Precise Hyperfine Pressure-Shift Measurements for Hydrogen Isotopes in Argon

Abstract

The pressure shift of the hyperfine splitting $\ensuremath{\nu}$ in the ground state of the hydrogen isotopes for an argon buffer gas has been measured with about 0.1% accuracy by an optical-pumping method with improvements in sample design, temperature control, and magnetic field stabilization. If the shift is expressed as $(\frac{1}{{\ensuremath{\nu}}_{0}})(\frac{\ensuremath{\delta}\ensuremath{\nu}}{\ensuremath{\delta}\ensuremath{\rho}})=A+B(T\ensuremath{-}{T}_{0})$, the results for hydrogen, deuterium, and tritium are, respectively, ${A}_{H}=(\ensuremath{-}4.800\ifmmode\pm\else\textpm\fi{}0.006)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{torr}}^{\ensuremath{-}1}$ (0\ifmmode^\circ\else\textdegree\fi{}C); ${B}_{H}=(+0.956\ifmmode\pm\else\textpm\fi{}0.011)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ \ifmmode^\circ\else\textdegree\fi{}${\mathrm{C}}^{\ensuremath{-}1}$ ${\mathrm{torr}}^{\ensuremath{-}1}$ (0\ifmmode^\circ\else\textdegree\fi{}C); ${A}_{D}=(\ensuremath{-}4.802\ifmmode\pm\else\textpm\fi{}0.022)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{torr}}^{\ensuremath{-}1}$ (0\ifmmode^\circ\else\textdegree\fi{}C); ${B}_{D}=(+1.091\ifmmode\pm\else\textpm\fi{}0.047)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ ${\mathrm{torr}}^{\ensuremath{-}1}$ (0\ifmmode^\circ\else\textdegree\fi{}C); ${A}_{T}=(\ensuremath{-}4.795\ifmmode\pm\else\textpm\fi{}0.012)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{torr}}^{\ensuremath{-}1}$ (0\ifmmode^\circ\else\textdegree\fi{}C); ${B}_{T}=(+0.929\ifmmode\pm\else\textpm\fi{}0.021)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ ${\mathrm{torr}}^{\ensuremath{-}1}$ (0\ifmmode^\circ\else\textdegree\fi{}C); where the arbitrary reference temperature ${T}_{0}=26\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ has been used in every case. The density $\ensuremath{\rho}$ is quoted in units of torr (0\ifmmode^\circ\else\textdegree\fi{}C), the equivalent of 3.536\ifmmode\times\else\texttimes\fi{}${10}^{16}$ atoms/${\mathrm{cm}}^{3}$. The absence of isotope dependence supports existing theories of the shift and encourages comparison with the measurements of muonium hyperfine splitting.