Precision determination of the fine-structure interval in the ground state of positronium. IV. Measurement of positronium fine-structure density shifts in noble gases

The fine-structure interval $\Delta \nu$ of ground state ($n=1\mathrm{}$) positronium has been measured to high precision, yielding $\Delta \nu =203.3849\mathrm{}\left(12\right)\mathrm{}$ GHz (6 ppm). Comparison with theory is at present limited by uncalculated terms of order ${\alpha }^2\Delta \nu$. Values for the linear coefficient of the fine-structure density shift, $a\equiv \left(\frac{1}{\Delta \nu }\right)\frac{\partial \Delta \nu }{\partial D}$, have been measured for positronium in nitrogen and the noble gases: $a\left({\mathrm{N}}_2\right)=(-3.2\mathrm{}\pm 0.5)\times {10}^{-5\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$ (0°C), $a\left(\mathrm{He}\right)=(+1.6\mathrm{}\pm 0.3)\times {10}^{-5\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$ (0°C), $a\left(\mathrm{Ne}\right)=(-1.9\mathrm{}\pm 0.4)\times {10}^{-5\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$ (0°C), $a\left(\mathrm{Ar}\right)=(-6.2\mathrm{}\pm 0.3)\times {10}^{-5\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$ (0°C), $\left|a\right(\mathrm{Kr})=(-6.6\mathrm{}\pm 0.5)\times {10}^{-5\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$(0°C), and $a\left(\mathrm{Xe}\right)=(-7.3\mathrm{}\pm 1.7)\times {10}^{-5\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$ (0°C). The positronium density shifts differ markedly from those of hydrogen.