Distorted Cluster States in Scattering Theory

Abstract

Difficulties connected with the asymptotic behavior of adiabatic wave functions in the scattering theory of slow collisions are discussed in the time-independent formalism. It is shown that the Born-Oppenheimer approximation, and its generalization involving a finite number of adiabatic states, cannot satisfy the correct asymptotic boundary conditions. A slightly different basis set of distorted cluster states is constructed which avoids this difficulty and yet fully contains the distortion effect. Symmetric treatment of the three-particle scattering system is given in the multidimensional form, and the nonadiabatic corrections and their approximations are discussed. Resonances as complex energy poles of the amplitudes are shown to be contained in the nonadiabatic correction terms and analyzed in terms of the effective potentials. An application of the method to high-energy fast collisions is briefly discussed.