Asymptotic wave function for three charged particles in the continuum

We present an improved version of the wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A 47, 2004 (1993)] that satisfies the Schr\"odinger equation up to terms of order O(1/${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\alpha}}}^{2}$) in the region where the pair \ensuremath{\alpha}=(\ensuremath{\beta},\ensuremath{\gamma}) remains close, while the third particle \ensuremath{\alpha} moves to infinity (${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\alpha}}}$\ensuremath{\rightarrow}\ensuremath{\infty}). The new wave function contains the zeroth- and all the first-order O(1/${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\alpha}}}$) terms, and matches smoothly Redmond's asymptotics and the Redmond-Merkuriev wave function when all three particles are well separated. \textcopyright{} 1996 The American Physical Society.

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