http://arxiv.org/abs/2210.11763
The spatial structure of the lowest 0$_1^+$, 0$_2^+$, 2$_1^+$ and 2$_2^+$ states of the $^{12}$C nucleus is studied within the 3$\alpha$ model with the Buck, Friedrich, and Wheatley $\alpha \alpha$ potential with Pauli forbidden states in the $S$ and $D$ waves. The Pauli forbidden states in the three-body system are treated by the exact orthogonalization method. The largest contributions to the ground and excited 2$_1^+$ bound states energies come from the partial waves $(\lambda, \ell)=(2,2)$ and $(\lambda, \ell)=(4,4)$. In contrast to the bound states, for the Hoyle resonance 0$_2^+$ and its analog state 2$_2^+$, dominant contributions come from the $(\lambda, \ell)=(0,0)$ and $(\lambda, \ell)=(2,2)$ configurations, respectively. The estimated probability density functions for the $^{12}$C(0$_1^+$) ground and 2$_1^+$ excited bound states show mostly a triangular structure, where the $\alpha$ particles move at a distance of about 2.5 fm from each other. However, the spatial structure of the Hoyle resonance and its analog state have a strongly different structure, like $^8$Be + $\alpha$. In the Hoyle state, the last $\alpha$ particle moves far from the doublet at the distance between $R=3.0$ fm and $R=5.0$ fm. In the Hoyle analog 2$_2^+$ state the two alpha particles move at a distance of about 15 fm, but the last $\alpha$ particle can move far from the doublet at the distance up to $R=30.0$ fm.
E. Tursunov, M. Saidov and M. Begijonov
Mon, 24 Oct 22
32/56
Comments: 12 pages, 4 figures, 2 tables