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

TL;DR

This paper demonstrates that a single $0^+$ THSR wave function with 2$5$ correlation accurately describes the ground state of $^{12}$C, aligning closely with the full 3$5$ cluster model solution, emphasizing the container picture's validity.

Contribution

It shows that including 2$5$ correlation in the THSR wave function provides a nearly complete description of the $^{12}$C ground state, simplifying the cluster model.

Findings

High squared overlap (98%) between the extended THSR and full 3$5$ wave functions.

Including 2$5$ correlation significantly improves the wave function's accuracy.

The container picture effectively describes the $^{12}$C ground state with 2$5$ correlation.

Abstract

It is shown that the single $0^+$ THSR (Tohsaki-Horiuchi-Schuck-R\"{o}pke) 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.