Integral Relations for Multichannel Reactions

Multichannel scattering reactions can be described through two integral relations based on the Kohn variational principle. When used in combination with the hyperspherical adiabatic expansion method the pattern of convergence of the corresponding K-matrix is similar to the one found when applied to obtain bound states. We have generalized the two integral relations, introduced in this article, to multichannel processes and l ≥0 partial waves. These relations, derived from the Kohn variational principle, speed up the pattern of convergence when used together with the hyperspherical adiabatic expansion method. This is because they do not require knowledge of the asymptotic part of the wave function. The efficiency of the method has been illustrated with applications to the 4He - 4He2 reaction (with only the elastic channel open) and the 4He - 4He - 6Li system with the elastic and the rearrangement channels open. (author)