Leading asymptotic terms of the three-body Coulomb scattering wave function

The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A54, 3078 (1996)] has been refined in the region where the pair $(\beta ,\gamma )$ remains close to each other while the third particle $\alpha$ is far away from them $({\rho }_{\alpha }\to \infty ,r_{\alpha }∕{\rho }_{\alpha }\to 0)$. The improved wave function satisfies the Schrödinger equation up to the terms of order $O(1∕{\rho }_{\alpha }^3)$, provides the leading asymptotic terms of the three-body scattering wave function with Coulomb interactions, and gives further insight into the continuum behavior of the three-charged-particle wave function, and helps to obtain the $3\to 3$ scattered wave. This opens up further ways of solving and analyzing the three-body Schrödinger equation by numerical means.