Precise Determination of the Cooper-Pair Mass

The ratio $\frac{h}{m^{\prime }}$ of Panck's constant to the observable Cooper-pair mass ($\sim 2m_e$) is determined directly using a rotating superconducting ring by measuring the London moment flux $\left(\frac{2m^{\prime }c}{e^{*}}\right)\omega S$, where $S$ is the area bounded by the ring, in units of the flux quantum ($\frac{\mathrm{hc}}{e^{*}}$). The flux in the ring is zero for a set of rotation frequencies which are equally spaced by $\Delta \nu$, and $\frac{h}{m^{\prime }}=2S\Delta \nu$. We have measured $\Delta \nu$ and $S$ with a precision of 5 ppm and an accuracy of 21 ppm. Our result for niobium, ${\left(\frac{m^{\prime }}{2m_e}\right)}_{\mathrm{Nb}}=1.000\mathrm{}084\left(21\right)\mathrm{}$, disagrees with theoretical predictions of 0.999 992.