Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function

Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg–Klein–Rees (RKR) results and vibrational energies of NaK, $$K_2$$ K 2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit $$D_e=2508cm^{-1}$$ D e = 2508 c m - 1 , $$254cm^{-1}$$ 254 c m - 1 and $$4221cm^{-1}$$ 4221 c m - 1 , respectively. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Few-Body Systems Springer Journals

Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function

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Publisher
Springer Vienna
Copyright
Copyright © 2018 by Springer-Verlag GmbH Austria, part of Springer Nature
Subject
Physics; Particle and Nuclear Physics; Nuclear Physics, Heavy Ions, Hadrons; Atomic, Molecular, Optical and Plasma Physics
ISSN
0177-7963
eISSN
1432-5411
D.O.I.
10.1007/s00601-018-1329-3
Publisher site
See Article on Publisher Site

Abstract

The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg–Klein–Rees (RKR) results and vibrational energies of NaK, $$K_2$$ K 2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit $$D_e=2508cm^{-1}$$ D e = 2508 c m - 1 , $$254cm^{-1}$$ 254 c m - 1 and $$4221cm^{-1}$$ 4221 c m - 1 , respectively.

Journal

Few-Body SystemsSpringer Journals

Published: Jan 31, 2018

References

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