Local Momentum and a Three-Body Gauge

Abstract

In recent years researchers have attempted to improve the continuum state three-body wavefunction for three, mutually interacting Coulomb particles by including, so called, local momentum effects, which depend upon the logarithmic gradient of the continuum, two-body Coulomb waves. Using the exact three-body wavefunction in the region where two of the three particles remain close, a revised description of these local momenta, is attained which predicts that a quantum-mechanical impulse may develop in the reaction zone, causing like-sign-charged particles to decrease their radial separation and opposite-sign-charged particles to increase their radial separation. The consequences of these predictions are investigated through both quantum and semi-classical techniques where the total energy of a two-body continuum Coulomb system in the presence of a third, mutually interacting body are analyzed. Numerical calculations confirm that while ignoring these local effects for light-ion-atom processes, may be appropriate, three-body effects may dominate in the reaction zone for heavy-ion-atom processes. This hypothesis is investigated and it is shown that a real-valued, position-dependent phase is added to the wavefunction. Further analysis shows that one may detect asymptotic variations in the scattering amplitudes for massive systems at near-threshold energies. These results provide convincing theoretical and physical evidence for a formal three-body gauge.