Intense-Laser-Field Ionization of the Hydrogen Molecular Ions $\mathrm{H}_2{}^{+}$ and $\mathrm{D}_2{}^{+}$ at Critical Internuclear Distances

Fragmentation of $\mathrm{H}_2{}^{+}$ and $\mathrm{D}_2{}^{+}$ in ion beams has been studied with short intense laser pulses (100 fs, $I=5\times {10}^{13}–1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$) and by a high-resolution two-dimensional velocity imaging technique. In the Coulomb explosion channel, at intensities just above the threshold for this process, we observe a clear structure in the kinetic energy spectra not previously found or predicted. The peaks can be attributed to single vibrational levels. We interpret this observation as a dissociative allocation of the electron to a proton followed by enhanced ionization at a well-defined “critical” overstretched internuclear distance. When using longer pulses we observe three separate Coulomb explosion velocity groups corresponding to critical distances of about 8, 11, and 15 a.u.

Figure 1

Velocity distribution of $\mathrm{H}_2{}^{+}$ fragments as projected onto the two-dimensional detector at a peak laser intensity of $1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$. The two fragmentation channels are discerned by their kinetic energies and angular distributions. The laser polarization is in the detector plane along the horizontal axis of the image. The kinetic energies of the fragments ejected along this axis are marked by the inserted scale. The measured right-hand side is mirrored to simulate the real complete distribution.

Figure 2

Kinetic energy spectra of protons from the Coulomb explosion of $\mathrm{H}_2{}^{+}$. The spectra are obtained by radial integration of the velocity distributions over $\pm 2°$ around the laser polarization axis. The error bars shown for the uppermost spectra are calculated from the difference in spectra for integration over positive and negative angles. Peak laser intensities are given in the figure together with the scaling factors of the proton yield.

Figure 3

Coulomb explosion spectra of (a) $\mathrm{H}_2{}^{+}$ at an intensity of $8.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$; (b) $\mathrm{D}_2{}^{+}$ at an intensity of $6.4\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The vertical lines mark the fragment energies as expected after one-photon absorption from different vibrational levels, followed by a Coulomb explosion at a critical distance.

Figure 4

Projected velocity distribution of the fragments from the photodissociation and Coulomb explosion channel of $\mathrm{D}_2{}^{+}$ at an intensity of $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and pulse duration of 350 fs. Three Coulomb explosion groups are discerned corresponding to enhanced ionization at about 8, 11, and 15 a.u. The color scale is adjusted to the signal in the CE channel.