Analytical computation of amplification of coupling in relativistic equations with Yukawa potential
- Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)
The approximate analytic solutions to the Klein-Gordon and Dirac equations with the Yukawa potential were derived by using the quasilinearization method (QLM). The accurate analytic expressions for the ground state energies and wave functions were presented. These high-precision approximate analytic representations are obtained by first casting the proper relativistic equation into a nonlinear Riccati form and then solving that nonlinear equation in the first QLM iteration. The choice of zero iteration is based on general features of the exact solutions near the origin and infinity. To estimate the accuracy of the QLM solutions, the exact numerical solutions were found, as well. The analytical QLM solutions are found to be extremely accurate for a small exponent parameter w of the Yukawa potential. The reasonable accuracy is kept for the medium values of w. When w approaches the critical values, the precision of the QLM results falls down markedly. However, the approximate analytic QLM solution to the Dirac equation corresponding to the maximum relativistic effect turned out to be very accurate even for w close to the exact critical w{sub ex}{sup Dir}=1.6767, whereas the QLM calculations yield w{sub qlm}{sup Dir}=1.6763. This effect of 'amplification' in compare with the Schroedinger equation critical parameter w{sub ex}{sup Sch}=1.1906 was investigated earlier [S. De Leo, P. Rotelli, Phys. Rev. D 69 (2004) 034006]. In this work, it was found that the 'amplification' for the Klein-Gordon equation became all the more evident. The exact numerical value is w{sub ex}{sup KG}{approx_equal}2.25, whereas the QLM approximation yields w{sub qlm}{sup KG}{approx_equal}2.15.
- OSTI ID:
- 21167715
- Journal Information:
- Annals of Physics (New York), Vol. 324, Issue 2; Other Information: DOI: 10.1016/j.aop.2008.08.004; PII: S0003-4916(08)00122-X; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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