Generalization of the Determinantal Method to Continuous Channels

The procedure by which all elements of the S matrix in multichannel scattering problems are expressed in terms of the Fredholm determinant of the Lippmann-Schwinger equation, is generalized to the case of ``continuous channels.'' This is a preliminary step toward its generalization to three (or more)-particle problems, in which the possibility of ``ionizing'' an initial bound state always introduces such a continuum. It is found that, whereas in the case of discrete channels the necessary functions can be obtained from the Fredholm determinant either by analytic continuation in the total energy, or by a ``substitution rule,'' for continuous channels only the latter procedure works, and it is not equivalent to an analytic continuation.