Relativistic corrections to the three-body problem

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 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 (a_1/2) versus the two-body strength parameter (λ) is slightly shifted to the right as a result of the relativistic correction.