The three-body rigid rotator and multipole expansions of the three-body continuum

Two approaches in the derivation of multipole expansions of the three-body continuum wavefunction are considered. These approaches are determined by the basis of angular functions used. The two angular bases considered are bipolar harmonics and Wigner D-functions. In the asymptotic region of large inter-particle separations the continuum wavefunction tends to be a product of two plane waves. It is shown that the coefficients in the multipole expansion of the product of two plane waves in terms of D-functions are equivalent to the wavefunctions of the three-body rigid rotator in momentum representation. Possible applications of the developed formalism to the theory of angular distributions in molecular photo and predissociation processes are discussed. Several novel relations between integrals with two Bessel functions are discovered during the calculations.