Microscopic study of 4-alpha-particle condensation with proper treatment of resonances

The 4 alpha condensate state for O-16 is discussed with the Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave function which has alpha-particle condensate character. With a treatment of resonances, it is found that the 4 alpha THSR wave function yields a fourth 0(+) state in the continuum above the 4 alpha-breakup threshold, in addition to the three 0(+) states obtained in a previous analysis. It is shown that this fourth 0(+) [(0(4)(+))(THSR)] state has a structure analogous to that of the Hoyle state because it has a very dilute density and a large component of alpha + C-12(0(2)(+)) configuration. Furthermore, single-alpha motions are extracted from the microscopic 16-nucleon wave function, and the condensate fraction and momentum distribution of alpha particles are quantitatively discussed. It is found that for the (0(4)(+)) THSR state a large alpha-particle occupation probability concentrates on a single-alpha 0S orbit and the alpha-particle momentum distribution has a delta-function-like peak at zero momentum, both indicating that the state has a strong 4 alpha condensate character. It is argued that the (0(4)(+)) THSR state is the counterpart of the 0(6)(+) state which was obtained as the 4 alpha condensate state in the previous 4 alpha orthogonality condition model calculation and therefore is likely to correspond to the 0(6)(+) state observed at 15.1 MeV. The necessity of including alpha + C-12 configurations in the THSR wave function is pointed out.