Relativistic Corrections to the Three-Body Problem

H. Jacob, V. S. Bhasin, and A. N. Mitra
Phys. Rev. D 1, 3496 – Published 15 June 1970
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Abstract

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 vc) 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 p22m(m2+p2)12m 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 nd scattering length (a12) versus the two-body strength parameter (λ) is slightly shifted to the right as a result of the relativistic correction.

  • Received 15 January 1970

DOI:https://doi.org/10.1103/PhysRevD.1.3496

©1970 American Physical Society

Authors & Affiliations

H. Jacob, V. S. Bhasin, and A. N. Mitra

  • Department of Physics and Astrophysics, University of Delhi, Delhi-7, India

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Issue

Vol. 1, Iss. 12 — 15 June 1970

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