We investigate the existence of weakly coupled gaslike states comprised of three $\alpha$ particles around an ${}^{16}$O core in ${}^{28}$Si. We calculate the excited states in ${}^{28}$Si using the multiconfiguration mixing method based on the ${}^{16}$O+3$\alpha$ cluster model. We also include the ${}^{16}$O+${}^{12}$C and ${}^{24}$Mg+$\alpha$ basis wave functions prepared by the generator coordinate method. To identify the gaslike states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the ${}^{16}$O+${}^{12}$C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-square radii for these states also suggest that a layer of gaslike three $\alpha$ particles could exist around the surface of the ${}^{16}$O core, which can be described as a “two-dimensional gas” in the intermediate state before the Hoyle-like three-$\alpha$ states emerge.

• Received 10 June 2012

DOI:https://doi.org/10.1103/PhysRevC.86.031303