Structure, excitations and impurity states of liquid helium
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abstract
The authors study the quantum liquid [sup 4]He with and without impurities using optimized Hypernetted Chain theory. The first part of this dissertation concerns pure liquid [sup 4]He. First a precision calculation for bulk [sup 4]He, including elementary diagrams and three-body correlations, is reviewed. Then the formalism is extended to the inhomogeneous system of [sup 4]He on a planar substrate. Results are presented for the new calculation that includes the elementary diagrams and three-body correlations in the inhomogeneous system. It is found that the density profile, the chemical potential, and the third sound velocity are quite close to the experimental values. The second part of this dissertation studies the system of [sup 4]He with a single [sup 3]He impurity. The authors review the system of static [sup 3]He impurity in bulk [sup 4]He and develop a theory for the self-energy of the impurity. They are able to calculate, in a self-consistent manner, the complex self-energy of the impurity at finite momentum. From this they can find the effective mass and compare it to that found using a Feynman-Cohen backflow formalism. It is shown how to relate the backflow effective mass to that found from the low-momentum limit to the self-energy. Finally, the authors study the system of a single [sup 3]He impurity in a film of [sup 4]He. They begin with a static impurity and then use a backflow formalism to find the effective mass of the impurity. They next calculate the complex self-energy of the [sup 3]He in the film. The results for the self-energy are used to calculate the observable effective mass and magnetic susceptibility.
