QC137 : Spherical symmetries of the Dirac Hamiltonian in the nuclear shell model
Thesis > Central Library of Shahrood University > Physics > PhD > 2013
Authors:
Majid Hamzavi [Author], Ali Akbar Rajabi[Supervisor]
Abstarct: Relativistic symmetries of the Dirac Hamiltonian had been discovered many years ago, but only recently these symmetries have been recognized empirically in nuclear and hadronic spectroscopy. Within the frxamework of Dirac equation, pseudospin symmetry used to feature deformed nuclei, superdeformation, to establish an effective shell-model and spin symmetry is relevant for mesons. Spin symmetry occurs when the scalar potential is nearly equal to the vector potential or equivalently and pseudospin symmetry occurs when . The pseudospin symmetry refers to a quasi-degeneracy of single nucleon doublets with non-relativistic quantum number and , where , and are single nucleon radial, orbital and total angular quantum numbers, respectively. The total angular momentum is , where is pseudo-angular momentum and is pseudospin angular momentum . Tensor potentials were introduced into the Dirac equation with the substitution and a spin-orbit coupling is added to the Dirac Hamiltonian. In this thesis, we introduce the Dirac equation with scalar and vector potential with arbitrary spin-orbit coupling number including tensor interaction under spin and pseudospin symmetry limits. The Pekeris approximation is discussed for some exponential potentials. The Nikiforov-Uvarov method and its generalized form are presented in this thesis too. The energy eigenvalue equations and corresponding eigenfunctions of are obtained for some important potential as Eckart, Mie-Tpe, Pseudoharmonic, Morse, generalized Woods-Saxon, Cornell and Killingbeck potentials. The analytical results have been compared with other results and methods and we see that our calculations are in good agreement with those obtained before.
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