⁴He effective interaction for dilute solutions of ⁴He in liquid ³He at low temperatures

Abstract

The authors present for the first time an effective interaction between two ⁴He atoms in a bath of liquid ³He at temperatures below 0.1 K. This interaction turns out to be, in its long-range limit, an oscillatory function of the ⁴He interatomic separation, the oscillations arising essentially from the sharp discontinuity in the momentum distribution at the Fermi surface. In addition, an expression is formulated for the oscillations in the density of the ³He bath induced by one ⁴He impurity, as well as a modified Friedel sum rule, which relates the relative amount of matter displaced by this impurity to the phase shifts pertaining to the impurity ³He quasiparticle scattering at the Fermi surface. Finally, the dependence of the results on temperature and on the ³He superfluidity gap is discussed.