Spectral fluctuations in ²⁴Mg nucleus using the framework of the nuclear shell model

Random matrix theory is used to study the chaotic properties in nuclear energy spectrum of the ²⁴Mg nucleus. The excitation energies (which are the main object of this study) are obtained via performing shell model calculations using the OXBASH computer code together with an effective interaction of Wildenthal (W) in the isospin formalism. The ²⁴Mg nucleus is assumed to have an inert ¹⁶O core with 8 nucleons (4protons and 4neutrons) move in the 1d_5/2, 2s_1/2 and 1d_3/2 orbitals. The spectral fluctuations are studied by two statistical measures: the nearest neighbor level spacing distribution P(s) and the Dyson-Mehta statistics (∆₃ statistics). For calculations with the full diagonalization of the Hamiltonian, the spectral fluctuations are found to be in agreement with the Gaussian orthogonal ensemble of random matrices.