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Direct evidence of the $\alpha$-cluster manifestation in bound states has notbeen obtained yet, although a number of experimental studies were carried outto extract the information of the clustering. In particular in conventionalanalyses of $\alpha$-transfer reactions, there exist a few significant problemson reaction models, which are insufficient to qualitatively discuss the clusterstructure. We aim to verify the development of the $\alpha$-cluster structurefrom observables. As the first application, we plan to extract the spatialinformation of the cluster structure of the $^{20}$Ne nucleus in its groundstate through the cross section of the $\alpha$-transfer reaction$^{16}$O($^6$Li,~$d$)$^{20}$Ne. For the analysis of the transfer reaction, wework with the coupled-channel Born approximation (CCBA) approach, in which thebreakup effect of $^6$Li is explicitly taken into account by means of thecontinuum-discretized coupled-channel method based on the three-body $\alpha +d + {}^{16}$O model. The two methods are adopted to calculate the overlapfunction between $^{20}$Ne and $\alpha + {}^{16}$O; one is the microscopiccluster model (MCM) with the generator coordinate method, and the other is thephenomenological two-body potential model (PM). We show that the CCBAcalculation with the MCM wave function gives a significant improvement of thetheoretical result on the angular distribution of the transfer cross section,which is consistent with the experimental data. Employing the PM, it isdiscussed which region of the cluster wave function is probed on the transfercross section. It is found that the surface region of the cluster wave functionis sensitive to the cross section. The present work is situated as the firststep in obtaining important information to systematically investigate thecluster structure.

Probing surface distributions of $\alpha$ clusters in $^{20}$Ne via $\alpha$-transfer reaction