Energies of States of the Ground State Band of Nuclear Rotation with Microscopic Approximations
12 Pages Posted: 25 Apr 2019 Last revised: 31 May 2019
Date Written: April 24, 2019
In our work, we have theoretically calculated the nuclear energies of the rotational band states of the heavy Plutonium nucleus 240 ((_94^240)Pu), using the following approximations: HF + BCS, HTDA and routhian (Cranking). We divide our study into two parts named A and B. Part A is devoted to the determination of some static properties of studied nucleus ((_94^240)Pu) as; the axial deformation energy curves and also the potentiel energy surface, using the HF + BCS method and its comparison with HTDA treatment.This approach is conserving the number of particles. The calculations that were done in part A allowed us to determine the ground state of our studied nucleus.This ground state is used for the determination of the nuclear rotation band (spectrum) as well as some other rotational properties of this nucleusas the nuclear rotation velocity Ω and the moment of inertia I as a function of the state.The part Bis organized from a code called Hartree-Fock and Routhian. We performed the Routhian calculations with the SIII Skyrme force in first, then with the SkM* force, and we compare the results with the experimental data. We found in part A that the results obtained by HTDA are closer to the experimental results than those given by HF + BCS, and the nucleus is an axial nucleuswith absolute minimum and a prolatedeformation ( i.e : elongated ellipsoid along one of the main axes ) in its ground state. Finally we determined the rotation spectrum, when using SkM* force ;the spectrum is closer to the experimental one than that obtained with the SIII force. This means that the SkM* force translates more realistically the rotation in the atomic nucleus.
Keywords: HTDA Aproche, HF+BCS approche, routhian (cranking) approche
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