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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 {\deg}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 knock-off type double ionization process. The Coulomb explosion imaging of He_2 provides a direct view of the nuclear wave function of this by far most extended and most diffuse of all naturally existing molecules.

The helium dimer ( 4 He 2 ) is an outstanding example of a fragile molecule whose existence was disputed for a long time because of the very weak interaction potential [1] (see black curve in Fig. 1). Unequivocal experimental evidence for 4 He 2 was first provided in 1994 in diffraction experiments [2] by a nano-structured transmission grating. Subsequently the average dimer bond length and dimer binding energy could be determined to be 52Å and 10 −7 eV (0.9·10 −3 cm −1 or 1.3 mK) [3]. This very large bond length, a factor 100 larger than the hydrogen bond length, goes along with a prediction of very widely delocalized wave function, unseen in any other molecule [4] (see blue function in Fig. 1). It is because of these exotic properties that "as the hydrogen molecule in the past, the helium dimer today became a test case for the development of new computational methods and tools" [5] in quantum chemistry. Despite this fundamental nature of the diffuse helium dimer wave function, it has escaped direct experimental observation until now, as the diffraction grating experiment measure the mean value and not the shape of the wave function itself. Our experiment provides a direct view of this diffuse object.
The large distance between the two helium atoms and the minuscule binding energy make the Helium dimer an unique model system to explore electron correlations over large distances. The most sensitive tool for such studies is multiple photoionization. Since photoabsorption is described by a single electron operator the photon energy and angular momentum is best thought of as being initially given to one electron of the atom only. In the absence of electron correlation the ejection of a single electron would be the only possible outcome of the photoabsorption process. Due to the ubiquity of electron correlation, however, the ejection of electron pairs by a single photon is a wide spread phenomenon seen in atoms [6], molecules [7,8] and solids [9]. This two electron process poses at least two central questions: what is the correlation mechanism by which the photon energy is distributed among the two electrons and over which distance are such correlations active? In the present work we report the surprising observation that a single photon can lead to nonsequential ejection of two electrons from two atoms which are separated by many atomic radii and where the overlap of the electronic wave functions is negligible. By measuring the internuclear distance for each ionization event together with the emitted electron pair, we show that as much as 39.3 eV of energy can be transferred up to a distance of 10Å. The energy is transferred by a type of "interatomic billiard". Our measured angular distributions suggest that primarily one electron absorbs the energy and is ejected from one of the atoms of the dimer. In some cases it is emitted towards the neighboring atom where it transfers part of its energy to a second electron which is knocked off.
A supersonic jet is crossed with a linearly polarized photon beam inside a spectrometer at beamline UE112PGM2 of the BESSY synchrotron.. By means of homogenous electric (E = 12 V/cm) and magnetic fields (B = 10 G) all charged particles created in the reaction are mapped towards two position and time sensitive detectors [13]. By measuring the positions of impact and the times-of-flight of all particles in coincidence the vector momentum of each particle is obtained during offline-analysis. In order to create Helium dimers we have expanded Helium gas through a 5 µm nozzle cooled to a temperature of 18 K. A driving pressure of 1.8 bar and a pressure of 1.2·10 −4 mbar on the low pressure side of the nozzle yielded a dimer fraction of 1-2 % in the gas beam.
If both He atoms of a dimer are ionized the dimer will undergo Coulomb explosion. In that case both He + ions are emitted back-to-back with a momentum of same magnitude. This is a clear signature for the breakup of a dimer, thus reactions of trimers and lager clusters can be excluded from the dataset. In the absence of electron correlation no He + -He + coincidences would be expected. Therefore already the observation of He + -He + coincidences proves experimentally the electron correlation that exists between electrons from the two distant atomic centers of the dimer. It is able to transfer at least 24.59 eV of energy (which equals the ionization energy of Helium) across the bond length of the dimer.
To unravel the energy transfer mechanisms we now examine how the photon energy is distributed among the two electrons and two ions.   [14] or a covalently bound molecule [15], suggesting similar correlation mechanisms to be at work. For the long studied atomic case knock-off and shake-off are the He + He He + He ) of the helium dimer (blue) is spread over a range up to several hundred Angstrom (out of scale). Via photoionization a transition from the ground state (black) to the repulsive potential of two He-ions (red) is possible (path A to B). In the classical reflection approximation, dissociation (path B to C) leads to a certain kinetic energy release (KER) of the two ions. In a quantum mechanical description the one-to-one relation of R and KER along path A-B-C is replaced by the overlap of Ψ i (R) with the final state wave function Ψ KER f (R) (green) for the respective KER.
two well established mechanisms mediating double electron ejection [16][17][18][19]. In the knockoff process the energy is transferred by a binary type collision between the two electrons.
For shake-off the rapid change of the correlated wave function caused by the photo ejection of one electron leads to shake off of the second electron upon the relaxation of this wave function to the new eigenstates of the altered potential. In the case of a knock-off process, the second ionization step can be considered as the impact of a 39.3 eV electron on a single helium atom (compare [19,20]). This (e,2e) type process has been examined in multiple experiments (i.e. [21][22][23]) and is well understood by theory. The dashed line in Fig. 2 shows The angular distribution of the dimer axis with respect to the photon polarization ( Fig.   3a) allows to distinguish between shake-off and knock-off. Shake-off is polarization independent resulting in an isotropic distribution of the ionic fragments in the laboratory frame.
For the knock-off however a simple billiard type scenario suggests that the photoelectron Continuous line: CCC calculation for electron impact ionization (e,2e) of He at 40eV initial energy.
The calculation is integrated over the secondary electron energies at 1, 4, 7.7, 12.7 and 15 eV from [24]. The theory has been mirrored to account for the indistinguishability of the two centers in the helium dimer.
of the He monomer. For the case of ionization of an 1s state as in helium this is a dipolar distribution given by cos 2 (ϑ),where ϑ is the angle between the photoelectron and the polarization axis. The measured experimental angular distribution of the dimer axis ( Fig.   3a) resembles strikingly that distribution and thus gives a clear evidence for the knock-off process ruling out the shake off mechanism.
As we have argued above, the primary photoelectron has to be emitted approximately along the dimer axis to facilitate the knock-off at the neighbor. Thus in the present case the dimer axis is the equivalent to the electron beam axis in the (e,2e) experiment at an atom. We therefore compare angular distributions of the electron with the dimer axis in the present experiment with the electron angular distribution with respect to the beam axis in the (e,2e) case (Fig. 3b). As it is not possible to distinguish from which atomic center the photoelectron is emitted, the intensities I(θ) and I(180-θ) add. Hence the data of the CCC calculation [24] for the (e,2e) collision with He has been mirrored accordantly. The theory (line in Fig. 3b) is in excellent agreement with the measured distribution.
Our identification of the knock-off mechanism as being responsible for the observed single photon double ionization is hence supported by three independent experimental observables: the energy sharing between the electrons, the angular distribution of the molecular axis and the angular distribution of the electrons with respect to the molecular axis.
We now use this knowledge of the correlation mechanism and the measured coulomb The classical physics reflection approximation [7,25] is successfully used e.g. in Coulomb explosion imaging in ion beams [26] and strong laser fields [27].
Quantum mechanically the classical relationship KER = 1/R has to be replaced by the overlap of the bound initial state wave function Ψ i (R) of the dimer with the continuum wave function Ψ f KER (R) for the respective KER (see Fig. 1). The probability distribution P(KER) is then given by: Since the second (target) atom can only be ionized if the photoelectron is emitted within a certain solid angle, the knock-off correlation mechanism underlies a classical 1/R 2 depen- dency. In the quantum treatment accordingly a geometrical factor 1/R has to be inserted to the integral of eq. 1. Classical and quantum sampling of the ground state wave function are shown by the blue and red line in Fig. 4. While the classical approximation introduces only a small error when the reflecting potential is very steep and the initial state is confined to a narrow region of R as in covalently bound molecules [7] the extreme dimensions of the Helium dimer require the full quantum treatment. The good agreement of the present coulomb explosion data with the full quantum calculation confirms the unique delocalized character of the He 2 wave function as predicted by theory. Our experiment samples this wave function in the region of approximately 2.5-10 Angstrom. We note that the typical confined gaussian wave function of all standard ground state molecules and also of all other van-der-Waals Systems would lead to a near gaussian peak in the KER. For comparison singly photon double ionization of neon dimers leads to a near Gaussian peak as narrow as ∆E/E= 0.2 peaked at 4.4 eV. The differences between classical and quantum calculation is negligible in Ne 2 (see dotted lines in Fig 4).
In conclusion we have observed the electron correlation mediated direct ejection of two electrons from two distant sites upon absorption of a single photon. The underlying mechanism of a knock-off type process which has its analogy in double ionization of atoms. For the extreme conditions of the helium dimer the knock off can be split into a photoionization at one center (the photoelectron gun) followed by an e,2e collision at the neighbor. This e,2e collision occurs in the static field of the neighboring coulomb charge, which can be controlled by the internuclear distance. This distance also controls the phase of the photoelectron as it hits the neutral. With very strong external field and phase, two new control parameters are introduced in e,2e. The influence of these parameters escaped observation and also theoretical attention so far. It is related to the rescattering process in a strong laserfield, where the intermediate electron is additionally driven by the field.
We want to thank the staff of BESSY II for experimental support. This work was funded by the Koselleck project of the Deutsche Forschungsgemeinschaft. R. E. G. and M. K. acknowledge support by the Helmholtz society, grant VH-NG-331. We acknowledge helpful discussions with Igor Bray.