RUI: Path Integrals and Charged Particle Dynamics

Board Of Trustees Of Illinois State University, Normal IL

Investigators

Abstract

Atomic collisions are a well-established method for probing the structure of atoms and molecules, as well as understanding the dynamics of how charged particles interact with matter. Due to their quantum mechanical nature, the particles involved in the collision must be modeled as matter waves, not as individual point particles. In the last decade, particles with unique waveforms have been created. These new matter waveforms (known as vortex waves or twisted particles) have properties that offer the opportunity for control and rotation of nanoparticles and improved resolution in electron microscopy, as well as the study of fundamental atomic properties, such as the magnetic moment and atomic transitions. Currently, there is a very limited understanding of how twisted particles interact with individual atoms or molecules. In order to realize the proposed applications, it is necessary to develop theoretical models that describe the particles' interaction with atoms at the most basic level. The researchers will develop and apply theoretical models to describe the physics of collisions between twisted particles and atoms in order to explain recently observed quantum phenomena and provide guidance for future experiments and applications. In addition to the science, another key aspect of the project is the inclusion of undergraduate students in cutting-edge research and the training of the next generation of physicists. Participation in this project provides students with valuable hands-on research experience through conceptual development of the models, as well as implementation and analysis. The students will also present their results at regional and national conferences, giving them a more global view of scientific research and encouraging them to pursue careers in STEM fields. The goals of the project will be accomplished through the development of two distinct computational models. All of the models will be designed for use on high performance computers and will be parallelized to improve efficiency. One of the models is based on the time-dependent Path Integral Quantum Trajectory (PIQTr) method that utilizes a Lagrangian approach to quantum mechanics. This model will be applied to phenomena such as electron capture, coherence, diffraction, tunneling, and quantum reflection. Application of the PIQTr model to higher dimensional systems will require the implementation of numerical techniques, such as adaptive stepsize, Monte Carlo integration, and boundary matching techniques. The results of the PIQTr model will provide a time-dependent analysis of collision processes allowing researchers to view the evolution of the interaction. A second model will be developed for the study of electron vortex beam collisions with atoms. This model will provide insight into orbital angular momentum transfer, as well as orientation and rotation effects that may occur during the collision process. A multipole expansion of the collision transition amplitude will yield information regarding potential selection rules or the possibility of state selectivity. The results of the electron vortex beam studies will be in the form of collision cross sections that can be used to provide guidance to experimentalists and others interested in applications of electron vortex beams. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.