Ph.D., Harvard, 1967

Associate Research Scientist and Adjunct Assistant Professor, NYU, 1967-70.

Assistant Professor to Professor, University of Arkansas, 1970-1983.

Chair of Department 1983-86.

Visiting member, Institute for Theoretical Physics, U.C. Santa Barbara, 1988.

Vice Chairman of Department 1992 to 1999.

Professor Lieber obtained his doctorate under the direction of Nobel Laureate Julian Schwinger. His current research interests are in theoretical and mathematical physics, with particular emphasis on quantum electrodynamics and atomic scattering theory.

QUANTUM MECHANICAL THREE-BODY PROBLEM

Primary research areas have been quantum electrodynamics, elementary particles and scattering theory, the latter with an emphasis on three-body problems with applications in atomic physics.

The three-body problem is famous in both classical and quantum mechanics, but my research has concentrated on the quantum case, especially involving three electrically charged particles. I have been interested in so-called "capture" reactions, in which an energetic projectile captures a particle from a composite target, e.g., A + (BC) -> (AB) + C, and "break-up" (or in the atomic case, "ionization"): A + (BC) -> A + B + C. An example of capture from atomic physics would be a proton projectile capturing an electron from a target atom, emerging as a neutral hydrogen atom. In ionization all three particles would be free. These processes are very fundamental, and experiments studying them are done in many laboratories around the world. The theory proves to be extremely difficult and many approximate techniques have been developed. Recently, I have discovered that for certain masses of the three particles, capture is kinematically forbidden by means of the simplest double collision process. The allowed and forbidden regions are shown in what has come to be called the "Lieber diagram." Recently, together with a graduate student, I showed that capture was still possible in the forbidden regions by triple or higher-order collisions. How these considerations affect the quantum mechanical cross sections is under investigation.

In the case of breakup reactions involving three charged particles in the final state, such as ionization of an atom by electron collision, calculations require accurate approximate wave functions, since no exact ones exist. Important contributions come from situations where one pair of particles emerges with nearly the same velocity. I have recently published an improved wavefunction which is valid in this region, and which goes smoothly into the wavefunction valid when all three particle are moving apart. I am currently applying similar techniques to study the bound state asymptotic wavefunction for three charged particles such as the helium atom.