We present the asymptotic solution of the Schrödinger equation for three charged particles in the region ${\Omega }_{\alpha }$ in which ${\rho }_{\alpha }\to \infty$ and $r_{\beta \gamma }/{\rho }_{\alpha }\to 0,$ where $r_{\beta \gamma }$ is the distance between particles β and γ, and ${\rho }_{\alpha }$ is the distance between particle α and the center of mass of the pair (β,γ) $\left(\alpha \ne \beta \ne \gamma \right).\mathrm{}$ Our asymptotic wave function in ${\Omega }_{\alpha }$ satisfies the Schrödinger 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 wave function is applicable in regions of ${\Omega }_{\alpha }(\alpha =1,2,3)$ up to terms of order $O(1/{\rho }_{\alpha }).\mathrm{}$

• Received 10 February 1997

DOI:https://doi.org/10.1103/PhysRevA.56.521