Measurement of Spin-Exchange Cross Sections for ${\mathrm{Cs}}^{133}$, ${\mathrm{Rb}}^{87}$, ${\mathrm{Rb}}^{85}$, ${\mathrm{K}}^{39}$, and ${\mathrm{Na}}^{23}$

This paper reports measurements to determine the spin-exchange cross section for collisions between like alkali atoms. The spin-exchange cross section is determined for ${\mathrm{Cs}}^{133}$, ${\mathrm{Rb}}^{87}$, ${\mathrm{Rb}}^{85}$, ${\mathrm{K}}^{39}$, and ${\mathrm{Na}}^{23}$. The lifetime of the alkali atoms in the Zeeman sublevels of the ground-state hyperfine levels is dominated by spin-exchange collisions. The spin-exchange collision rate is therefore reflected by the linewidth of the microwave absorption spectrum observed in the magnetic dipole transitions between various of the Zeeman sublevels. The measurements employed an $X$-band electron paramagnetic resonance spectrometer. The alkali metal was distilled into a sample bulb which was placed inside a Dewar in a resonant cavity. The bulb was then heated to a temperature corresponding to an equilibrium vapor density of approximately ${10}^{15}$ alkali atoms/c.c. and the microwave absorption spectrum was recorded. In order to relate the spin-exchange rate to a cross section, it is necessary to determine the alkali density. This was done by comparing the intensity of the alkali EPR absorption to that of a weighed and oriented copper sulfate crystal. For ${\mathrm{Cs}}^{133}$ and ${\mathrm{Rb}}^{87}$, interpretation of the linewidth data is complicated by the fact that the transitions occur in a region where there is appreciable mixing of the high-field spin states by the hyperfine interaction. A density-matrix description of spin exchange which corrects for this intermediate field mixing is discussed, and the corrections are applied to the measured cross sections for two transitions in ${\mathrm{Cs}}^{133}$ and ${\mathrm{Rb}}^{87}$. Relative cross sections, referred to that of ${\mathrm{Na}}^{23}$, are also given.