Abstract
In this research, we have been obtained the Dirac equation for second Pöschl–Teller-like potential including a Coulomb-like tensor interaction with arbitrary spin–orbit coupling quantum number κ. Under the condition of spin and pseudospin (p-spin) symmetries, we use the basic concept of the supersymmetric shape invariance formulism in quantum mechanics and the function analysis method to obtain energy eigenvalues and corresponding two-component spinors of the Dirac particle. We have also shown that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.
Highlights
The spin and pseudospin symmetry concepts introduced in nuclear theory [1, 2] have been used to explain the features of deformed nuclei [3] and superdeformation [4], and to establish an effective shell-model coupling scheme [5]
Alhaidari et al [9] have investigated in detail physical interpretation on the three-dimensional Dirac equation in the case of spin symmetry limit (V(r) - S(r) = 0) and pseudospin symmetry limit (V(r) ? S(r) = 0)
As far as we know, one has not reported the investigation of the spin and pseudospin symmetries solutions of the Dirac equation with the Poschl–Teller-like potential including a Coulomblike potential as a tensor interaction for the arbitrary spin– orbit quantum number j
Summary
The spin and pseudospin symmetry concepts introduced in nuclear theory [1, 2] have been used to explain the features of deformed nuclei [3] and superdeformation [4], and to establish an effective shell-model coupling scheme [5]. We attempt to study the spin and pseudospin symmetry solutions of the Dirac equation for arbitrary quantum number j with the Poschl–Teller-like potential. As far as we know, one has not reported the investigation of the spin and pseudospin symmetries solutions of the Dirac equation with the Poschl–Teller-like potential including a Coulomblike potential as a tensor interaction for the arbitrary spin– orbit quantum number j. Dr = dR(r)/dr = 0) or R(r) = Cps = constant and p-spin symmetry is exact in the Dirac equation [8, 48,49,50] In this part, we consider D(r) as the Poschl–Teller-like potential, the equation obtained for the lower component of the Dirac spinor, Gnj(r), becomes. Using the expression given in Eq (20), we construct the following two supersymmetric partner potentials: VÆðrÞ
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