The Theory of the Excitation of Atomic Mercury by Electron Impact

The probability of excitation by electron impact of the four $P$ levels ($2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, $2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, $2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, $2{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$) of Hg has been calculated. It is found that, although with increasing velocities the excitation of two of the triplet levels vanishes compared with that of the singlet, that of the middle triplet level approaches a small constant value ($\frac{1}{25}$), which can be calculated from the singlet-triplet separation. It is also possible to calculate the number of dispersion electrons $f$ for these transitions by the use of approximate wave functions. Although the absolute magnitude of $f$ is too large by a factor 2, the relative magnitudes are fixed by the singlet-triplet separation and are in good agreement with experiment. An estimate is made of the relative probability of excitation of all four $P$ levels for fairly slow electrons, and these are roughly all of the same order of magnitude, the ratios at 10 volts being 7.0:3.5:1.9:0.4. The variation of the cross sections with voltage are shown in the figure. A brief comparison with experiment is given.