D-state amplitudes of three-nucleon systems using single-nucleon transfer reactions

New determinations of the D-state amplitudes for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and the triton have been made by studying the tensor analyzing powers for the ground state transitions in ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$(d→${,}^3$He${)}^{30}$Si and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$(d→,t${)}^{30}$P reactions at $E_{\mathrm{d}\mathrm{\simeq }16}$ MeV. Exact finite range distorted-wave Born approximation analyses of these data for an angular range of 20° to 135° yields $D_2$ ${(}^3$He)=-0.24±0.04 ${\mathrm{fm}}^2$ and $D_2$(t)=-0.25±0.05 ${\mathrm{fm}}^2$. The asymptotic D/S-state ratios, η, are also determined and compared with predictions of Gibson-Lehman wave functions for the three-nucleon system. We obtain η${(}^3$He)=-0.042±0.007 and η(t)=-0.050±0.010. .AE