Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions

Abstract

We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As relativistic symmetries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2-and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.

Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

“…These symmetries were discovered in the first half of 1970's independently by Smith et al [4] and Bell et al [5]. Since then, SS and PSS are being investigated in various scientific papers [6][7][8][9][10][11][12][13][14][15], detailed reports have been published by Ginocchio [16] and recently by Liang et al [17]. The origin of these symmetries basically depends on the investigated system's Hamiltonian, that is constituted with the external potential energy term limited with a Lorentz scalar, V s , and a non-zero time component Lorentz vector, V v , [18].…”

An investigation of the bound-state solutions of the Klein-Gordon equation for the generalized Woods-Saxon potential in spin symmetry and pseudo-spin symmetry limits

“…Initially, these symmetries are asserted by Smith et al [6] and Bell et al [7] in their independent studies. Afterwards, the subject became more and more popular and was studied by many authors [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Detailed reviews of using these symmetries in nuclear structure phenomena, including the open problems, were given by Ginocchio [27] and recently by Liang et al [28].…”