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Cold Collision Frequency Shift of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi mathvariant="italic">S</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi mathvariant="italic">S</mml:mi></mml:math>Transition in Hydrogen
We have observed the cold collision frequency shift of the $1S$- $2S$ transition in trapped spin-polarized atomic hydrogen. We find $\ensuremath{\Delta}{\ensuremath{\nu}}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}3.8\ifmmode\pm\else\textpm\fi{}0.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}n\mathrm{Hz}{\mathrm{cm}}^{3}$, where $n$ is the sample density. From this we derive the $1S$- $2S$ $s$-wave triplet scattering length, ${a}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1.4\ifmmode\pm\else\textpm\fi{}0.3\mathrm{nm}$, which is in fair agreement with a recent calculation. The shift …