Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical-pumping process, both with and without buffer gas present. The observed transients are single exponentials with no buffer gas present, and double exponentials with buffer gas present, over a wide range of pumping intensities and relaxation times. These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin is included and a single relaxation time is assumed. From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section ${\ensuremath{\sigma}}_{\mathrm{eff}}$ is deduced for the disorientation of rubidium-87 within the
52P21 state as a result of its collision with a buffer-gas atom. It is shown that ${\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}_{\frac{1}{2}}+{\ensuremath{\sigma}}_{\frac{3}{2}}$, where ${\ensuremath{\sigma}}_{\frac{1}{2}}$ is the cross section for disorientation within the
52P21 level, and ${\ensuremath{\sigma}}_{\frac{3}{2}}$ is the cross section for transfer from the
52P21 level to the
52P23 level by means of collisions with the buffer gas. On the basis of recently measured values for ${\ensuremath{\sigma}}_{\frac{3}{2}}$, values are deduced for ${\ensuremath{\sigma}}_{\frac{1}{2}}$. The cross sections are: ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{H}\mathrm{e})=1.5(0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$
cm2, ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{N}\mathrm{e})=4.4(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$
cm2, and ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{A}\mathrm{r})=3.5(1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$
cm2. These cross sections are deduced from a model in which the probabilities for
Rb87 to relax from any hyperfine level to any other are all equal. This model gives a better fit with the observed transients than the assumption that the electron spin only is randomized in the
P21 state with the nuclear spin unaffected. We show that accurate relaxation-time measurements can be made by measuring the time constants associated with the double exponentials as a function of light intensity, and extrapolating them to zero light intensity. Moreover, since no shutter is required, relaxation times ${10}^{\ensuremath{-}3}$ sec can be easily observed.
Rate equations for the optical pumping of alkali-metal vapors simultaneously subject to pumping, relaxation in the excited state, and relaxation in the ground state are shown to yield analytic solutions for the alkali-metal electronic and nuclear-spin polarizations in the limit of weak pumping. Nuclear-spin and hyperfine-interaction effects are properly included. Analysis of the double-exponential form of the pumping transient of the ground-state electronic-spin polarization is shown to yield new methods for the measurement of cross sections for collisional relaxation in both the ground and excited states. Formulas are derived that relate relaxation cross sections to experimentally measurable parameters. Formulas describing the influence of nuclear spin on signals obtained from standard depolarization of resonance-radiation experiments also are provided. Ambiguities in earlier optical-pumping experiments and calculations arising from oversimplified descriptions of relaxation processes are discussed.
Short spin relaxation times for rubidium atoms, oriented by optical pumping, have been observed in the presence of benzene, ammonia, and dimethyl ether buffer gases. The disorientation cross sections of these gases in rubidium are obtained from relaxation times measured in mixtures with molecular nitrogen. The partial pressures of the gases were low compared to the nitrogen pressures in the mixtures, and the diffusion coefficient of rubidium in the mixtures was assumed to be the same as in pure nitrogen. The disorientation cross sections at 55°C are 7±1×10—19 cm2 for benzene, 8±2×10—18 cm2 for ammonia, and 3±1×10—18 cm2 for dimethyl ether. The cross section of carbon monoxide has also been obtained from the longer rubidium spin relaxation time in this gas. These measurements, complicated by a slow reaction of carbon monoxide with liquid rubidium, yield a cross section of 1±0.5×10—22 cm2 for carbon monoxide. The cross sections of ammonia, dimethyl ether, and benzene are much larger than cross sections of other molecular buffer gases. A discussion of the relaxation processes in these gases is given. The large cross sections of polar gases with appreciable dipole moments are found to result from an interaction of the rubidium atoms with the electric field of the polar molecules during a collision. Virtual excitation to the p states of the atom by the electric field gives rise to an interaction of the spin of the valence electron with the orbital angular momentum of the p states. The direct contribution of the magnetic field of the moving polar molecule is also considered and found to be small compared to the electric interaction. The large cross section of benzene is assumed to result from a spin exchange interaction with a charge transfer complex of rubidium and benzene formed in very small amounts. If the assumed complex is responsible for the large benzene cross section, the equilibrium constant for its formation can be calculated from an estimate of the spin exchange cross section.
The hyperfine relaxation of a population difference, produced by optical pumping, between the
F=1 mF=0 and
F=2 mF=0 energy levels of the ground state of
Rb87, has been studied in cells containing neon, argon, helium, or krypton as a buffer gas. The relaxation times
T1 and
T2 have been measured as a function of the rubidium vapor pressure in the cell. The relaxation rate due to spin exchange in
Rb87-
Rb87 collisions has been found equal to 65 ${\mathrm{sec}}^{\ensuremath{-}1}$ at 44\ifmmode^\circ\else\textdegree\fi{}C, and the diffusion coefficients of
Rb87 atoms in He, Ne, and Ar evaluated as 0.6, 0.31, and 0.22
cm2 ${\mathrm{sec}}^{\ensuremath{-}1}$, respectively. The cross section for
Rb87-Ne and
Rb87-Ar collisions are found to be 1.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$
cm2 and 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$
cm2. These values are in general agreement with values previously obtained by other methods. The extrapolated values of
T21 for zero vapor pressure of rubidium are 185, 237, and 318 ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne, He, or Ar, respectively. Relaxations by the pumping light or by the magnetic field inhomogeneities are also discussed.
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) 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.