6533b7d7fe1ef96bd126901b

RESEARCH PRODUCT

Definition of an appropriate free dynamics and the physical S-matrix in multichannel hyperradial adiabatic scattering

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In the hyperradial adiabatic (HA) treatment of the three-body problem the total wave function is i expanded as ΨHA(R, ξ, η) = R−5/2 ∑iχi(R)φi(R|ξ, η),where R denotes the hyperradius and (ξ , η) are internal hyperangles. Integration over ξ and η converts the Schrödinger equation into a system of coupled hyperradial equations. It is a well-known fact that, within the HA approach, the non-adiabatic corrections that couple channels converging to the same asymptotic configuration can show an unphysical long-range behavior ∼ 1/R. Though the latter is of purely kinematic origin and arises from the use of the hyperradius instead of the pertinent Jacobi variables, it is nevertheless the source of the considerable difficulties inherent in this approach. Here we propose, following the analysis of [1, 2], to define appropriate hyperradial-distorted free incoming and outgoing waves (H DF W ) that incorporate these unphysical long-range effects. Using them the physical S−matrix can be found in a straightforward manner.