RELATIVISTIC 2-BODY PLUS POTENTIAL PROBLEM - COMPATIBLE EQUATIONS AND DOUBLE BOUND-STATE SOLUTIONS (2-FERMION CASE)

We write a pair of coupled Dirac equations, containing each an external attractive interaction term eJ i (i=1,2), a mutual interaction term ωV i, and a three-body term eωW i . These interaction terms can be chosen freely, within some restrictions imposed by the compatibility requirement. After eliminating the dependence on the relative time by performing an inversible transformation, we are ready to compute the double bound-state solutions by perturbations in the parameter ω, as in the corresponding nonrelativistic problem. These manipulations suggest for the three-body terms W i a well-adapted choice, leading to an energy eigenvalue equation which is compact and has a clear nonrelativistic limit. © 1990 Società Italiana di Fisica.