Dr. Madison is a theoretical atomic physicist and his work focuses on understanding the fundamental interactions between atoms and their environment. Since atomic particles are too small to observe, the only way to study these interactions is to collide beams of particles of interest and then observe the results of the collision. The role of a theorist is to predict and interpret the results of such collisions. Unfortunately, the collision of even the most elementary projectile with the most elementary atom is a very difficult quantum mechanical problem which cannot be solved analytically. Consequently, work in this area requires extensive use of computers and Dr. Madison's students typically work with computer codes several thousand lines long.

The recent work of Madison's research group has concentrated on the interactions of electrons, positrons and protons with both light and heavy atoms. This type of work is important to various types of practical applications such as building more efficient light sources, diamond coating tools for longer life, laser development and cancer treatment. The work has been continuously supported by the National Science Foundation since the early eighties.