The method of interpolating integral equations for quantum Fluids.—III

Summary A method for interpolating between the (F)HNC and (F)PY approaches in order to take into account elementary contributions has been presented in two preceding papers concerned with the properties of zero-temperature quantum fluids, described by short-range correlated wave functions. In the present paper, both for Bose and for Fermi systems, the technique is extended to the case in which the two-body radial distribution function contains a long-range tail, going asr ⁻⁴. The results obtained for the energy per particle and momentum distribution of liquid⁴He, polarized hydrogen and³He are presented in correspondence to variational wave functions containing only two-particle correlations.

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Riassunto In due precedenti lavori è stata sviluppata una tecnica di interpolazione tra le approssimazioni (F)HNC e (F)PY per tenere conto dei cosiddetti contributi elementari nel calcolo delle proprietà dei fluidi quantistici a temperatura zero e descritti da funzioni d’onda con fattori di correlazione a corto raggio. Nel presente lavoro il metodo è esteso, per sistemi sia bosonici che fermionici, al caso in cui la funzione radiale di distribuzione contenga una coda con andamentor ⁻⁴. Sono presentati i risultati ottenuti per l’energia per particella e la distribuzione di quantità di moto dell’⁴He liquido, dell’idrogeno polarizzato e dell’³He liquido, in corrispondenza a funzioni d’onda variazionali contenenti solo correlazioni di coppia.

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Резюме В двух предыдущих работах был предложен метод интерполяции между (F)HNC и (F)PY подходами. В этих работах рассматривались свойства квантовых жидкостей при нулевой температуре, которые описываются волновыми функциями с короткодействующими корреляциями. В данной работе, для Бозеи Ферми-систем, предложенная тенхика обобщается на случай, когда двух-частичная радиальная функция распределения содержит длиннодействующий хвост, который спадает какr ⁻⁴. Приводятся результаты для энергии на одну частицу и импульсное распределение для жидкого⁴He, поляризованного водорода и³H, причем соответствующие вариационные волновые функции содержат только двух-частичные корреляции.

     

The boundary value problem in fermion systems

The half-space boundary value problem for fermions near zero temperature in plane geometry is solved for diffuse boundary scattering by numerically constructing the spatial propagator in terms of the eigenfunctions of a generalized eigenvalue problem for the linearized Uehling-Uhlenbeck collision integral. The slip length is calculated for several interparticle scattering laws and compared with a relaxation time ansatz result and the experimental values for normal fluid³He. It is shown that the nonsingular part of the collision operator is relatively compact to the singular part.     

Normal Liquid Helium-3 in the Static Fluctuation Approximation

In this paper normal liquid helium-3 is studied for the first time within the framework of the so-called static fluctuation approximation. This is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for neutral many-fermionic systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The thermodynamic properties are then obtained for normal liquid helium-3. The quadratic-fluctuation approximation is found to be valid for this system in the low-temperature limit (0.25 K). Our results are presented in a set of figures. The role of the interaction is emphasized, and the functional dependence on the temperature of key thermodynamic quantities is derived for normal liquid helium-3.     

饱和液体氦-3的粘度性质

文中揭示了低温液态氦-3在其饱和蒸气压下粘度随温度状态参数变化的反常规律,首次提出了3He在0.003K至其临界温度3.3157K温区内完整的气液相平衡曲线粘度方程。该方程计算值与高精度实验数据偏差小于±0.7%,并且在极低温条件下光滑过渡为由量子理论预测的理论极限。这项工作是研究氦-3在整个温度和压力区间上粘度性质行为特性的起点,不仅是构建全区间粘度方程的重要边界,而且对于理解费米-狄拉克量子统计规律在低温下的作用规律具有指导意义。     

Ground state of liquid helium-3: off-shell effects due to non-local potentials

It is shown that by incorporating the off-shell effects through the introduction of phase equivalent nonlocal potentials, (that are essentially equivalent so far as two-body properties are concerned) one could obtain a much better agreement regarding the important properties of the ground state of liquid helium-3, in lowest order Brueckner-Goldstone theory. The binding energy, equilibruim density and the convergence character of Brueckner-Goldstone series improve drastically.     

Mott–Hubbard transition in a 2D He fluid monolayer

We discuss recent observations of the heat capacity and magnetization of a fluid ³He monolayer adsorbed on graphite plated with a bilayer of HD. Approaching the density at which the monolayer solidifies into a commensurate solid, we observe an apparent divergence of the effective mass. However, the inferred values of F₀^a tend to a constant. We interpret this in terms of a Mott–Hubbard transition between a 2D Fermi liquid and a magnetically disordered solid occurring via the Brinkman–Rice–Anderson–Vollhardt scenario.     

Fluctuation effects in spin diffusion measurements in liquid He

We have measured spin diffusion coefficients of liquid ³He at a frequency of 920 kHz by pulsed NMR. By analyzing our data in the framework of the Leggett–Rice theory we got a spin diffusion coefficient and a Leggett–Rice parameter =λωτ simultaneously at each temperature. On approaching the superfluid transition the spin diffusion coefficients showed a deviation from predictions of the Fermi liquid theory. The deviation at low pressure was larger than that at high pressure. This anomaly may be due to the effects of fluctuations of superfluidity which were recently observed in the viscosity measurement of liquid ³He.     

Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one-dimensional systems

We develop a perturbation theory formalism for the theory of the Fermi surface in a Fermi liquid of particles interacting via a bounded short-range repulsive pair potential. The formalism is based on the renormalization group and provides a formal expansion of the large-distance Schwinger functions in terms of a family of running couplings consisting of one- and two-body quasiparticle potentials. The flow of the running couplings is described in terms of a beta function, which is studied to all orders of perturbation theory and shown to obey, in thenth order,n! bounds. The flow equations are written in general dimensiond1 for the spinless case (for simplicity). The picture that emerges is that on a large scale the system looks like a system of fermions interacting via a-like interaction potential (i.e., a potential approaching 0 everywhere except at the origin, where it diverges, although keeping the integral bounded); the theory is not asymptotically free in the usual sense and the freedom mechanism is thus more delicate than usual: the technical problem of dealing with unbounded effective potentials is solved by introducing a mathematically precise notion ofquasiparticles, which turn out to be natural objects with finite interaction even when the physical potential diverges as a deltalike function. A remarkable kind of gauge symmetry is associated with the quasiparticles. To substantiate the analogy with the quasiparticle theory we discuss the mean field theory using our notion of quasiparticles: the resulting self-consistency relations are closely reminiscent of those of the BCS model. The formalism seems suited for a joint theory of normal states of Fermi liquids and of BCS states: the first are associated with the trivial fixed point of our flow or with nearby nontrivial fixed points (or invariant sets) and the second may naturally correspond to really nontrivial fixed points (which may nevertheless turn out to be accessible to analysis because the BCS state is a quasi free state, hence quite simple, unlike the nontrivial fixed points of field theory). Thed=1 case is deeply different from thed> 1 case, for our spinless fermions: we can treat it essentially completely for small coupling. The system is not asymptotically free and presents anomalous renormalization group flow with a vanishing beta function, and the discontinuity of the occupation number at the Fermi surface is smoothed by the interaction (remaining singular with a coupling-dependent singularity of power type with exponent identified with the anomalous dimension). Finally, we present a heuristic discussion of the theory for the flow of the running coupling constants in spinlessd> 1 systems: their structure is simplified further and the relevant part of the running interaction is precisely the interaction between pairs of quasiparticles which we identify with the Cooper pairs of superconductivity. The formal perturbation theory seems to have a chance to work only if the interaction between the Cooper pairs is repulsive: and to second order we show that in the spin-0 case this happens if the physical potential is repulsive. Our results indicate the possibility of the existence of a normal Fermi surface only if the interaction is repulsive.     

The normal liquid 3He one-body momentum distribution at zero and finite temperature

The normal liquid helium 3 one-body momentum distribution, n(k), at zero and finite temperature is evaluated by using the cluster expansion theory for the occupation probability of Ristig-Clark formalism. The lowest order constrained variational (LOCV) and the extended LOCV (ELOCV) method are used to calculate the correlation functions at zero and finite temperatures. The input inter-atomic potential is the familiar 6–12 Lennard-Jones interaction. The gap in n(k) at the Fermi surface is found to be about 0.41 comparing to 1.0 (0.72) for the noninteracting (dilute hard-sphere) Fermi gas model at zero temperature and it decreases by increasing the temperature. It is also demonstrated that the high-momentum tail of n(k) gets larger as we increase the temperature and finally, we find a good agreement between present calculated n(k) and those coming from more sophisticated approaches such as Diffusion and Green-function Monte Carlo techniques.     

Average partial level density based on the random matrix model. Inclusion of realistic one-body spectrum and effect of particle escape

The effect of the realistic one-body spectrum is included in calculating the average partial level density, which has been so far obtained assuming degenerate one-body spectrum and GDE for the residual interaction. We show that such partial level densities are obtained by solving the extended saddle point equations which need inputs of the realistic one-body spectrum as well as the second moment of the ensemble. It is seen that the average partial level density is expressed in a convolution form of the partial level density for realistic one-body spectrum with the distribution which describes the effect by the random residual interaction. Calculations numerically performed show the improvement over the previous results. The effect of particle escape on the level density is also investigated and turns out to be practically negligible in precompound reactions.     

Critical velocities and two mechanisms of transition in superfluid liquid He

Two mechanisms of transition of the superfluid liquid ⁴He to quantum turbulence regimes are proposed for the case when the influence of the normal fluid on superfluid flow is suppressed by introducing superleaks at the ends of the capillary. Using dimensional analysis it is found that in the roton mechanism the critical velocity depends on channel size as vc∝d−1/4, matching the experiments. For the second, super-flow mechanism, the analysis of independent parameters relevant for this phenomena leads to critical velocity depending on d as vc∝d−1. It is shown that turbulence for super-flow mechanism arises when a “quantum Reynolds number” exceeds some critical value which is about 10³ for 1D geometry. The dimensional analysis of the equation for critical velocity of superfluid flow without superleaks at the ends of the capillary is also presented.     

Pseudoclassical approach to electron and ion density correlations in simple liquid metals

Il Nuovo Cimento D - Electron-electron and electron-ion structural correlations in simple liquid metals are treated by using effective pair potentials to incorporate quantal effects into a...     

He accumulation effect in solid and liquid D-T mixture

This article reports the accumulation effect of the ³He originating from tritium β decay; ³He created in solid remains in it, while one in liquid diffuses and goes out to the vapor gas. We observed this effect through the neutron detection from muon catalyzed fusion phenomenon (μCF), and gave it qualitative understanding, by which the muon transfer rate from (dμ) and (tμ) to helium was derived. This revised version was published online in August 2006 with corrections to the Cover Date.     

Elastic and inelastic scattering of 270 MeV3He particles from58Ni,90Zr,116Sn and208Pb

Differential cross-section angular distributions for the elastic scattering of 270 MeV³He particles from⁵⁸Ni,⁹⁰Zr,¹¹⁶Sn and²⁰⁸Pb have been measured. Optical model analysis of the cross-sections has yielded the optical model parameters for³He particles at 270 MeV. Angular distributions have also been measured for the inelastic excitation of the low-lying levels in the above mentioned nuclei. A collective model analysis using the distorted wave Born approximation (DWBA) of these cross-sections with the distorted waves generated by the optical model parameters determined from the elastic scattering analysis, has yielded the reduced transition probability (B(EL)) values consistent with those reported in the literature.     

The density maximum in liquid He4 and its relationship to the lambda point

The lambda point in liquid He⁴ is a very well-established phenomenon. London, in 1938, suggested that the effect might be an example of Bose–Einstein condensation and it is this model that is generally accepted nowadays. There are, however, serious discrepancies between the theory and experimental results. Here we present an alternative model based on the existence of the density maximum in liquid He⁴ near 2.18 K, that explains the anomaly in the specific heat capacity but does not have the failings of the BEC model. In addition the theory explains the occurrence of the density maximum in liquid He⁴.     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.