Determination of the asymptoticD- toS-state ratio for6Livia(6Li→,d)transfer reactions

Abstract

Measurements of cross section, vector analyzing power ${A}_{y},$ and tensor analyzing powers ${A}_{\mathrm{zz}}$ and ${A}_{\mathrm{xz}}$ over the angular range $10\ifmmode^\circ\else\textdegree\fi{}<~{\ensuremath{\theta}}_{\mathrm{lab}}<~40\ifmmode^\circ\else\textdegree\fi{}$ have been performed at ${E(}^{6}\mathrm{Li})=34 \mathrm{MeV}$ for the ${}^{58}\mathrm{Ni}{(}^{6}\mathrm{Li}\ensuremath{\rightarrow}{,d)}^{62}\mathrm{Zn}$ and ${}^{40}\mathrm{Ca}{(}^{6}\mathrm{Li}\ensuremath{\rightarrow}{,d)}^{44}\mathrm{Ti}$ reactions leading to the ground state and first excited state of both residual nuclei. The reactions are described by distorted-wave Born approximation calculations, assuming a direct $\ensuremath{\alpha}$-particle transfer mechanism. The asymptotic $D/S$ state ratio $\ensuremath{\eta}$ for the $d+\ensuremath{\alpha}$ relative wave function in ${}^{6}\mathrm{Li}$ is determined. In this one-step analysis, the best fit to the tensor observables leads to a value of $\ensuremath{\eta}=+0.0003\ifmmode\pm\else\textpm\fi{}0.0009.$ This value is in disagreement with most of the previous theoretical and empirical determinations of $\ensuremath{\eta}.$ An investigation of two-step reaction mechanisms is performed, allowing the ${J}^{\ensuremath{\pi}}{=3}^{+},$ ${2}^{+},$ and ${1}^{+}$ states in ${}^{6}\mathrm{Li}$ to contribute to the transfer reaction channel. Reasonable agreement is achieved with the cross section and vector analyzing power data for several possible two-step amplitudes. It is found that the fitted magnitude of $\ensuremath{\eta}$ increases with increasing two-step amplitude, giving $\ensuremath{\eta}=\ensuremath{-}0.0030\ifmmode\pm\else\textpm\fi{}0.0022$ for unit amplitude, therefore not changing significantly from our one-step result.