From measurements of the velocity of second sound and the osmotic pressure the inertia! mass of 3 He in superfluid 4 He has been obtained as a function of temperature and concentration. The results indicate that (i) the 3 He quasiparticle spectrum is not quite parabolic and (ii) part of the quasiparticle effective interaction is velocity dependent or "nonlocal" and resembles the interaction of spheres moving through a nonviscous classical fluid.As usually interpreted, the Landau and Pomeranchuk 1 (LP) and Bardeen, Baym, and Pines 2 (BBP) theories of liquid 3 He-4 He mixtures predict that at low temperatures, where the phonon and roton densities are negligible, the normalfluid density p" should be given bywhere n 3 is the 3 He number density and the mass m should be independent of temperature and 3 He concentration. This result depends on two assumptions: (i) The quasiparticle energy e, which is the energy change on adding one 3 He of momentum p to a very weak solution of 3 He in 4 He, is given byand terms in higher powers of p 2 may be neglected. (ii) In the BBP theory, which takes into account an effective interaction between 3 He quasiparticles, the interaction v(r) is assumed to i to depend only on the interparticle distance r and not on the particle velocities with respect to the superfluid. The interaction energy is thus unchanged when the quasiparticles are accelerated with respect to the superfluid, and therefore v(r) (or its Fourier transform V k ) does not contribute to the normal-fluid inertial mass.If we define an empirical inertial mass m^Pn/ns,determination of the temperature and concentration dependence of m i allows one to test assumptions (i) and (ii). In this Letter we obtain p" and m { from measurements of the velocity of second sound. An equation for the velocity of second sound in the low-frequency, hydrodynamic limit has been derived by Khalatnikov. 3 This rather complicated equation, which depends only on thermodynamic and Galilean-in variance arguments, can be written as (l^){~(^4/91n^) r ,p + (^T/C)(aS/ain|) r ,p 2 } Pn/Ps+P? where Z=n 3 /n 40 =X/(l + aX), /= 1 +a-m 3 /m 4 = 0.53. (4) (5) (This result assumes that n 3 =n 40 X/(l + aX) and it therefore neglects, among other things, thermal expansion. The approximations involved have been investigated and can be justified.) In Eqs. (3)-(5), X is the atomic concentration of 3 He, n 40 is the number density of pure 4 He, a is the BBP parameter 0.284 (see, for instance, Edwards, Ifft, and Sarwinski 4 ), M 4 is the 4 He chemical potential, and S and C are the entropy and specific heat per atom of 3 He. [Using £ «1 and V 4 (T,X) = M 4 (?\ 0)-7r/w 4O , where ir is the osmotic pressure of the solution, Eq. (3) can be trans-formed to p n u 2 2 -(87r/ain£) s , P .The analogy between second sound in the mixture and ordinary sound in the quasiparticle gas is quite clear. 5 The derivative 37r/8ln| can be regarded as the "osmotic bulk modulus" of the mixture.] To determine p" from the second-sound velocities we used Eq. (3) with 3pt 4 /31n4 and 9S/ 31ni...

The heat evolved when He 3 is added to liquid He 3~H e 4 mixtures at the saturated vapor pressure has been measured for temperatures in the region of 0.05° K. The starting concentrations varied between zero and six atomic percent of He 3 . Since the variation of the energy with temperature (the specific heat) is known, the experiments give the ground-state energy and the He 3 and He 4 chemical potentials at 0°K as a function of concentration. The measurements were made in a calorimeter connected by a wire of high thermal resistance to a dilution refrigerator operating at ~ 0.02°K. The He 3 was added through a long tube containing thermal anchors connected to the refrigerator.The results give the difference in binding energy for one He 3 atom in He 4 relative to pure He 3 as (£3 -L^/kg^ (0.312 ± 0.007) degK, in excellent agreement with the theoretical value of Massey and Woo. The concentration dependence of the energy and chemical potentials agrees with predictions using the Bardeen, Baym, and Pines empirical interaction. The osmotic pressure in a saturated solution at 0°K is found to be (17.8 ± 0.9) mmHg.

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