Energy spectrum of the nucleus73Ta181 by a canonical transformation

Abstract

The quasi-particle creation and annihilation operators introduced in the BCS formalism for the sake of convenience in the calculations, are taken as a function of a parameter (σ). This parameter is also a function of an arbitrary parameter in terms of the probability of the states being occupied or unoccupied. The canonical transformation of the general Hamiltonian of the nucleus has been performed in terms of this new parameter. Using the Hamiltonian obtained, the matrix elements of the odd-mass nucleus are calculated. The energy spectra are determined with the values 0.25; 0.50; 0.75; 1.00; 1.25; 1.50; 1.75; 2.00 of the parameterz which is function of σ. The single-particle energies appearing in the matrix elements are taken separately for the 0.20; 0.25; 0.30 values of the deformation parameter of the nucleus. The single-particle energies are calculated by diagonalization of the Lamm Hamiltonian with the asymptotic base wave function. With this procedure it is observed that the energy values can be found in a rational manner by a suitable choice of all the parameters.