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Highly efficient double ionization of mixed alkali dimers by intermolecular Coulombic decay

Nature Physics (2019) | Download Citation


As opposed to purely molecular systems where electron dynamics proceed only through intramolecular processes, weakly bound complexes such as He droplets offer an environment where local excitations can interact with neighbouring embedded molecules leading to new intermolecular relaxation mechanisms. Here, we report on a new decay mechanism leading to the double ionization of alkali dimers attached to He droplets by intermolecular energy transfer. From the electron spectra, the process is similar to the well-known shake-off mechanism observed in double Auger decay and single-photon double ionization1,2, however, in this case, the process is dominant, occurring with efficiencies equal to, or greater than, single ionization by energy transfer. Although an alkali dimer attached to a He droplet is a model case, the decay mechanism is relevant for any system where the excitation energy of one constituent exceeds the double ionization potential of another neighbouring molecule. The process is, in particular, relevant for biological systems, where radicals and slow electrons are known to cause radiation damage3.


The correlated action of multiple electrons after photon absorption in atomic and molecular systems has led to the discovery of a variety of radiation-induced decay processes (for example multiple excitation and/or ionization or various autoionization channels)1,4,5. When the system complexity is increased to larger, more complex systems, new and diverse intermolecular decay mechanisms open up. In particular, processes such as intermolecular Coulombic decay (ICD)6 where energy is exchanged between electronically excited atoms or molecules and their neighbours have been of broad interest (for reviews, see refs. 7,8). ICD and related intermolecular processes are a potentially important channel for radiation damage of biologically relevant systems9,10. Recently, ICD was measured for the first time in a hydrated biomolecular system11.

Owing to their simple electronic structure and high ionization potential, weakly bound He complexes have served as a model system for studying intermolecular processes such as ICD12,13,14 and electron-transfer-mediated decay15,16. Additionally, He complexes have been used to observe a related type of ICD. In this case, when He droplets17,18 or He–Ne dimers19 are resonantly excited, the energy can be transferred to neighbouring constituents leading to their ionization. An example of such a process is shown in the electron kinetic energy distribution in Fig. 1d for K atoms attached to the surface of He droplets. A photon ( = 21.6 eV) is initially absorbed by a He nanodroplet at the resonance correlating to the 1s2p1P-state of atomic He (ref. 20). Through ultrafast intraband relaxation within the droplet21,22, an excited 1s2s1S He atom (Ee = 20.6 eV) is formed. The excess energy is then transferred by ICD to the K atom leading to its ionization while the He atom relaxes to its ground state. The characteristic electron kinetic energy is the difference between the He excited state and the acceptor’s ionization potential. For the case of K atoms, this results in a kinetic energy of about 16.3 eV, which matches the position of the pronounced peak in the spectrum (black line in Fig. 1d). A question that arises is how the situation changes for systems where double ionization is energetically allowed. For endofullerenes, it has been theoretically proposed that double ICD (dICD) can become a viable decay mechanism23. Here, we show that, indeed, dICD is not only a possible decay path, but can even be the dominant decay mechanism occurring with efficiencies equal to, if not exceeding, single ionization.

Fig. 1: Coincidence spectra for discriminating possible involved decay mechanisms applied while measuring the energetics of the constituent ions and electrons. The ionization process is triggered by energy transfer from the excited 1s2s1S He atom (Ee = 20.6 eV).
Fig. 1

a, Ion–ion coincidence time-of-flight spectrum for K–Rb dimers attached to the surface of He droplets. b, K+, Rb+ and electron VMIs taken in triple (e, 39K, 85Rb) coincidence. The momenta scales are given in atomic units. c, Kinetic energy distributions for K+ (blue line) and Rb+ (grey line) taken in triple (e, 39K, 85Rb) coincidence. d, Electron kinetic energy distributions taken in triple (e, 39K, 85Rb) coincidence (red line) and double (e, 39K) coincidence (black line). Note that the black line in d was a separate measurement where single K atoms were attached to the surface of He droplets. The expected electron kinetic energy from single K atoms is given by a dashed vertical line. The filled lines in c and d correspond to the respective ion and electron kinetic energy distributions for K–Rb dimers calculated from FCF simulations (see text for details).

To gain detailed insight into the process, we investigated alkali dimers, the simplest metal cluster. Furthermore, to circumvent issues with detector dead times, the dimers were composed of alkali atoms of different mass, K and Rb. The process of dICD is schematically shown in Fig. 2 along with the potential energy curves of free K–Rb dimers in the ground 1Σ+ state (black line)24 and dicationic state (red line). The dicationic curve was calculated using a Coulomb potential shifted to match the asymptotic ionization energy of the free atoms, shown as dashed lines in Fig. 2. Similar to the ICD ionization of K atoms described above, dICD occurs by a transfer of energy from the excited 1s2s1S He atom (Ee = 20.6 eV) to the K–Rb dimer. However, in this case, the double ionization potential of the K–Rb dimer is energetically less than the excited He atom, resulting in the emission of two electrons along with the dicationic dissociation of the ions.

Fig. 2: The potential energy curve of K–Rb dimers in the ground (black) and dicationic (red) state.
Fig. 2

The asymptotic limit of the dicationic state is given by the dashed red line along with the individual ionization potentials of K (dashed blue line) and Rb (dashed grey line). A schematic of the process is given where the K–Rb dimer is represented by blue and grey spheres, the He atom by a red sphere, and the He droplet by a yellow sphere. The photon ( = 21.6 eV) is initially absorbed by the He droplet at the 1s2p1P resonance. Through ultrafast intraband relaxation within the droplet21,22, an excited 1s2s1S He atom (Ee = 20.6 eV) is formed. The excess energy is then transferred by dICD to the K–Rb dimer leading to its double ionization while the He atom relaxes to its ground state.

Direct evidence for dICD is thus determined by measuring multiple coincidences of electrons and ions produced by this process. Figure 1a shows the electron–ion–ion coincidence time-of-flight spectrum for K–Rb dimers attached to the surface of He droplets for a photon energy of 21.6 eV. In general, distributions observed in ion–ion coincidence maps identify ions created by multiple ionization while the shape of the distribution gives information about the dissociation process25. In this case, the coincidence map is centred around the respective masses of K and Rb where several sharp, negative sloping features are observed. These distributions indicate that fragmentation occurs through dicationic dissociation of the dimers leading to back-to-back emission of the ions. The primary ion pair originates from dimers of 39K and 85Rb while the neighbouring distributions come from the isotopes, 41K and 87Rb. There are additional, weaker distributions due to complexes of an alkali ion with a few He atoms attached. For cases where the He droplet is not resonantly excited, no such distributions are observed indicating that ionization proceeds through excited He atoms. Additionally, using electron–ion–ion coincidence imaging techniques, one can extract electron/ion kinetic energy spectra from the individual ion pairs in the coincidence map (Fig. 1c,d).

Figure 1b shows the raw velocity map images (VMIs) of ions and electrons measured in triple (e, 39K, 85Rb) coincidence. VMIs are two-dimensional projections of the charged particle’s momentum sphere that are then inverted to obtain kinetic energy distributions for the respective electrons and ions26. The left and middle images show VMIs of K+ and Rb+ ions, and the right image shows the electron VMI. The clearly visible ring structure in all VMIs indicates a non-zero kinetic energy component.

From the VMIs, we determine the kinetic energy distributions by Abel inversion26. Figure 1c shows the ion kinetic energy distributions for the 39K ion (blue line) and 85Rb ion (grey line) measured in triple (e, 39K, 85Rb) coincidence. The ions have broad kinetic energies centred around 3.75 eV and 1.5 eV, respectively. The sum of these energies corresponds to the kinetic energy release of the ion pair in the dicationic state, as illustrated in Fig. 2. To assess this conjecture, we performed Franck–Condon factor (FCF) simulations of the ion and electron kinetic energy distributions assuming vertical transitions between the potential energy curves given in Fig. 2. The initial state is assumed to be an excited He atom in the 1s2s1S-state (Ee = 20.6 eV) interacting with the alkali dimer in its vibronic ground state17,18. The results are shown as filled peaks in Fig. 1c. Note that the 1s2s1S-state of a He atom in a droplet is still dipole-coupled to the ground state20, thereby allowing ICD-like energy transfer to occur. The kinetic energy release from the FCF simulations, shown in Fig. 1c, gives quantitatively similar results to the measured values, but drastically underestimates the width. Broadening of the experimental distributions is likely due to perturbations of the initial and final ionic state by dopant–He droplet interactions. In particular, the transient attachment of the localized excited He atom to the K–Rb dimer may lead to its stabilization. Depending on the configuration of the state, dICD proceeds at different internuclear distances of the K–Rb dimer, resulting in a broader distribution of the fragmented ions.

Figure 1d shows the electron kinetic energy distribution (red line) measured in triple (e, 39K, 85Rb) coincidence. The spectrum shows two peaks centred at 0 eV and 8 eV, which arise from double ionization of alkali dimers. The simulated excess electron energy for double ionization of K–Rb dimers is 8 eV (filled peak in Fig. 1d) fitting well with the sum electron energy. The measured kinetic energy spectrum shows a U-shaped distribution indicating one electron takes nearly all of the excess energy while the second electron is emitted with nearly zero kinetic energy. Similar distributions have previously been observed in single-photon double ionization of atoms (SPDI)2,5 and double Auger decay (DAD)1,27. In those cases, the mechanism, known as shake-off, is due to the sudden removal of the primary electron leaving the system in a perturbed ionic state; the secondary electron then has a probability of relaxing to an unbound state resulting in an unequal sharing of the excess energy. The electron energy distribution in Fig. 1d shows a similar distribution to shake-off, but, in contrast, occurs relatively close to the double ionization threshold. This could, in part, be due to the low ionization potential of the valence electron for alkali atoms. The overall similarity to shake-off indicates that dICD proceeds through a one-step process as opposed to other two-step electron impact ionization mechanisms in SPDI such as knockout2.

We verified dICD for several mixed alkali dimer systems (K–Rb, Na–K, Na–Rb), small homogeneous alkali clusters (Li, Na, K, Rb and Cs), and even alkaline earth atoms (Ba). Figure 3 shows the electron kinetic energy distributions of small, homogeneous clusters of Li, Na, K and Rb attached to the surface of a He droplet. The excited 1s2s1S He atom (Ee = 20.6 eV) triggers the energy transfer process. The black filled lines were taken in double (e, Ak+) coincidence and the red filled lines were taken in triple (e, Ak+, Ak+) coincidence with the alkali metal ions, Ak+, where Ak denotes Li, Na, K, Rb. The red filled lines show electrons emitted from dICD and the black filled lines show electrons emitted from ICD, occurring at higher kinetic energies, as well as dICD. Owing to the comparable electronic structure and ionization potentials of alkali metals, their distributions exhibit similar features. In all cases shown, dICD is a prominent decay channel, leading one to conclude that the process is ubiquitous and not limited specifically to K–Rb dimers where the excited ionic state of Rb could also lead to double ionization through a cascade mechanism. In particular, the asymmetric distribution observed in dICD is evidence of a similar one-step, shake-off-type ionization mechanism.

Fig. 3: Electron kinetic energy distributions from the ionization of small, homogeneous clusters of alkali metals attached to the surface of a He droplet.
Fig. 3

ad, Independent spectra for Li (a), Na (b), K (c) and Rb (d). The black filled lines were taken in double (e, Ak+) coincidence and the red filled lines were taken in triple (e, Ak+, Ak+) coincidence, where Ak are the alkali metals shown in ad. The excited 1s2s1S He atom (Ee = 20.6 eV) triggers the energy transfer process.

Surprisingly, as can be seen in Fig. 3, dICD is a highly efficient process showing comparable, if not larger, ionization rates to ICD. In contrast, for SPDI near threshold, the branching ratio to single ionization is much less than 1% for atoms28 and small molecules29. For DAD, the branching ratio to Auger decay is typically a few per cent for atoms30. As such, one can conclude that dICD can even be the dominant process in weakly bound systems for cases where it is energetically allowed. In general, dICD should not be limited to outer valence shell excited atoms; Auger-forbidden, inner-valence-shell excited/ionized atoms, which have even higher excitation energies, have the potential for dICD as well. Additionally, the multiple ions and electrons formed in the process of dICD should play an important role in biological systems. For instance, core–shell ionization of a solvated magnesium dication leads to a variety of cascade channels where Auger and intermolecular decay processes occur31. For each step where ICD is allowed, dICD could also be an energetically open decay channel leading to an enhancement in the production of neighbouring water ions and low-energy electrons. The subsequent ionization of water typically leads to proton transfer and the formation of the hydroxyl radical, a highly reactive damage centre32, while the production of low-energy electrons is a known source of radiation damage for proteins and DNA3.


Experimental set-up

The experiment was performed using a mobile He droplet machine attached to a velocity map imaging photoelectron photoion coincidence spectrometer33 at the GasPhase beamline of Elettra-Sincrotrone Trieste, Italy. The set-up is described in detail in ref. 18, and only significant points will be addressed here. In short, a beam of He nanodroplets was produced by continuously expanding pressurized He (50 bar) of high purity (He 6.0) out of a cold nozzle (T = 7–40 K) with a diameter of 5 μm into vacuum. Under these expansion conditions, the mean droplet sizes ranged from 101 to 108 He atoms per droplet34. For the current experiment, a droplet size of 50,000 He atoms was used. After passing a skimmer (0.4 mm) and a mechanical beam chopper used for discriminating the droplet beam signal from the He background, the droplets were doped using the ‘pick-up’ technique35 with subsequent heated doping cells filled with alkali metals. While most atomic and molecular species become submerged in the interior of the He nanodroplets, the alkali atoms remain weakly bound on the surface36. The He droplet beam next crosses the synchrotron beam inside of a photoelectron photoion coincidence (PEPICO) detector consisting of an ion time-of-flight detector and velocity map imaging detector (5% ΔE/E resolution). With this set-up, either electron or ion kinetic energy distributions can be recorded, depending on the polarity, in coincidence with one specific ion mass or with several ion masses in multicoincidence mode33. When electrons are recorded on the VMI, only one electron for each coincidence event can be detected. The kinetic energy distributions were reconstructed using the Maximum Entropy Legendre Reconstruction method26. The polarization axis was perpendicular to the VMI axis to ensure cylindrical symmetry that is required for the inversion process. The photon energy was set to 21.6 eV and a tin filter was used to eliminate any higher-order light contamination. The pulse repetition rate was 500 MHz.

FCF simulations of the dicationic dissociation and related ion/electron kinetic energy distributions of alkali dimers created by double ICD on He nanodroplets

The simulation of the kinetic energy distributions of the alkali metal ions K+ and Rb+ generated by dICD and the spectra of emitted electrons is based on the FCF for the vertical bound-continuum transition from the K–Rb dopant ground state 1Σ+ into the doubly ionized state [K–Rb]2+ (Fig. 2):

$$F(V) = \left| {{\int}_0^\infty {\kern 1pt} {\it{\Psi }}_{X,v = 0}(R){\it{\Psi }}^V_{\left[ {{\mathrm{KRb}}} \right]^{2 + }}(R){\mathrm{{d}R}}} \right|^2$$

Here, ΨX,ν=0 is the vibrational wavefunction of the neutral K–Rb dimer, \(\Psi^{V}_{[\rm{KRb}]^{2+}}\) is the continuum wavefunction of the dissociating [KRb]2+ dication at potential energy V, and R is the K–Rb interatomic distance. Owing to the low temperature of the He nanodroplet (0.37 K)34, we assumed K–Rb to be initially prepared in the vibrational ground state (v = 0). Since alkali atoms and small clusters are attached to He nanodroplets in weakly bound surface states36, the perturbation of the intramolecular potential energy curves by the He droplet is neglected in the simulation.

F(V) is calculated numerically using the program BCONT 2.2 (ref. 37). From F(V), we obtained the kinetic energy distribution of the K ionic fragment, \({\rm{P}}_{{\rm{K}}^{+}}({\rm{E}}_{{\rm{K}}^{+}})\), by linear transformation of the argument:

$$P_{{\mathrm{K}}\,^ +\, }(E_{{\mathrm{K}}^+}) = F\,\left[ {\frac{{m_{{\mathrm{Rb}}}}}{{m_{\mathrm{K}} + m_{{\mathrm{Rb}}}}}\left( {V - E(v = 0) - I_{\mathrm{p}}({\mathrm{K}}) - I_{\mathrm{p}}({\mathrm{Rb}})} \right)} \right]$$

where mRb and mK are the respective masses of Rb and K atoms. Here, E(v = 0) = −0.50 eV is the energy of the v = 0 lowest vibrational level in the 1Σ+ state potential of K–Rb (ref. 24) and Ip(K) = 4.34 eV and Ip(Rb) = 4.18 eV denote the ionization energies of K and Rb, respectively. Note the same transformation can be applied to obtain the kinetic energy distribution of the Rb ionic fragment. Assuming maximally unequal energy sharing between the two electrons generated by dICD, the energy distribution of the energetic electron, \(P_{e_{1}}(E_{e_{1}})\), is obtained from:

$$P_{{\rm{e}}_1}(E_{{\rm{e}}_1}) = F\left[ {E_{\rm{e}} - V} \right]$$

Here Ee denotes the energy of the excited 1s2s1S He atom (20.6 eV).

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on request.

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This work was financially supported by the Carl-Zeiss-Stiftung and the Deutsche Forschungsgemeinschaft (project MU 2347/10-1). The authors thank L. Cederbaum, K. Gokhberg, N. Kryzhevoi and N. Berrah for stimulating discussions.

Author information


  1. Physikalisches Institut, Universität Freiburg, Freiburg, Germany

    • A. C. LaForge
    •  & F. Stienkemeier
  2. Department of Physics, University of Connecticut, Storrs, CT, USA

    • A. C. LaForge
  3. Department of Physics and Astronomy, Aarhus University, Aarhus C, Denmark

    • M. Shcherbinin
    •  & M. Mudrich
  4. Elettra-Sincrotrone Trieste, Basovizza, Italy

    • R. Richter
  5. Max-Planck-Institut für Kernphysik, Heidelberg, Germany

    • R. Moshammer
    •  & T. Pfeifer


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A.C.L. and M.M. conceived the experiment. A.C.L., M.S. and R.R. conducted the experiment. A.C.L., M.S. and M.M. analysed the data. M.M. performed the FCF calculations. A.C.L. interpreted the data with help from R.R., F.S., R.M., T.P. and M.M. A.C.L. wrote the paper. All authors reviewed the manuscript.

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The authors declare no competing interests.

Corresponding author

Correspondence to A. C. LaForge.

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