Asymptotic continuum wave function for three charged particles

We present the asymptotic solution of the Schrodinger equation for three charged particles in the region Omega(alpha) in which rho(alpha)-->infinity and r(beta gamma)/rho(alpha)-->0, where r(beta gamma) is the distance between particles beta and gamma, and rho(alpha) is the distance between particle alpha and the center of mass of the pair (beta,gamma) (alpha not equal beta not equal gamma). Our asymptotic wave function in Omega(alpha) satisfies the Schrodinger equation up to terms of order O(1/rho(alpha)(2)) and contains the zeroth-order terms and all, of the first-order O(1/rho(alpha)) terms. The new wave function contains additional terms which are absent in previous wave functions derived recently by others. The additional terms can be expressed in terms of solutions of a two-body problem with boundary conditions which do not correspond to the conventional boundary conditions for two-body states. We also prove that the leading term of our asymptotic wave function in Omega(alpha) is equal to the leading term of the Redmond-Merkuriev (RM) wave function in Omega(alpha), and hence the RM wavefunction is applicable in regions of Omega(alpha) (alpha = 1,2,3) up to terms of order O(1/rho(alpha)).