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Journal de physique

Hyperfine and electronic spin waves in atomic hydrogen : the role of the spin exchange process

J. P. Bouchaud, C. Lhuillier

Published Jan 1, 1985• 7 citations
Publisher

Abstract

The identical spin rotation effect is the quantum mechanical collisional effect underlying the transverse nuclear spin waves recently seen in dilute non degenerate gases in Paris [3He] and at Cornell University [H↓]. This mechanism could in principle give rise, at low enough temperatures, to hydrodynamic oscillatory modes associated with any non diagonal elements of the atomic internal density matrix (generalized spin waves or coherences waves). Starting from a quantum Boltzmann equation recently derived for the study of 4-component atomic hydrogen, we show that the current of any transverse quantity (hyperfine or Zeeman coherence) does indeed precess around molecular exchange fields. Unhappily, in most cases, the oscillatory modes associated with these transverse quantities are heavily damped. The first intrinsic cause of damping of these waves is spin exchange. We study the conditions under which this damping is minimized in both zero field and in high magnetic field. Numerical values of all relevant parameters for the description of spin transport properties in atomic hydrogen are given in the appendices.

DOI
10.1051/jphys:0198500460110178100

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The general results obtained in the preceding article are applied to the study of transport phenomena in a spin polarized gas at low temperatures, with particular emphasis on the particle indistinguishability effects in collisions. The effects of the nuclear orientation M are treated exactly (no M expansion). First, a simple theory of spin diffusion is presented and the response of the gas to a spin orientation gradient is calculated. The spin coherences and their evolution due to the « identical-spin rotation effect » are taken into account; it is found that they can play an important role, especially in the low temperature limit. The hydrodynamic equations of evolution of M are non-linear and anisotropic. Particle indistinguishability effects give an oscillatory character to the evolution of the transverse components of M (spin oscillations). Then, a more elaborate variational method is used to study the coupling between spin diffusion and heat conduction. This effect is, again, a sheer consequence of quantum interference phenomena introduced by particle indistinguishability. Finally, isotopic mixtures of 3He and 4He are considered In addition to coupling between isotopic diffusion and heat conduction, which exists for classical systems, quantum collision effects introduce a coupling between these two modes and spin diffusion.

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The identical spin rotation effect is the quantum mechanical collisional effect underlying the transverse nuclear spin waves recently seen in dilute non degenerate gases in Paris [3He] and at Cornell University [H↓]. This mechanism could in principle give rise, at low enough temperatures, to hydrodynamic oscillatory modes associated with any non diagonal elements of the atomic internal density matrix (generalized spin waves or coherences waves). Starting from a quantum Boltzmann equation recently derived for the study of 4-component atomic hydrogen, we show that the current of any transverse quantity (hyperfine or Zeeman coherence) does indeed precess around molecular exchange fields. Unhappily, in most cases, the oscillatory modes associated with these transverse quantities are heavily damped. The first intrinsic cause of damping of these waves is spin exchange. We study the conditions under which this damping is minimized in both zero field and in high magnetic field. Numerical values of all relevant parameters for the description of spin transport properties in atomic hydrogen are given in the appendices.
The general results recently obtained for the Boltzmann collision term in a gas of atomic hydrogen are applied to the study of longitudinal spin diffusion in high magnetic fields. This phenomenon can be described as a diffusion of concentration in a four component reactive mixture (the reaction being here the electronic transfer between nuclei). A numerical discussion of all the coefficients of the diffusion matrix between 100 mK to 100 K is given in the text, together with a discussion of the nature of the hydrodynamic modes in such a situation. The variations of the diffusion coefficients with the internal state of the gas are important for temperatures lower than 500 mK or higher than 10 K, when the spin exchange process is not negligible compared to the direct process. Finally, the relative importance of these two processes determines the nature of the hydrodynamic modes in the system.
We present an experimental study of electron spin waves in atomic hydrogen gas compressed to high densities of ∼5 × 10 18 cm −3 at temperatures ranging from 0.26 to 0.6 K in the strong magnetic field of 4.6 T. Hydrogen gas is in a quantum regime when the thermal de-Broglie wavelength is much larger than the s -wave scattering length. In this regime the identical particle effects play a major role in atomic collisions and lead to the identical spin rotation effect (ISR). We observed a variety of spin wave modes caused by this effect with strong dependence on the magnetic potential caused by variations of the polarizing magnetic field. We demonstrate confinement of the ISR modes in the magnetic potential and manipulate their properties by changing the spatial profile of the magnetic field. We have found that at a high enough density of H gas the magnons accumulate in their ground state in the magnetic trap and exhibit long coherence, which has a profound effect on the electron spin resonance spectra. Such macroscopic accumulation of the ground state occurs at a certain critical density of hydrogen gas, where the chemical potential of the magnons becomes equal to the energy of their ground state in the trapping potential.
The quantum Boltzmann equation governing the evolution of the one-body internal density matrix of an atomic hydrogen (or alkali) gas is established. Indistinguishability of both nuclei and electrons explains the presence in the collision term of a large number (eleven) of « exchange cross sections ». The different collision terms fall into two categories : these which contribute to the damping of perturbations (similar to the usual collision term in the classical regime) and those which are Hamiltonian like and originate from the « identical spin rotation effect ». Due to those numerous exchange terms, all transport properties in atomic hydrogen are very sensitive to the internal state of the gas.
The effect of spin exchange collisions on the internal variables (orientation, alignment, etc.) of colliding atoms is discussed, with particular emphasis on the role played by the Pauli principle. The calculation presented is valid for distinguishable or identical particles, and the initial introduction of an effective exchange hamiltonian for the spins is avoided. The one-atom density matrix of the internal variables is calculated after collision, in an operatorial form which enables the discussion of various physical effects. The first term in the density matrix evolution is a transfer term which does not originate from particle indistinguishability. The following terms are indeed introduced by the Pauli antisymmetrization principle applied to electrons and nuclei, and they can be described as electronic or nuclear apparent magnetic field (or electric gradient). In addition, terms arising from the combined exchange of electrons and nuclei are obtained, in particular from the exchange of identical whole atoms (bosons in the case of hydrogen). The evolution equations for the density operators are applied to a few particular cases in order to evaluate spin exchange effects in various situations : weak or strong hyperfine decoupling, Zeeman or hyperfine resonances, etc...
The general results obtained in the preceding article are applied to the study of transport phenomena in a spin polarized gas at low temperatures, with particular emphasis on the particle indistinguishability effects in collisions. The effects of the nuclear orientation M are treated exactly (no M expansion). First, a simple theory of spin diffusion is presented and the response of the gas to a spin orientation gradient is calculated. The spin coherences and their evolution due to the « identical-spin rotation effect » are taken into account; it is found that they can play an important role, especially in the low temperature limit. The hydrodynamic equations of evolution of M are non-linear and anisotropic. Particle indistinguishability effects give an oscillatory character to the evolution of the transverse components of M (spin oscillations). Then, a more elaborate variational method is used to study the coupling between spin diffusion and heat conduction. This effect is, again, a sheer consequence of quantum interference phenomena introduced by particle indistinguishability. Finally, isotopic mixtures of 3He and 4He are considered In addition to coupling between isotopic diffusion and heat conduction, which exists for classical systems, quantum collision effects introduce a coupling between these two modes and spin diffusion.