Multichannel variational expressions of scattering theory

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Abstract
We have compared variational functionals for multichannel scattering. The functionals considered were Schwinger-type functionals based on the close-coupling equations, the Schwinger-type variational functionals of Takatsuka and McKoy [Phys. Rev. A 24, 2473 (1981)], and a Kohn-type variational functional. The results for a simple Huck-model potential containing both open and closed channels indicate that the Schwinger-type variational functionals yielded very similar results and that all the methods considered converged at a similar rate with respect to the closed-channel expansion. To obtain good convergence with any of these methods it was essential to include separate trial functions outside the range of the Huck square-well potential in the channels where a correct asymptotic form of the wave function was required, those being only the closed channels for the Schwinger-type functionals and both open and closed channels for the Kohn-type functionals. These asymptotic functions were needed to reproduce the discontinuity in the second derivative of the wave function due to the discontinuities in the model potential. Convergence characteristics of these methods with respect to target-state expansions were also considered.