarrow{t}·\overrightarrow{\mathrm{T}}$ is spherically symmetric, a microscopic interaction with individual nucleons allows higher multipole transfers and can lead to alignment of the isobaric analog state. The alignment of the isobaric analog state is sensitive to the relative importance of the higher multipole transfers that contribute to the formation of the IAS. The importance of these higher multipoles depends on the properties of the nucleon-nucleon interaction and also on the angle of neutron emission, which affects the momentum transfer. The alignment of the isobaric analog state can be inferred from the study of the decay channels of the isobaric analog state. For $A\gtrsim 60$, the isobaric analog state can decay by particle emission. Thus, the alignment of the isobaric analog state can be studied by the measurement of angular distributions of the decay protons in coincidence with the neutrons. Illustrative calculations of the alignment of the isobaric analog state and the angular distribution of decay protons are presented here for several nuclei, and comparisons with experimental measurements of $n-p$ coincidence angular distributions for ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ and ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$ are presented. The anisotropies in these two cases are weak. However, strong alignments of the isobaric analog state found theoretically for $A\lesssim 60$ suggest that ($p,n\gamma$) correlation experiments for those nuclei would be interesting.

NUCLEAR REACTIONS ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{99}{}_{}{}^{}\mathrm{Tc}(p,n\overline{p})$, $E=17\mathrm{}$ MeV, calculated $n-\overline{p}$ angular correlation; ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{99}{}_{}{}^{}\mathrm{Ru}$ (${}_{}{}^{99}{}_{}{}^{}\mathrm{Ru}(p,n\gamma )$) IAS, $E=17\mathrm{}$ MeV, calculated alignment of magnetic substates; ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$ (${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}(p,n\overline{p})$), $E=17\mathrm{}$ MeV, measured $n-\overline{p}$ angular correlation.