| More

A renormalized HVT approach for a class of central potential wells

Views: 14 Downloads: 8
C. A. Efthimiou, M. E. grypeos, C, G. Koutroulos, W. J. Oyewumi, Th. Petridou
C. A. Efthimiou, M. E. grypeos, C, G. Koutroulos, W. J. Oyewumi, Th. Petridou


An investigation is carried out to consider a renormalized HVT approach in the context of s-power series expansions for the energy eigenvalues of a particle moving non-relativistically in a central potential well belonging to the class V(r)=−Df(rR), D>0 where f is an appropriate even function of x=r/R and the dimensionless quantity s = (h^2/2μDR)^{1/2} is assumed to be sufficiently small. Previously, the more general class of central potentials of even power series in r is considered and the renormalized recurrence relations from which the expansions of the energy eigenvalues follow, are derived. The s-power series of the renormalized expansion are then given for the initial class of potentials up to third order in s (included) for each energy-level Enl . It is shown that the renormalization parameter Κ enters the coefficients of the renormalized expansion through the state-dependent quantity a_{nl}χ^{1/2} =a_{nl}(1+K ((−d_1D)R^2))^{½}, a_{nl}=(2n+l+32). The question of determining χ is discussed. Our first numerical results are also given and the utility of potentials of the class considered (to which belong the well-known Gaussian and reduced Poschl- Teller potentials) in the study of single–particle states of a Λ in hypernuclei is pointed out.

Full Text:



J.O. Hirschfelder Journal of Chemical Physics 33 (1960) 1462

F.M. Fernandes and E.A. Castro Hypervirial Theorems, Lecture Notes in Chemistry Vol. 43, Springer-Verlag, ( 1987), Berlin.

G. Marc and W.G. McMillan Advances in Chemical Physics 58 (1985) 209

J. Killingbeck J. Phys. A Math. Gen.14 (1981) 1005

E.J. Austin and J. Killingbeck J.Phys.A Math. Gen.15 (1982) L443

J.P. Killingbeck, A.Grosjean and Jolicard J. Phys. A Math.Gen. 34(2001)8309

Th.E. Liolios and M.E. Grypeos International. Journal of Theoretical. Physics


M.E. Grypeos and Th.E. Liolios, Phys. Lett. A 252 (1999) 125

DOI: http://dx.doi.org/10.12681/hnps.2587


  • There are currently no refbacks.

Copyright (c) 2019 C. A. Efthimiou, M. E. grypeos, C, G. Koutroulos, W. J. Oyewumi, Th. Petridou

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.