Coulomb spheroidal representation in the hyperspherical approach to the three-body problem

摘要

The construction of the most simple representation coordinated with thephysical asymptotic conditions is considered for the Coulomb three-body scatteringwave function at energies below the threshold of the three-particle breakup. It isshown that such a representation can be constructed with the use of the well-knownsolutions of the separable Coulomb two-centre (CTC) problem if the role of theintercentre distance is given to the hyperradius. For the simplest version of theapproach (Abramov, J Phys B 41:175201, 2008) the corresponding system of radialdifferential equations and the statement of the three-body scattering problem for thetotal angular momentum J > 0 are presented.