The energy dependence of two-step distorted-wave Born approximation calculations is studied for unnaturalparity state excitations by the ($p,t$) reaction involving ($p,p^{\prime },t$), ($p,t,t^{\prime }$), and ($p,d,t$) processes. The calculations which provide rapidly decreasing cross sections with an increase in the incident energy are found to be quite consistent with the observed results for the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (8.88 MeV, $2^{-}$) reaction at the energy range of $E_p=20\mathrm{}-45$ MeV. The remarkable difference of kinematical features between one-step and twostep processes is pointed out and the importance of higher-order effects for one-step allowed transitions is apparently indicated.

NUCLEAR REACTIONS Energy dependence of second-order DWBA cross sections, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}(p,t){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ (8.88 MeV, $2^{-}$) and (9.85 MeV, $2^{+}$) $E=20.0\mathrm{}-43.6$ MeV.

• Received 22 June 1977

DOI:https://doi.org/10.1103/PhysRevC.17.1271