Nuclear magnetic susceptibility measurements of the
3He in dilute
3He-
4He mixture films are presented. At low
3He coverages (
d3<0.1 layer), the
3He behaves approximately as a 2D ideal Fermi gas. For larger submonolayer
3He coverages, the low-temperature susceptibility is enhanced, increasing with increasing amounts of
3He, contrary to the 2D ideal Fermi-gas model. No evidence for a phase transition in the
3He is seen.
Dilute mixtures of
He3 in liquid
He4 are regarded as a set of
He3 atoms intereacting with elementary excitations of the
He4. The coupling between the
He3 and the
He4 is chosen phenomenologically and it is not weak but, for low temperatures, its main effects may be eliminated by means of two canonical transformations. The equations which determine the transformations describe the motion of a
He4 excitation in the presence of one or two
He3 atoms and, in the latter case, they resemble Faddeev's equations in the three-body problem. At low temperatures, there are few
He4 excitations and many of the properties of the mixture are determined by the effective
He3 Hamiltonian produced by the transformation. In this respect, the system behaves like a Fermi liquid. The
He3-
He3 potential is essentially momentum-independent and consists of the Van der Waals interaction together with an effectively repulsive potential induced by the
He4. It is suggested that a Fermi-liquid analysis is the best way of obtaining information about this potential, and the possible existence of a fermion superfluid phase transition is discussed from that point of view.
We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.
Simultaneous continuous-wave NMR and total-pressure measurements on spin-polarized atomic hydrogen gas in a 5-T magnetic field are reported. During sample loading we observe positive nuclear polarization. The rf susceptibility of the decaying sample is nonlinearly related to the density. This and the anomalous NMR line shape are discussed in light of the identical spin-rotation effect and the hydrodynamic spin-wave model. The analysis of the time evolution of the NMR signal area and of the pressure gives the two-body exchange recombination-rate coefficients
Kaa=1.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and
Kab=1.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, and the one-body relaxation rate
G1=1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ in the absence of rf field, at T=370 mK.
We have studied NMR spin echoes in
3He liquid in a magnetic field
B0=8 T for temperatures T\ensuremath{\ge}4.5 mK. The data are analyzed in terms of the Leggett-Rice effect to obtain the transverse spin-diffusion coefficient ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$(T). For T20 mK we find that ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ is less than measured in earlier experiments at lower
B0. This phenomenon has been predicted for degenerate Fermi systems, due to the phase space created for quasiparticle scattering by spin polarization. The effect we have measured is more pronounced than suggested by scaling a dilute-gas theory result by a Fermi-liquid factor.
We present neutron-scattering measurements of the momentum distribution of liquid $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixtures. The experiments were performed at wave vectors
Q, $26\ensuremath{\leqslant}Q\ensuremath{\leqslant}29\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with
3He concentrations
x between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction
n0 and the momentum distributions of
3He and
4He atoms. We find that
n0 increases somewhat above the pure
4He value when
3He is added; e.g., from ${n}_{0}=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ at
x=0 to $(11\ifmmode\pm\else\textpm\fi{}3)%$ at
x=15−−20. This agrees with predictions but is less than the only previous measurement. We find a
4He kinetic energy
K4 for pure
4He that agrees with previous determinations.
K4 decreases somewhat with increasing
3He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The
3He response is not well reproduced by a Fermi-gas momentum distribution,
n(k). Rather an
n(k) having a small step height at the Fermi surface and a substantial high-momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This
n(k) is consistent with calculated
n(k). Thus agreement between theory and experiment is obtained comparing
n(k) in contrast to earlier findings based on comparing calculated and observed
3He kinetic energies.