Determination of the Meson Spectra in the Dirac Equation with Power Law Potential
Main Article Content
Abstract
The pseudo-shifted ℓ-expansion technique was used in the Dirac equation to derive a Schrodinger-like equation. The equation was solved using a non-QCD based power potential of the form; with to obtain the mass spectra for bottom quark . The mass spectra of both light and heavy mesons obtained in this work were in good agreement with both the experiment and other theoretical works. However, the mass spectra of 10.1564 and 10.3039 obtained for bottom quark were small when compare with the experimental results for the same orbits. Other discrepancies observed were the 9.9252 for bottom quark and 3.9715 for charmonium that were higher than experimental results. This model has successfully mimicked the mass spectra of both light and heavy mesons and also predicts the mass spectra of mixed mesons
Downloads
Article Details
References
Hall, R.L. (2005). Exact solutions for semi relativistic problems with non-local potentials. Math-Phys/0512079; 1.
Ikhdair, S.M. & Falaye, B.J. (2014). Bound States of Spatially Dependent Mass Dirac Equation with the Eckart Potential including Coulomb Tensor Interaction. Europ. Physical J. Phys. 129(1).
Jena, S.N. (1983). Mass Spectra of Light and Heavy Mesons in the Dirac Equation with Power Law Potential. Pramana, 21(4): 247-255.
Jena, S.N and Tripati, T. (1983). Dirac Mass Spectra of Qq-Like Mesons in a Power Law Potential. Phys. Letter B, 122(2): 181-184.
Kang, J.S. and Schnitzer, H.J. (1975). Dynamics of light and heavy bound quarks Phys. Rev. D 12, 841.
Magyari E (1980), relativistic consistency of the logarithmic Heavy quark model, Physics letter B 95,295.
Mustafa, O. & Odeh, M. (2001). Magnetic Finger Print on the spectra of one electron and two electrons interacting in parabolic quantum dots. Czech. J Phys., 52; 795.
Mustafa, O. & Znojil, M. (2002). PT-Symmetric Pseudo-Perturbation recipe: An Imaginary Cubic Oscillator with Spikes. J. Phys. A Math. Gen. 35(42); 1-23.
Mustafa, O. (2003). Perturbed Coulombic Potentials in Dirac and Klein-Gordon equations. Czechoslovakia Journal of Physics, 54(5): 1-20.
Mustafa, O. (2004), perturbed columbic potential in the Dirac and Klein Gordon equations. Czech. J. Phys. 54 (5).
Mustafa, O. (2008). Perturbed Coulombic potentials in Dirac and Klein-Gordon equations. Czech. J. Phys. 3.
Ram, B. and Halasa, R. (1979). Meson spectra with harmonic- oscillator potential in the Klein Gordon equation. Phys. Rev. D 19, 3467.
Sharma, G.S. and Sharma, L.K (1984). Meson spectra with a power law potential in the Dirac equation. Pramana, 22(6): 533-537.
Sharma L.K & J.O Fiase (2003), meson spectra, power law potential model in the Dirac Equation. Botswana J. Tech., 12(2); 14-20.
Schiff, L. I. (1968). Quantum Mechanics 3rd Edition, McGraw, New York
Ushie, P.O. (2021). Eigen Solutions of the Schrodinger equation in the presence of ring-shaped Hellmann Potential. J. Sc. & Eng. Research, 8(5); 132-148.