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The Journal of Chemical Physics

The quantal collision integrals and transport coefficients of dilute gaseous spin-polarized hydrogen and its admixtures with the isotopes of helium

T. K. Lim

Published Dec 15, 1982• 7 citations
Publisher

Abstract

The collision integrals and transport coefficients of spin-polarized hydrogen H↑ and its admixtures with the isotopes of helium are calculated with representative Lennard-Jones interatomic potentials at temperatures below 2 K. Diffractive features are predicted for these systems which are attributable to their extreme quantal characteristics.

DOI
10.1063/1.443820

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Journal of Physics B Atomic Molecular and Optical Physics•Jan 20, 2004•22 citations
The collision integrals and transport coefficients of spin-polarized hydrogen H↑ and its admixtures with the isotopes of helium are calculated with representative Lennard-Jones interatomic potentials at temperatures below 2 K. Diffractive features are predicted for these systems which are attributable to their extreme quantal characteristics.
The potential of Meyer and Frommhold describing the interaction between hydrogen and helium atoms is used to calculate the diffusion coefficients of hydrogen atoms in helium gas and helium atoms in hydrogen gas as functions of temperature, taking into account higher-order corrections of transport theory. Comparison with experiment suggests that the interaction potential should be steepened at small nuclear separations. Calculations of the diffusion coefficients for temperatures between zero and 1000 K with the modified potential are reported. The corresponding H-He scattering length resulting from the zero-temperature value of the diffusion coefficients has the magnitude 0.359a0.{0.359a}_{0}.0.359a0​. Direct calculation shows it to be negative.
We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.
A complete quantum phase shift calculation of several transport coefficients in spin polarized quantum gases (3He, H↑ and D↑) has been carried out for temperatures ranging from 0.04 K to 10 K and nuclear polarizations M varying from 0 to 1. After a detailed analysis of the dynamical features of the collision, the various direct and exchange « cross sections » necessary to describe the collision between two spin-polarized atoms are studied Emphasis is then placed on some particle-indistinguishability consequences that could be seen in 3He or H↑ systems, such as the strong M dependence of the heat capacity, a mode coupling between heat capacity and longitudinal spin diffusion and the oscillatory character of the evolution of the transverse components of M.
Systems of spin-aligned hydrogen isotopes are studied. They are shown to exhibit even more extreme "quantum" behavior than the helium isotopes. Spin-aligned hydrogen is predicted to be a gas at all temperatures and its Bose-Einstein condensation and possible superfluidity are discussed. Spin-aligned deuterium is predicted to show critical behavior strongly influenced by quantum mechanics. The preparation of spin-aligned hydrogen (in the presence of large magnetic fields) is also discussed.
Spin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« less
Upper and lower bounds are estimated for the scattering length, a , for the various isotopes of spin-polarized metastable helium. From a previous study involving various large basis sets and two ab initio approaches, and paying special attention to combine them with the accurate long-range potential, we get, for 4 He*– 4 He* collisions (in Bohr) 152 < 4−4 a < 230 and for 3 He*– 3 He* collisions 94 < 3−3 a < 113, while a surprising result arises for mixed collisions, 3 He*– 4 He*, 3−4 a < −488 and 3−4 a > 865. Indeed, the scattering length for this species is very close to the divergence occurring at the binding of a 14th vibrational level. Within these limits, our approach suggests that the values for 4−4 a and 3−3 a are closer to their upper bounds than to their lower bounds, and that the value for 3−4 a is negative and very large (>500) in magnitude. Sympathetic cooling could therefore be very efficient for the mixed species. Cooling-rate coefficients are also evaluated: they are large, of order 10 −9 cm 3 s −1 at mK temperatures for all combinations.