On a Dilute Solution of He^3 in Superfluid He^4. I : A Dilute Gas Model Calculation

概要

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An investigation is given about the properties of the fermion quasiparticles in a dilute solution of fermion in a low density boson gas at the absolute zero of temperature, assuming that a bare interaction between any pair of particles is identical isotropic potential of repulsion. An approximation of scattering amplitudes to the interactions is employed. Formulae for the chemical potential, the effective mass and the excitation spectrum of the fermion quasiparticle are given noting the differences between the case of a single impurity and the case of a dilute uniform solution. The effective interaction between the fermion quasiparticles in the limit of small momentum transfer is given by the sum of the direct interaction between the quasiparticles and the induced interaction due to the exchange of a virtual excitation of bosons, and becomes weakly attractive. The dependences of the effective interaction on the momentum transfer and the velocities of the interacting quasiparticles are also studied. Furthermore the expression for the ground state energy of the system is given.
理論物理学刊行会の論文
1967-10-25