The container picture with two-alpha correlation for the ground state of 12C

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