Three alpha-particle space correlations in C12

The three-alpha structure of the ground (Jπ,T=0+,0) and first excited (2+,0) states of the C12 nucleus was investigated in the framework of the shell-model theory. The probability density for the space distribution of the three alphas was obtained by projecting three-alpha states from the intermediate-coupling model wavefunctions of the C12 nucleus. The projection procedure was done with the use of three-alpha coefficients of fractional parentage of the translationally invariant shell model. The main result is that the triangular and linear configurations of the three alphas are present in the intermediate-coupling model wavefunctions of the analysed states. The intermediate-coupling model privileges a linear oscillations in the ground state, while a triangular oscillations are more probable in the first excited state. The probability of the three-alpha clusterization of C12, predicted with the aid of intermediate-coupling model wavefunctions, is equal to 0.47 and 0.52 for the ground and the first excited state, respectively. 42 refs., 7 figs., 1 tab. (author)