A microscopic model for the description of the giant multipole resonances in light deformed nuclei and their excitation via ($p, \gamma$) reactions is proposed. A version of Feshbach's formalism of nuclear reactions is used for which the bound states of the target and compound systems are described as linear combinations of angular momentum projected deformed hole and particle-hole configurations, respectively. The theory is applied to study the giant multipole resonances in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ as seen via ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(p, \gamma ){}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reactions. Results for both the transitions to the ground state as well as the first $2^{+}$ excited state of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ are calculated and a number of approximations are tested. The 90° yields are found to be in good agreement with experiment. Gross features as well as intermediate structures of the experimental cross sections are reasonably well reproduced.

NUCLEAR STRUCTURE ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$; Calculated spectra and $E1\mathrm{}$ transitions. Angular momentum projected Hartree-Fock and Tamm-Dancoff methods.

NUCLEAR REACTIONS ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}(p, \gamma )$; radiative capture. Calculated cross sections to ground and first excited state.

• Received 1 November 1976

DOI:https://doi.org/10.1103/PhysRevC.15.1515