The hyperfine relaxation of a population difference, produced by optical pumping, between the $F=1\mathrm{}$ $m_F=0\mathrm{}$ and $F=2\mathrm{}$ $m_F=0\mathrm{}$ energy levels of the ground state of ${\mathrm{Rb}}^{87}$, has been studied in cells containing neon, argon, helium, or krypton as a buffer gas. The relaxation times $T_1$ and $T_2$ have been measured as a function of the rubidium vapor pressure in the cell. The relaxation rate due to spin exchange in ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ collisions has been found equal to 65 ${\sec }^{-1\mathrm{}}$ at 44°C, and the diffusion coefficients of ${\mathrm{Rb}}^{87}$ atoms in He, Ne, and Ar evaluated as 0.6, 0.31, and 0.22 ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$, respectively. The cross section for ${\mathrm{Rb}}^{87}$-Ne and ${\mathrm{Rb}}^{87}$-Ar collisions are found to be 1.6×${10}^{-22\mathrm{}}$ ${\mathrm{cm}}^2$ and 9×${10}^{-22\mathrm{}}$ ${\mathrm{cm}}^2$. These values are in general agreement with values previously obtained by other methods. The extrapolated values of $\frac{1}{T_2}$ for zero vapor pressure of rubidium are 185, 237, and 318 ${\sec }^{-1\mathrm{}}$ for Ne, He, or Ar, respectively. Relaxations by the pumping light or by the magnetic field inhomogeneities are also discussed.

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