Relativistic corrections to the three-body problem

Jacob, H. ; Bhasin, V. S. ; Mitra, A. N. (1970) Relativistic corrections to the three-body problem Physical Review D - Particles, Fields, Gravitation and Cosmology, 1 (12). pp. 3496-3501. ISSN 1550-7998

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Relativistic corrections are evaluated for a model three-body problem consisting of three identical bosons in s-wave pairs through separable potentials. For the potentials, Shirokov's second-order (in v/c) correction, which vanishes in the c.m. frame of a two-body system, is considered. No corrections are considered for the kinetic energy, as it is argued that any such correction is intimately linked with the precise structure assumed for a three-particle dynamics and cannot merely be incorporated through the modification p2/2m→(m2+p2)1/2-m for each particle, which affects even the two-particle dynamics on the energy shell (and hence also the parameters of the two-body potential). The reduction in the quantity analogous to the binding energy of the triton is found to be of the order of 5%, while the curve for the counterpart of the doublet n-d scattering length (a1/2) versus the two-body strength parameter (λ) is slightly shifted to the right as a result of the relativistic correction.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:34688
Deposited On:09 Apr 2011 07:24
Last Modified:09 Apr 2011 07:24

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