Computational study of channel coupling arrays: Low energy e−–H scattering parameters in the 1S approximation

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Abstract
Low energy electron–hydrogen scattering parameters have been calculated using the new set of coupled equations for the transition operators for different arrangement channels derived recently. A key feature of this approach to multichannel scattering is the use of the channel coupling array W, whose elements link the various channels together and thus determine which arrangements are explicitly coupled in the equations. In this work, the dependence of the low energy scattering parameters on the elements Wij is studied numerically within an approximation retaining only the n=1, hydrogen ground state in the expansion of the channel Green’s operator. Because of the channel coupling, this is not the same approximation as the familiar static or static exchange approximation of more conventional calculations. The best results for singlet and triplet parameters taken together occur for the channel permuting array values W11=W22=0, W21=W12=1; these are the values that guarantee a connected integral equation for the matrix of transition operators. In particular, we find singlet and triplet scattering length values (in a.u.) of 6.230 and 2.077, which compare well with the variational results of Schwartz, 5.96 and 1.77.