The $4\alpha$ condensate state for ${}^{16}\mathrm{O}$ is discussed with the Tohsaki-Horiuchi-Schuck-Röpke (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 $0^{+}$ $[(0_4^{+}){}_{\mathrm{THSR}}]$ state has a structure analogous to that of the Hoyle state because it has a very dilute density and a large component of $\alpha +{}^{12}\mathrm{C}(0_2^{+})$ 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 $(0_4^{+}){}_{\mathrm{THSR}}$ 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 $(0_4^{+}){}_{\mathrm{THSR}}$ 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 $\alpha +{}^{12}\mathrm{C}$ configurations in the THSR wave function is pointed out.

• Received 15 April 2010

DOI:https://doi.org/10.1103/PhysRevC.82.024312