Nuclear collective level density and shape of thorium isotopes

The nuclear level density gives information about the structure of nuclei. We have calculated the effective and collective level density of thorium nuclei in the mass range 204–280, lying on the β -stability and drip lines. Here, we have used the phenomenological model for the level density calculations. The level density parameter is found to decrease toward neutron number N = 126 and 184. Hence, 126 and 184 may be neutron magic numbers. The present evaluated data will be useful in understanding the mechanism of nuclear reactions taking place under extreme conditions, including those in nucleosynthesis. The shape and deformation of thorium nuclei lying in between the drip lines are also included in this study. Here, we have used a relativistic mean-field theory for the shape evolution. This study will be useful for identifying the variation of level density parameter and shape variation of thorium nuclei toward the drip lines and around the shell closure. The nuclear level density variation may be attributed to the variation of nuclear shape. From this study, we noticed a correlation between nuclear level density parameter and nuclear shapes. So, it points to the fact that 126 and 184 could be neutron magic numbers. The total binding energy is calculated as a function of the deformation parameter β 2 , and most of the thorium nuclei in the studied region are found to be having prolate shapes.