Relativistic symmetries in Yukawa-type interactions with Coulomb-like tensor

Keywords: Dirac equation Yukawa potential Coulomb-like tensor potential Spin and p-spin symmetry Nikiforov–Uvarov method a b s t r a c t This study presents the solutions of the Dirac equation with a new suggested Yukawa-type potential for any spin–orbit quantum number j interacting with a Coulomb-like tensor interaction. In the presence of spin and pseudospin (p-spin) symmetries, the approximate energy eigenvalues and wave functions are obtained by means of the parametric Nikiforov–Uvarov (pNU) method and the asymptotic iteration method (AIM). The numerical results show that the Coulomb-like tensor interaction removes degeneracies between spin and p-spin state doublets. The bound state solutions of the Schrödinger and Klein–Gordon equations for this new potential have also been presented. Our analytical results are in exact agreements with previous works. Relativistic symmetries of the Dirac Hamiltonian had been discovered many years ago. However, these symmetries have been recently recognized empirically in nuclear and hadronic spectroscopies [1]. Within the framework of Dirac equation, the p-spin symmetry used to feature deformed nuclei and the superdeformation to establish an effective shell-model [2– 4]. The spin symmetry is relevant to mesons [5] and occurs when the difference of the scalar S(r) and vector V(r)potentials are constant, i.e., D(r) = C s and the p-spin symmetry occurs when the sum of the scalar and vector potentials are constant, i.e., R(r) = C ps [6,7]. The p-spin symmetry refers to a quasi-degeneracy of single nucleon doublets with non-relativistic quantum number (n, l, j = l + 1/2) and (n À 1, l + 2, j = l + 3/2), where n, l and j denote the single nucleon radial, orbital and total angular quantum numbers, respectively [8,9]. Furthermore, the total angular momentum is j ¼ ~ l þ ~ s, where ~ l ¼ l þ 1 pseudo-angular momentum and ~ s is p-spin angular momentum [10]. Recently, the tensor potential has been introduced into the Dirac equation with the substitution ~ p ! ~ p À imxb:^ rUðrÞ and a spin–orbit coupling is added to the Dirac Hamiltonian [11,12]. Lisboa et al. [13] have studied a generalized relativistic harmonic oscillator for spin-1/2 particles by considering a Dirac Hamilto-nian that contains quadratic vector and scalar potentials together with a linear tensor potential under the conditions of p-spin and spin symmetry. Alberto et al. [14] studied the contribution of the isoscalar tensor coupling to the realization of p-spin symmetry in nuclei. …