${\text{HD}}^{+}$ in a beam in intense pulsed laser fields: Dissociation and ionization with high-energy resolution of the fragments

The isotopically mixed hydrogen molecular ion ${\text{HD}}^{+}$ was investigated in intense pulsed laser fields with high, i.e., vibrational resolution of the fragments. An ion beam of ${\text{HD}}^{+}$ with a translational energy of 11.1 keV was exposed to femtosecond laser pulses (100 fs) of intensities in the range from ${10}^{13}–{10}^{15}\text{W}/{\text{cm}}^2$. Fragments from the two dissociation channels ${\text{HD}}^{+}\to \text{H}+{\text{D}}^{+}$, and ${\text{HD}}^{+}\to \text{D}+{\text{H}}^{+}$, as well as the Coulomb explosion channel, ${\text{HD}}^{+}\to {\text{H}}^{+}+{\text{D}}^{+}+e^{-}$, were projected onto a two-dimensional multichannel plate detector to measure their velocity distributions. The fragments from the three channels were spatially clearly distinguished because of the different velocities of H $\left({\text{H}}^{+}\right)$ and D $\left({\text{D}}^{+}\right)$ fragments. Fragments from most of the populated vibrational states of ${\text{HD}}^{+}$ can be discerned as well-resolved peaks in the speed and angular distributions. The typical light induced potential (LIP) effects such as bond softening and level shifting already observed in the studies of ${\text{H}}_2^{+}$ and ${\text{D}}_2^{+}$ are here also observed. In addition to these one-photon peaks, also peaks due to three- (net two-) and finally also to direct two-photon absorption, typical of the asymmetric ${\text{HD}}^{+}$, were found in the vibrationally resolved fragment spectra of the dissociation channels. Besides the fragments from one-photon bond softening, also fragments formed by two- and three-photon processes were found to have narrow angular distributions, in contrast to the approximately ${\text{cos}}^2$ distribution of fragments from vibrational levels above the LIP crossing being fragmented by classical dissociation. The relative probability of the two dissociation channels was investigated, addressing the question of the higher electron affinity to the proton or the deuteron during the dissociation, but could not be decided because of too low accuracy here. The Coulomb explosion channel was also clearly discerned by its fragment velocities as well as the narrow angular distributions of ${\text{H}}^{+}$ and ${\text{D}}^{+}$ fragments, which is quite analogous to those found in the cases of ${\text{H}}_2^{+}$ and ${\text{D}}_2^{+}$.

Figure 1

(Color) The unperturbed potential curves $1s\sigma$ and $2p\sigma$ of ${\text{HD}}^{+}$. The dashed lines indicate the $2p\sigma$ curve shifted by one-, two-, and three-photon energies, leading to three crossings with the $1s\sigma$ curve in the vicinity of the vibrational levels $v=4$, $v=6$, and $v=10$. In the strong-field regime, gaps open up at these crossings (so-called anticrossings) and molecules from the vibrational levels below the crossings start to dissociate by so-called bond softening.

Figure 2

(Color) The measured two-dimensional velocity distribution of (a) neutral fragments and (b) neutral together with charged fragments. The laser polarization is horizontal in the plane of the image. The laser intensity was $1\times {10}^{15}\text{W}/{\text{cm}}^2$ and the pulse length was 100 fs in both measurements. The scale in (a) indicated the fragment velocity in km/s along the horizontal axis. Only one-half of the distribution is measured, which was then mirrored along the axis perpendicular to the polarization axis. In (b) the Coulomb explosion fragments, ${\text{D}}^{+}$ (at velocities of 8–16 km/s) and ${\text{H}}^{+}$ (above 20 km/s) are clearly seen. In (b) the color scale was adjusted to show the ${\text{H}}^{+}$ Coulomb explosion channel.

Figure 3

(Color) Measured two-dimensional velocity distributions of the neutral photofragments. The peak laser intensities were $3\times {10}^{13}\text{W}/{\text{cm}}^2$ (a), $2\times {10}^{14}\text{W}/{\text{cm}}^2$ (b), $5\times {10}^{14}\text{W}/{\text{cm}}^2$ (c), and $1\times {10}^{15}\text{W}/{\text{cm}}^2$ (d). The maximum velocity along the horizontal axis is 12 km/s.

Figure 4

(Color) Speed distributions of the neutral photofragments for the measurements in Fig. 3. The distributions were obtained by integrating the Abel-inverted velocity distributions over $\pm 4°$ around the polarization axis at each speed. The vertical lines represent the classically expected velocities for the H and D fragments after one- and net two-photon absorption as calculated from Eq. (4).

Figure 5

(Color) Measured two-dimensional velocity distributions of the neutral and charged fragments together in three- (left-hand column) and two- (right-hand column) dimensional representation for laser intensities from $3\times {10}^{13}\text{W}/{\text{cm}}^2$ to $2\times {10}^{14}\text{W}/{\text{cm}}^2$. Each measurement contains fragments from about $4.5\times {10}^6$ laser pulses. The three-dimensional distributions on the left-hand side show most impressively the relative development of the four peaks being due to one-photon bond softening $\left(A\right)$, “classical” one-photon $\left(B\right)$, three- (net two-) photon $\left(C\right)$, and direct two-photon absorption $\left(D\right)$, and also Coulomb explosion $\left(E\right)$.

Figure 6

(Color) Speed distributions of the neutral and charged fragments together for the measurements in Fig. 5. The distributions were obtained by integrating the Abel-inverted velocity distributions over $\pm 4°$ around the polarization axis at each speed. The vertical lines represent the classically expected velocities for the H and D fragments after one- and net two-photon absorption as calculated from Eq. (4) using field-free energies of vibrational states. The ${\text{H}}^{+}$ fragments from the Coulomb explosion channel are around 25 km/s and are not displayed here.

Figure 7

(Color) Angular distributions of the fragments from different vibrational levels as extracted from the Abel-inverted velocity distributions. The peak laser intensity is $3\times {10}^{13}\text{W}/{\text{cm}}^2$ in (a) and (b), and $9\times {10}^{13}\text{W}/{\text{cm}}^2$ in (c). The large scattering of the signal in the midst of the experimental curve is an artifact of the inversion algorithm, resulting from data containing asymmetric contributions.

Figure 8

(Color) Speed distributions for the neutral fragments only and neutral and charged fragments together used for calculation of the branching ratio between the two dissociation channels [Eq. (11)]. The distributions were obtained by integrating the measured velocity distributions over $\pm 45°$ around the polarization axis and normalizing them by the integrated ion currents (total charges).