Competing decay-channel fluorescence, dissociation, and ionization in superexcited levels of ${\mathrm{H}}_2$

The absolute cross sections for the competing decay-channel fluorescence, dissociation, and ionization of photoexcited long-lived superexcited ${\mathrm{H}}_2$ molecular levels have been measured from the ionization threshold of ${\mathrm{H}}_2$ up to the H($1s$) $+$ H($n=3$) dissociation limit. The total and partial natural widths of these levels have been determined. Good agreement is found with first principles calculations carried out with the multichannel quantum defect theory for excited levels of ${}^1{\Pi }_u^{-}$ symmetry, which represent $70\%$ of the levels studied experimentally. The calculations reproduce the balance between the competing decay processes as well as its substantial evolution from level to level.

Figure 1

Selected potential energy curves for ${\mathrm{H}}_2$ illustrating various photon emission pathways relevant in the present experiments. Double arrows correspond to the range of the accessible fluorescence window; see the text for details.

Figure 2

A section of the excitation spectra of ${\mathrm{H}}_2$ above the ionization threshold. The spectra in (a)–(d) are on an absolute scale. (a) Photoabsorption, (b) photoionization, (c) photodissociation, (d) molecular fluorescence cross section obtained by subtraction, and (e) molecular fluorescence excitation spectrum recorded with a visible-sensitive detector.

Figure 3

Molecular (solid lines) and ion (dashed line) potential energy curves with vibronic levels [black horizonal solid lines and dark gray (blue online) horizontal dotted lines] and vibrational ionization thresholds [light gray (red online) horizontal dotted lines], illustrating the discretization of the dissociation continuum through application of a fixed boundary condition at $R=R_c$. $E$ [medium gray (green online) horizontal solid line] is the total energy under consideration. Rydberg levels with $n>3$ are not shown, for clarity.

Figure 4

Level energies as functions of the boundary condition $b$ applied to the vibrational wave functions at $R=R_c$. The anticrossing between a physical level ($D^1{\Pi }_u^{-},v=15,N=1$ level, flat portions of the curves) and a fictitious continuum level ($C^1{\Pi }_u^{-}$, steep portions of the curves) permits extraction of the predissociation width (see text for details).

Figure 5

Histogram illustrating the overall comparison between measured and calculated $Q$($N$) absorption line positions. Hatched (red online) bars show the present measurements. The curve is the Gaussian that fits the histogram. Black cross-hatched bars show spectrographic measurements [13, 14, 15] normalized to fit the maximum of the curve.

Figure 6

Measured (solid squares, in blue online) and calculated (open squares connected by lines) Einstein $A$ coefficients for the $3p\pi D$, $4p\pi D^{\prime }$, and $5p\pi D^{″}$ ${}^1\Pi {}_u^{-},N=1-3$ levels, plotted as functions of the vibrational quantum number $v$.

Figure 7

Histogram illustrating the overall comparison between measured and calculated absorption line intensities (Einstein $A$ coefficients). The three outliers probably correspond to blended lines. The curve is the Gaussian that fits the histogram.

Figure 8

Comparison between measured and calculated yield values for the $3p\pi D$, $4p\pi D^{\prime }$, and $5p\pi D^{″}$ ${}^1{\Pi }_u^{-}$ levels, plotted as functions of the excited-state vibrational quantum number $v$. Triangles (green online, dashed lines) refer to fluorescence, squares (blue online, solid lines) refer to dissociation, and circles (red online, dotted lines) refer to ionization, respectively. Open symbols connected by lines are calculated values, whereas solid symbols are measured values. Previously measured values [4, 37] are also indicated and, for better visibility, slightly offset to the right on the abscissa scale.

Figure 9

Measured and calculated partial widths for the $3p\pi D$ ${}^1{\Pi }_u^{-}$ levels plotted as functions of $v$. The symbols have the same meanings as in Fig. 8.

Figure 10

Measured and calculated partial widths for the $4p\pi D^{\prime }$ ${}^1{\Pi }_u^{-}$ levels plotted as functions of $v$. The symbols have the same meanings as in Fig. 8. Note the logarithmic ordinate scale.

Figure 11

Measured and calculated partial widths for the $5p\pi D^{″}$ ${}^1{\Pi }_u^{-}$ levels plotted as functions of $v$. The symbols have the same meanings as in Fig. 8. Note the logarithmic ordinate scale.

Figure 12

Photoionization cross section calculated for $Q$(1) transitions plotted on a logarithmic scale. The dissociation and fluorescence decay channels have not been taken into account in this calculation.

Figure 13

Upper traces (green online): experimental fluorescence excited spectrum plotted on a linear scale (arbitrary units). Lower traces: theoretical photoionization cross sections calculated for the $Q$(1), $Q$(2), and $Q$(3) transitions [in black, light gray (red), and dark gray (blue), respectively] plotted on a linear scale (in units of ${10}^{-13}$ cm${}^2$).