Shell-Model Theory of Nuclear Reactions in Deformed Nuclei

Abstract

A theoretical study has been made of the intermediate-structure resonances observed in neutron scattering and proton capture by ${\mathrm{F}}^{19}$ in terms of simple excitations of the compound nucleus using Feshbach's formalism for nuclear and photonuclear reactions. The simple excitations were taken to be particle-hole states in the deformed-level scheme, including the excitation of rotational bands. The average resonance widths, and spacing, and average total cross section ($\ensuremath{\Delta}E=0.5$ MeV) observed for $n+{\mathrm{F}}^{19}$ with neutron energy between 0.5 and 2.5 MeV is reasonably well reproduced by the model. In particular, the agreement with the average total cross section indicates that an optical potential can be derived from the above model. In proton capture by ${\mathrm{F}}^{19}$, though the calculated widths of the resonances are of the correct order of magnitude, the relative spacing of the resonances and magnitude of the cross sections is not in agreement with experiment.