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Journal de physique

The role of the Pauli principle in metastability exchange collisions

M. Pinard, Franck Laloë

Published Jan 1, 1980• 11 citations
Publisher

Abstract

In optical pumping experiments, metastability exchange collisions are used to transfer orientation, alignment, ... between different atomic levels. This article studies the effect of such collisions on the atom internal variables density operator by a method used in a previous publication for spin exchange collisions. The calculations are valid when the nuclei of the two atoms are distinguishable as well as when they are identical particles, which allows a detailed discussion of nuclear identity effects (apparent magnetic field, etc...). Two cases are successively studied : no depolarization of the electronic angular momentum (He*-He collisions) and partial depolarization (Ne*-Ne collisions for example). The nuclear identity effects should be observable in low temperature optical pumping experiments with noble gases. In an Appendix, another particle identity effect is studied, which can be observed in atomic beam experiments : during the collision of two 3He atoms, both in the ground state, the spin state of the atoms scattered in a particular direction can be changed by nuclear indistinguishability effects.

DOI
10.1051/jphys:01980004108079900

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Physical Review A•Dec 1, 1976•13 citations
In optical pumping experiments, metastability exchange collisions are used to transfer orientation, alignment, ... between different atomic levels. This article studies the effect of such collisions on the atom internal variables density operator by a method used in a previous publication for spin exchange collisions. The calculations are valid when the nuclei of the two atoms are distinguishable as well as when they are identical particles, which allows a detailed discussion of nuclear identity effects (apparent magnetic field, etc...). Two cases are successively studied : no depolarization of the electronic angular momentum (He*-He collisions) and partial depolarization (Ne*-Ne collisions for example). The nuclear identity effects should be observable in low temperature optical pumping experiments with noble gases. In an Appendix, another particle identity effect is studied, which can be observed in atomic beam experiments : during the collision of two 3He atoms, both in the ground state, the spin state of the atoms scattered in a particular direction can be changed by nuclear indistinguishability effects.
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...
In the collision of spin-polarized atoms, the transmission of electron polarization between colliding particles is possible. A similar situation occurs in a collision, for example, between alkali atoms in the ground state. If one of the colliding particles is in an excited state and its energy is sufficient for ionization of the collision partner, then along with the elastic process (spin exchange), an inelastic process (ionization) is also possible, as a result of these processes polarization can also be transferred to the partner. Simultaneously occurring elastic and inelastic processes at the collision between two helium atoms are possible if these atoms are in the metastable (23S1) state. The paper discusses the interaction between spin-polarized metastable atoms of helium-3 and helium-4 isotopes under conditions of optical pumping of atoms. Complex interaction potentials of the atoms under consideration were constructed and on their basis, the spin exchange and chemo-ionization cross-sections were calculated. Using these cross-sections, expressions for the transfer of orientation and alignment from one atom to another were obtained.
Three further types of collision between atomic systems in which no change of internal energy takes place are considered. These are collisions in which transfer of excitation occurs between two similar atoms, spin exchange collisions, and collisions in which the direction but not the magnitude of the orbital angular momentum of an excited atom is changed on impact. An account is given of the theory of these processes in relation to that for other processes, elastic scattering and symmetrical charge exchange, discussed in the earlier articles, in which no change of internal energy occurs. Methods for measuring the relevant cross sections are described. These make use of optical pumping and nuclear magnetic resonance techniques. Comparison is made between observed and calculated cross sections.
Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, Fd{F}_{d}Fd​ and Fx{F}_{x}Fx​. All cross sections must be expressible in terms of ∣Fd∣|{F}_{d}|∣Fd​∣ and ∣Fx∣|{F}_{x}|∣Fx​∣, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.
Cross sections for relaxation of circular and linear polarization of 62P326^{2}P_{\frac{3}{2}}62P23​​ cesium atoms, induced in collisions with ground-state He, Ne, Ar, and Xe, have been determined by Zeeman scanning techniques. A fluorescence cell containing low-pressure cesium vapor together with a buffer gas was irradiated with circularly or linearly polarized 8521-\AA{} Cs resonance radiation, producing excited and polarized Cs atoms which became depolarized in subsequent collisions with the buffer-gas atoms. The resulting depolarization of the cesium resonance fluorescence was monitored in relation to buffer-gas pressure (0-10 Torr) and to the strength of the ambient magnetic field (0-10 kG). At low fields at which the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$ is coupled to the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$, the measurements yielded depolarization cross sections Q(circ.)Q(\mathrm{circ}.)Q(circ.) and Q(lin.)Q(\mathrm{lin}.)Q(lin.), which agree within experimental error with theoretical values calculated for spin-coupled conditions. At kilogauss fields with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ decoupled, the experiments produced cross sections for disorientation and disalignment, which are also in satisfactory agreement with the appropriate theoretical predictions. The results indicate that the nuclear spin has a more pronounced effect on the collisional relaxation of the atomic dipole than of the quadrupole.