Laser-wavelength and intensity dependence of electron-nuclear energy sharing in dissociative ionization of ${\mathrm{H}}_2$

We experimentally and theoretically study the photoelectron-nuclear energy sharing mechanism of the correlated dynamics between the photoelectrons and the fragmented ions in the dissociative ionization of ${\mathrm{H}}_2$ with respect to the laser intensity at the wavelengths $\lambda =395\mathrm{nm}$ and $\lambda =790\mathrm{nm}$. We show that the prominent photoelectron-nuclear energy sharing along the back-diagonal lines is only observed for 395 nm at lower intensities, which is absent for increased intensities at 395 nm and for 790 nm lasers over a wide range of intensities. Based on a quantum mechanical model that includes the correlation between the photoelectron and the parent ion, we show that bond hardening has a significant effect on the photoelectron-nuclear energy sharing. The resonant states of the neutral hydrogen molecule during strong-field ionization and the distribution of vibrational states of molecular ions determine the joint energy spectrum of photoelectrons and nuclei. The study provides an intuitive and comprehensive description and understanding of the correlated photoelectron-nuclear dynamics in the dissociative ionization.

Figure 1

The potential energy curves of ${\mathrm{H}}_2$ and ${{\mathrm{H}}_2}^{+}$. Heavy solid black curves in (a) and (b) are the diabatic potential energy curves. The thin blue or red curves in (a) and (b) are adiabatic dressed potential energy curves of ${{\mathrm{H}}_2}^{+}$ at $\lambda =395\mathrm{nm}$ and at $\lambda =790\mathrm{nm}$, respectively.

Figure 2

(a), (b) the joint energy spectra measured at $\lambda =395\mathrm{nm}$ for different laser intensities. (c), (d) the photoelectron energy spectra corresponding to the dissociative and the single ionization channels. (a), (c) $I=1.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$; (b), (d) $I=1.96\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 3

(a),(b) the joint energy spectra measured at $\lambda =790\mathrm{nm}$ for different laser intensities. (c), (d) the photoelectron energy spectra corresponding to the dissociative and the single ionization channels. (a), (c) $I=0.93\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$; (b), (d) $I=2.20\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 4

(a) and (b) are the calculated joint energy spectra at λ = 395nm for different laser intensities. (c) and (d) are the energy of populated vibrational states with respect to the photoelectron energy. (e) and (f) are the calculated photoelectron energy spectra of the single ionization and the dissociative ionization channels. (a), (c) and (e) $I=1.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$; (b), (d) and (f) $I=2.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 5

(a) and (b) are the calculated joint energy spectra at $\lambda =790\mathrm{nm}$ for different laser intensities. (c) and (d) are the energy of populated vibrational states with respect to the photoelectron energy. (e) and (f) are the calculated photoelectron energy spectra of the single ionization and the dissociative ionization channels. (a), (c) and (e) $I=1.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$; (b), (d) and (f) $I=2.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 6

The laser-intensity-dependent photoelectron energy spectra of the single ionization (a) and the dissociative ionization (b) channels at the wavelength of 790 nm.