Coupled-channel Born approximation andl=2jdependence inSi28(d,p)Si29from 10 to 18 MeV

We discuss the general problem of $j$ dependence in nuclear reactions, and evidence that $l=2\mathrm{}j$ dependence seen in ($d,p$) reactions is, at least in many cases, connected with the collective character of the target and residual nuclei in the reaction. To test this idea, we present analyses of three sets of data for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}(d,p){}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, at 10, 13, and 18 MeV incident deuteron energy. These analyses are performed in terms of the coupled channel Born approximation (CCBA), and include inelastic excitations of vibrational character both in entrance and exit channels. It is shown that the observed $l=2\mathrm{}j$ dependence, particularly for the 1.28 MeV ${\frac{3}{2}}^{+}$ and 2.03 MeV ${\frac{5}{2}}^{+}$ states in ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, can be well explained by CCBA. Evidence is also presented that the 2.03 MeV ${\frac{5}{2}}^{+}$ and 2.43 MeV ${\frac{3}{2}}^{+}$ states have to a large extent the character [${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}\left(2_1^{+}\right)\times {\left(s_{\frac{1}{2}}\right)}_n$].