Microscopic theory of quantum fluid at nonzero temperature. The momentum distribution,liquid-structure factor and ground-state energy of liquid4He

Summary Employing theU-matrix theory in the present form we have presented a microscopic theory of an interactingN-boson system at nonzero temperature. The Hamiltonian includes a term describing the external influence, a term for a two-particle interaction and one pertaining to the dipole-type interaction. To study the ground state of liquid⁴He, only the two-particle interaction is included. Based on scattering data, we have deduced the two-particle potential function. With that we calculate numerically the momentum atT=1.1 K for several sets of parameters. It is shown that the theoretical curves agree well with the observed results. The corresponding liquid-structure-factor curves fit the measured data very well and the best result for the ground-state energy is −7.12K.

---

Riassunto Impiegando la teoria della matriceU nella forma presente, abbiamo presentato una teoria microscopica di un sistema interagente diN bosoni a temperatura non nulla. L'hamiltoniana include un termine che descrive l'influenza esterna, un termine per un'interazione a 2 particelle e une che riguarda l'interazione di tipo dipolare. Per studiare lo stato fondamentale dell'⁴He liquido s'include solo l'interazione a 2 particelle. Basandoci su dati di scattering, abbiamo dedotto la funzione potenziale a 2 particelle. Con quella, calcoliamo numericamente la distribuzione dell'impulso aT=1.1K per diversi gruppi di parametri. Si mostra che le curve teoriche sono in buon accordo con i risultati osservati. Le corrispondenti curve del fattore di struttura del liquido si adattano benissimo ai dati misurati e il risultato migliore per l'energia dello stato fondamentale è − 7.12K.

---

Резюме Используь теориюU-матрицы, мы предлагаем микроскопическую теорию взаимодеюствующейN-бозонной системы при ненулевых температурах. Гамильтониан включает член, описывающий внешнее влияние, член двух-частичного взаимодействия и член, относящийся к дипольному типу взаимодействия. При исследовании основного состояния шидкого⁴He учитяватся только двух-частичное взаимодействие. Основываясь на данных по рассеянию, мы выводим двух-частичную потенциальную функцию. Мы численно определяем распределение по импульсам приT=1.1K для некоторых систем параметров. Показывается, что теоретические кривые согласуются с наблюденными результатами. Соответст вующий структурный фактор зидкости хорошо согласуется с экспериментальными данными. Полученная величина энергии основного состояния составляет −7.12 K.

     

Enhanced thermal conductance at a copper-liquid helium interface in the presence of acoustic streaming

In a conventional Kapitza resistance experiment involving heat transfer across a copper surface into liquid helium, an acoustic streaming velocity field (at 10 MHz) was directed transverse to the surface normal. Ultrasound had no observable effect on the heat transfer to the superfluid phase (He-II), but in the normal fluid phase (He-I) the thermal conductance increased linearly with acoustic velocity amplitude, reaching a value 2.5 times the zero sound conductance for a sound velocity amplitude of 0.8 cm s^?1.     

Elastic scattering of electrons by helium atoms in high energy higher order Born approximation

The differential cross-sections forē-helium elastic scattering are calculated by using Yateshigh-energy higher order Born approximations, through 0 (K _i ^{Emphasis>−2} ) of the incident electron momentum, and comparisons have been made with the recent theoretical and experimental results.     

On the summation of the Brillouin-Wigner type perturbation series

It is shown that if the ‘mean excitation energy’ assumption is introduced in the Brillouin-Wigner perturbation series, then the resulting series can be exactly summed. The implications of the result for calculating energy shift and for constructing trial functions are examined with special reference to the ground state of the helium atom.     

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models⁴He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of⁴He with the product (Jastrow) form that corresponds to a classical 1/r ^b pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10^–5 for 1/r ⁹ and 6.36×10^–6 for 1/r ⁶, while the interstitial fractional concentrations are 1.32×10^–3 and 1.08×10^–5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r ⁹ potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)⁴He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in⁴He is probably much lower than our results.     

Spherically compressed helium atom described by perturbative and variational methods

We analyze the energy spectrum of the three lowest-lying S symmetry states for the spherically confined helium atom as a function of the box radius by using an approach based on a time independent perturbation theory and two variational methods. The first treatment depends on exact solutions for confined one-electron atoms, whereas in the latter two methods exponents and linear coefficients are variationally optimized via {s,t,u}-Hylleraas functions and Generalized {r₁,r₂,r₁₂}-Hylleraas basis sets that fulfill appropriate boundary conditions. Although it is found that throughout most of the box radii here analyzed the variational energies for the three states lie below those perturbatively obtained, an opposite trend occurs toward the weak and strong confinement regions for the singlet excited and triplet states, respectively.     

Experiments with solid He

The possibility of supersolid behavior in ⁴He was predicted many years ago, but negative experiments in the 1970’s removed motivation for further experimental efforts to explore the possibility until the work of Goodkind’s group renewed attention. Kim and Chan found unambiguous evidence for a period shift in a torsional oscillator filled with solid ⁴He and this observation and its interpretation have created substantial interest in the study of solid ⁴He. Here, recent work with an experimental design that allows for superfluid ⁴He to be in direct contact with solid ⁴He off the melting curve will be discussed and evidence for the flow of helium atoms through a cell filled with solid ⁴He, caused by an applied chemical potential difference will be briefly reviewed.     

A low-temperature high-pressure apparatus with a temperature control system

Abstract

A low-temperature high-pressure apparatus was designed using commercial cryogenic equipment. Pressures up to 1 GPa and temperatures down to 40 K can be obtained in a volume of up to 30 cm³. The apparatus is of the piston-cylinder type with a piston diameter of 45 mm, and the pressure can be varied at all temperatures, An adaptive temperature control system keeps the temperature inside the pressure cylinder constant to within ±0.1 K.     

AN APPROXIMATION OF THE KINETIC ENERGY OF A SUPERFLUID FILM ON A RIEMANN SURFACE

The flow of a superfluid film adsorbed on a porous medium can be modeled by a meromorphic differential on a Riemann surface of high genus. In this paper, we define the mixed Hodge metric of meromorphic differentials on a Riemann surface and justify using this metric to approximate the kinetic energy of a superfluid film flowing on a porous surface.     

Recent developments in polyetherimide membrane for gas separation

Polyetherimide (PEI) is an extraordinary type of polyimide with excellent thermal and mechanical properties. The polymer is also gas permeable and is considered one of the best membranes for gas separation. Despite the high selectivity, PEI suffers from low permeability due to the trade‐off between phenomena in polymers. To overcome this limitation, fillers are added during the membrane preparation to create voids for better gas transport. In this paper, permeability and selectivity data of PEI membranes for the separation of oxygen, carbon dioxide, and helium are discussed. The paper also summarizes the reported studies for adding fillers to improve the membrane performance.