Investigation of spatial manifestation of $\alpha$ clusters in ${}^{16}$O via $\alpha$-transfer reactions

Abstract

Recently, we have determined surface distributions of $\alpha$ clusters in the ground state of ${}^{20}\mathrm{Ne}$ from $\alpha$-transfer cross sections, without investigating the properties of its excited states. In this paper we extend our comprehension of $\alpha$-cluster structures in excited states of nuclei through reaction studies. In particular we focus on ${}^{16}\mathrm{O}$, for which attention has been paid to advances of structure theory and assignment regarding $4^{+}$-resonance states. We study the surface manifestation of the $\alpha$-cluster states in both the ground and excited states of ${}^{16}\mathrm{O}$ from the analysis of the $\alpha$-transfer reaction ${}^{12}\mathrm{C}{(}^6\mathrm{Li},d{)}^{16}\mathrm{O}$. The $\alpha$-transfer reaction is described by the distorted-wave Born approximation. We test two microscopic wave functions as an input of reaction calculations. Then a phenomenological potential model is introduced to clarify the correspondence between cluster-wave functions and transfer-cross sections. Surface peaks of the $\alpha$-wave function of ${}^{16}\mathrm{O}(0^{+})$ are sensitively probed by transfer-cross sections at forward angles, while it remains unclear how we trace the surface behavior of ${}^{16}\mathrm{O}(4^{+})$ from the cross sections. We are able to specify that the $\alpha$-cluster structure in the $0_1^{+}$ and $0_2^{+}$ states prominently manifests itself at the radii $\sim 4$ and $\sim 4.5$~fm, respectively. It is remarkable that the $4_1^{+}$ state has the ${}^{12}\mathrm{C}+\alpha$-cluster component with the surface peak at the radius $\sim 4$ or outer, whereas the ${}^{12}\mathrm{C}+\alpha$-cluster component in the $4_2^{+}$ state is found not to be dominant. The $4_2^{+}$ state is difficult to be interpreted by a simple potential model assuming the ${}^{12}\mathrm{C}+\alpha$ configuration only.

Comments: 14 pages, 7 figures