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A four-body coincident measurement of carbonyl sulfide dimers is conducted using a femtosecond laser-induced Coulomb explosion. Sequential and concerted processes that occur during the Coulomb explosion are distinguished. Four isomers of carbonyl sulfide dimer are resolved, and their structures are retrieved from the measured coincident momenta of the fragment ions generated in the concerted process, with the help of a classical trajectory simulation. As a result of our study, we can resolve the isomers of a weakly bound molecular cluster and determine their stereo configuration by using the Coulomb explosion. There is also the potential in femtosecond time-resolved imaging for structural evolution of molecular complexes in dissociation.

We study the fragmentation of very large dimers into two singly charged ions caused by absorption of a photon. In this process a photo electron emitted from one atom of the dimer has certain chances to hit the other atom knocking out one of its electrons. This results in the production of two singly charged ions and the consequent Coulomb explosion of the residual doubly charged system. We develop a theory of this process and apply it to calculate the fragmentation of $^4$He$_2$, $^7$Li - $^4$He and $^6$Li - $^4$He dimers. Our results for the helium dimer are in good agreement with available experimental data. For the Li-He dimers (where experimental data are still absent) our results predict that this fragmentation mechanism becomes much more efficient than in the case of He$_2$. We also show that, provided the recoil effects are of minor importance, the so called reflection approximation is very accurate also for large dimers., 13 pages, 6 figures

We present experimental results that show the secondary-ion yield depends on the structure and orientation of incident cluster ions. A beam of carbon-cluster ions ${{\mathrm{C}}_{n}}^{+}$ ($n\ensuremath{\le}4$) with an energy of 0.9 MeV per atom, which were obtained from a tandem electrostatic accelerator, was incident on a glycine target deposited on a carbon foil. The structure and orientation of the cluster ions after passing through the target were determined by the Coulomb explosion imaging method, and the positive secondary ions were simultaneously measured by time-of-flight mass spectrometry. When looking at the orientation dependence of linear structured ${{\mathrm{C}}_{2}}^{+}, {{\mathrm{C}}_{3}}^{+}$, and ${{\mathrm{C}}_{4}}^{+}$ projectiles, parallel orientations with respect to the beam direction were found to enhance the secondary-ion yield compared with perpendicular orientations. Additionally, comparison of the structure dependence of ${{\mathrm{C}}_{3}}^{+}$ and ${{\mathrm{C}}_{4}}^{+}$ projectiles with linear and ring structures showed that the secondary-ion yield was larger for linear structures. Interestingly, there was a clear correlation between the secondary-ion yield and the deposited energy density in the cluster-ion track. The energy density was calculated with electronic stopping power for incident cluster ions using linear-response dielectric theory and the cross section of the track of the incident cluster considering its geometrical structure and orientation. These results suggest that the deposited energy density in the cluster-ion track is a key parameter in the secondary-ion emission process induced by swift cluster-ion impacts.

We studied the ultrafast nuclear dynamics during the dissociation of ${\mathrm{OCS}}^{+}$ molecules using a strong IR-laser pump and probe technique in combination with the coincidence measurement. The nuclear movement is tracked by analyzing the time-dependent kinetic energy release (KER) spectra. The involved dissociation states and pathways are assigned with the help of the semiclassical Landau-Zener surface hopping calculations. The real-time bond-breaking dynamics of the ${3}^{2}\phantom{\rule{0.16em}{0ex}}A{}^{\ensuremath{'}}$ coupling to other states are observed for the two-body dissociation channel and the three-body dissociation channel but with high KER. The three-body dissociation channel with low KER is assigned to the direct breaking process from the ${3}^{2}\phantom{\rule{0.16em}{0ex}}A{}^{\ensuremath{''}}$ state. The overall agreements between the experimental and theoretical results demonstrate that the time-resolved Coulomb-explosion imaging is a valuable way to monitor the bond breaking and structural evolution of complex molecules.

We report on the fragmentation of multiply charged ${\mathrm{CH}}_{3}\mathrm{I}$ ions through dissociative ionization and Coulomb explosion induced by moderately intense (${10}^{12}--{10}^{13} \mathrm{W}/{\mathrm{cm}}^{2}$) ultrashort laser fields. Velocity map imaging of the fragment ions as a function of pulse duration, ranging from 25 fs to 1.5 ps, leads to kinetic energies, angular distributions, and the relative ion yield in different channels of these fragments. We propose possible pathways for the fragmentation channels based on the kinetic energies and theoretical potential energy curves. For the energetic fragments, we observe an enhanced yield with increasing pulse duration. A simple one-dimensional classical model of wave-packet propagation over the proposed intermediate state potential energy curve is used to estimate the ionization probability as a function of pulse duration. Our results suggest that a delayed enhanced ionization is a consequence of rearrangement of the energies of the molecular orbitals following bond stretching. The resultant energy upshift of the inner orbitals at larger internuclear separation gives rise to resonant multiorbital coupling at a critical distance, which enables enhanced ionization for longer pulses.

We report on electron removal calculations for 2.81 keV/amu ${\mathrm{Li}}^{3+}$ and ${\mathrm{O}}^{3+}$ ion collisions with neon dimers. The target is described as two independent neon atoms fixed at the dimer's equilibrium bond length, whose electrons are subjected to the time-dependent bare and screened Coulomb potentials of the classically moving ${\mathrm{Li}}^{3+}$ and ${\mathrm{O}}^{3+}$ projectile ions, respectively. Three mutually perpendicular orientations of the dimer with respect to the rectilinear projectile trajectories are considered and collision events for the two ion-atom subsystems are combined in an impact parameter by impact parameter fashion and are orientation averaged to calculate probabilities and cross sections for the ion-dimer system. The coupled-channel two-center basis generator method is used to solve the ion-atom collision problems. We concentrate the ion-dimer analysis on one-electron and two-electron removal processes which can be associated with interatomic Coulomb decay, Coulomb explosion, and radiative charge transfer. We find that the calculated relative yields are in fair agreement with recent experimental data for ${\mathrm{O}}^{3+}\text{\ensuremath{-}}{\mathrm{Ne}}_{2}$ collisions if we represent the projectile by a screened Coulomb potential, but disagree markedly for a bare Coulomb potential, i.e., for ${\mathrm{Li}}^{3+}$ impact. In particular, our calculations suggest that interatomic Coulomb decay is a significant reaction channel in the former case only, since capture of a $\mathrm{Ne}(2s$) electron to form hydrogenlike ${\mathrm{Li}}^{2+}$ is unlikely.

The dynamics of four-body Coulomb explosion of acetylene in collision with 50 keV/u ${\mathrm{Ne}}^{8+}$ are investigated by detecting all four ionic fragments and the scattered projectile in quintuple coincidence. Six different breakup channels of ${\mathrm{C}}_{2}{{\mathrm{H}}_{2}}^{q+}$ cations with $4\ensuremath{\leqslant}q\ensuremath{\leqslant}8$ are identified. The kinetic energy (KE) distributions of all ionic fragments as well as the total kinetic energy release (KER) distributions are obtained and compared with the calculation results of the point-charge (PC) approximation model for each channel. For symmetric charge distribution channels, the calculations of PC model, in general, agrees well with the peak positions of the measured KER and KE distributions for all three channels with the largest deviation appearing in the breakup of ${\mathrm{C}}_{2}{{\mathrm{H}}_{2}}^{4+}$. However, for asymmetric charge distribution channels, although the KER values calculated by the PC model for the breakup of ${\mathrm{C}}_{2}{\mathrm{H}}_{2}^{5+}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{2}^{7+}$ fit very well with experiment, the KEs of the two protons and the two C cations exhibit noticeable discrepancy between experiment and PC model. In addition, it is found that the fragmentation of ${\mathrm{C}}_{2}{{\mathrm{H}}_{2}}^{6+}$ which may lead to either two ${\mathrm{C}}^{2+}$ cations or one ${\mathrm{C}}^{+}$ and one ${\mathrm{C}}^{3+}$ cation shows a strong preference for symmetric charge distribution between the two C cations.

Coulomb-explosion imaging is a broadly employed technique to reconstruct the geometry of molecules from the direct multibody breakups of its ions. However, we reveal that this technique fails for a large class of systems, such as (${\mathrm{CO})}_{2}{}^{3+}$ and ${\mathrm{ArCO}}^{3+}$, since the events of the ``direct breakup channel'' are not the real direct breakups but the rapid sequential breakups with a short-lived and ultrafast-rotational fragment. Using Ar-CO as a prototype, we have investigated theoretically its Coulomb-explosion process. We find that due to the interfield between the metastable ${\mathrm{CO}}^{2+}$ and ${\mathrm{Ar}}^{+}$, ${\mathrm{ArCO}}^{3+}$ changes from its initial T shape into the more stable linear shape within 100 fs; such a rotation of ${\mathrm{CO}}^{2+}$ is hundreds of times faster than the field free case. Further, the advanced three-body surface hopping simulations indicate that the angle ${\ensuremath{\angle}}_{(\mathrm{Ar},\mathrm{CO})}$ has rotated from an initial ${95}^{\ensuremath{\circ}}$ to $110.6{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$ on average before the Coulomb explosion, which agrees well with the one (${115}^{\ensuremath{\circ}}$) detected by Gong et al. [Phys. Rev. A 88, 013422 (2013)]. Furthermore, we point out that correct geometry of ArCO can be obtained from the three-body breakups with high kinetic-energy release ($g20$ eV).

Interatomic Coulombic decay (ICD) is a fundamental process between atoms or molecules via a neighbor interaction that produces a relaxation of an electronically excited atom or molecule when embedded in an environment. Due to the physical nature of the process, the electronic and nuclear degrees of freedom are coupled. In this paper, we study the ICD process for a lithium dimer by means of the electron and nuclear dynamics (END) approach. The END approach incorporates a full time-dependent description of the electronic and nuclear degrees of freedom, although its current version does not properly account for continuum states and has limitations in the electronic description by using a single determinantal wave function. Despite this, we confirm that the ICD process takes place via a dipole interaction that induces the nuclear motion of the dimer with a consequent electronic population transfer to higher excited states simulating the ionization process. When the dimer approaches a distance of around 11.5 a.u. (6 \AA{}), this ionization process takes place due to the dipole coupling and occurs at the place of the strongest attractive dipole force. Passing that point, we find that the two lithium atoms repel each other via a Coulomb explosion process followed with a consequent kinetic-energy release (KER). We determine the KER and the timing of the ICD process. We point out the strengths and weaknesses of the END approach and the required enhancements to account for a better description of the ICD process in a coupled electron and nuclear dynamics.

In a momentum coincidence measurement experiment, we studied the three-body fragmentation dynamics of carbon dioxide dimers in intense femtosecond laser fields. The three-dimensional momentum vectors and kinetic energies of the fragments were recorded in a cold-target recoil-ion momentum spectrometer. An analysis shows that ${({\mathrm{CO}}_{2})}_{2}{}^{3+}$ breaks up into ${\mathrm{CO}}_{2}{}^{+}+{\mathrm{CO}}^{+}+{\mathrm{O}}^{+}$ ions through both concerted and sequential fragmentation channels. These two fragmentation channels are consistent with the instantaneous and metastable dissociation channels in the dissociation dynamics of ${\mathrm{CO}}_{2}{}^{2+}$ ion breakup into ${\mathrm{CO}}^{+}$ and ${\mathrm{O}}^{+}$ ions. From Coulomb explosion imaging, our results show that, for the parallel sliding structure of the carbon dioxide dimer molecules, the angle between the C=O bond and the van der Waals bond is $48{}^{\ensuremath{\circ}}$, and the intermolecular nuclear distance $R({\mathrm{CO}}_{2}\text{\ensuremath{-}}{\mathrm{CO}}_{2})$ is 4.0 \AA{}. By tracing the direction of the fragmentation ions, the ${\mathrm{O}}^{+}$ was found to be produced from the C=O bond that is closer to the center of the C-C bond during direct dissociation. These results indicate that the dynamic characteristics of the monomer is retained and gives rise to new dynamics in the molecular cluster complexes. Finally, we have measured angular distributions of ion fragments produced by different dissociation channels of ${({\mathrm{CO}}_{2})}_{2}$, and the results reveal that the structure of the dimer and its relative orientation in the laser field govern the ionization dynamics.

A coincidence momentum imaging method is used to investigate the dissociative ionization of carbonyl sulfide (OCS) irradiated by linearly polarized 800 nm femtosecond laser pulses. As a typical asymmetric molecule, kinetic-energy release (KER) distributions of two-body Coulomb explosion (CE) along C-S or C-O bond breakage from $\mathrm{OC}{\mathrm{S}}^{q+}$ ($q=2$, 3, 4) exhibit a different behavior when the parent charge state increases. Two processes, i.e., concerted enhanced multiple ionization and ladder-climbing-type sequential ionization, are proposed for the C-S and C-O bond breakage, respectively. With the help of the potential-energy curves (PEC) obtained from the multistate density-functional-theory method, the KER values are calculated for these CE channels of $\mathrm{OC}{\mathrm{S}}^{q+}$. The overall good quantitative agreement between the experiment and calculation confirms the validity of the ionization mechanism assumed. In our approach, the global minimum of cationic PEC for the OCS can be treated as ${R}_{c}$ for enhanced ionization. Furthermore, a bimodal KER distribution was observed for the channel of $\mathrm{OC}{\mathrm{S}}^{2+}\ensuremath{\rightarrow}{\mathrm{O}}^{+}+\mathrm{C}{\mathrm{S}}^{+}$, and with the help of PEC, we believe that both of the ionization processes are involved in the dynamics of its formation.

Author(s): Martin, L; Bello, RY; Hogle, CW; Palacios, A; Tong, XM; Sanz-Vicario, JL; Jahnke, T; Schoffler, M; Dorner, R; Weber, T; Martin, F; Kapteyn, HC; Murnane, MM; Ranitovic, P | Abstract: Understanding electron-electron correlations in matter ranging from atoms to solids represents a grand challenge for both experiment and theory. These correlations occur on attosecond timescales and have only recently become experimentally accessible. In the case of highly excited systems, the task of understanding and probing correlated interactions is even greater. In this work, we combine state-of-the-art light sources and advanced detection techniques with ab initio calculations to unravel the role of electron-electron correlation in D2 photoionization by mapping the dissociation of a highly excited D2+ molecule. Correlations between the two electrons dictate the pathways along which the molecule dissociates and lead to a superposition of excited ionic states. Using 3D Coulomb explosion imaging and electron-ion coincidence techniques, we assess the relative contribution of competing parent ion states to the dissociation process for different orientations of the molecule with respect to the laser polarization, which is consistent with a shake-up ionization process. As a step toward observing coherent superposition experimentally, we map the relevant nuclear potentials using Coulomb explosion imaging and show theoretically that such an experiment could confirm this coherence via two-path interference.

We experimentally investigate the dissociative double ionization of hydrogen chloride (HCl) molecules in intense femtosecond laser pulses. In addition to the prompt dissociation channels which occur on femtosecond timescales, long-lived hydrogen chloride dications which Coulomb-explode in flight towards the detector are clearly identified in the photoion-photoion coincidence spectrum. Different pathways leading to these prompt and delayed dissociation channels involving various bound and repulsive states of the HCl dication are discussed based on the observed kinetic energy release and momentum distributions. Our results indicate that the specific features of the HCl dication potential energy curves are responsible for the generation of the delayed fragmentation channels, which are expected to be general processes for the hydrogen halides.

Much of our knowledge of molecular geometry and interaction dynamics comes from indirect measurements of the molecular fragments following breakup. This technique---Coulomb-explosion imaging (CEI), i.e., determining the initial molecular configuration of a system from the momenta of the resulting fragments using knowledge of the particle interactions---is one of the fundamental tools of molecular physics. Moreover, CEI has been a staple of molecular studies for decades. Here we show that one often cannot assign a unique initial configuration to the few-body breakup of a polyatomic molecule given the measurement of the resulting fragments' momenta. Specifically, multiple initial configurations can result in identical momenta for a molecule breaking into three or more parts. Further, the nonunique and nonuniform mapping from the initial configuration to the measured momenta also significantly complicates the determination of molecular alignment at the time of breakup.

International audience; Almost ten years ago, energetic neutral hydrogen atoms were detected after a strong-field double ionization of H2. This process, called 'frustrated tunneling ionization', occurs when an ionized electron is recaptured after being driven back to its parent ion by the electric field of a femtosecond laser. In the present study we demonstrate that a related process naturally occurs in clusters without the need of an external field: we observe a charge hopping that occurs during a Coulomb explosion of a small helium cluster, which leads to an energetic neutral helium atom. This claim is supported by theoretical evidence. As an analog to 'frustrated tunneling ionization', we term this process 'frustrated Coulomb explosion'.

The dynamics following laser-induced molecular photodissociation of gas-phase CH2BrI at 271.6 nm were investigated by time-resolved Coulomb-explosion imaging using intense near-IR femtosecond laser pulses. The observed delay-dependent photofragment momenta reveal that CH2BrI undergoes C-I cleavage, depositing 65.6% of the available energy into internal product states, and that absorption of a second UV photon breaks the C-Br bond of CH2Br. Simulations confirm that this mechanism is consistent with previous data recorded at 248 nm, demonstrating the sensitivity of Coulomb-explosion imaging as a real-time probe of chemical dynamics.

We have measured fully differential cross sections for dissociative single capture and Coulomb explosion through double capture in 75 keV $p+{\mathrm{H}}_{2}$ collisions. Data were analyzed for fixed kinetic energy releases and molecular orientations as a function of scattering angle. Two-center interference was identified for dissociative single capture. The interference pattern is not inconsistent with the symmetry of the dissociative electronic state affecting the phase angle of the interference term. No clear signatures of single-center interference were observed for either process. For double capture at most only a very weak two-center interference structure was found. This very small (or zero) visibility can probably be attributed to a convolution of two independent scatterings of the projectile with the two electrons yielding the measured scattering angle.

The fragmentation dynamics of an endohedral fullerene, $\mathrm{S}{\mathrm{c}}_{3}\mathrm{N}@{\mathrm{C}}_{80}$, after absorption of a soft-x-ray photon, has been studied with an ion-ion-coincidence momentum-imaging technique. Molecular inner-shell ionization at 406.5 eV, targeting the Sc ($2p$) shell of the encapsulated $\mathrm{S}{\mathrm{c}}_{3}\mathrm{N}$ moiety and the C ($1s$) shell of the ${\mathrm{C}}_{80}$ cage, leads to the cage fragmentation through evaporation of ${\mathrm{C}}_{2}$, emission of small molecular carbon ions (${\mathrm{C}}_{n}{}^{+}$, $n\ensuremath{\le}24$), and release of Sc and Sc-containing ions associated with the carbon cage opening or fragmentation. The predominant charge states of Sc and Sc-containing ionic fragments are $+1$ despite an effective Sc valence of 2.4, indicating that charge transfer or redistribution plays an important role in the fragmentation of the encaged $\mathrm{S}{\mathrm{c}}_{3}\mathrm{N}$. Sequential emission of two out of the three Sc atoms of the encaged moiety, via Coulomb explosion in the form of $\mathrm{S}{\mathrm{c}}^{+}$ or Sc-containing ions, is significant. We also find that the resonant excitation of the Sc ($2p$) shell electrons significantly increased the yield of the parent $\mathrm{S}{\mathrm{c}}_{3}\mathrm{N}@{\mathrm{C}}_{80}$ and its fragment ions, partially attributed to the collision of the energetic Auger electrons from the Sc site with the carbon cage.

Interatomic Coulombic decay (ICD) is induced in helium nanodroplets by photoexciting the $n=2$ excited state of ${\mathrm{He}}^{+}$ using XUV synchrotron radiation. By recording multiple-coincidence electron and ion images we find that ICD occurs in various locations at the droplet surface, inside the surface region, or in the droplet interior. ICD at the surface gives rise to energetic ${\mathrm{He}}^{+}$ ions as previously observed for free He dimers. ICD deeper inside leads to the ejection of slow ${\mathrm{He}}^{+}$ ions due to Coulomb explosion delayed by elastic collisions with neighboring He atoms, and to the formation of ${\mathrm{He}}_{k}{}^{+}$ complexes.

By theoretical calculation, we demonstrate the possibility to control and partially suppress the Coulomb explosion of ${\mathrm{N}}_{2}$ molecules after core-level photoionization by an x-ray laser and subsequent Auger decay. This is achieved by means of a femtosecond infrared laser pulse interacting with the ${\mathrm{N}}_{2}{}^{2+}$ dication produced by the x-ray pulse. Suppression of molecular fragmentation requires few-femtosecond IR pulses interacting with the system either during or shortly after the arrival of the x-ray pulse. The IR pulse suppresses fragmentation mostly by optically coupling the electronic routes to ultrafast molecular dissociation with electronic channels able to support long-lived vibrational resonances. The effect is strongly dependent on the orientation of the molecule with respect to the polarization axis of the IR field. Our calculations are motivated by x-ray pump--IR probe experiments performed at an x-ray free-electron laser [J. M. Glownia et al., Opt. Express 18, 17620 (2010)], where only enhancement of ${\mathrm{N}}_{2}{}^{2+}$ fragmentation as a function of the pump-probe delay time was reported. The opposite effect reported here becomes apparent when the various electronic channels are considered separately. In practice, this corresponds to a coincident measurement of the energy of the ejected Auger electron.

We report a quantitative study of the effect of nonaxial recoil during Coulomb explosion of laser-aligned molecules and introduce a method to remove the blurring caused by nonaxial recoil in the fragment-ion angular distributions. Simulations show that nonaxial recoil affects correlations between the emission directions of fragment ions differently from the effect caused by imperfect molecular alignment. The method, based on analysis of the correlation between the emission directions of the fragment ions from Coulomb explosion, is used to deconvolute the effect of nonaxial recoil from experimental fragment angular distributions. The deconvolution method is then applied to a number of experimental data sets to correct the degree of alignment for nonaxial recoil, to select optimal Coulomb explosion channels for probing molecular alignment, and to estimate the highest degree of alignment that can be observed from selected Coulomb explosion channels.

We have experimentally and theoretically studied the fragmentation dynamics of argon trimer $(\mathrm{A}{\mathrm{r}}_{3})$ in intense laser fields. By coincidently measuring the momentum vectors, we obtained the emission geometry of the three fragmental ions produced in the three-body fragmentation process. In addition to the direct Coulomb explosion channels, we observed the indirect Coulomb explosion channels with Rydberg excitation. We have further developed a classical polyatomic molecular ensemble model, in which all interactions among electrons and nuclei are fully included, to simulate the fragmentation dynamics of argon trimer in intense laser fields. The experimental observations have been reproduced by the model calculation. The simulations show that the Rydberg excitation modifies the kinetic energy release as well as the emission geometry of fragmental ions during the explosion process. The study provides insight into the correlation dynamics of electrons and nuclei of many-body physics driven by intense laser fields.

The Coulomb explosion of small cluster beams can be used to measure the dwell time of fragments traversing amorphous films. Therefore, the thickness of thin films can be obtained with the so-called Coulomb depth profiling technique using relatively high cluster energies where the fragments are fully ionized after breakup. Here we demonstrate the applicability of Coulomb depth profiling technique at lower cluster energies where neutralization and wake effects come into play. To that end, we investigated 50--200 keV/u ${{\mathrm{H}}_{2}}^{+}$ molecular ions impinging on a 10 nm ${\mathrm{TiO}}_{2}$ film and measured the energy of the backscattered ${\mathrm{H}}^{+}$ fragments with high-energy resolution. The effect of the neutralization of the ${\mathrm{H}}^{+}$ fragments along the incoming trajectory before the backscattering collision is clearly observed at lower energies through the decrease of the energy broadening due to the Coulomb explosion. The reduced values of the Coulomb explosion combined with full Monte Carlo simulations provide compatible results with those obtained at higher cluster energies where neutralization is less important. The results are corroborated by electron microscopy measurements.

We study the formation of highly excited neutral atoms during the breakup of strongly driven molecules. Past work on this significant phenomenon has shown that during the formation of highly excited neutral atoms (${\mathrm{H}}^{*}$) during the breakup of ${\mathrm{H}}_{2}$ in a linear laser field the electron that escapes does so either very quickly or after remaining bound for a few periods of the laser field. Here, we address the electron-nuclear dynamics in ${\mathrm{H}}^{*}$ formation in elliptical laser fields, through Coulomb explosion. We show that with increasing ellipticity two-electron effects are effectively ``switched off.'' We perform these studies using a toolkit we have developed for semiclassical computations for strongly driven multicenter molecules. This toolkit includes the formulation of the probabilities of strong-field phenomena in a transparent way. This allows us to identify the shortcomings of currently used initial phase-space distributions for the electronic degrees of freedom. In addition, it includes a three-dimensional method for time propagation that fully accounts for the Coulomb singularity. This technique has been previously developed in the context of celestial mechanics and we currently adopt it to strongly driven systems. Moreover, we allow for tunneling during the time propagation. We find that this is necessary in order to accurately describe the fragmentation of strongly driven molecules.

A study of impulsive alignment of noble-gas dimers using picosecond laser pulses shows how to extract rotational constants and estimate polarizability anisotropies from measurements and provides detailed insight into the temporal evolution of the laser-induced alignment.

We report the direct observation of the orientation of jet-cooled molecules induced by a THz pulse. The intense THz field ($\ensuremath{\sim}$30 kV/cm) creates a superposition between the rotational ground state ($J=0$) and the excited state ($J=1$) of HBr molecules. The rotational dynamics is probed by Coulomb explosion imaging of the fragment ions produced by a near-infrared femtosecond laser pulse. Comparing with the simulations based on a time-dependent Schr\"odinger equation, the rotational wave packets are completely reconstructed, which reveal that $\ensuremath{\sim}$$7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ of the ground-state population is transferred to the $J=1$ state at an initial temperature of 8 K, achieving a degree of orientation of $\ensuremath{\langle}cos\ensuremath{\theta}\ensuremath{\rangle}\ensuremath{\sim}0.017$.

We report on the observation of a high-energy ``shoulder'' in the kinetic-energy distribution of ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ ions formed in the interaction of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ with ultrashort light pulses of an intensity higher than approximately ${10}^{15} {\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}.$ It extends up to a kinetic energy of $\ensuremath{\approx}8 \mathrm{eV}.$ The ``shoulder'' ions are formed by Coulomb explosion after photoionization of the respective molecular ion. The shape of the ``shoulder'' indicates that photoionization of ${\mathrm{H}}_{2}^{+}$ in the vibrational ground state $v=0$ and of ${\mathrm{D}}_{2}^{+}$ in $v=0,1$ is the mechanism for atomic ion formation near the ``shoulder'' cutoff.

A five-body classical trajectory Monte Carlo model has been developed to study fragmentation of diatomic molecules after double electron removal by highly charged ion impact. A systematic study of the final-state deuteron energy and momentum spectra has been conducted for Xe19+ + D-2 collisions at impact energies ranging from 1 eV/u to 100 keV/u. At the highest projectile energies, the fragment energies and momenta are determined by the Coulomb explosion of the doubly-ionized molecule via the known Franck-Condon transition for the isolated molecule. The deuterons are emitted back-to-hack with nearly equal energies. At the lowest projectile energies, the final state behavior is due mainly to the collisional momentum transfer from the slow-moving projectile. The deuterons are strongly scattered in the direction opposite to the transverse momentum of the projectile with energies far greater than those produced in the Franck-Condon transition. At energies around 150 eV/u, both slow and fast deuterons are predicted. This is due to the vector addition of the collisional momentum transfer to the center of mass of the molecule with that due to the two-body Coulomb breakup of the dissociating ions. [S1050-2947(99)01009-4].

We have developed a one-dimensional time-dependent Thomas-Fermi model of atoms, molecules, and small clusters exposed to an intense subpicosecond laser field. In this model, the dynamics of an electronic cloud is governed by the hydrodynamic equations of motion, whereas the nuclei move in accordance with the Newton equations. The quantum mechanics enters in this approach only through the constitutive relation between the pressure and the density, which is derived from the application of Fermi-Dirac statistics to a noninteracting $T=0$ temperature electron gas. The time-independent version of the model, formulated in terms of the integral equation for the electric potential, is also discussed. We present numerical results for diatomic molecules and small clusters irradiated by the strong laser pulses. In the case of molecules, we observe the multielectron ionization accompanied by dissociation. The kinetic energy defect, understood as a reduction of the energy of resulting ions in comparison with a simple Coulomb explosion picture, is explained in terms of a screening effect of escaping fragments by the ejected electrons. For small clusters we find that the explosion of the cluster has a stepwise character; the consecutive layers of atoms are stripped off one by one. We observe the highly energetic (as compared with diatomic systems) atomic fragments even for relatively low laser intensities and a few atoms clusters. Also, the model predicts the nonuniform energy distribution among the same charge state ions and supports the idea of hot electrons generated in the cluster via a mechanism of inverse bremsstrahlung.

The high-order multielectron ionization of ${\mathrm{Xe}}_{531},$ ${\mathrm{Xe}}_{1061},$ and ${\mathrm{Xe}}_{2097}$ clusters in a strong laser field is studied using classical dynamics. The simulations are performed in the frozen geometry approximation for fixed ionic charges, so that only the evolution of the electrons, which are unbound to the ions, is examined. The dependence of the ionization efficiency on the laser frequency and cluster radius is manifested by pronounced maxima. The presence of these maxima favors the quasiresonance ionization mechanism, which is related to the motion of the unbound electrons in the entire cluster. The high level of ionization $(q\ensuremath{\sim}8--18$ per atom) is realized in the expanded cluster, due to the Coulomb explosion.

The Coulomb explosion of ${\mathrm{CO}}_{2}$ in collisions with ${\mathrm{Ar}}^{8+}$ ions of 120 keV has been examined experimentally using a position sensitive detector with a triple coincidence technique. The technique has allowed the full characterization of the structure of the exploding molecule. Purely Coulombic fragment energies fit the experimental results well, across the range of fragment energies. Modifications to the molecular geometry are observed, in the form of widening of the zero point bend distribution and sequential processes are found to be unimportant in the dissociation process.

Highly charged molecular ions are generated in Coulomb explosion experiments involving multielectron dissociative ionization, but little is known about the precise mechanisms involved in their formation. To help improve the understanding of such experiments, potential energy curves are calculated in this paper for diatomic chlorine $({\mathrm{Cl}}_{2})$ and its ions ${\mathrm{Cl}}_{2}^{n+},$ where $n=1,2,3,4,6,8,10$. Bound vibrational states are obtained in three low-lying electronic states for ${\mathrm{Cl}}_{2}^{2+}$ and one state for ${\mathrm{Cl}}_{2}^{3+}.$ Vertical excitation energies are given for stepwise excitations up to ${\mathrm{Cl}}_{2}^{10+}.$ For all the ions examined there is a significant energy defect $(\ensuremath{\Delta})$ from the corresponding Coulomb potential, in one case reaching magnitudes of over 20 eV. We analyze the origin of these energy defects in terms of residual chemical bonding, and discuss the contribution of strongly bonding configurations at short internuclear distance. Finally, we present a simple physical model which describes the qualitative behavior of $\ensuremath{\Delta}(R,Q)$.

The Coulomb explosion of ${\mathrm{H}}_{2}\mathrm{O}$ in laser pulses of 50 fs and intensity of $3\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ has been investigated using an ion momentum-imaging technique to determine the shape of the exploding molecule. The molecule is found to straighten substantially during the ionization process with the bend distribution at a maximum between $130\ifmmode^\circ\else\textdegree\fi{}$ and $180\ifmmode^\circ\else\textdegree\fi{}.$

Laser-induced molecular coulomb explosion of ${\mathrm{N}}_{2}$ and ${\mathrm{CO}}_{2}$ is studied experimentally using linearly and circularly polarized laser light in the ${10}^{15}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ intensity range at $\ensuremath{\lambda}=800\mathrm{nm}.$ The fragmentation kinetic energy releases are found to be identical in both cases using two different experimental methods. These results show that the molecular relaxation is independent of the respective directions of the laser electric field and of the internuclear axis. These results are confirmed by varying the linear laser polarization direction relative to the explosion direction of ${\mathrm{N}}_{2}$ and ${\mathrm{CO}}_{2}.$ Moreover, since in the linear case the molecular reorientation occurs along the laser electric field direction, these results show that inertial effects are not responsible for the possible elongation of the internuclear distances.

We study the interaction of ${\mathrm{C}}_{60}$ molecules with intense $(10--1000{\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2})$ femtosecond pulses of 790-nm wavelength. High charge states of carbon up to ${\mathrm{C}}^{4+}$ are produced in this intensity range, as determined by time-of-flight spectroscopy. These high charge states of carbon are produced at intensities more than an order of magnitude lower than would be required based on optical field ionization of isolated carbon atoms. From a line-shape analysis of the time-of-flight data, we derive the kinetic-energy distribution of the C ions. We find average energies of up to a few hundred eV, indicating that these ions are released through Coulomb explosion of the ${\mathrm{C}}_{60}$ molecules once the charge buildup due to ionization becomes sufficiently high. Ionic potentials of up to 200 V are derived from the kinetic-energy distributions. The ionic potential needed to retain electrons energetic enough to cause K-shell impact ionization is 392 V. This potential is not reached in case of ionization of ${\mathrm{C}}_{60}$ with 790-nm, 45-fs pulses since the disintegration of the cluster occurs on a time scale of a few femtoseconds, much shorter than the optical pulse. In this short time span, the heating of the cluster is not efficient enough for higher charge states to be ionized.

The analysis of electron potentials in multicharged molecules and small clusters allows one to determine which of these systems may be ionized in a strong laser field by the quasiresonance mechanism. The presence of moderately transparent interionic potential barriers ~for electron tunneling! is necessary for the quasiresonance electron energy enhancement and, consequently, for ionization @Zuo and Bandrauk, Phys. Rev. A 52, R2511 ~1995!#. In multicharged systems, which spatially expand by Coulomb explosion, the interionic barriers increase with time. The simulation of electron motion in such systems demonstrates the presence of a different kind of charge resonance enhanced ionization mechanism whose efficiency depends on the dynamics of the increase of the interionic barriers. This dynamic charge resonance enhanced ionization mechanism is of classical origin and its efficiency is higher than that of the static ~frozen geometry! mechanism. @S1050-2947~98!06410-5# PACS number~s!: 33.80.Rv

We study the effects on the electronic stopping power of large clusters in solids, resulting from multiple elastic scattering of each particle in the cluster by the target atoms, in the small-angle approximation. Evaluation of the cluster vicinage self-energy at the entrance of the target shows that large clusters may stabilize against the Coulomb explosion for a range of cluster sizes and speeds, so that the change of the cluster structure, due to multiple scattering, may have a noticeable influence on the vicinage, or interference, energy losses of clusters due to collective electronic excitations in the target. Stopping power calculations are presented for ${\mathrm{C}}_{60}$ and $({\mathrm{H}}_{2}{)}_{50}$ clusters in an Al target, together with the results on stabilization conditions against the Coulomb explosion for $({\mathrm{H}}_{2}{)}_{{N}_{m}}$, based on self-energy considerations.

The dynamical interaction effects on the Coulomb explosion and the stopping power are studied for MeV ${\mathrm{H}}_{2}^{+}$ ions in grazing collisions with a solid surface. The surface dynamical potential induced by the molecular ions is obtained by using a local frequency-dependent dielectric function for a semi-infinite electron gas with damping. A set of equations describing the motion of the center of mass and the Coulomb explosion is obtained by including the repulsive force of the surface atoms, the bare Coulomb force, and the dynamical forces. The total energy loss for the molecular ion is calculated, taking into account a contribution from both the collective excitations of the conduction electrons and the single-electron excitations of each of the substrate atoms.

The time-dependent Schr\"odinger equation for the one-dimensional ${\mathrm{H}}_{2}^{+}$ molecule (with both nuclear and electronic degrees of freedom included) was solved numerically to study dissociative ionization. A wave-function splitting technique was used with projections onto Volkov states, which allows one to circumvent the problem of lost information on electron flux due to absorbing boundary methods. This technique allows us to calculate the above-threshold ionization (ATI) photo electron kinetic-energy spectra in the presence of moving nuclei, as well as complete spectra of dissociating protons, beyond the Born-Oppenheimer approximation. The ATI spectra are considerably enhanced with respect to the H-atom spectra due to electron molecule interaction. The peaks seen in calculated Coulomb explosion spectra of protons agree well with recent theoretical and experimental work related to the phenomenon of charge-resonance-enhanced ionization in molecules.

By considering a laser-induced dipole layer along the surface of a metal and its action on an electron of the metal, it is shown that at moderate laser field intensities of some ${10}^{10} {\mathrm{W}\mathrm{}\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ energetic electrons of a few 100 eV can be produced, which explains recent observations of Farkas et al. [Phys. Rev. A 41, 4123 (1990); Opt. Eng. 32, 2476 (1993)] without necessarily resorting to the mechanism of Coulomb explosion, taking place after the completion of the ionization process.

Atomic clusters have long been studied by chemists and physicists because of the unique position that clusters hold as an intermediate state between molecules and solids [1]. Many studies have traced the properties of materials from their monatomic characteristics to their bulk state characteristics through an examination of the material as it forms larger and larger clusters. Recently, there has been much activity in extending these studies to very high intensity, ultrashort laser pulses with peak laser intensities >1015 Wcm −2 and pulse widths of 0.1 to 10 ps [2–11]. There has also been some preliminary theoretical work in this area as well [6,12]. In this parameter regime the physics governing the laser cluster interaction is fundamentally different than in previous studies. At these intensities the laser interaction is non-perturbative and very high order multiphoton ionization and strong electric field tunnel ionization are possible. Consequently, highly charged ions can be produced [2,5,8,10]. Furthermore, the short pulses used are comparable to or shorter than the disassembly times of a cluster in the laser field [6] and, so, the entire laser pulse interacts with an inertially confined body of atoms.

The Coulomb explosion of 173-MeV HeH{sup +} molecular ions traversing thin carbon foils has been measured for foil thicknesses ranging from 2 to 200{mu}g/cm{sup 2}. In contrast with measurements at lower energies, the energy spectra for protons observed emerging in the incident beam direction show distinct components that correspond to the partner helium ions being in charge states 0, 1, and 2. From an analysis of the variation of the yields of these components as functions of the target thickness, we extract electron-loss cross sections that are in good agreement with theoretical estimates. {open_quotes}Wake effects{close_quotes} that increase with increasing target thickness are observed as asymmetries in the yields and energy shifts for {open_quotes}backward-going{close_quotes} as compared to {open_quotes}forward-going{close_quotes} protons. {copyright} {ital 1997} {ital The American Physical Society}

We present a quantitative model to describe the formation of hydrogen atoms (1s and 2p states) following the dissociation of fast (30{endash}120 keV/u) hydrogen cluster ions H{sub n}{sup +} (n=2 and n= 3 {endash} 21, odd) induced by a thin carbon foil. The model includes Coulomb explosion, multiple scattering, energy loss, and a simplified description of charge-exchange processes inside the solid. This description takes into account the dynamic screening of the moving protons by the target electrons and the relative position of the protons during the charge-exchange process. The results of the calculations performed with a Monte Carlo computer code reproduce remarkably well the experimental data.

We simultaneously probe the molecular structure and the symmetry of valence electronic orbital of an anisotropic atomic-molecular complex of ArCO by tracing its three-body Coulomb breakup following triple ionization in a phase-controlled elliptically polarized two-color pulse. The geometry of ArCO is found to be tilted T shaped, where the angle between the covalent and van der Waals bonds is 65\ifmmode^\circ\else\textdegree\fi{} with oxygen pointing towards argon. The asymmetric profiles of the outmost orbitals from the CO site are probed by directional dissociation of the contained CO subunit as a function of the laser phase. Our results clearly image the asymmetric geometry of ArCO and thus reveal the anisotropic interaction between a rare-gas atom and a heteronuclear diatomic molecule.

In recent years it was demonstrated that the negative hydrogen molecular ions H${}_{2}{}^{\ensuremath{-}}$ and D${}_{2}{}^{\ensuremath{-}}$ exist in long-lived states with lifetimes exceeding 1 $\ensuremath{\mu}$s (H${}_{2}{}^{\ensuremath{-}}$) and 1 ms (D${}_{2}{}^{\ensuremath{-}}$). These metastable ions exhibit very large internuclear distances and possess high angular momenta, which stabilizes them against autodetachment. Here we present the results of a foil-induced Coulomb explosion imaging experiment that allows for the measurement of the rovibrational wave functions of the metastable D${}_{2}{}^{\ensuremath{-}}$ ions. We compare our results to previous predictions from a nonlocal resonance theory. Our measurements do not confirm the discrepancy between experiment and theory that was inferred from previous photofragmentation studies. In fact, we find good agreement between the experiment and calculated wave functions for the most long-lived states with rotational quantum numbers $J=37$ and 38.

The time-dependent Schr\"odinger equation for ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ in a 600-nm, intense (I\ensuremath{\geqslant}${10}^{14}$ W/${\mathrm{cm}}^{2}$) laser field is solved numerically for a model which uses the exact three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser electric field and three-dimensional electronic motion. High ionization rates of ${\mathrm{H}}_{2}$${\mathrm{}}^{+}$ are found, exceeding those of neutral atomic hydrogen. This confirms, by the rigorous, full dynamical calculation, the recently discovered charge-resonance-enhanced ionization (CREI)---all previous demonstrations of CREI were based on the ``frozen nuclei'' model. The numerical kinetic-energy spectra of dissociating fragments are compared with recent experimental results. They can be interpreted by a simple bond softening mechanism (or laser-induced avoided crossing in a dressed-state representation), in which the binding forces are completely suppressed by the strong electric field and thus the dissociating fragments move as free particles with a kinetic energy close to their initial vibrational energy until they reach a critical distance R=${\mathit{R}}_{\mathit{c}}$\ensuremath{\cong}8 bohr, where they are rapidly ionized, due to CREI. The harmonic generation spectra calculated from our non-Born-Oppenheimer simulations show that the high harmonics are also generated when the nuclei cross this critical distance R=${\mathit{R}}_{\mathit{c}}$. \textcopyright{} 1996 The American Physical Society.

The structure of ${\mathrm{C}}_{3}$${\mathrm{H}}_{3}^{+}$ and ${\mathrm{C}}_{3}$${\mathrm{H}}_{4}^{+}$ ions produced by nonresonant multiphoton ionization is determined using laser-induced Coulomb explosion and associated multicharged atomic ion momenta correlations. Both cations exhibit the same ${\mathrm{C}}_{3}$ average elongated linear carbon geometry. Stretched and bent nuclear configurations around the average structure are included in the calculations in order to reproduce the observed ion-ion correlation peak shapes.