Four-particle correlations in nuclei on the sd-f7/2 levels

The four-body J = 0 and T = 0 or T = 2 interacting term was explicitly introduced into the shell-model pairing Hamiltonian for nuclei whose protons and neutrons fill up the same harmonic oscillator shell. Due to the quasi-spin symmetry SO(5) the Hamiltonian was analytically diagonalised for one j-shell and it was applied to the schematic two-level model sd-f7/2. It was found that even the small admixture of the four-body interaction provides a possibility for theoretical description of the excited 0+ levels for nuclei with A≥ 40. State vectors obtained by diagonalisation were then used for transfer probability calculations leading to comparison of the probabilities of the cluster and step by step transfer reactions. The predicted new ''four-body superfluidity'' could be interpreted as a background for a possible two-paired boson ''abnormal state'' within Interacting Boson Model. 18 refs., 7 figs. (author)