Precise Hyperfine Pressure-Shift Measurements for Hydrogen Isotopes in Argon

Abstract

The pressure shift of the hyperfine splitting $\nu$ 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 $\left(\frac{1}{{\nu }_0}\right)\left(\frac{\delta \nu }{\delta \rho }\right)=A+B(T-T_0)$, the results for hydrogen, deuterium, and tritium are, respectively, $A_H=(-4.800\mathrm{}\pm 0.006)\times {10}^{-9\mathrm{}}$ ${\mathrm{torr}}^{-1\mathrm{}}$ (0°C); $B_H=(+0.956\mathrm{}\pm 0.011)\times {10}^{-11\mathrm{}}$ °${\mathrm{C}}^{-1\mathrm{}}$ ${\mathrm{torr}}^{-1\mathrm{}}$ (0°C); $A_D=(-4.802\mathrm{}\pm 0.022)\times {10}^{-9\mathrm{}}$ ${\mathrm{torr}}^{-1\mathrm{}}$ (0°C); $B_D=(+1.091\mathrm{}\pm 0.047)\times {10}^{-11\mathrm{}}$ ${\mathrm{torr}}^{-1\mathrm{}}$ (0°C); $A_T=(-4.795\mathrm{}\pm 0.012)\times {10}^{-9\mathrm{}}$ ${\mathrm{torr}}^{-1\mathrm{}}$ (0°C); $B_T=(+0.929\mathrm{}\pm 0.021)\times {10}^{-11\mathrm{}}$ ${\mathrm{torr}}^{-1\mathrm{}}$ (0°C); where the arbitrary reference temperature $T_0=26\mathrm{}°\mathrm{C}$ has been used in every case. The density $\rho$ is quoted in units of torr (0°C), the equivalent of 3.536×${10}^{16}$ 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.