Spin-exchange Cross Section Research Articles

Scattering amplitudes for atomic collisions, with application to spin-exchange between hydrogen atoms

Calculations of the scattering amplitudes for collisions between one-electron atoms are presented. The main emphasis is on the scattering of two hydrogen atoms, including the spin-exchange process. The interaction between the atoms is represented by a potential V S ( r), where r is the separation and S is the total electronic spin of the atoms. The corresponding scattering amplitudes f S are obtained from exact (numerical) solutions of the radial Schrödinger equation. Detailed comparisons are made with various approximations, such as the JWKB method, the high-energy approximation to it, and the model of Purcell and Field and Wittke and Dicke. The JWKB approximation works surprisingly well, but begins to break down at thermal energies. The other approximations are not nearly as accurate. The Purcell and Field model, for example, predicts total spin-exchange cross sections too small by about 35%, and a total unpolarized scattering which has the wrong energy dependence and is typically incorrect by a factor of two. The defects in this model are analyzed in some detail and a number of changes proposed which make it more useful. Along these lines a phenomenological model for the unpolarized scattering is formulated which should be useful in analyzing the scattering between any pair of atoms. A detailed discussion, based on the exact calculations, is also given of various differential cross sections and of the energy dependence of the total cross sections. This includes the effects of the identity of the atoms and the occurrence of resonances.

Spin Relaxation of Optically Pumped Rubidium Atoms in Molecular Buffer Gases

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.

Spin-Exchange Cross Section forRb85-Rb87Collisions

The spin-exchange cross section for ${\mathrm{Rb}}^{85}$-${\mathrm{Rb}}^{87}$ collisions has been measured to be (1.70\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ using the techniques of optical pumping and an interferometric method for measuring the Rb vapor density. The ${\mathrm{Rb}}^{87}$ constituent in a vapor of natural Rb was polarized through absorption of circularly polarized resonance radiation, and the ${\mathrm{Rb}}^{87}$ polarization was partially transferred to the ${\mathrm{Rb}}^{85}$ constituent through spin-exchange collisions. A phenomenological theory of the optical pumping plus the exchange polarization process which neglects nuclear spin was used to relate the cross section to the ratio of the signal strengths for the ${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{85}$ Zeeman resonances, the relaxation time, and the ${\mathrm{Rb}}^{87}$ vapor density. The density was measured by comparing spectral profiles of the resonance radiation transmitted through the optical pumping cell at room temperature with the resonance radiation transmitted at the temperature at which the signal strengths were measured. These spectral profiles were obtained through use of a scanning Fabry-Perot interferometer.

Study of the Spin-Relaxation Times and the Effects of Spin-Exchange Collisions in an Optically Oriented Sodium Vapor

The spin-relaxation time of an optically oriented sodium vapor diffusing in a helium or neon buffer gas has been measured and analyzed by the method of Franzen. The diffusion coefficients for sodium in helium and neon are 1.0\ifmmode\pm\else\textpm\fi{}0.3 and 0.50\ifmmode\pm\else\textpm\fi{}0.17 ${\mathrm{cm}}^{2}$/sec, respectively. The disorientation cross sections for sodium colliding with helium and neon are (3\ifmmode\pm\else\textpm\fi{}4)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}26}$ and (1.8\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$, respectively. The radio-frequency (rf) Zeeman transitions of the sodium atoms in the ground state have been examined. An analysis of the effects of spin-exchange collisions between sodium atoms on the intensities and line shapes of the various Zeeman transitions is presented. From these studies a spin exchange cross section of (1-3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ is estimated for two sodium atoms colliding. The main source of error in this measurement is probably lack of knowledge of the sodium vapor pressure in the sodium-absorption cells.

Effect of Spin-Exchange Collisions on the Optical Orientation of Atomic Sodium

The effect of spin-exchange collisions on the state populations obtained in an optically pumped ${\mathrm{Na}}^{23}$ vapor is studied in the limit of low light intensity. These state populations and hence the intensity of the rf Zeeman transitions are found theoretically to depend strongly on the spin-exchange cross sections. The various Zeeman rf transitions are found experimentally to be very different in intensity and this is interpreted as being partially due to spin-exchange collisions. From the intensity of the rf transitions in a magnetic field large enough to separate the six Zeeman components and from the observed relaxation time a spin-exchange cross section for two sodium atoms of $\ensuremath{\pi}{{S}_{0}}^{2}=6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ is found.