As an undergraduate, graduate and later a staff member at the University of Adelaide, Robert Crompton developed techniques for studying collisions between extremely low energy electrons and atoms and molecules. In 1961 he was invited to continue this work at The Australian National University, where he later became Professor and Head of the Atomic and Molecular Physics Laboratories until his retirement in 1991.
The award of a Fulbright Scholarship in 1968 began his close collaboration with US scientists in a number of laboratories, including the University of Oklahoma where he holds the appointment of Adjunct Professor.
Robert Crompton has been Secretary for Physical Sciences of the Australian Academy of Science (1984-88) and President of the Australian Institute of Physics (1993-94). He is a Fellow of the Academy and the British Institute of Physics as well as of the Australian Institute (elected as an Honorary Fellow in 2001) and of the American Physical Society. He is presently a Visiting Fellow at the ANU and Chairman of the Board of the Australian Science Olympiads.