Isotope effects in low-pressure Hg–rare-gas discharges

Measurements of the Hg (253.7 nm) output ($P_{\mathrm{uv}}$) and output per arc watt ($P_{\mathrm{uv}}$/$P_W$) as a function of ${}_{}{}^{196}{}_{}{}^{}\mathrm{Hg}$ concentration in a low-pressure Hg-Ar electrical discharge are reported. A peak increase of 7.9% and 6.8% for $P_{\mathrm{uv}}$ and $P_{\mathrm{u}\mathrm{v}/\mathrm{PW}}$, respectively, has been found at 2.6 wt. % ${}_{}{}^{196}{}_{}{}^{}\mathrm{Hg}$. A modified Holstein-Biberman formalism that takes into account emission and absorption line shapes, energy transfer between Hg isotopes, rare-gas hyperfine mixing, and overlap between different isotopic components has been developed. Based on this formalism the calculated hyperfine structure (hfs) of the Hg(6 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$→6 ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$) transition is in very good agreement with our measured hfs. Furthermore our calculations predict a saturation in $P_{\mathrm{uv}}$ and $P_{\mathrm{uv}/P_W}$ for relatively low ${}_{}{}^{196}{}_{}{}^{}\mathrm{Hg}$ concentrations. This formalism is applicable to various problems involving resonance radiation transfer in metal-vapor–rare-gas combinations containing more than one isotope.