Cold Collision Frequency Shift of the 1S-2S Transition in Hydrogen

We have observed the cold collision frequency shift of the 1S-2S transition in trapped spin-polarized atomic hydrogen. We find $\Delta \nu_{1S-2S} = -3.8(8)\times 10^{-10} n Hz cm^3$, where $n$ is the sample density. From this we derive the 1S-2S s-wave triplet scattering length, $a_{1S-2S}=-1.4(3)$ nm, which is in fair agreement with a recent calculation. The shift provides a valuable probe of the distribution of densities in a trapped sample.