Gauge transformations for coupled-channel calculations applied to pair production in relativistic atomic collisions.

Abstract

It is shown that for single-center coupled-channel calculations, it is not possible to remove some unwanted part ${\mathit{W}}^{\ensuremath{'}}$ of the interaction by a gauge transformation, even if the coupled equations do not exhibit an explicit dependence on ${\mathit{W}}^{\ensuremath{'}}$. This dependence necessarily exists and enters implicitly via the convergence property of the basis expansion. In two-center expansions, an explicit dependence on the gauge function associated with ${\mathit{W}}^{\ensuremath{'}}$ always remains because of the nonorthogonality of the basis states belonging to different centers in the reaction zone. The observation discussed here and supported by physical examples is relevant to the assessment of the asymptotic cross-section behavior for electron-positron pair production in relativistic atomic collisions. \textcopyright{} 1996 The American Physical Society.