Investigation of strong force influence on behavior of nuclear energy levels in Calcium and Titanium isotopes: Based on quantum chaos theory

The atomic nucleus is a complex many-body system that consists of two types of fermion (neutron and proton). They are in the strong interaction. The statistical properties of energy levels and influence of strong force between these fermions are well described by random matrix theory. Resonance of energy levels depends on the Hamiltonian symmetry placed in one of the GOE, GUE and GSE ensembles or in the integrable system in a Poissonian ensemble. We can study resonance of energy levels of one system with eigenvalues of the Hamiltonian. This paper by using the nuclear shell model investigate the influence of strong force on the nuclear structure in Calcium and Titanium isotopes with quantum chaos theory. Difference between these isotopes is in their Valance particles. Investigation the energy levels of them is show that behavior of the nuclear system in   Ti48 is very close to GOE ensemble but in Ca48 is a little bit far from this behavior