Complete photo-fragmentation of the deuterium molecule

Step-by-step state-selective tracking of fragmentation dynamics of water dications by momentum imaging

The double photoionization of a molecule by one photon ejects two electrons and typically creates an unstable dication. Observing the subsequent fragmentation products in coincidence can reveal a surprisingly detailed picture of the dynamics. Determining the time evolution and quantum mechanical states involved leads to deeper understanding of molecular dynamics. Here in a combined experimental and theoretical study, we unambiguously separate the sequential breakup via D⁺ + OD⁺ intermediates, from other processes leading to the same D⁺ + D⁺ + O final products of double ionization of water by a single photon. Moreover, we experimentally identify, separate, and follow step by step, two pathways involving the b ¹Σ⁺ and a ¹Δ electronic states of the intermediate OD⁺ ion. Our classical trajectory calculations on the relevant potential energy surfaces reproduce well the measured data and, combined with the experiment, enable the determination of the internal energy and angular momentum distribution of the OD⁺ intermediate.

Determining the time evolution of reactions at the quantum mechanical level improves our understanding of molecular dynamics. Here, authors separate the breakup of water, one bond at a time, from other processes leading to the same final products and experimentally identify, separate, and follow step by step two breakup paths of the transient OD⁺ fragment.

A modified magnetic bottle electron spectrometer for the detection of multiply charged ions in coincidence with all correlated electrons: decay pathways to Xe3+ above xenon-4d ionization threshold

Single-photon multiple photoionization results from electron correlations that make this process possible beyond the independent electron approximation. To study this phenomenon experimentally, the detection in coincidence of all emitted electrons is the most direct approach. It provides the relative contribution of all possible multiple ionization processes, the energy distribution between electrons that can reveal simultaneous or sequential mechanisms, and, if possible, the angular correlations between electrons. In the present work, we present a new magnet design of our magnetic bottle electron spectrometer that allows the detection of multiply charged Xeⁿ⁺ ions in coincidence with n electrons. This new coincidence detection allows more efficient extraction of minor channels that are otherwise masked by random coincidences. The proof of principle is provided for xenon triple ionization.

Zeptosecond birth time delay in molecular photoionization

Photoionization is one of the fundamental light-matter interaction processes in which the absorption of a photon launches the escape of an electron. The time scale of this process poses many open questions. Experiments have found time delays in the attosecond (10−18 seconds) domain between electron ejection from different orbitals, from different electronic bands, or in different directions. Here, we demonstrate that, across a molecular orbital, the electron is not launched at the same time. Rather, the birth time depends on the travel time of the photon across the molecule, which is 247 zeptoseconds (1 zeptosecond = 10−21 seconds) for the average bond length of molecular hydrogen. Using an electron interferometric technique, we resolve this birth time delay between electron emission from the two centers of the hydrogen molecule.

Absence of Triplets in Single-Photon Double Ionization of Methanol

Despite the abundance of data concerning single-photon double ionization of methanol, the spin state of the emitted electron pair has never been determined. Here we present the first evidence that identifies the emitted electron pair spin as overwhelmingly singlet when the dication forms in low-energy configurations. The experimental data show that while the yield of the CH2O+ + H3+ Coulomb explosion channel is abundant, the metastable methanol dication is largely absent. According to high-level ab initio simulations, these facts indicate that photoionization promptly forms singlet dication states, where they quickly decompose through various channels, with significant H3+ yields on the low-lying states. In contrast, if we assume that the initial dication is formed in one of the low-lying triplet states, the ab initio simulations exhibit a metastable dication, contradicting the experimental findings. Comparing the average simulated branching ratios with the experimental data suggests a >3 order of magnitude enhancement of the singlet:triplet ratio compared with their respective 1:3 multiplicities.

Quantum Effects Dominating the Interatomic Coulombic Decay of an Extreme System

LiHe is an extreme open-shell system. It is among the weakest bound systems known, and its mean interatomic distance extends dramatically into the classical forbidden region. Upon 1s → 2p excitation of He, interatomic Coulombic decay (ICD) takes place in which the electronically excited helium atom relaxes and transfers its excess energy to ionize the neighboring lithium atom. A substantial part of the decay is found to be to the dissociation continuum producing Li⁺ and He atoms. The distribution of the kinetic energy released by the ICD products is found to be highly oscillatory. Its analysis reveals that quantum phase shifts between the decaying states and the dissociating final states are controlling this ICD reaction. The semiclassical reflection principle, which commonly explains ICD reactions, fails. The process is expected to be amenable to experiment.

Subfemtosecond Tracing of Molecular Dynamics during Strong-Field Interaction

We introduce and experimentally demonstrate a method where the two intrinsic timescales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photoelectron photoion coincidence experiment. In our experiment, elliptically polarized, 750 nm, 4.5 fs laser pulses were focused to an intensity of 9×10^{14}  W/cm^{2} onto H_{2}. Using coincidence imaging, we directly observe the nuclear wave packet evolving on the 1sσ_{g} state of H_{2}^{+} during its first round-trip with attosecond temporal and picometer spatial resolution. The demonstrated method should enable insight into the first few femtoseconds of the vibronic dynamics of ionization-induced unimolecular reactions of larger molecules.

Invited Review Article: Photofragment imaging

Photodissociation studies in molecular beams that employ position-sensitive particle detection to map product recoil velocities emerged thirty years ago and continue to evolve with new laser and detector technologies. These powerful methods allow application of tunable laser detection of single product quantum states, simultaneous measurement of velocity and angular momentum polarization, measurement of joint product state distributions for the detected and undetected products, coincident detection of multiple product channels, and application to radicals and ions as well as closed-shell molecules. These studies have permitted deep investigation of photochemical dynamics for a broad range of systems, revealed new reaction mechanisms, and addressed problems of practical importance in atmospheric, combustion, and interstellar chemistry. This review presents an historical overview, a detailed technical account of the range of methods employed, and selected experimental highlights illustrating the capabilities of the method.

Development of an electron-ion coincidence apparatus for molecular-frame electron energy loss spectroscopy studies

We report details of an electron-ion coincidence apparatus, which has been developed for molecular-frame electron energy loss spectroscopy studies. The apparatus is mainly composed of a pulsed electron gun, an energy-dispersive electron spectrometer, and an ion momentum imaging spectrometer. Molecular-orientation dependence of the high-energy electron scattering cross section can be examined by conducting measurements of vector correlation between the momenta of the scattered electron and fragment ion. Background due to false coincidences is significantly reduced by introducing a pulsed electron beam and pulsing scheme of ion extraction. The experimental setup has been tested by measuring the inner-shell excitation of N₂ at an incident electron energy of 1.5 keV and a scattering angle of 10.2°.

Imaging the square of the correlated two-electron wave function of a hydrogen molecule

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H₂ two-electron wave function in which electron–electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.

Electron-electron correlation is a complex and interesting phenomenon that occurs in multi-electron systems. Here, the authors demonstrate the imaging of the correlated two-electron wave function in hydrogen molecule using the coincident detection of the electron and proton after the photoionization.

Two-Particle Interference of Electron Pairs on a Molecular Level

We investigate the photodouble ionization of H_{2} molecules with 400 eV photons. We find that the emitted electrons do not show any sign of two-center interference fringes in their angular emission distributions if considered separately. In contrast, the quasiparticle consisting of both electrons (i.e., the "dielectron") does. The work highlights the fact that nonlocal effects are embedded everywhere in nature where many-particle processes are involved.

Time resolved 3D momentum imaging of ultrafast dynamics by coherent VUV-XUV radiation

We present a new experimental setup for measuring ultrafast nuclear and electron dynamics of molecules after photo-excitation and ionization. We combine a high flux femtosecond vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) source with an internally cold molecular beam and a 3D momentum imaging particle spectrometer to measure electrons and ions in coincidence. We describe a variety of tools developed to perform pump-probe studies in the VUV-XUV spectrum and to modify and characterize the photon beam. First benchmark experiments are presented to demonstrate the capabilities of the system.

Electron and recoil ion momentum imaging with a magneto-optically trapped target

A reaction microscope (ReMi) has been combined with a magneto-optical trap (MOT) for the kinematically complete investigation of atomic break-up processes. With the novel MOTReMi apparatus, the momentum vectors of the fragments of laser-cooled and state-prepared lithium atoms are measured in coincidence and over the full solid angle. The first successful implementation of a MOTReMi could be realized due to an optimized design of the present setup, a nonstandard operation of the MOT, and by employing a switching cycle with alternating measuring and trapping periods. The very low target temperature in the MOT (∼2 mK) allows for an excellent momentum resolution. Optical preparation of the target atoms in the excited Li 2(2)P3/2 state was demonstrated providing an atomic polarization of close to 100%. While first experimental results were reported earlier, in this work, we focus on the technical description of the setup and its performance in commissioning experiments involving target ionization in 266 nm laser pulses and in collisions with projectile ions.

Enhanced one-photon double ionization of atoms and molecules in an environment of different species

The correlated nature of electronic states in atoms and molecules is manifested in the simultaneous emission of two electrons after absorption of a single photon close to the respective threshold. Numerous observations in atoms and small molecules demonstrate that the double ionization efficiency close to threshold is rather small. In this Letter we show that this efficiency can be dramatically enhanced in the environment. To be specific, we concentrate on the case where the species in question has one or several He atoms as neighbors. The enhancement is achieved by an indirect process, where a He atom of the environment absorbs a photon and the resulting He(+) cation is neutralized fast by a process known as electron transfer mediated decay, producing thereby doubly ionized species. The enhancement of the double ionization is demonstrated in detail for the example of the Mg · He cluster. We show that the double ionization cross section of Mg becomes 3 orders of magnitude larger than the respective cross section of the isolated Mg atom. The impact of more neighbors is discussed and the extension to other species and environments is addressed.

Spatial imaging of the H2(+) vibrational wave function at the quantum limit

We experimentally obtained a direct image of the nuclear wave functions of H(2)(+) by dissociating the molecule via electron attachment and determining the vibrational state using the cold target recoil ion momentum spectroscopy technique. Our experiment visualizes the nodal structure of different vibrational states. We compare our results to the widely used reflection approximation and to quantum simulations and discuss the limits of position measurements in molecules imposed by the uncertainty principle.

Angular distributions for the complete photofragmentation of the Li atom

We explore the complete breakup of the Li atom after absorption of a single photon, the purest example of the so-called four-body Coulomb problem. The resulting strongly correlated three-electron continuum is investigated by calculating the angular distributions of the ionized electrons using advanced close-coupling techniques. We find that the distributions are dominated by the Coulomb interactions between the electrons, that multiple break-up processes can be identified, and that the complex dynamics of the fragmentation process are evident for most scattering geometries.

Electron pair density in the lowest 1Σ(u)(+) and 1Σ(g)(+) states of H2

We demonstrate and advocate the use of observable quantities derived from the two-electron reduced density matrix - pair densities, conditional densities, and exchange-correlation holes--as signatures of the type of electron correlation in a chemical bond. The prototype cases of the lowest (1)Σ(u)(+) and (1)Σ(g)(+) states of H(2), which exhibit large variation in types of bonding, ranging from strongly ionic to covalent, are discussed. Both the excited (1)Σ(g)(+) and (1)Σ(u)(+) states have been interpreted as essentially consisting of (natural) orbital configurations with an inner electron in a contracted 1sσ(g) orbital and an outer electron in a diffuse (united atom type, Rydberg) orbital. We show that nevertheless totally different correlation behavior is encountered in various states when comparing them at a common internuclear distance. Also when following one state along the internuclear distance coordinate, strong variation in correlation behavior is observed, as expected. Switches between ionic to covalent character of a state occur till very large distances (40 bohrs for states approaching the 1s3[script-l] asymptotic limit, and 282 bohrs for states approaching the 1s4[script-l] limit).

Two-center resonant photoionization

Photoionization of an atom A, in the presence of a neighboring atom B, can proceed both directly and via resonant excitation of B with subsequent energy transfer to A through two-center electron-electron correlation. We show that in such a case the photoionization process can be very strongly enhanced and acquire interesting characteristic features, both in its time development and the electron spectrum.

Single photon double ionization of the helium dimer

We show that a single photon can ionize the two helium atoms of the helium dimer in a distance up to 10 A. The energy sharing among the electrons, the angular distributions of the ions and electrons, as well as comparison with electron impact data for helium atoms suggest a knockoff type double ionization process. The Coulomb explosion imaging of He2 provides a direct view of the nuclear wave function of this by far most extended and most diffuse of all naturally existing molecules.

Fully differential molecular-frame measurements for the electron-impact dissociative ionization of H2

We present fully differential state-resolved experimental data for the dissociative ionization of molecular hydrogen induced through electron impact. Molecular-frame ionization cross sections are derived for transitions from the X{1}Sigma{g}{+} molecular ground state to the 1ssigma{g}, 2psigma{u}, 2ssigma{g}, and 2ppi{u} states of H2+. For transitions to the 2ssigma{g} and 2ppi{u} states, a strong orientation dependence in the cross sections is revealed, with "side-on" preferred to "end-on" collisions and a propensity for the fragment proton to emerge along the normal to the scattering plane.

Electron-pair excitations and the molecular Coulomb continuum

Electron-pair excitations in the molecular hydrogen continuum are described by quantizing rotations of the momentum plane of the electron pair about the pair's relative momentum. A heliumlike description of the molecular photodouble ionization is thus extended to higher angular momenta of the electron pair. A simple three-state superposition is found to account surprisingly well for recent observations of noncoplanar electron-pair, molecular-axis angular distributions.

Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules

Present experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) for ionization from the outermost valence orbitals of molecules. We show that the details of MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.

Physical interpretation of the "kinetic energy release" effect in the double photoionization of H(2)

A physical interpretation is given for the variation with internuclear separation of the fully differential cross section for double photoionization of H2. This effect is analyzed in a geometry where the fourbody interaction is completely probed. Excellent agreement is found between experiment and time-dependent close-coupling theory after convoluting the latter over the relevant solid angles. We show the observed variations are purely due to the epsilon(Sigma) component of the polarization vector epsilon along the molecular axis, a conclusion which is supported through calculations of the photoionization of H2(+).

Interference in the collective electron momentum in double photoionization of H2

We investigate single-photon double ionization of H(2) by 130 to 240 eV circularly polarized photons. We find a double slitlike interference pattern in the sum momentum of both electrons in the molecular frame which survives integration over all other degrees of freedom. The difference momentum and the individual electron momentum distributions do not show such a robust interference pattern. We show that this interference results from a non-Heitler-London fraction of the H(2) ground state where both electrons are at the same atomic center.

The simplest double slit: interference and entanglement in double photoionization of H2

The wave nature of particles is rarely observed, in part because of their very short de Broglie wavelengths in most situations. However, even with wavelengths close to the size of their surroundings, the particles couple to their environment (for example, by gravity, Coulomb interaction, or thermal radiation). These couplings shift the wave phases, often in an uncontrolled way, and the resulting decoherence, or loss of phase integrity, is thought to be a main cause of the transition from quantum to classical behavior. How much interaction is needed to induce this transition? Here we show that a photoelectron and two protons form a minimum particle/slit system and that a single additional electron constitutes a minimum environment. Interference fringes observed in the angular distribution of a single electron are lost through its Coulomb interaction with a second electron, though the correlated momenta of the entangled electron pair continue to exhibit quantum interference.

Experimental separation of virtual photon exchange and electron transfer in interatomic coulombic decay of neon dimers

We investigate the interatomic Coulombic decay (ICD) of neon dimers following photoionization with simultaneous excitation of the ionized atom (shakeup) in a multiparticle coincidence experiment. We find that, depending on the parity of the excited state, which determines whether ICD takes place via virtual dipole photon emission or overlap of the wave functions, the decay happens at different internuclear distances, illustrating that nuclear dynamics heavily influence the electronic decay in the neon dimer.

Soft X-ray-Driven Femtosecond Molecular Dynamics

The direct observation of molecular dynamics initiated by x-rays has been hindered to date by the lack of bright femtosecond sources of short-wavelength light. We used soft x-ray beams generated by high-harmonic upconversion of a femtosecond laser to photoionize a nitrogen molecule, creating highly excited molecular cations. A strong infrared pulse was then used to probe the ultrafast electronic and nuclear dynamics as the molecule exploded. We found that substantial fragmentation occurs through an electron-shakeup process, in which a second electron is simultaneously excited during the soft x-ray photoionization process. During fragmentation, the molecular potential seen by the electron changes rapidly from nearly spherically symmetric to a two-center molecular potential. Our approach can capture in real time and with angstrom resolution the influence of ionizing radiation on a range of molecular systems, probing dynamics that are inaccessible with the use of other techniques.

Electron correlation in the GK state of the hydrogen molecule

The second excited (1)Sigma(g)(+) state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the 1s3d configuration of He. At large internuclear distances R, it dissociates to two separated atoms, one in the ground state and another in the 2p excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the K minimum of the potential energy curve. As R>2.0 a.u., a natural orbital of sigma(u) symmetry joins the two natural orbitals of sigma(g) symmetry at smaller R. The average interelectronic distance decreases as the internuclear distance increases from R=2.0 to 3.0 a.u. Around R=3.0 a.u. the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration (1s)(2), where both 1s electrons are on the same nucleus. As the two 1s electrons run into different nuclei, one of the two 1s electrons is promoted to the 2p state, which results in the outer peak in the pair density curve. The Rydberg 1s2p configuration persists as the nuclei stretch, and becomes dominant at large R where four natural orbitals, two of sigma(g) and two of sigma(u) symmetry, become responsible.

Few-photon multiple ionization of ne and ar by strong free-electron-laser pulses

Few-photon multiple ionization of Ne and Ar atoms by strong vacuum ultraviolet laser pulses from the free-electron laser at Hamburg was investigated differentially with the Heidelberg reaction microscope. The light-intensity dependence of Ne2+ production reveals the dominance of nonsequential two-photon double ionization at intensities of I<6x10(12) W/cm2 and significant contributions of three-photon ionization as I increases. Ne2+ recoil-ion-momentum distributions suggest that two electrons absorbing "instantaneously" two photons are ejected most likely into opposite hemispheres with similar energies.

(e,3e) on helium at low impact energy: the strongly correlated three-electron continuum

Double ionization of the helium atom by slow electron impact (E(0)=106 eV) is studied in a kinematically complete experiment. Because of a low excess energy E(exc)=27 eV above the double ionization threshold, a strongly correlated three-electron continuum is realized. This is demonstrated by measuring and calculating the fully differential cross sections for equal energy sharing of the final-state electrons. While the electron emission is dominated by a strong Coulomb repulsion, also signatures of more complex dynamics of the full four-body system are identified.

Triple differential cross sections for the double photoionization of H2

Triple differential cross sections arising from the break up of the H2 molecule by a single photon are presented. The time-dependent close-coupling technique is used to calculate differential cross sections for various geometries. Excellent agreement is found between current work and recent exterior complex-scaling calculations, confirming, for the first time, the absolute magnitude of the triple differential cross sections. Our calculations also compare favorably with recent synchrotron light source measurements.

Role of nuclear motion in double ionization of molecular hydrogen by a single photon

We examine the origin of recently observed variations with internuclear distance (R) of the fully differential cross sections for double ionization of aligned H2 by absorption of a single photon. Using the results of fully converged numerical solutions of the Schrödinger equation, we show that these variations arise primarily from pronounced differences in the R dependence of the parallel and perpendicular components of the ionization amplitude. We also predict that R dependences should be readily observable in the asymmetry parameter for photodouble ionization, even in experimental measurements that are not differential in the energy sharings between ejected photoelectrons.

Interferences from fast electron emission in molecular photoionization

We present a theoretical study of fast-electron emission produced in H2 and H2+ photoionization. We show that, when the electron wave length is comparable to the molecular size, the electron angular distributions arising from fixed-in-space molecules exhibit pronounced interference effects that critically depend on orientation and energy sharing between electrons and nuclei. In particular, for molecules oriented parallel to the polarization direction, the angular patterns reveal a complex nodal structure, while for molecules oriented perpendicularly, typical Young's double-slit interferences are observed. These patterns change dramatically as the molecule vibrates.

Kinematically complete study of dissociative ionization of by ion impact

We present a kinematically complete study of dissociative ionization of D(2) by 13.6 MeV/u S(15+) ions. The experiment allows us to unravel the competing mechanisms, namely, direct single ionization, autoionization of doubly excited states, ionization excitation, and double ionization, and to analyze the corresponding electron angular distribution from fixed-in-space molecules. The conclusions are supported by theoretical calculations in which the correlated motion of all electrons and nuclei and the interferences between them are described from first principles.

Photodouble ionization dynamics for fixed-in-space H2

The Coulomb explosion of the hydrogen molecule, after absorption of a 76 eV photon, has been studied by momentum imaging the two electrons and the two protons. Absolute fully differential cross sections of high statistical quality are obtained. A subset of the overall data, namely, equal electron-energy sharing, is used to investigate the effects of molecular orientation on the photoelectron angular distribution. Departures from the first-order helium-like model are evident in detection geometries where electron-electron correlation is "frozen."

Complete Photo-Induced Breakup of the H 2 Molecule as a Probe of Molecular Electron Correlation

Despite decades of progress in quantum mechanics, electron correlation effects are still only partially understood. Experiments in which both electrons are ejected from an oriented hydrogen molecule by absorption of a single photon have recently demonstrated a puzzling phenomenon: The ejection pattern of the electrons depends sensitively on the bond distance between the two nuclei as they vibrate in their ground state. Here, we report a complete numerical solution of the Schrödinger equation for the double photoionization of H2. The results suggest that the distribution of photoelectrons emitted from aligned molecules reflects electron correlation effects that are purely molecular in origin.