The superfluid transition temperature of liquid 3He

The superfluid transition temperature, T_c, is calculated from a scattering amplitude (constructed from the polarization potentials of Aldrich and Pines) which has been shown to yield agreement with experiment for transport properties. Our calculated values agree with experiment at all pressures up to 34 atm.     

High temperature spontaneous ferromagnetism and other magnetic phenomena in liquid 3He and 3He4He dilute mixtures

Equilibrium ferromagnetic ordering in liquid ³He at temperatures T ? 0.3 K due to long-wavelength spin fluctuations is predicted. The magnetocaloric effect and other thermodynamic properties of ³He↑ are discussed. The properties of ³He↑⁴He solutions are considered in the case of a restricted geometry.     

Superfluidity of 3He in dilute solutions of 3He in liquid 4He

The possibility of superfluidity of ³He in dilute solutions of ³He in liquid ⁴He is investigated, and the corresponding critical temperature is estimated. The results indicate S-state pairing, i.e., for small concentrations of ³He, the highest transition temperature is obtained for L = 0, but the obtained critical temperatures are very low.     

Adsorption on a solid surface dilute liquid mixtures of 4He in 3He at low temperature

Numerical calculations show the ⁴He adsorption near the walls. Superfluid film observations can then be explained by a surface separation.     

This mysterious liquid 3He

The spin contribution to the heat capacity and entropy of ³He has been singled out. With increasing T the spin entropy reaches a constant value, different from ln 2. The spin contribution ≈ ln T can be observed in the temperature dependence of the pressure.     

Separable interactions and liquid 3He

A rigorous expression is given for the free energy of a system of fermions in the presence of a magnetic field interacting via a pairing hamiltonian in the weak-coupling limit. Starting from this expression Landau expansions are derived in two special cases, i.e. the case of general l-wave pairing in zero field and the case of l = 1 pairing, which applies to liquid ³He, in non-zero field.     

The elastic scattering of 3He on 4He at medium energies

The differential cross section of the elastic scattering ³He(⁴He, ⁴He)³He has been measured at center of mass energies E_c.m. between 28 and 44 MeV and in the c.m. angular range of 20° to 160°. The ³He polarization P at E_c.m. = 42 MeV and θ_c.m. = 132° was determined in a double scattering experiment. The analysis of the cross section data with the optical and the cluster model has been described previously. The phase shifts obtained in the cluster model calculations were used as starting values in a phase shift analysis. The resulting final real phase shifts and elasticity parameters give good fits to the cross section data. At 44 MeV the elasticity parameters show a pronounced odd-even dependence on angular momentum which had been found already in the case of the real phase shifts. The result of the polarization experiment |P| < 0.22 is consistent with cluster model predictions.     

The momentum distribution of the neutron in 2H and 3He as determined by quasi-elastic scattering

The momentum distribution of the neutron in ²H was determined in the range 0 to 365 MeV/c and in ³He in the range 0–295 MeV/c, by quasi-elastic scattering of 667 MeV/c protons. The measurements were analyzed by the plane wave impulse approximation and a correction was made for multiple scattering in the target nucleons. The results for ²H fit the Hulthén-Yamaguchi wave function quite well but show deviations similar to those found by other workers. For ³He there are no previously published measurements for comparison, but the results fit several expressions for the wave function, proposed for reasons of plausibility and analytical tractability, with parameters close to those obtained by electron scattering. The momentum distribution in ³He has a small but significant dip around 100 MeV/c which is not found in any of the theoretical expressions.     

Quasiparticle interaction in liquid 3He

The quasiparticle interaction in liquid ³He is studied. It is shown that part of the interaction can be considered induced through the exchange of density and spin-density excitations. The coupling of these excitations to quasiparticles is shown to be given rigorously by the quasiparticle interaction itself in the long wavelength limit. The induced part of the interaction is then calculated by determining the density-density and spin-density-spin-density response functions assuming that the irreducible particle-hole vertex functions are frequency independent. The remainder of the interaction is shown to be given by a vertex function which does not have certain singularities and it is argued that it can be approximated by the Brueckner G-matrix. From the net interaction Landau parameters are extracted and compared with the experimentally known ones. Since the agreement was not satisfactory, the consequences of making a theory in terms of “paramagnons” is explored. This leads to much better numerical results, but the theory is less satisfactory. Consideration of the density-density response function arrived at here shows it to be similar to one proposed by Pines and Nozières [3, 24], who assumed a local relation between a density fluctuation and the potential it produces. We come to the conclusion that the numerical discrepancies between our calculated Landau parameters and the experimental ones probably arise from neglect of the exchange of two and more spin fluctuations. In the paper following this one, O. Sjöberg makes application of our theory to calculate the Landau parameters of nuclear matter. No “soft” excitations such as the spin fluctuations of liquid ³He exist in nuclear matter, and the theory appears to be quantitatively much better there, although some of the crucial Landau parameters are not directly measurable, and a direct check is not possible.     

Transverse zero sound propagation in superfluid 3He

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

Specific heat of liquid 3He at 29.4 bar

The specific heat of liquid ³He has been measured from 4 to 300 mK. Even at very low temperature, it deviates from a pure γT behavior. The effective mass $\text{m}{}^1\text{= 5.8m}{}_3$ is in good agreement with previous results, but disagrees with recent measurements around T_A.     

Anomalous nuclear spin relaxation in liquid 3He4He mixtures

The longitudinal relaxation time, T₁, was measured in liquid ³He⁴He mixtures with molar concentrations of ³He of 0.12, 0.20 and 0.45 under saturated vapor pressure. λ-anomaly was clearly observed in the temperature dependence of T₁.     

Continuum energy spectra of 3He scattered by 3He at 120 MeV

Bump structure was observed in the continuum energy spectra of ³He from the ³He(τ, τ') reaction at 120 MeV. The angular dependence of the cross sections at around the peak of the bump was reproduced by calculations based on the simple impulse approximation. It is also shown that the effects of multiple scattering are important to reproduce the energy spectrum of the lower-energy side of the bump.     

Thermal relaxation in liquid 3He/4He mixtures near the tricritical point

Very long relaxation times τ were observed in our earlier specific heat measurements on liquid ³He/⁴He mixtures in two-phase-states near the tricritical temperature T_O. It appear that 1/τ ∝ (T_O ? T).     

The 4He(p,d)3He reaction at 770 MeV

The differential cross section of the ⁴He(p, d)³He pick-up reaction has been measured at E_p = 770 MeV. The data are analysed in the framework of the DWBA; both one-nucleon and one-N¹ transfers are considered.     

Ions at the critical interface of 3He4He mixtures

Trapping of ions at the interface of ³He⁴He mixtures has been studied near the tricritical point. The “soft” critical interface leads to a strong dependence of the trapping times both on temperature and on the applied electric field.     

On the superfluidity of 3He in dilute mixtures of 3He4He

It is shown on the basis of the experimental data on thermodynamic and transport properties under pressure that the temperatures of the transition of ³He to the superfluid state for ³He-⁴He solutions with concentrations 0.6-3% lie in the range 0.4–1.4 mK.     

Elastic electron scattering from 3He and 4He

The cross sections for elastic electron scattering from ³He and ⁴He were measured for the momentum transfer range from 0.45–2.0 fm^?1. The cross sections were separated into their longitudinal (charge) and transverse (magnetic) contributions using the Rosenbluth formula. The charge and magnetic form factors were obtained model-independently.The rms charge radii were found to be 1.671 (14) fm for ⁴He and 1.976 (15) fm for ³He, and the magnetic rms radius of ³He is 1.99 (6) fm. The mis charge radius for ⁴He is in excellent agreement with the latest muonic data.Comparison of the form factors was made with Faddeev three-body calculations using realistic two-body NN interactions. At present the theoretical calculation is not able to reproduce the experimental data.     

Coherent pion production in 3He3He collisions

A model is proposed to describe the near-threshold production of pions in the ${}^3\text{He}\text{(}{}^3\text{He}\text{, π}{}^{\mathrm{+}}\text{)}{}^6\text{Li}$ reaction. Taking experimental data on the ${}^3\text{He}\text{(p, π}{}^{\mathrm{+}}\text{)}{}^4$He process as input the cross sections for the first three levels of ⁶Li are reproduced semi-quantitatively.     

Spectrum of 3He atoms in superfluid 4He

It is suggested that at a wave vector near the inverse average interparticle separation, the spectrum of a ³He atom in superfluid ⁴He has a roton like dip. The results of light scattering and transport measurements in liquid ³He-⁴He mixtures can thereby be reconciled.