Statistical Fluctuations of Energy Spectra in 32A Nuclei using the Proton-Neutron Formalism Interaction

Statistical fluctuations of nuclear energy spectra in 32A (32S, 32P and 32Si) nuclei are probed by the framework of the nuclear shell model. Energy levels of considered nuclei are evaluated via performing sd-shell model calculations using the OXBASH computer code with the realistic effective interaction of WPN in the proton-neutron formalism. Here, we assume the 32A nuclei consists of an inert 16O core with 16 nucleons move in the 1d5/2, 2s1/2 and 1d3/2 orbitals. For full hamiltonian calculations of 32A nuclei, we have found an intermediate behavior between Wigner and Poisson limits for both the distributions and statistics as a result of the absence of mixing and repulsion between levels with different isospin. Further, they transfer gradually toward the GOE limit when going over and nuclei, individually (i. e. through changing the numbers of valence protons and neutrons in 32A). Moreover, they are independent of the spin (universal for different spins). For unperturbed hamiltonian (the non-interacting particles case) calculations, we have found a regular behavior for both the distributions and statistics due to the absence of mixing and repulsion between levels with different isospin (as a result of using the proton-neutron formalism interaction) and also due to the nonexistence of the off-diagonal residual interaction.