Relativistic Treatment of Loosely Bound Systems in Scattering Theory

An approximate method for treating loosely bound systems is discussed, with the deuteron form factor in the impulse approximation treated as an example. Major advantages of the method are that it is simple and unambiguous, and leads to a quantitative estimate of its accuracy. The principal physical assumption behind the method is that the bound system can be regarded as coupled to only one channel at low energies. One can use this to obtain simple, relativistically invariant expressions for scattering amplitudes in which the bound state is described by a relativistic wave function. For the deuteron this wave function is related to the $d-\mathrm{np}$ vertex with one nucleon off the mass shell. A method by which this wave function can be determined from phenomenological nonrelativistic wave functions is discussed.