James Sternberg

Quantum treatment of continuum electrons in the fields of moving charges

An ab initio, three-dimensional quantum mechanical calculation has been performed for the time evolution of continuum electrons in the fields of moving charges. Here the essential singularity associated with the diverging phase factor in the continuum wave function is identified and removed analytically. As a result, the continuum components of the regularized wave function are slowly varying with time. Therefore, one can propagate continuum electrons to asymptotically large times and obtain numerically stable, well-converged ejected electron momentum spectra with very low numerical noise. As a consequence, our approach resolves outstanding controversies concerning structures in electron momentum distributions. The main conclusions are general and are illustrated here for ionization of atomic hydrogen by proton impact. Our results show that in order to obtain the correct long-time free-particle propagation, the essential singularity identified here should be removed from the continuum components of solutions to the time-dependent Schroedinger equation.

Quantum Mechanical Models Of The Fermi Shuttle

The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron’s orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi‐classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.

Recent Applications Of The Lattice, Time‐Dependent Schrödinger Equation Approach For Ion‐Atom Collisions

Contemporary computational methods, such as the lattice, time‐dependent Schrodinger equation (LTDSE) approach, have opened opportunities to study ion‐atom collisions at a new level of detail and to uncover unexpected phenomena. Such interactions within gaseous, plasma, and material environments are fundamental to diverse applications such as low temperature plasma processing of materials, magnetic confinement fusion, and astrophysics. Results are briefly summarized here stemming from recent use of the LTDSE approach, with particular emphasis on elucidation of unexpected vortices in the ejected electron spectrum in ion‐atom collisions and for an atom subject to an electric field pulse.

Evolution of Quantum Systems from Microscopic to Macroscopic Scales

Even though the static properties of quantum systems have been known since the early days of quantum mechanics, accurate simulation of the dynamical break‐up or ionization remains a theoretical challenge despite our complete knowledge of the relevant interactions. Simulations are challenging because of highly oscillatory exponential phase factors in the electronic wave function and the infinitesimally small values of the continuum components of electronic probability density at large times after the collision. The approach we recently developed, the regularized time‐dependent Schrodinger equation method, has addressed these difficulties by removing the diverging phase factors and transforming the time‐dependent Schrodinger equation to an expanding space. The evolution of the electronic wave function was followed to internuclear distances of R = 100,000 a.u. or 5 microns, which is of the order of the diameter of a human hair. Our calculations also revealed unexpected presence of free vortices in the electr...

Hyperspherical Theory of Three-Body Recombination in Cold Collisions

Three‐body recombination in cold atomic collisions has been successfully modeled using the hyperspherical close‐coupling theory. This representation maps many‐body fragmentation channels onto simple radial equations similar to those for two‐body processes. Computation of hyperspherical adiabatic energy eigenvalues is a major task using this theory. We have developed asymptotic representations of the adiabatic eigenvalues based upon energy dependent zero‐range potentials. Our asymptotic expressions are compared with ab initio calculations as well as hyperspherical adiabatic calculations using zero range potentials with constant M that have appeared in the literature.