Perturbed Bound-State Poles in Potential Scattering. I

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Abstract
The perturbation formula of Dashen and Frautschi is studied in nonrelativistic potential scattering. A formalism based on the Jost function is presented and is shown to be equivalent to the Dashen-Frautschi approach. It is shown for both cases that unless the Born approximation is satisfied for the unperturbed problem, the mass shift cannot be calculated in a simple way. It is pointed out that the Born approximation is not expected to be valid if the bound state is assumed to exist. The formalism is illustrated by the use of a soluble square-well potential. The infrared problem is also discussed. It is pointed out that the infrared divergence is automatically eliminated at the binding energy and is not "spurious."