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Relativistic two-body plus potential problem: Compatible equations and double bound-state solutions (two-fermion case)

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Il Nuovo Cimento A (1965-1970)

Summary

We write a pair of coupled Dirac equations, containing each an external attractive interaction termeJ i (i=1,2), a mutual interaction term ωV i , and a three-body termeωW 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 termsW i a well-adapted choice, leading to an energy eigenvalue equation which is compact and has a clear nonrelativistic limit.

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  1. J. Bijtebier

    Present address: Bevoegdverklaard navorser bij het National Fonds voor Wetenschappelijk, Onderzoek, Belgium

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  1. Theoretische Natuurkunde, Vrije Universiteit Brussel, Brussels, Belgium

    J. Bijtebier

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Bijtebier, J. Relativistic two-body plus potential problem: Compatible equations and double bound-state solutions (two-fermion case). Nuov Cim A 103, 639–651 (1990). https://doi.org/10.1007/BF02789017

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