Superfluid transition temperature in a Fermi gas with repulsion allowing for higher orders of perturbation theory

Higher-order perturbation-theory corrections to the superfluid transition temperature in a weakly nonideal Fermi gas with repulsion are determined. This involves calculating the contribution of third-and fourth-order diagrams in terms of the gas parameter ap _F to the effective interaction which determines the super-fluid transition temperature and also allowing for effects associated with retardation and renormalization of the polar part of the Green’s function. The expressions obtained provide evidence in support of attraction in the effective interaction in the second, third, and fourth orders of perturbation theory. It is shown that the critical temperature is mainly determined by second-and third-order terms of perturbation theory. Calculations are made of the superfluid transition temperature for a gas comprising neutral Fermi particles in a magnetic field. The limits of validity of the theory are analyzed and the possibility of applying the results to dilute solutions of ³He in ⁴He and neutral-particle Fermi gases in magnetic traps is discussed.     

Shear viscosity of superfluid He-A1 at low temperatures

The shear viscosity tensor of the A₁-phase of superfluid ³He is calculated at low temperatures and melting pressure, by using the Boltzmann equation approach. The two normal and superfluid components take part in elements of the shear viscosity tensor differently. The interaction between normal and Bogoliubov quasiparticles in the collision integrals is considered in the binary, decay, and coalescence processes. We show that the elements of the shear viscosities η_xy, η_xz, and η_zz are proportional to (T/T_c)⁻². The constant of proportionality is in nearly good agreement with the experimental results of Roobol et al.     

Self-consistent approximations for correlation functions in the theory of triplet pairing superfluidity in3He

A self-consistent and “spin conserving” approximation scheme is developed for the two-particle correlation functions in superfluid³He. It is shown that the irreducible vertex part occuring in the Bethe-Salpeter equation for the generalized correlation function (having 4⁴ components) must be equal to the functional derivative of the approximate self-energy part with respect to the Green's function. The theory is specialized to the Hartree-Fock approximation yielding the RPA susceptibility belowT _c . An important feature of the resulting diagrammatic expansion is that the spin-fluctuation effects in the superfluid phase arise from infinite iteration of pairs of anomalous propagators inboth the particle-hole and in the particle-particle channels.     

Doppler-shift of fourth sound in flowing 3He4He mixtures

The Doppler-shift Δu₄ of fourth sound propagating in flowing superfluid ³He⁴He mixtures is calculated for arbitrary ³He concentration c. For c ? 0.15 and at T ? 1.4 K a cancellation of the dominant terms in the equation for Δu₄ results in a concentration independent shift.     

Anisotropic superconductivity in PrOs4Sb12

Recently two anisotropic superconducting gap functions have been observed in the skutterudite PrOs₄Sb₁₂. These order parameters are spin-triplet. There are at least 2 distinct phases in a magnetic field, bearing some resemblance to superfluid ³He. Here we present an analysis of the thermodynamic properties in these two superconducting states within the weak-coupling BCS theory.     

Quasiclassical approach to kinetic equations for superfluid 3hellum: General theory and application to the spin dynamics

Using the method of the quasiclassical Green function, we derive a set of kinetic equations which describe general nonequilibrium situations in the quasiclassical regime, i.e., when the external frequency and wave vector, ω and q are small compared to the atomic scale (ω ? μ, ∥ q ∥ ? pf. The equations consist of a Boltzmann equation for the quasiparticle distribution function, labeled by the energy and the direction of the momentum (particle representation), coupled to a time dependent Ginzburg-Landau equation for the order parameter. We discuss extensively the properties of these equations, and apply them to orbital and spin dynamics. Solving the Boltzmann equation in a well defined approximation, we are able to derive the expressions for the linewidths for all temperatures, with the correct identification of the phenomenological relaxation times. Furthermore, we discuss the connection between various relaxation times used in non-equilibrium situations, and we give a detailed comparison of the particle representation with the excitation representation which is used frequently in other work on non-equilibrium phenomena in superfluid ³He and in superconductors.     

Phenomenological phase diagram of superfluid 3He in a stretched aerogel

Highly anisotropic “nematically ordered” aerogel induces global uniaxial anisotropy in superfluid ³He. The anisotropy lowers symmetry of 3He in the aerogel from spherical to axial. As a result, instead of one transition temperature in a state with an orbital moment l = 1, there are two, corresponding to projections l _z = 0 and l _z = ±1. This splitting has a pronounced effect on the phase diagram of superfluid ³He and on the structures of the appearing phases. Possible phase diagrams obtained phenomenologically on the basis of Landau expansion of the thermodynamic potential in the vicinity of the transition temperature are presented here. The order parameters corresponding to each phase and their temperature dependences are found.     

Effect of correlated disorder on the temperature of unconventional cooper pairing: 3He in aerogel

It has been shown by the example of ³He in aerogel that the correlation in the position of impurities may have a considerable effect on the transition temperature T _c of a Fermi fluid to an unconventional superfluid or superconducting state if the correlation radius of the system of impurities exceeds the correlation length ξ₀ of the emerging superfluid phase. A decrease in T _c of ³He in aerogel has been expressed in terms of the structure factor of aerogel. Taking into account the fractal structure of aerogel provides a simple formula that satisfactorily describes the observed decrease in T _c.     

Evolution of the nucleon structure in the lightest nuclei

We show that the pattern of the oscillation of the structure functions ratio r^A(x)=F₂^A/F₂^N(D) varies with A by changing the position of the cross-over point x₃ in which r^A(x)=1, unlike the pattern for nuclei with masses A>4, where only the amplitude of the oscillation changes. In particular we find that the pattern of F₂(x) modifications is controlled with the values (1−x₃)=0.32 (D/N), 0.16 (³He/D) and 0.08 (⁴He/D). The obtained results follow from the relativistic approach and allow one to define the class of modifications of the bound nucleon structure.     

Transverse zero sound propagation in superfluid 3He

Transverse zero sound should propagate in superfluid ³He only in a rather narrow range below T_c.     

Stability of helical textures in 3HeA in the presence of superflow

We analyze the stability of a variety of uniform textures in superfluid ³HeA in the presence of superflow p. We find below T_ins a class of stable helical l? textures, where l? is no longer aligned with p but winds around it with a constant pitch .     

Cooling dilute 3He4He mixtures to 0.6 mK

We have cooled a ³He⁴He solution to the lowest temperatures yet achieved, 0.58 mK, and find no evidence for a superfluid transition in the dissolved ³He. We have measured the thermal boundary resistance between this solution and sintered 700 Å silver powder, and find that R is proportional to T^?2 between 0.8 mK and 4 mK.     

Low-temperature spin-relaxation time in normal liquid 3He

We calculate the low-temperature (T ? T_F) spin-relaxation time T₁ in normal liquid ³He, expressed in terms of the perturbations of the scattering amplitudes due to nuclear dipole-dipole interactions. These perturbations are obtained using the induced interaction model, yielding good agreement with experiment, as well as with previous calculations.     

Static susceptibility and longitudinal resonance frequency of superfluid 3He B

The static susceptibility and the longitudinal resonance frequency of superfluid ³He B have been measured at 18.7 bar from T_c to 0.27 T_c using continuous wave transverse NMR.     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

Thermodynamics of textures in superfluid 3He

The contribution of the textures in the B-phase of superfluid ³He to the specific heat has been calculated. The specific heat is found to be divergent near T_c.     

On the specific heat of Fermi liquids

The contributions of long-wavelength spin fluctuations to the specific heat of Fermi liquids is consistently calculated on the basis of the Landau theory of Fermi liquids. More satisfactory estimations of the Landau parameter F₁^a for liquid ³He are obtained.     

The superfluidd transition temperature of a Fermi liquid: 3He and 3He4He mixtures

The superfluid transitions temperature is calculated from the microscopic theory of a Fermi liquid in terms of the Landau parameters and one unknown scale factor. Determining the latter from the observed transition in ³He leads to an estimate that the superfluid transition in ³He⁴He mixtures may be presently observable.     

High-precision evaluation of the magnetic moment of the helion

NMR spectra of samples containing a mixture of hydrogen deuteride HD with pressure of about 80 atm and helium-3 with partial pressure of about 1 atm are analyzed. The ratio of the resonance frequencies of the nuclei, F(³He)/F(H₂), is determined to be 0.761786594(2), which is equal to the magnetic moment of the helion (bound in a helium atom) in the units of the magnetic moment of a proton (bound in molecular hydrogen). The uncertainty of two digits in the last place corresponds to a relative error of ??[F(³He)/F(H₂)] = 2.6 × 10^?9. The use of the known calculated data on the shielding of nuclei in the helium-3 atom (??(³He) = 59924(2) × 10^?9) and on the shielding of protons in hydrogen (??(H₂) = 26288(2) × 10^?9) yields a value of ??(³He)/?? _p = ?0.761812217(3) for the free magnetic moment of the helion in the units of the proton magnetic moment.