Higher-Precision Determination of the Fine-Structure Interval in the Ground State of Positronium, and the Fine-Structure Density Shift in Nitrogen

The fine-structure interval $\Delta \nu$ in the ground state of positronium has been remeasured with higher precision to obtain $\Delta {\nu }_{\mathrm{expt}}=203.396\mathrm{}\pm 0.005$ GHz (24 ppm). The current theoretical value is $\Delta {\nu }_{\mathrm{theor}}=203.4155\mathrm{}$ GHz. The difference $\Delta {\nu }_{\mathrm{expt}}-\Delta {\nu }_{\mathrm{theor}}=-19\mathrm{}\pm 5$ MHz is about 4 standard deviations of the experimental error, indicating the need for calculations of higher-order radiative contributions. Values are given for both the linear and quadratic coefficients of the fine-structure density shift in ${\mathrm{N}}_2$.