Abstract
We present exact solutions of the Dirac equation with Yukawa potential in the presence of a Coulomb-like tensor potential. For this goal we expand the Yukawa form of the nuclear potential in its mesonic clouds by using Taylor extension to the power of seventh and bring out its simple form. In order to obtain the energy eigenvalue and the corresponding wave functions in closed forms for this potential (with great powers and inverse exponent), we use ansatz method. We also regard the effects of spin-spin, spin-isospin, and isospin-isospin interactions on the relativistic energy spectra of nucleon. By using the obtained results, we have calculated the deuteron mass. The results of our model show that the deuteron spectrum is very close to the ones obtained in experiments.
Highlights
It is well known that the exact energy eigenvalues of the bound state play an important role in quantum mechanics
Tensor couplings have been used widely in the studies of nuclear properties [12,13,14,15,16,17,18,19,20,21,22], and they were introduced into the Dirac equation by substitution P⃗ → P⃗ −imωβ⋅x U(r) [16, 23], where m is one of the particles, mass and ω refers to harmonic oscillator
The deuteron mass are given by two nucleons masses, and the eigenenergies of the Dirac equation E, (E is a function of η, δ, τ, h, m) with the first-order energy correction from potential Hint can be obtained by using the unperturbed wavefunction (33), (35), and (36)
Summary
It is well known that the exact energy eigenvalues of the bound state play an important role in quantum mechanics. The Dirac equation which describes the motion of a spin-1/2 particle has been used in solving many problems of nuclear and high-energy physics. Tensor couplings have been used widely in the studies of nuclear properties [12,13,14,15,16,17,18,19,20,21,22], and they were introduced into the Dirac equation by substitution P⃗ → P⃗ −imωβ⋅x U(r) [16, 23], where m is one of the particles, mass and ω refers to harmonic oscillator. We solve the resulting equations for deuteron nuclei and obtain the parameters for it. We are able to number the mass of Deuteron by using obtained parameters, and the equation is in conformity with experimental measure
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