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

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