³He dimers in two-dimensional ³He-⁴He mixture films

We have studied the ground state properties of two-dimensional ³He-⁴He mixtures at zero temperature. ³He atoms with opposite spins form loosely bound dimers in free space and in low concentration mixtures with ⁴He. The binding energy of the dimer ranges from milli-Kelvins near the saturation density to micro-Kelvins at the solidification density. The radius of such a weakly bound dimer is tens of Ångstöms. We also calculate the phase diagram of the mixture. The maximum solubility of ³He ≈ 7% is determined by comparing chemical potentials in the pure and mixed fluids. The upper stability limit of the super-saturated mixture is obtained from the second derivative of the enthalpy. It becomes negative at the concentration 10-15 % depending of the pressure, indicating a softening of the concentration-fluctuation mode. We also find an indication of the phase transition from the dimerized to atomic mixture.