Clusters under strong vuv pulses: A quantum-classical hybrid description incorporating plasma effects

The quantum-classical hybrid description of rare-gas clusters interacting with intense light pulses which we have developed is described in detail. Much emphasis is put on the treatment of screening electrons in the cluster which set the time scale for the evolution of the system and form the link between electrons strongly bound to ions and quasifree plasma electrons in the cluster. As an example, we discuss the dynamics of an ${\text{Ar}}_{147}$ cluster exposed to a short vuv laser pulse of 20 eV photon energy.

Figure 1

Atomic photoionization cross sections extrapolated below the threshold according to [19] (dashed lines) and by interpolation of the discrete spectrum (solid lines). The dash-dotted lines are an approximation with hydrogenic wave functions; see text. The initial configuration is displayed in each panel.

Figure 2

Time intervals $T_i$ of the averaged localized motion of the screening electrons as a function of real time for an ${\text{Ar}}_{147}$ cluster with laser parameter as specified in Sec. 4.

Figure 3

(Color online) Sketch for the construction of the equivalent electronic configuration (right panel) from the actual configuration (left panel) of a cluster ion with three localized electrons (red) around a $3s^{1}3p^1$ (upper row) and $3s^2{p}^1$ (lower row) configuration. Holes are shown as open circles.

Figure 4

Total energies (circles) for ions with one of the electrons in a Rydberg state with quantum number $n$ and angular momentum $\ell =1$. The valence shell configuration $C_q$ is specified for each set of energies. Fitted curves (thick lines) according to Eq. (13). As an example, the energy $E^{\ast }$ for an equivalent configuration (dotted line) as defined in Sec. 3A and the corresponding energy $\Delta E^{\ast }$ for ionization (dashed line) are shown.

Figure 5

Sketch of the energy balance for the photoionization of a cluster ion $\alpha$. The cluster environment is symbolized by a single neighboring ion. The thick solid line indicates the full cluster potential, and the thin long dashed line represents the cluster environment $V\left(\mathbf{r}\right)$—i.e., the cluster potential without the contribution from the ion itself. The dotted line is the Coulomb potential for $q_{\alpha }+1$—i.e., the field of the ion if the electron were ionized. The interaction of the bound electron with the nucleus is represented by $\Delta E_{\text{ip}}^{\ast }$. The saddle point of $V\left(\mathbf{r}\right)-\left(q_{\alpha }+1\right)v\left(\alpha ,\mathbf{r}\right)$ defines the position ${\mathbf{r}}_{\text{bar}}$ of the barrier.

Figure 6

Number of localized quasifree electrons $n_{\text{loc}}$ and the corresponding energy $E^{\ast }$ according to Eq. (10) for the central ion and a surface ion of an ${\text{Ar}}_{147}$ cluster from the microscopic calculation in Sec. 4.

Figure 7

Close-up of Fig. 6 for $143<t<151\text{fs}$. The upper panel shows the number of localized electrons (엯 for the central atom, where $q=6$, and $\times$ for the surface atom, $q=4$). The lower panel shows the total energy $E^{\ast }$ of the ions and their localized electrons. The solid lines show here the average of $E^{\ast }$ over the time intervals $T_i$, as introduced in Sec. 2C. The gray line shows the electric field of the laser; it corresponds to the gray-shaded area of Fig. 6.

Figure 8

Explosion of ${\text{Ar}}_{147}$ exposed to a 100-fs-long vuv laser pulse with intensity $I=7\times {10}^{13}\text{W}∕{\text{cm}}^2$ and photon energy $\hslash \omega =20\text{eV}$: (a) solid line, total absorbed energy per atom; dashed line, energy absorbed due to photoionization; (b) solid line, total number of ionized electrons per atom; $◇$, quasifree electrons; ◯, localized electrons; (c) temperature of the quasifree electrons; (d) expansion, average interionic distance [see Eq. (22)].

Figure 9

Ion charge distribution (top panel) and kinetic energy distribution of the released electrons (bottom) after the cluster explosion for the same pulse as in Fig. 8. The propagation time was $t=6.4\text{ps}$. The electron signal can be exponentially fitted by $\text{exp}\left(-E_{\text{kin}}∕E_0\right)$ with $E_0=5.4\text{eV}$ (dashed line).