Observation of the Interference Effect in Vibrationally Resolved Electron Momentum Spectroscopy of ${\mathrm{H}}_2$

We report the first measurement on vibrationally resolved electron momentum spectroscopy of ${\mathrm{H}}_2$ by using a high-resolution ($e$, $2e$) spectrometer. The vibrational-specific experimental momentum profiles have been obtained and shown to be in agreement with calculations of ($e$, $2e$) ionization cross sections taking into account the vibrational wave functions. Distinct deviations from Franck-Condon predictions have been observed in vibrational ratios of cross sections, which can readily be ascribed to the Young-type two-center interference. Unlike previous ($e$, $2e$) work, the present observation of an interference effect does not rely on the comparison with the one-center atomic cross section.

Figure 1

(a) Vibronic transitions from the $X{}^1{\mathrm{\Sigma }}_g^{+}$ ground state of ${\mathrm{H}}_2$ to the ${}^2{\mathrm{\Sigma }}_g^{+}(1s{\sigma }_g)$ ground state of ${\mathrm{H}}_2^{+}$. The wave functions of some of the vibrational states are also shown. (b) The high-resolution photoelectron spectrum of ${\mathrm{H}}_2$ [23]. (c) The BES of ${\mathrm{H}}_2$ obtained in the present experiment. The dashed lines indicate the Gaussian peaks, and the solid line is the summed fit.

Figure 2

(a) The TMPs for different ${\mathrm{H}}_2^{+}$ vibrational states (shown by different colors). The inset shows the summed XMP for all vibrational states compared with the TMP calculated at equilibrium nuclear distance. The XMPs and corresponding TMPs for ${\mu }^{\prime }=0–8$ are shown in (b)–(j), respectively. The XMP and TMP presented in (k) are the sum of XMPs and TMPs for ${\mu }^{\prime }>8$. All profiles are area-normalized to unity.

Figure 3

The experimental and theoretical ratios of the EMS cross sections for different groups of vibrational states over the calculated cross section for ${\mu }^{\prime }=15$: (a) the low quantum number group $X=L$; (b) the intermediate quantum number group $X=I$; (c) the high quantum number group $X=H$. Solid circles and curves represent experimental and theoretical results. Dashed lines are Franck-Condon predictions. Chained lines are fitted curves of the model.