Spin-exchange frequency shift in alkali-metal-vapor cell frequency standards

In this paper we calculate the effect of spin-exchange collisions in alkali-metal vapors. In the framework of the high-energy approximation, we evaluate the spin-exchange cross sections related to the line broadening and to the frequency shift of the ground state hyperfine transition. We do the calculation for the four isotopes, ²³Na, ³⁹K, ⁸⁷Rb, and ¹³³Cs. The results are used in particular to evaluate the spin-exchange frequency shift in Rb vapor cell frequency standards used in many applications. It turns out that, due to possible fluctuations in the atomic density, spin exchange may affect significantly the medium and long term frequency stability of the frequency standard.