Angular Distribution ofγRadiation Following Direct Nuclear Reaction

The $\gamma$-ray angular distributions following the direct reaction ${\mathrm{C}}^{12}(p, p^{\prime }{\gamma }_{4.43\mathrm{M}\mathrm{e}\mathrm{V}}){\mathrm{C}}^{12}$ have been calculated for the cases of single-particle excitation and collective excitation using Glendenning's optical potential and the surface interaction model. In the case of particle excitation, the effective two-body potential has been assumed to have the form $V_d\mathrm{}\left(\right|\mathrm{}{\mathrm{r}}_p-{\mathrm{r}}_n\mathrm{}\left|\right)[a_0+a_1\sigma \mathrm{}(p\left)\mathrm{}·\sigma \mathrm{}\right(n\left)\right]$. Comparison with experiments at this laboratory for incident proton energies $E_p=6.69, 8.46, 8.71, \mathrm{and} 9.72$ MeV shows remarkably good fits for $\frac{a_1}{a_0}=\pm 0.67$. For the case of collective excitation, the agreement has been found to be poor. The plane-wave Born approximation for the incoming and outgoing waves does not yield satisfactory results for either mechanism.