This paper discusses two levels of generalization of the parallel axis theorem for rotational inertia. The first relates the moments of inertia about any two parallel axes, whether or not they are passing through the center of mass. The second relates the inertia tensors about any two points.
The energy density formalism is implemented to study the binding energy of some heavy, superheavy and hyperheavy nuclei. The macroscopic contribution of binding energy is derived in the presence of a depression parameter in the nuclear density distribution, and the total energy is obtained by adding the shell and pairing correction to the macroscopic part. Total energy is studied with the variation of quadrupole β 2 and hexadecapole β 4 deformation parameters using different values of depression parameter. The addition of the shell and pairing corrections affects the behavior of the total energy especially the minimum position at specific deformation parameters, a second minimum in some cases are close to the first one, suggesting the possible existence of shape isomers. We minimized the total energy with respect to deformation and density depression parameters and obtained the binding energy of 208
The experimental charge densities of atomic nuclei show fluctuations in their distributions. This paper investigates the limits of accuracy of two-parameter Fermi and three-parameter Fermi distributions in describing the charge density. An improved analytical function for density distribution is proposed, which allows for density fluctuation. The experimental charge densities of 40 Ca, 60 Ni, 100 Mo, 152 Sm and 208 Pb, representing the various shapes of density fluctuation, are used to assess the accuracy of the proposed formula. The proposed function reproduces the experimental charge densities with significant improvement in accuracy over other commonly used formulae. A compilation of charge density distribution parameters of 73 nuclei is presented based on the proposed formula.
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