Inelastic scattering of photoelectrons from He nanodroplets
M. V. Shcherbinin, F. Vad Westergaard, M. Hanif, S. R. Krishnan, A. C. LaForge, R. Richter, T. Pfeifer, M. Mudrich
IInelastic scattering of photoelectrons from He nanodroplets
M. V. Shcherbinin , F. Vad Westergaard , M. Hanif , S. R.Krishnan , A. C. LaForge , R. Richter , T. Pfeifer , and M. Mudrich Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark Department of Physics, Indian Institute of Technology, Madras, Chennai 600 036, India Department of Physics, University of Connecticut, Storrs, Connecticut, 06269, USA Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy and Max-Planck-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany (Dated: December 20, 2018)We present a detailed study of inelastic energy-loss collisions of photoelectrons emitted from Henanodroplets by tunable extreme ultraviolet (XUV) radiation. Using coincidence imaging detectionof electrons and ions, we probe the lowest He droplet excited states up to the electron impactionization threshold. We find significant signal contributions from photoelectrons emitted fromfree He atoms accompanying the He nanodroplet beam. Furthermore, signal contributions fromphotoionization and electron impact excitation/ionization occurring in pairs of nearest-neighboratoms in the He droplets are detected. This work highlights the importance of inelastic electronscattering in the interaction of nanoparticles with XUV radiation.
I. INTRODUCTION
Energetic electrons created inside a condensed phasesystem primarily interact with the individual atoms ofthat substance and their scattering can be predicted quiteaccurately. In contrast, low-energy electrons interactwith the whole molecular network, and their scatteringis currently too complex to make accurate predictions.In particular, inelastic and elastic scattering of slow elec-trons in water is lacking a complete understanding [1].Therefore, precise measurements using simple model sys-tems can add to the fundamental understanding of elec-tron scattering in the condensed phase. Here, we presentexperiments with helium (He) nanodroplets which fea-ture (i) an extremely simple electronic structure of the Heconstituent atoms, (ii) a homogeneous, superfluid den-sity distribution [2, 3], and (iii) a high electrophobicity,which facilitates the emission of slow electrons out of thedroplets and thus allows for their sensitive detection.He nanodroplets are commonly regarded as “idealspectroscopic matrices” providing a transparent, cold,and weakly perturbing environment for the spectroscopyof embedded molecular species [3, 4]. They can be seenas flying nano-cryostats in which individual moleculesare isolated and cooled upon pickup of a single moleculeper droplet. When doping two or more molecules perdroplet at elevated vapor pressure of the dopant species,aggregation into ultracold complexes with sometimes un-usual configurations occurs [5–7]. Thus, applying ad-vanced spectroscopic techniques to dopants inside Henanodroplets may open new ways of probing the struc-ture and dynamics of unconventional molecular com-plexes and nanoparticles [8–11].While photoionization combined with ion detection hasproven to be a useful technique to probe neutral andcationic molecules [12–17], the powerful technique of pho-toelectron spectroscopy is less established. Most pho-toelectron studies have been carried out using resonanttwo-photon ionization by nanosecond laser pulses, where local rearrangement of the He solvation shell around theintermediate excited dopant may impact the spectra [18–22]. A few studies of photoelectron spectra using one-photon ionization by XUV radiation have been reportedfor pure [23–26] and doped He droplets [27–30]. However,in the latter case, dopants were ionized indirectly eitherby Penning ionization or by charge transfer from ionizedHe nanodroplets. Therefore, no information about thedopants was extracted from the measured electron spec-tra.One difficulty in performing ultraviolet photoelectronspectroscopy (UPS) or even x-ray photoelectron spec-troscopy (XPS) of doped He nanodroplets is that theemitted photoelectrons interact with the He matrix ontheir way from the photoionized dopant to the detec-tor. This can lead to unwanted loss of angular infor-mation (anisotropy), to distortions of the electron spec-tra, or even to electron-ion recombination. Note thatHe droplets are even capable of trapping electrons whenbombarding the droplets with electrons of several eV ofkinetic energy [31]. Anionic He droplets as well as anionicatomic and molecular He ions are also detected at elec-tron impact energies around 22 and 44 eV [32]. At theseenergies, the impinging electron excites one or even twoHe atoms inside the droplet and subsequently attachesto one excited He ∗ atom. Similarly, by photoionizing Hedroplets at photon energies hν >
44 eV, we have pre-viously found indications that the photoelectron under-goes inelastic collisions with the He thereby losing around22 eV of kinetic energy [24]. In contrast, the spectra ofelectrons originating from ionization and correlated de-cay processes revealed only weak perturbations by the Hedroplets [26]. The present study is devoted to inelasticscattering of photoelectrons with He nanodroplets. Weresolve individual components of the electron energy-lossspectra measured at various photon energies. From theanalysis of peak positions and amplitudes, we infer vari-ous inelastic scattering scenarios. a r X i v : . [ phy s i c s . a t m - c l u s ] D ec II. METHODS
The experiments are performed using a He nan-odroplet apparatus combined with a velocity map imag-ing photoelectron-photoion coincidence (VMI-PEPICO)detector at the GasPhase beamline of Elettra-SincrotroneTrieste, Italy. The apparatus has been described in detailelsewhere [24, 28]. Briefly, a beam of He nanodropletsis produced by continuously expanding pressurized He(50 bar) of high purity out of a cold nozzle (10-28 K)with a diameter of 5 µ m into vacuum. At these expan-sion conditions, the mean droplet sizes range between (cid:104) N (cid:105) = 700 and ∼ × He atoms per droplet. Fur-ther downstream, the beam passes a mechanical beamchopper used for discriminating droplet-beam correlatedsignals from the background.In the detector chamber, the He droplet beam crossesthe synchrotron beam perpendicularly in the center of theVMI-PEPICO detector. By detecting either electrons orions with the VMI detector in coincidence with the corre-sponding particles of opposite charge on the TOF detec-tor, we obtain either ion mass-correlated electron VMIsor mass-selected ion VMIs. Kinetic energy distributionsof electrons or ions are obtained from the VMIs by Abelinversion [33]. The energy resolution of the electron spec-tra obtained in this way is ∆
E/E (cid:38) hν = 44-64 eV. Ion mass distributions from the He droplet beamrecorded at these photon energies contain a series of clus-ter masses He + n , n = 1 , , . . . ; but by far the mostabundant fragments are He + and He +2 [24]. All electronand ion spectra discussed in this work are measured ata He nozzle temperature of T = 14 K which correspondsto a mean number of atoms per droplet of N = 23 , III. RESULTS AND DISCUSSION
Photoelectron spectra and photoelectron angular dis-tributions of He nanodroplets near the ionization thresh-old have been studied before [23, 24, 34]. In the exper-iment using PEPICO-VMI recorded in coincidence withHe + , both the electron energy and the anisotropy wasfound to match that of the free He atom ( β = 2) [24].In contrast, electrons measured in coincidence with He +2 were slightly upshifted in energy and their anisotropy wasreduced to β ≈
1. Therefore, we concluded that He + ionscreated near the ionization threshold predominantly orig-inate from free He atoms accompanying the He dropletbeam, whereas He +2 and larger molecular ions He + n , n > hν (cid:38)
44 eV, ad-ditional peaks and broad features appear in the electronspectra which are shifted to lower energies by (cid:38) . Inelastic / direct
D r o p l e t r a d i u s ( n m )
E l e c t r o n e n e r g y ( e V )
Droplet corr. electrons (arb. units)
T [ K ] / R [ n m ] 1 2 / 1 8 1 3 . 5 / 1 0 1 5 / 4 . 7 1 9 / 3 . 7 2 1 . 5 / 3 . 1 2 4 / 2 . 5 2 8 / 2 . 0
Figure 1. Spectra of total electrons emitted from He nan-odroplets at a photon energy hν = 55 eV. The mean size ofthe droplets is varied by changing the temperature of the Henozzle. The inset shows the ratio of integrals over the low-energy peak (inelastic scattering) vs. the high-energy peak(direct photoemission). continuum. The fraction of inelastically scattered elec-trons with respect to those emitted directly with a ki-netic energy around hν − E i rises from 0 up to > R of the He droplets is increased from2 to about 20 nm by lowering the temperature of theHe nozzle from 28 to 12 K, see inset in Fig. 1. Here, E i = 24 .
59 eV is the atomic ionization energy of He.The red line depicts the estimated fraction of inelasticcollisions, exp( σn He R ) −
1. Here, σ = 0 .
29 ˚A is the to-tal inelastic collision cross section at hν = 55 eV [35], and n He = 0 . − is the density of He atoms in He nan-odroplets [2]. The reasonable agreement of our simple es-timate with the experimental data confirms our interpre-tation. Accordingly, the mean free path of electrons witha kinetic energy of hν − E i = 30 .
41 eV in He nanodropletsdue to inelastic scattering is 1 / ( σn He ) = 15 . >
100 nm(not shown), this ratio of inelastic collisions versus di-rectly emitted electrons further rises to >
10, but an ad-ditional feature eventually dominates the electron spec-trum which will be discussed elsewhere.
A. Electron energy-loss spectra
Typical raw spectra recorded at higher resolution andin coincidence with He + and He +2 are shown in Fig. 2a) and b), respectively. The photon energy is set to hν = 51 eV. In accordance with our previous interpreta-tion, we attribute those electrons detected in coincidencewith He + atomic ions to photoionization of mainly freeHe atoms. The fact that very similar electron energy lossspectra are measured in coincidence with He + and He +2 ions indicates that electrons are emitted from the free Heatoms in the vicinity of the He droplets where they scat- Electron yield (arb. units)
E x p e r i m e n t a l d a t a 1 s 2 s 2 S 1 s 2 p P 1 s 2 p P 1 s 2 s S H e * - H e + (cid:1) u H e * - H e + (cid:1) g 1 s 3 s P i o n i z a t i o n a ) H e + b ) H e +2 E l e c t r o n k i n e t i c e n e r g y ( e V )
Figure 2. Photoelectron spectra recorded in coincidencewith He + and He +2 ions at a photon energy hν = 51 eV. Onlythe low-energy part is shown, where a multi-peak structureis generated by inelastic scattering of the primary photoelec-tron with He atoms thereby exciting them into various excitedstates. ter inelastically. This interpretation is supported by thedependence of the yield of inelastically scattered elec-trons detected in coincidence with He + in proportionto those detected in coincidence with He +2 , depicted inFig. 3. As the temperature of the He nozzle is increasedfrom 12 to 22 K and thus the mean droplet size decreasesfrom about 1 . × to 2,700 He atoms per He droplet,the ratio of inelastically scattered electrons (integral overelectron spectra from 0 to 8 eV) in coincidence with He + versus He +2 rises by nearly a factor of 2.The smooth bell shaped curves in Fig. 2 depict gaus-sian functions which are simultaneously fitted to the ex-perimental spectrum. Due to the limited quality of theexperimental data, only 8 peaks can be identified withhigh confidence. We attribute them to the lowest ex-cited states 1s2s S up to 1s3p P as well as the ionizationcontinuum. As these states have the highest impact exci-tation cross sections [35], they are expected to dominatethe spectrum. From the peak positions of the fit curves,we infer the energy loss which equals the excitation en-ergy of the respective state (see legend). The peak inte-grals correspond to the relative probabilities of excitingthe various states by electron impact, see Sec. III C.The broad feature in Fig. 2 b) reaching from zero up to3.5 eV electron energy is due to electrons created by elec-tron impact ionization of He. The flat structure of thisfeature indicates that the energy is shared between thetwo electrons according to a uniform distribution func-tion, in accordance with previous findings [36]. Note thatin our experiment, we detect only one of the two elec-trons due to the finite deadtime of the detector. While Scattered photoelectrons He+ / He2+
D r o p l e t s i z e ( a t o m s p e r d r o p l e t )N o z z l e t e m p e r a t u r e ( K )
Figure 3. Ratio of inelastically scattered electrons detectedin coincidence with He + versus He +2 as a function of the Henozzle temperature (bottom axis) which controls the He nan-odroplet size (top axis). the peaks in Fig. 2 a) and b), corresponding to excitedstates, are similar in positions and amplitudes, the distri-bution assigned to impact ionization is more pronouncedin the coincidence measurement with He +2 .Another significant difference between the spectra incoincidence with He + and with He +2 is the occurrence oftwo small peaks at an electron energy between 7 and 8 eVin the He + electron spectrum [Fig. 2 a)], not present inthe He +2 electron spectrum. These peaks are present inall He + -correlated spectra except for those recorded atexpansion conditions when large He droplets ( N > )are formed (nozzle temperature T <
14 K).To get an overview of the results at all measured pho-ton energies ranging from 44 up to 56 eV, we plot in Fig. 4the energies of the He states excited by electron impact, E ∗ = hν − E i − E p , obtained from the fitted peak posi-tions E p . The error bars indicate the widths of the fittedpeaks (standard deviation). The choice of the atomicionization energy as the value of E i is well justified whenanalyzing the He + coincidence electron spectra which areprimarily due to photoionization of free He atoms. As forthe He +2 coincidence data, the corresponding value of E i may be slightly reduced by about 0.1 eV as observed inphotoelectron spectra recorded near-threshold [24, 34].However, for the sake of consistency with the represen-tation of the He + data, and since the shift of E i is smallcompared to the resolution of our spectrometer, we usethe same value E i = 24 .
59 throughout.The horizontal dashed lines in Fig. 4 represent the Heexcited state energies E ∗ for the He atomic values E p [37].The slanted dashed lines tangent to the onset of the datapoints at low photon energies represent the highest pos-sible energy that the primary photoelectron can transferby exciting a He atom, hν − E i . The slanted dashed ( a ) H e + P h o t o n e n e r g y ( e V )
Excitation energy (eV) S 1 s 2 s S 1 s 2 p P 1 s 2 p P H e * + H e + (cid:1) u H e * + H e + (cid:1) g 1 s 3 s S i o n i z a t i o n h (cid:1) -E i He h (cid:1) -E i He ( b ) H e +2 Figure 4. Compilation of the fitted peak positions E p inelectron spectra recorded in coincidence with He + a) and withHe +2 b) as a function of the photon energy hν . The results arerepresented as energies of the He states excited by electronimpact, E ∗ = hν − E i − E p , where E i denotes the atomicionization energy of He. lines that nearly match the fitted positions of the broadimpact ionization feature represents the linear function hν − E i /
2, that is the expected energy of electrons cre-ated by impact ionization when assuming equal energysharing between the two electrons.Overall we find a good correspondence between the + (cid:1) +u H e * + H e + (cid:1) +g H e + H e + A (cid:1) +g H e + H e + X (cid:1) +u H e + H e
Potential energy (eV)
I n t e r a t o m i c d i s t a n c e ( Å ) H e + + H e + Figure 5. Selected potential energy curves for the He ground state up to the doubly ionized state He + +He + , takenfrom [41, 42]. The thick vertical dashed line indicates theaverage distance between He atoms inside He nanodroplets. fitted peak energies and the literature values [37]. How-ever, the experimental atomic excitation energies are sys-tematically up-shifted in energy by 0.2-1 eV, where thehigher excited states are up-shifted more than the lowestHe excited state 1s2s S. We attribute this up-shifting tothe repulsive interaction of He ∗ excited atoms (assum-ing prompt localization of the excitation on one atom)with the surrounding ground state He atoms inside theHe nanodroplet. This concept is commonly adoptedto explain the broad, blue-shifted features in photoab-sorption spectra of He nanodroplets [38–40]. For thehigher excitations into 1s n(cid:96) -states with principal quan-tum number n = 3 , (cid:96) = 0 , ,
2, even the ejec-tion of free Rydberg atoms was observed [40]. In ourexperiment we find an average up-shift of the excita-tion energy of the 1s2p P-state of ∆ E P = 0 . ± . S and 1s2p Pto ∆ E S = 0 . ± . E P = 0 . ± . . ± . S and 1s2p , P), 0 . ± . S) to 1 . ± . P). The peak widths forthe optically allowed states are in good agreement withthose measured by photoabsorption spectroscopy.
B. Nearest-neighbor excitation and ionization byelectron collision
In addition to the peaks corresponding to atomic exci-tations of He, we find two small peaks at energies about1 eV below the lowest excited atomic level 1s2s S in theHe + coincidence spectra [Fig. 2 a)]. How can an electronlose less energy than the lowest He excitation in an inelas-tic collision with a He nanodroplet? We have mentionedthat the presence of neutral He atoms around the impact-excited He atom can only cause an up-shift of the energyof the low-lying levels. The interpretation we propose isbased on the peculiar shape of potential curves for a pairof He atoms where one is excited and the other is ion-ized, see the green and blue lines in Fig. 5. In the rangeof most probable He-He interatomic distances inside Henanodroplets, around 3.6 ˚A [34], the lowest two potentialcurves 2 Σ + g,u correlating to the pair of atoms He ∗ +He + feature a shallow well with a depth of 0.6 and 1.0 eV withrespect to the He ∗ (1s2s S)+He + atomic asymptote, re-spectively. Thus, we assume that the primary photoelec-tron undergoes an inelastic collision with a neighboringHe atom whose excitation energy is down-shifted by thepresence of the nearby photoion. We mention that thisprocess resembles the well-known shake-up and knock-up processes in an atom or a molecule, where an electronis emitted by the absorption of an energetic photon andsimultaneously the remaining photoion is electronicallyexcited [43]. Shake-up, which is driven by electron cor-relation, is less likely to play a role here given the largedistance between two He atoms [44]. However, we can-not exclude its contribution to the measured signal giventhat more than one atom surrounds the ionization centerwhich may lead to a collective enhancement.According to our interpretation of the two additionalpeaks in terms of He ∗ +He + molecular excitations, wehave added dashed horizontal lines at excitation energiesof 18.8 and 19.2 eV in Fig. 4 a). The good agreementof these values with the experimental peak energies con-firms our model. The missing up-shift for these states isdue to the fact that now the nearest neighbor of the He ∗ is the He + photoion which down-shifts the level. This isin contrast to the more frequent cases where the photoionis at some distance away from the He ∗ , and the nearestneighbor to the He ∗ is a neutral He atom causing anup-shift of the He ∗ level, as discussed above. Note thatthere may be more down-shifted features due to molec-ular excitations correlating to the higher-lying excitedatomic levels superimposing on the electron energy-lossspectrum. However, given their low relative amplitudesand the limited quality of our data, we cannot unambigu-ously identify any.But why are the two He ∗ -He + molecular featuresobserved only in coincidence with He + atomic ions?Clearly, the combined process of photoionization andscattering on the next neighbor occurs inside the dropletswhere we expect He +2 and larger He cationic clustersto form. Note that the penetration depth of the XUV (cid:1) = ( a ) H e + Ion signal (arb. units)
I o n k i n e t i c e n e r g y ( e V ) h (cid:1) = ( b ) H e +2 Figure 6. He + (a) and He +2 (b) ion kinetic energy distribu-tions recorded at various photon energies. photons 1 / ( σ abs n He ) (cid:38) σ abs = 0 . .
012 ˚A is the photoionization cross sec-tion of He in the photon energy range 44-64 eV [45]. Ourspeculative explanation is that the bound He ∗ -He + pairof atoms is expelled towards the He droplet surface whereit decays into an unbound pair of atoms He+He + . In thebound excited state, the excited electron is delocalizedover the two He atoms and therefore the system repre-sents a vibronically excited molecular ion. Vibrationallyexcited [15, 46] as well as electronically excited molecu-lar ions [47] and even excited atomic ions [48] have beenfound to be efficiently ejected out of He nanodropletsby a nonthermal, impulsive process. The He ∗ -He + sys-tem either detaches from the droplet, or it stays veryweakly bound at the surface until it radiatively decaysinto an unbound pair of atoms He+He + with an inter-atomic spacing around 4 ˚A given by the minima of thepotential wells (green and blue curves in Fig. 5). Ourobservation of the disappearance of the He ∗ -He + molec-ular features for large He droplets is in line with previousobservations of reduced ion yields for larger droplets [15].Our interpretation in terms of inelastic scattering ofthe photoelectron with a He atom next to the atomfrom which it is emitted inside the droplet is supportedby measurements of the He + and He +2 ion kinetic en-ergy distributions, shown in Fig. 6 a) and b), respec-tively. In these experiments the He nozzle temperaturewas set to 16 K which corresponds to a mean num-ber of He atoms per droplet of 5,500. At photon en-ergies below the threshold for electron inelastic scatter-ing, hν = 44 eV, He + ions predominantly have low ki-netic energies < . +2 cations are distributed around 0.15 eV with the high-est energies reaching up to about 1 eV. The more ex-tended low-energy distribution for He +2 ions as comparedto He + is due to nonthermal ejection of vibrationally ex-cited He +2 [15, 49]. At hν = 50 eV, where various electronimpact excitation channels open up, the He + and He +2 ion kinetic energy distributions are nearly unchanged. Incontrast, at hν = 55 and 64 eV, where electron impactionization is the dominant channel, the ion kinetic en-ergy distributions qualitatively change; a second maxi-mum appears as a shoulder in the ion spectrum of He + which is peaked around 0.7 eV and reaches up to about2.7 eV. Similarly, the He +2 spectrum develops a shoulderpeaked around 0.6 eV which extends up to about 1.7 eV.The higher kinetic-energy component of the ion energydistributions associated with electron impact ionizationresults from Coulomb explosion of pairs of ions createdat relatively short distance. This is no surprise given therelatively large ionization cross section σ i = 0 .
15 ˚A at hν = 64 eV [35], which yields a probability of electronscattering with a neighboring He atom in a droplet ata distance of d = 3 . − exp( − σ i n He d ) = 1 . + ion of about 2 eV when assuming binarydissociation.The experimental higher kinetic-energy shoulder in theHe + distribution at hν = 64 eV contains 50 % of thetotal signal (25 % at hν = 55 eV) and spans the wideenergy range 0.35 - 2.7 eV. How can we rationalize thisfinding? The high-energy edge (2.7 eV) matches wellthe maximum energy that a He + ions can acquire whenCoulomb explosion starts at the minimum distance be-tween nearst neighbors (2.4 ˚A) [34]. The low-energy on-set (0.35 eV) corresponds to a distance between He + ionsof about 20 ˚A, which roughly coincides with the meanHe nanodroplet radius (32 ˚A). Thus, it seems that allelectron-impact ionization events contribute to the shoul-der structure in the He + energy distribution. Consider-ing that scattering of the photoelectron with any atom inthe entire He droplet may occur, we set d = 32 ˚A and ob-tain an estimated scattering probability of 20 %, whichcomes close to the experimental value. As in the caseof electron-impact excitation of a neighboring atom dis-cussed above, a correlated or even collective one-photondouble ionization process akin to shake-off [50] may en-hance the signal amplitude.The shape of the shoulder distribution is given by thedistribution function of distances at which impact ion- ization occurs. In addition, collisions of the acceleratedions with neighboring He atoms on their way out of thedroplet likely cause a shift towards lower energies. Suchelastic ion-atom collisions have recently been observedfor pairs of ions created by interatomic Coulombic decay(ICD) inside He droplets at an even shorter distance [26].When an ion collides elastically with a neighboring Heatom it can lose all of its kinetic energy (head-on col-lision), in which case Coulomb explosion restarts at alarger distance and the final kinetic energy is reduced.An accurate modeling of the measured ion kinetic energydistributions would require a three-dimensional scatter-ing simulation, which goes beyond the scope of this pa-per, though. C. Electron impact cross sections
Finally, we inspect the relative intensities of the var-ious inelastic electron scattering channels as a functionof photon energy. Fig. 7 displays the integrals over in-dividual fitted peaks in the electron spectra recorded incoincidence with He + (a) and with He +2 (b). For compar-ison, the theoretical results by Ralchenko [35] is shown inpanel c). In the range 46 ≤ hν ≤
51 eV the order of theexperimental peak integrals roughly matches that of thetheoretical cross section. Thus, 1s2s S excitation is mostprobable, whereas 1s2p P is least. At hν >
51 eV, thepeak integrals are of similar order of magnitude, whichagrees with the theoretical cross sections.Likewise, the predicted pronounced rise of the crosssection for impact ionization for hν > . +2 .In the He + coincidence spectra, the impact ionizationsignals are slightly underrepresented with respect to theimpact excitation channels. Given that the ratio of de-tected He + ions and coincident electrons as compared toHe +2 ions is only 0.23, the overall agreement of the mea-sured peak integrals with the theoretical cross sectionsis satisfactory. This indicates that electron impact exci-tation and ionization proceed essentially with the sameprobabilities in He droplet as in free He atoms. IV. CONCLUSION
When He nanodroplets are irradiated by XUV lightat hν (cid:38)
44 eV, emitted photoelectrons undergo inelas-tic collisions with He atoms in the nanodroplets. Thefraction of scattered electrons can exceed that of directlyemitted electrons when the droplets grow large with radii (cid:38)
20 nm. The amplitudes of the individual inelasticchannels (excited states of He, ionization) roughly agreewith theoretical predictions for the He atom.Previously, we had concluded that photoionizationevents occurring inside the droplets mostly generate He +2 molecules and larger clusters in a process labeled by (1)in Fig. 8. In contrast, He + ions mostly originate from Cross section (Å2)Peak integral (arb. units)
P h o t o n e n e r g y ( e V ) S 1 s 2 s S 1 s 2 p P 1 s 2 p P H e * - H e + (cid:1) g H e * - H e + (cid:1) u 1 s 3 s S i o n i z a t i o n a ) H e + c ) T h e o r yb ) H e +2 Figure 7. Integrals of the fitted peaks in the electron spectrarecorded in coincidence with He + and He +2 [a) and b), respec-tively]. Panel c) shows the cross sections for electron impactexcitation and ionization of various states of He extractedfrom Ref. [35]. photoionization of free He atoms that accompany the Hedroplet beam, see process (2). However, when photoion-ization takes place inside the droplet and the photoelec-tron scatters off a He atom in the close vicinity of the pho-toion, He + ions and correlated electrons originating frominside the He droplets can be detected as well. In thecase that the next neighbor is excited into low-lying lev-els by collision with the photoelectron, a transient boundHe ∗ -He + molecular state is populated [process (3)]. Thisis seen as two small peaks in the electron spectrum corre-sponding to excited levels lying below the lowest excitedstate of the He atom. In case that the next neighbor is impact ionized, the two He + ions undergo Coulomb ex-plosion and both He + and He +2 ions are detected withhigher kinetic energy of up to 3 eV [process (4)]. Thus, e - e - e - e - hν * e - Figure 8. Schematic representation of four possible photoion-ization and electron-He inelastic scattering processes occur-ring upon photoionization of He nanodroplets at hν >
44 eV.Excited He ∗ atoms are marked by stars, He + ions are shownas circles containing crosses. See text for details. the two processes (3) and (4) are the pertinent new fea-tures related to He nanodroplets. The possibiliy thatcorrelated or even collective effects contribute to the am-plitudes of these processes is an intriguing thought thathopefully incites theoreticians to investigate this system.These results add to the fundamental understandingof the interaction of relatively low-energy electrons withcondensed phase systems. Electron scattering in biolog-ical matter plays a crucial role in radiation biology andDNA damage [51]. Besides, our findings show that elec-tron scattering may impose severe limitations for the useof He nanodroplets as a substrate for photoelectron spec-troscopy of embedded molecules and complexes when us-ing XUV or x-ray radiation. In a forthcoming study, wewill discuss the importance of elastic scattering of elec-trons created inside large He nanodroplets. ACKNOWLEDGMENTS
M.M. acknowledges financial support by DeutscheForschungsgemeinschaft (project MU 2347/10-1) andby Aarhus Universitets Forskningsfond (AUFF). A.C.Lgratefully acknowledges the support by Carl-Zeiss-Stiftung. S.R.K. thanks DST, Govt. of India, for sup-port.” [1] E. Alizadeh, T. M. Orlando, and L. Sanche, AnnualReview of Physical Chemistry , 379 (2015). [2] J. Harms, J. P. Toennies, and F. Dalfovo, Phys. Rev. B , 3341 (1998).[3] J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. , 2622 (2004).[4] F. Stienkemeier and K. Lehmann, J. Phys. B , R127(2006).[5] K. Nauta and R. E. Miller, Science , 1895 (1999).[6] K. Nauta and R. E. Miller, Science , 293 (2000).[7] A. Przystawik, S. G¨ode, T. D¨oppner, J. Tiggesb¨aumker,and K.-H. Meiwes-Broer, Phys. Rev. A , 021202(2008).[8] S. M¨uller, S. Krapf, T. Koslowski, M. Mudrich, andF. Stienkemeier, Phys. Rev. Lett. , 183401 (2009).[9] S. G¨ode, R. Irsig, J. Tiggesb¨aumker, and K.-H. Meiwes-Broer, New J. Phys. , 015026 (2013).[10] P. Thaler, A. Volk, D. Knez, F. Lackner, G. Haberfehlner,J. Steurer, M. Schnedlitz, and W. E. Ernst, J. Chem.Phys. , 134201 (2015).[11] L. Bruder, U. Bangert, M. Binz, D. Uhl, R. Vexiau,N. Bouloufa-Maafa, O. Dulieu, and F. Stienkemeier, Na-ture Comm. , 4823 (2018).[12] M. Mudrich, O. B¨unermann, F. Stienkemeier, O. Dulieu,and M. Weidem¨uller, Eur. Phys. J. D , 291 (2004).[13] A. Przystawik, P. Radcliffe, S. G¨ode, K. H. Meiwes-Broer, and J. Tiggesb¨aumker, J. Phys. B , S1183(2006).[14] E. Loginov, A. Braun, and M. Drabbels, Phys. Chem.Chem. Phys. , 6107 (2008).[15] S. Smolarek, N. B. Brauer, W. J. Buma, andM. Drabbels, J. Am. Chem. Soc. , 14086 (2010).[16] F. Lackner, G. Krois, T. Buchsteiner, J. V. Pototschnig,and W. E. Ernst, Phys. Rev. Lett. , 153001 (2014).[17] M. Mudrich and F. Stienkemeier, Int. Rev. Phys. Chem. , 301 (2014).[18] P. Radcliffe, A. Przystawik, T. Diederich, T. D¨oppner,J. Tiggesb¨aumker, and K.-H. Meiwes-Broer, Phys. Rev.Lett. , 173403 (2004).[19] E. Loginov, D. Rossi, and M. Drabbels, Phys. Rev. Lett. , 163401 (2005).[20] D. S. Peterka, J. H. Kim, C. C. Wang, and D. M. Neu-mark, J. Phys. Chem. B , 19945 (2006).[21] A. Przystawik, P. Radcliffe, T. Diederich, T. D¨oppner,J. Tiggesb¨aumker, and K.-H. Meiwes-Broer, J. Chem.Phys. , 184306 (2007).[22] J. von Vangerow, A. Sieg, F. Stienkemeier, M. Mudrich,A. Leal, D. Mateo, A. Hernando, M. Barranco, andM. Pi, J. Phys. Chem. A , 6604 (2014).[23] D. S. Peterka, A. Lindinger, L. Poisson, M. Ahmed, andD. M. Neumark, Phys. Rev. Lett. , 043401 (2003).[24] D. Buchta, S. R. Krishnan, N. B. Brauer, M. Drabbels,P. O’Keeffe, M. Devetta, M. Di Fraia, C. Callegari,R. Richter, M. Coreno, K. C. Prince, F. Stienkemeier,J. Ullrich, R. Moshammer, and M. Mudrich, J. Chem.Phys. , 084301 (2013).[25] M. P. Ziemkiewicz, D. M. Neumark, and O. Gessner,Int. Rev. Phys. Chem. , 239 (2015).[26] M. Shcherbinin, A. C. LaForge, V. Sharma, M. Devetta,R. Richter, R. Moshammer, T. Pfeifer, and M. Mudrich,Phys. Rev. A , 013407 (2017).[27] C. C. Wang, O. Kornilov, O. Gessner, J. H. Kim, D. S.Peterka, and D. M. Neumark, J. Phys. Chem. , 9356(2008).[28] D. Buchta, S. R. Krishnan, N. B. Brauer, M. Drabbels,P. O’Keeffe, M. Devetta, M. Di Fraia, C. Callegari,R. Richter, M. Coreno, K. C. Prince, F. Stienkemeier, R. Moshammer, and M. Mudrich, J. Phys. Chem. A , 4394 (2013).[29] A. C. LaForge, V. Stumpf, K. Gokhberg, J. vonVangerow, F. Stienkemeier, N. V. Kryzhevoi, P. O’Keeffe,A. Ciavardini, S. R. Krishnan, M. Coreno, K. C. Prince,R. Richter, R. Moshammer, T. Pfeifer, L. S. Cederbaum,and M. Mudrich, Phys. Rev. Lett. , 203001 (2016).[30] M. Shcherbinin, A. C. LaForge, M. Hanif, R. Richter,and M. Mudrich, J. Phys. Chem. A , 1855 (2018).[31] U. Henne and J. P. Toennies, J. Chem. Phys. , 9327(1998).[32] A. Mauracher, M. Daxner, J. Postler, S. E. Huber,S. Denifl, P. Scheier, and J. P. Toennies, J. Phys. Chem.Lett. , 2444 (2014).[33] B. Dick, Phys. Chem. Chem. Phys. , 570-580 (2014).[34] D. S. Peterka, J. H. Kim, C. C. Wang, L. Poisson, andD. M. Neumark, J. Phys. Chem. A , 7449 (2007).[35] Y. Ralchenko, R. Janev, T. Kato, D. Fursa, I. Bray, andF. de Heer, Atomic Data and Nuclear Data Tables ,603 (2008).[36] S. Cvejanovic and F. H. Read, J. Phys. B , 1841 (1974).[37] A. Kramida, Y. Ralchenko, J. Reader, and N. A. Team,“Nist atomic spectra database (version 5.5.6),” Avail-able: https://physics.nist.gov/asd [Fri Sep 21 2018]. Na-tional Institute of Standards and Technology, Gaithers-burg, MD (2018).[38] M. Joppien, R. Karnbach, and T. M¨oller, Phys. Rev.Lett. , 2654 (1993).[39] K. von Haeften, T. Laarmann, H. Wabnitz, T. M¨oller,and K. Fink, J. Phys. Chem. , 7316 (2011).[40] O. Kornilov, O. B¨unermann, D. J. Haxton, S. R. Leone,D. M. Neumark, and O. Gessner, J. Phys. Chem. ,7891 (2011).[41] J. Ackermann and H. Hogreve, Chem. Phys. , 75(1991).[42] A. R. Janzen and R. A. Aziz, J. Chem. Phys. , 914(1997).[43] V. G. Yarzhemsky and M. Y. Amusia, Phys. Rev. A ,063406 (2016).[44] K. Gokhberg, “private communication,” (2018).[45] L. Y. J. A. R. Samson, Z. X. He and G. N. Haddad, J.Phys. B: At. Mol. Opt. Phys. , 887 (1994).[46] B. E. Callicoatt, K. F¨orde, L. F. Jung, T. Ruchti, andK. C. Janda, J. Chem. Phys. , 10195 (1998).[47] N. B. Brauer, S. Smolarek, X. Zhang, W. J. Buma, andM. Drabbels, J. Phys. Chem. Lett. , 1563 (2011).[48] X. Zhang and M. Drabbels, J. Chem. Phys. , 051102(2012).[49] H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies,and C. Winkler, J. Chem. Phys. , 6875 (1990).[50] T. S. P. L. Chocian and J.-M. Rost, Phys. Rev. A ,073002 (2002).[51] B. Bouda¨ıffa, P. Cloutier, D. Hunting, M. A. Huels, andL. Sanche, Science287