${\mathrm{HD}}^{+}$ photodissociation in the scaled coordinate approach

The scaled coordinate approach is applied to the problem of $\mathrm{H}{\mathrm{D}}^{+}$ photodissociation in a short, intense, infrared laser pulse. Two- and three-dimensional models for the molecule aligned in the field of a linearly polarized laser are studied. Scaling allows substantial improvements in the numerical accuracy and provides a simple way to calculate the fragments’ energy spectra.

Figure 1

(Color online) Momentum distributions calculated from a Fourier transform (dashed lines) and from the scaled coordinate density function (solid lines). The left panel shows free particle evolution; and the right, photodetachment of a particle bound with a short-range potential. The scaling parameter is $v_x=1.414$ for the free particle case and $9.759\times {10}^{-3}$ for the photodetachment model, making convergence of scaled spatial distribution to the momentum distribution much faster for the free particle.

Figure 2

(Color online) Convergence of the ionization probability for a model system with respect to the number of grid points $N$. The solid line shows the scaled results and the dashed line the unscaled results.

Figure 3

Domains in configuration space corresponding to different final states. The asymmetry of the domains is due to the nuclear mass difference: $\mathrm{H}$ fragments move faster than $\mathrm{D}$ fragments with respect to the center of mass.

Figure 4

(Color online) Convergence of the dissociation probability in the 2D model. $P_H$ is the probability to dissociate to $\mathrm{H}+d$; and $P_{\mathrm{D}}$, to $p+\mathrm{D}$.

Figure 5

(Color online) Kinetic energy distribution of the dissociated fragments in the center of mass frame for a 2D model of ${\mathrm{H}}_2^{+}$. The eighth excited state was exposed to a laser pulse of 10 fs FWHM, $I={10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$, and $\omega =0.1\mathrm{a}.\mathrm{u}$. The vertical dotted line shows the position of the peak expected from energy conservation.

Figure 6

(Color online) Intensity dependence of the $\mathrm{H}{\mathrm{D}}^{+}$ (2D model) dissociation probability in the field of 10-fs FWHM, 785-nm laser pulse.

Figure 7

(Color online) Carrier-envelope phase dependence of the $\mathrm{H}{\mathrm{D}}^{+}$ (2D model) dissociation probability in the field of 10-fs FWHM, 785-nm laser pulse with peak intensity $I=7\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. The error bars are estimated from convergence tests like those shown in Fig. 4.

Figure 8

(Color online) Carrier-envelope phase dependence of the $\mathrm{H}{\mathrm{D}}^{+}$ dissociation probability in the field of 10-fs FWHM, 785-nm laser pulse with peak intensity $I=7\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, 3D model. The open symbols denote our previous [18] unscaled results (circles for $P_H$ and diamonds for $P_D$). The filled symbols denote the present scaled results (circles for $P_H$ and diamonds for $P_D$).

Figure 9

(Color online) Velocity distributions of the fragments in the center-of-mass frame after dissociation of the $\mathrm{H}{\mathrm{D}}^{+}$ ground state in 10-fs, 785-nm laser pulse with peak intensity $I=7\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$: (a) $\mathrm{H}+d$ channel and (b) $p+\mathrm{D}$ channel.

Figure 10

(Color online) Dissociation of the $\mathrm{H}{\mathrm{D}}^{+}$ ground state in 10-fs, 785-nm laser pulse with peak intensity $I=7\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$: CEPD dependence of the probability density at the fragment relative velocity 0.01 a.u.