The container picture with two-alpha correlation for the ground state of ${}^{12}$C

Abstract

It is shown that the single $0^{+}$ THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function which is extended to include 2$\alpha$ correlation is almost completely equivalent to the 3$\alpha$ wave function obtained as the full solution of 3$\alpha$ cluster model. Their squared overlap is as high as 98\% while it is 93\% if the 2$\alpha$ correlation is not included. This result implies that, by incorporating the 2$\alpha$ correlation in the 3$\alpha$ model, the ground state of ${}^{12}$C is describable in the container picture which is valid for the Hoyle state for which the 2$\alpha$ correlation is weak and a single $0^{+}$ THSR wave function without 2$\alpha$ correlation is almost completely equivalent to the full solution of 3$\alpha$ cluster model.

Comments: 6 pages, 2 figures