Reference measurements of hydrogen's dielectric permittivity

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Abstract
We used a quasi-spherical cavity resonator to measure the relative dielectric permittivity ε r of H2 at frequencies from 2.4 to 7.3 GHz, at pressures up to 6.5 MPa, and at the temperatures 273 K and 293 K. The resonator was calibrated using auxiliary measurements of ε r(p, T) for helium together with the accurate ab initio values of helium's dielectric permittivity. The measurements determine accurate values of hydrogen's molecular electric polarizability and its temperature dependence. At 273 K, we obtained = (8.9568 ± 0.0008) × 10−41 F m2 (all uncertainties reported here are one standard uncertainty), which agrees with the value (8.9566 ± 0.0026) × 10−41 F m2 that was obtained by combining Rychlewski's ab initio calculations with estimates of rotational level populations. Our results yield the temperature dependence = × (1.1 ± 0.3) × 10−5 K−1, which agrees with the calculated value × 1.0 × 10−5 K−1. Our data also determine hydrogen's second dielectric virial coefficient, = (0.03 ± 0.05) cm3 mol−1, a property that has not yet been calculated.