Origin, Evolution And Imaging Of Vortices In Atomic Processes

Calculations of the time‐dependent wave function for proton impact on atomic hydrogen using the Lattice‐Time‐Dependent‐Schrodinger‐Equation (LTDSE) method [1] follow the wave function from microscopic to macroscopic times. Isolated zeros, now identified as vortices, appear when the target and projectile nuclei are separated by a few atomic units [2]. Such structure has apparently been observed frequently in ab. initio. calculations. Our work shows that such structures persist to macroscopic distances and appear as “holes” in electron momentum distributions. They can, in principle, be observed in reaction microscope studies. Such observation is formally justified by the “imaging theorem”, which can be derived from first principles. Similarly, two‐electron momentum distributions as observed, e.g., in (e,2e) coincidence measurements may show isolated zeros [3]. Calculations using correlated wave functions support the interpretation that a minima in (e,2e) for helium targets corresponds to a vortex. In this case the “imaging theorem” can be applied to argue that there must be vortices in the two‐electron wave function[4]. A general discussion of vortices in quantum mechanics will be illustrated using exact LTDSE calculations, and, for interpretive purposes, the time‐dependent first Born approximation. These calculations show that the plane wave B1 amplitudes have no vortices, but the time‐dependent B1 amplitudes do. It will be further shown that angular momentum transfer is the key to forming vortices in the time‐dependent theory.