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Physical Review

Noble-Gas-Induced Rubidium Spin Disorientation

R. M. Herman

Published Dec 14, 1964• 62 citations
Publisher

Abstract

Cross sections for noble-gas-induced Rb spin disorientation are calculated, taking into account second-order cross terms in the spin-orbit and K\ifmmode\cdot\else\textperiodcentered\fi{}L couplings, as initially proposed by Bernheim. Contrary to Bernheim, it is argued that spin-orbit effects are negligible in first order. Using simple wave functions, it is shown that the spin-orbit coupling provided by the electric field of the Rb ionic core, when the valence electronic orbital is deformed in short-range encounters, is sufficient to yield the observed relaxation rates. For He, the calculated disorientation cross section shows agreement to within a factor of 6 with the experimentally determined cross section for depolarization of optically oriented Rb vapor. Moreover, if, for all Rb-rare-gas pairs, we assume the same proportionality between the short- and calculated long-range energies at the kinetic radius, agreement to within a factor of 6 for Ne, A, Kr and Xe is also obtained.

DOI
10.1103/physrev.136.a1576

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Experimental determination of the spin-rotation coupling in Na-Xe molecules

M. Hou, B. Feng, J. Zhang +3 more

A theory for calculating the spin–rotation coupling coefficient in alkali-metal–noble-gas van der Waals molecules was recently presented.1 It assumes the spin–rotation interaction in alkali-metal–noble-gas molecules to be mainly due to the spin–orbit interaction of the alkali-metal valence electron within the core of the noble gas, and predicts that the spin–rotation constant γ should depend on the spin–orbit interaction in the noble gas and be almost independent of the spin–orbit interaction of the alkali-metal atom. Experimentally, only a few of the possible pairs of the different alkali-metal atoms with different noble-gas atoms have been investigated. By measuring the sodium spin relaxation rate as a function of the helium buffer-gas pressure and the width of the sodium magnetic slowing-down curve, we report in this paper our experimentally determined value of the spin–rotation interaction constant in Na–Xe molecules γ = (1.1 ± 0.3)MHz. The measured value is nearly the same as was measured in K–Xe, Rb–Xe, and Cs–Xe.1 This result shows a reasonable agreement with the theoretical prediction.

International Laser Science Conference•Jan 1, 1986•0 citations
Cross sections for noble-gas-induced Rb spin disorientation are calculated, taking into account second-order cross terms in the spin-orbit and K\ifmmode\cdot\else\textperiodcentered\fi{}L couplings, as initially proposed by Bernheim. Contrary to Bernheim, it is argued that spin-orbit effects are negligible in first order. Using simple wave functions, it is shown that the spin-orbit coupling provided by the electric field of the Rb ionic core, when the valence electronic orbital is deformed in short-range encounters, is sufficient to yield the observed relaxation rates. For He, the calculated disorientation cross section shows agreement to within a factor of 6 with the experimentally determined cross section for depolarization of optically oriented Rb vapor. Moreover, if, for all Rb-rare-gas pairs, we assume the same proportionality between the short- and calculated long-range energies at the kinetic radius, agreement to within a factor of 6 for Ne, A, Kr and Xe is also obtained.
The cross sections for disorientation of 42P1/2 potassium atoms, induced in collisions with noble gas atoms, have been determined in zero magnetic field by studying the depolarization of K(7699 Å) resonance fluorescence in relation to noble gas pressures. Potassium vapor at low density, mixed with a noble gas in a fluorescence vessel, was irradiated with circularly polarized 7699 Å potassium resonance radiation and the resulting resonance fluorescence, observed in an approximately backward direction, was analyzed with respect to circular polarization. The variation of the degree of polarization with gas pressure was interpreted on the basis of a 'J randomization' model for the collisions and yielded the following disorientation cross sections which are appropriately corrected for the effect of nuclear spin: K–He, 24 ± 4 Å2; K–Ne, 21 ± 3 Å2; K–Ar, 37 ± 5 Å2; K–Kr, 51 ± 7 Å2; K–Xe, 69 ± 9 Å2. The cross sections are significantly smaller than values obtained previously in kilogauss fields.
The spin relaxation of optically pumped rubidium vapor induced by rubidium-rare-gas atomic collisions has been investigated in an ultraclean environment. The experiment was performed under conditions such that the partial pressure of nonrare-gas impurities was less than 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ Torr, and that the time between Rb-Rb spin exchange collisions was short compared to the spin relaxation time. The cross sections (in cm2{\mathrm{cm}}^{2}cm2) for disorientation of rubidium were found to be: He, 3.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}25}$; Ne, 3.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$; Ar, 1.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$; Kr, 7.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$; Xe, 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$. The fact that these cross sections are considerably smaller than previously reported values is attributed primarily to the low degree of impurity contamination in the present work. When compared with already existing values for cesium and sodium, the disorientation cross sections of these three alkali metals are seen to have a remarkably similar dependence on buffer-gas atomic number. The new experimental values are also compared with recent theoretical calculations.
Relaxation experiments have been performed between 0–200 G on optically polarized Rb atoms in argon, krypton or xenon, at pressures ranging from 0.1 to 20 torr. They clearly show the existence of Rb–Ar, Rb–Kr and Rb–Xe molecules of low binding energy (smaller than kT). Molecular parameters such as lifetime, spin-orbit coupling constant, formation rate, constant of mass action, etc., are measured, or evaluated when they cannot be directly measured. Experimental values of the diffusion coefficient of Rb in the gas (except xenon) and of the disorientation cross sections by usual binary collisions are also obtained.
The cross sections for disorientation of 32P1/2 sodium atoms, induced in collisions with noble gas atoms, have been determined by following the depolarization of Na–D1 resonance fluorescence in relation to noble gas pressure. Sodium vapor at low density, mixed with a noble gas in a fluorescence cell, was irradiated with circularly polarized D1 resonance radiation and the resulting D1 resonance fluorescence, observed in an approximately backward direction, was analyzed with respect to circular polarization. The variation of the degree of polarization with gas pressure was interpreted on the basis of a 'J randomization' model for the collisions, and yielded the following disorientation cross sections which are appropriately corrected for effects due to nuclear spin. Na–He: 28.1 ± 4.0 Å2; Na–Ne: 27.8 ± 4.0 Å2; Na–Ar: 57.0 ± 8.0 Å2; Na–Kr: 78.0 ± 10 Å2; Na–Xe: 87.0 ± 13 Å2.
Relaxation experiments performed on optically polarized Rb atoms in a rare gas have been previously reported; their detailed interpretation is given below. It is shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. Two processes of molecule formation are analyzed: binary resonant collisions leading to metastable states and three-body collisions producing actual bound states. A relaxation model valid for any disorientation probability per single Rb-Kr interaction is developed. Aside from clear evidence for the existence of alkali-rare-gas molecules, the success of the theoretical interpretation of the relaxation experiments yields the equilibrium constant $\mathcal{K}=1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ cm3{\mathrm{cm}}^{3}cm3/molecule for the reaction Rb+Kr \ensuremath{\rightleftharpoons} Rb-Kr at 300\ifmmode^\circ\else\textdegree\fi{}K, the average lifetime of a Rb-Kr molecule in the gas phase, $\ensuremath{\tau}=0.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ sec, at a krypton pressure of one Torr, and the average spin-orbit coupling constant in a Rb-Kr molecule, $\overline{\ensuremath{\gamma}}{h}^{\ensuremath{-}1}=0.63$ MHz. It is also shown that the spin-orbit potential is predominantly short-range.
A theory for calculating the spin–rotation coupling coefficient in alkali-metal–noble-gas van der Waals molecules was recently presented.1 It assumes the spin–rotation interaction in alkali-metal–noble-gas molecules to be mainly due to the spin–orbit interaction of the alkali-metal valence electron within the core of the noble gas, and predicts that the spin–rotation constant γ should depend on the spin–orbit interaction in the noble gas and be almost independent of the spin–orbit interaction of the alkali-metal atom. Experimentally, only a few of the possible pairs of the different alkali-metal atoms with different noble-gas atoms have been investigated. By measuring the sodium spin relaxation rate as a function of the helium buffer-gas pressure and the width of the sodium magnetic slowing-down curve, we report in this paper our experimentally determined value of the spin–rotation interaction constant in Na–Xe molecules γ = (1.1 ± 0.3)MHz. The measured value is nearly the same as was measured in K–Xe, Rb–Xe, and Cs–Xe.1 This result shows a reasonable agreement with the theoretical prediction.