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Geometric configurations of three-$alpha$ particles in the ground- and first-excited $J^pi=0^+$ states of $^{12}$C are discussed within two types of $alpha$-cluster models which treat the Pauli principle differently. Though there are some quantitative differences especially in the internal region of the wave functions, equilateral triangle configurations are dominant in the ground state, while in the first excited $0^+$ state isosceles triangle configurations dominate, originating from $^8{rm Be}+alpha$ configurations.
Lowest energy spectrum of the $^{12}$C nucleus is analyzed in the 3$alpha$ cluster model with a deep $alphaalpha$-potential of Buck, Friedrich and Wheatley with Pauli forbidden states in the $S$ and $D$ waves. The direct orthogonalization method is a
The ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction plays a key role in the evolution of stars with masses of $M >$ 0.55 $M_odot$. The cross-section of the ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction within the Gamow window ($E_
We present a new picture that the $alpha$-linear-chain structure for ${^{12}{rm C}}$ and ${^{16}{rm O}}$ has one-dimensional $alpha$ condensate character. The wave functions of linear-chain states which are described by superposing a large number of
Densities and transition densities are computed in an equilateral triangular alpha-cluster model for $^{12}$C, in which each $alpha$ particle is taken as a gaussian density distribution. The ground-state, the symmetric vibration (Hoyle state) and the
For more than half a century, the structure of $^{12}$C, such as the ground band, has been understood to be well described by the three $alpha$ cluster model based on a geometrical crystalline picture. On the contrary, recently it has been claimed th