Physics Letters A 374 (2010) 4303–4307 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method M. Hamzavi ∗ , A.A. Rajabi, H. Hassanabadi Physics Department, Shahrood University of Technology, Shahrood, Iran article info abstract Article history: Received 9 June 2010 Received in revised form 8 August 2010 Accepted 26 August 2010 Available online 27 August 2010 Communicated by R. Wu Keywords: Dirac equation Spatially-dependent mass Coulomb potential Tensor potential Pseudospin symmetry Asymptotic iteration method In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential in- cluding a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin–orbit coupling number κ . The energy eigenvalues and corresponding eigen- functions are obtained and some numerical results are given.  2010 Elsevier B.V. All rights reserved. 1. Introduction In the framework of the Dirac equation, the pseudospin sym- metry occurs when the magnitude of the attractive Lorentz scalar potential S (r ) and the time-component repulsive vector poten- tial V (r ), are nearly equal but in opposite sign, i.e. S (r ) ≃−V (r ), where the sum of the potential is Σ(r ) = S (r ) + V (r ) = C ps = constant [1–19]. Tensor potentials were introduced into the Dirac equation with the substituting  p → p − imωβ. ˆ rU (r ) and a spin– orbit coupling is added to the Dirac Hamiltonian [20–30]. In the relativistic and non-relativistic cases, the solution of Dirac, Klein– Gordon and Schrödinger equations with effective mass is useful for the investigation of some physical systems [31–50]. In this Letter, we consider both spatially-dependent mass and tensor potential for attractive scalar and repulsive vector Coulomb potential un- der pseudospin symmetry limit. In Section 2, the Dirac equation with tensor potential and spatially-dependent mass is briefly in- troduced. In Section 3, a brief introduction to asymptotic iteration method (AIM) [51–55] is given. We solve the Dirac equation and give some numerical results in Section 4. Finally, conclusion is given in Section 5. * Corresponding author. Tel.: +98 273 3395270; fax: +98 273 3395270. E-mail address: mhamzavi@shahroodut.ac.ir (M. Hamzavi). 2. Dirac equation with spatially-dependent mass and tensor coupling The spatially-dependent mass Dirac equation including tensor interaction for spin- 1 2 particles with scalar potential S (r ) and vec- tor potential V (r ), in units where ¯ h = c = 1, is   α .  p + β ( m(r ) + S (r ) ) − i β  α . ˆ rU (r )  ψ( r ) =  E − V (r )  ψ( r ) (1) where E is the relativistic energy of the system,  p =−i  ∇ is the three-dimensional momentum operator and m(r ) is the effective mass of the fermionic particle.  α and β are the 4 × 4 usual Dirac matrices give as  α =  0  σ  σ 0  , β =  I 0 0 −I  (2) where I is 2 × 2 unitary matrix and  σ are three-vector spin matri- ces σ 1 =  0 1 1 0  , σ 2 =  0 −i i 0  , σ 3 =  1 0 0 −1  (3) The total angular momentum operator  J and spin–orbit K = (  σ .  L + 1) commute with Dirac Hamiltonian, where  L is the orbital 0375-9601/$ – see front matter  2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.08.065