Approximate triangle amplitude for three-body charge exchange processes

The single-rescattering contribution to the amplitude pertaining to three-body charge exchange reactions (triangle amplitude) contains the off-shell Coulomb T-matrix ${\mathit{T}}^{\mathit{C}}$ describing the intermediate-state Coulomb scattering of charged subsystems. For ease of computation, the latter is usually replaced by the potential ${\mathit{V}}^{\mathit{C}}$ which, however, is unsatisfactory in many cases. An alternative approximation, obtained by ``renormalizing'' the ``triangle'' contribution with ${\mathit{V}}^{\mathit{C}}$ instead of ${\mathit{T}}^{\mathit{C}}$ by a simple analytic expression, is shown to yield results in excellent agreement with the numerically calculated exact amplitude, for atomic elastic exchange reactions, over a wide range of (medium to high) projectile energies and scattering angles (including the forward direction). \textcopyright{} 1996 The American Physical Society.

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