The number density of dilute 3He-4He solutions under saturated vapor pressure is calculated within the framework of quantum hydrodynamics. For temperatures T small compared to the 3He Fermi temperature TF, results are given for 3He concentrations large enough to manifest 3He quasiparticle interactions. The nondegenerate regime (T>>TF) is also considered in the limit of small 3He concentration. Relevance to experimental determination of quasiparticle energies and interactions is emphasized.
1. CALCULATION RESULTS
Accuracy in the measurement of liquid He densities at low temperatures has been much sharpened over the last few years. 1 In view of this advance in experimental technique, we have undertaken a calculation of the density of dilute 3He-4He solutions under a variety of conditions. Together with the corresponding experiments, our results should provide a means for a precise determination of the 3He single-fermion spectrum, its density dependence, and the interaction between 3He quasiparticles.
The first experimental and theoretical determinations of 3He-4He solution densities were carried out by Edwards, Ifft, and Sarwinski 2'3 (EIS). Pertinent to quantum hydrodynamic theory, the 4He displacement coefficient and pressure-dependent quasiparticle effective mass were determined in the limit of zero 3He concentration. Concentration dependences were also estimatecl, although with limited reliability, as the experimental accuracy was considerably less than is now available via high-quality resonant cavity techniques. Corresponding to these experimental limitations, a number of useful simplifications were adopted in the EIS theoretical treatment. Basically, EIS tacitly accepted the assumption, as in Bardeen, Baym, and Pines 4 (BBP), that the 3He quasiparticle energy