This award supports Professor Eckhard Krotscheck of Texas A & M University (TAMU) to collaborate in theoretical physics with Professor Mikko Saarela of the Department of Theoretical Physics of the University of Oulu, Finland. They have two principle lines of joint research. One is to produce a microscopic description of the structure and the excitations of uniform mixtures of the quantum fluids Helium-4 and Helium-3 in two and three dimensions. They are particularly interested in critical concentrations and in the collective excitations, the effective mass, and the dynamic form factor of the mixture. As a second line of research, they are working on questions related to the symmetry-broken geometry of films of these isotopic elements adsorbed to a substrate. Here they are seeking to produce a semi-quantitative description of the interface between the Helium-4 and the Helium-3 liquid and its collective excitation. This research relies heavily upon the complementary expertise of the collaborating scientists which is the basis for an effective division of labor. All of the numerical work on time-dependent correlation functions will be done in Finland, and all the work on non-uniform systems at TAMU. The work on bulk mixtures will continue to be done at both locations. Professor Saarela has derived most of the results necessary for the inclusion and optimization of three- body correlations, and Professor Krotscheck has worked out the CBF (correlated basis functions) corrections of ring diagrams and is presently working on the elementary diagrams. The proposed work builds on a productive collaboration in the general area of the theory of strongly interacting many-body systems. A thorough investigation of the problem of mixtures of Helium-3 and Helium-4 requires state-of-the-art many body theory at a level that is beyond what has been done previously in microscopic attempts to understand quantum liquid mixtures. The proposed research will contribute to such strengthening of many-body theory in quantum physics. It applies state-of-the- art approaches to several interesting questions and is linked in a timely fashion to experimental research being done by others which will refine the theory.
