EUV ionization of pure He nanodroplets: Mass-correlated photoelectron imaging, Penning ionization and electron energy-loss spectra
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, M. Mudrich
EEUV ionization of pure He nanodroplets: Mass-correlated photoelectron imaging,Penning ionization and electron energy-loss spectra
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 † Physikalisches Institut, Universit¨at Freiburg, 79104 Freiburg, Germany Max-Planck-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany Laboratoire de Chimie Physique Mol´eculaire, Swiss Federal Instituteof Technology Lausanne (EPFL), 1015 Lausanne, Switzerland CNR Istituto di Metodologie Inorganiche e dei Plasmi, CP10, 00016 Monterotondo Scalo, Italy CIMAINA and Dipartimento di Fisica, Universit`a di Milano, 20133 Milano, Italy Department of Physics, University of Trieste, 34128 Trieste, Italy and Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy (Dated: October 9, 2018)The ionization dynamics of pure He nanodroplets irradiated by EUV radiation is studied us-ing Velocity-Map Imaging PhotoElectron-PhotoIon COincidence (VMI-PEPICO) spectroscopy. Wepresent photoelectron energy spectra and angular distributions measured in coincidence with themost abundant ions He + , He +2 , and He +3 . Surprisingly, below the autoionization threshold of Hedroplets we find indications for multiple excitation and subsequent ionization of the droplets by aPenning-like process. At high photon energies we evidence inelastic collisions of photoelectrons withthe surrounding He atoms in the droplets. I. INTRODUCTION
Helium nanodroplets are intriguing many-body quan-tum systems which feature special properties such asvery low equilibrium temperature (0.38 K), superfluidity,and the ability to efficiently cool and assemble embed-ded species (‘dopants’). Therefore pure He nanodropletshave been extensively studied using electron impact ion-ization [1–5] as well as by photoexcitation and ioniza-tion with synchrotron radiation [6–11]. Recently, time-resolved experiments have become possible using fem-tosecond light pulses in the extreme ultraviolet (EUV)spectral range from high-order harmonic generation [12–15]. Based on the photoionization and dispersed fluores-cence emission measurements, the following three distinctregimes of excitation and ionization have been identified:(i) At photon energies 20 . < hν <
23 eV, He nan-odroplets are excited with high cross sections into per-turbed excited states (“bands”) derived from the 1s2s Sand 1s2p P He atomic levels. Fast droplet-induced intra-band and inter-band relaxation as well as He ∗ excimerformation follows the excitation [9, 10, 13, 14]. Due tothe repulsive interaction between excited He ∗ or He ∗ andthe He environment the excitation migrates to the surfacepresumably involving both resonant hopping of the elec-tronic excitation as well as nuclear motion of the excitedHe ∗ atom [3, 14–16]. Depending on the size of the Hedroplet, the He ∗ (1s2p P) state is trapped at the surfaceand eventually relaxes into the long-lived 1s2s , S statesor into vibrationally excited He ∗ molecules [2]. The lat-ter are subject to vibrational relaxation by coupling to ∗ Current address: IBM-India Semiconductor R&D Center, D3-F1, Manyata Park, Bangalore 560045, India † [email protected] the He droplet and eventually evaporate off the dropletsurface.(ii) At photon energies 23 < hν < . ∗ andHe ∗ in Rydberg states dominates [10, 14, 15], while thefraction of He ∗ dimers increases with rising excitationenergies [9, 10]. At hν >
24 eV population of tripletstates of He was also observed [9, 12]. As a further re-laxation channel, autoionization of He droplets sets inat hν >
23 eV leading to the formation of small ionicfragments (He + n , n ≤
17) as well as large cluster ions( N (cid:38) ) [6]. A peculiarity of the ionization of Hedroplets below the ionization energy E i, He = 24 .
59 eV ofatomic He is the emission of electrons with very low ki-netic energy < hν > . E i, He , He + ions (positive holes) are created in thedroplets. The positive charges subsequently migratethrough the He droplet by resonant hopping and eventu-ally localize by forming He +2 molecular ions or by ionizinga dopant if present [1, 3–5]. The internal energy of thenewly formed ion as well as the binding energy liber-ated upon formation of ‘snowball’ structures (He atomstightly bound around the ion core) is believed to stop thecharge-hopping process and causes massive droplet frag-mentation. Therefore, He + largely from background Heatoms and He +2 from droplets are the dominant speciesappearing in the mass spectra [6, 8, 16, 17].Detailed insight into the dynamics of photoexcitationand ionization of pure He nanodroplets has been gainedfrom ion mass spectra and velocity-map photoelectron a r X i v : . [ phy s i c s . a t m - c l u s ] M a y imaging [7, 8] as well as from dispersed fluorescence mea-surements [9–11, 18]. The photoelectron spectra (PES)recorded by ionizing He droplets at hν = 25 eV have re-vealed the presence of a high-energy component extend-ing to electron energies E e > hν − E i, He which was dis-cussed in terms of the direct single ionization of paired upneighboring He atoms to form He +2 dimer ions in boundvibrational levels [8]. Photoelectron angular distribu-tions measured for He droplets were found to be moreisotropic than those for free He atoms indicating elas-tic scattering of the escaping electrons from He in thedroplets. Apart from electrons created by direct pho-toionization, electrons with nearly vanishing kinetic en-ergy were observed which arise from an indirect ioniza-tion mechanism involving significant electron-He interac-tions. This component in the PES was most pronouncedfor large He droplets ionized in regimes (ii) and (iii) upto hν = 27 eV [7, 8]. Possible origins such as trappingof electrons in so called bubble states that decay whenthey approach the droplet surface [19–22], or vibrationalautoionization of highly excited electronic states of thedroplets were discussed [8].In the present paper we report on a synchrotron studyof pure He nanodroplets using Velocity-Map ImagingPhotoElectron-PhotoIon COincidence (VMI-PEPICO)spectroscopy. This method allows us to measure PESand angular distributions in coincidence with specific ionmasses which was not possible in previous experiments.The PES and angular distributions measured in correla-tion with the most abundant fragments He + n , n = 1 , , hν = 21 . S → P dropletabsorption band [6, 18, 23]. Upon ionization of Hedroplets at high photon energies hν (cid:38) × E i, He we ob-serve low-energy electrons in addition to those directlyemitted, which are generated by inelastic electron-He col-lisions. II. EXPERIMENTAL
The experiments presented here are performed using amobile He droplet machine attached to a VMI-PEPICOdetector at the GasPhase beamline of Elettra-SincrotroneTrieste, Italy [24]. The experimental setup is describedin more detail in a previous publication [16]. In short,a continuous beam of He nanodroplets with a mean sizeranging from 200 to 17000 He atoms per droplet is gen-erated by varying the temperature T of a cryogenic noz-zle [25, 26]. An adjacent vacuum chamber contains dop-ing cells, which are not used in the experiments reportedhere unless explicitly mentioned, and a mechanical beamchopper for discriminating ion and electron counts cor-related with the droplet beam from background countsdue to residual He and other residual gas components.In the detector chamber further downstream, the He droplet beam intersects the synchrotron light beam atright angle in the center of a velocity map imaging (VMI)spectrometer. The synchrotron radiation is linearly po-larized along the direction of the He droplet beam, thatis perpendicular to the symmetry axis of the VMI spec-trometer. The latter is composed of field plates that ac-celerate photoelectrons onto a position and time resolv-ing delay-line detector, while photoions are acceleratedonto a microchannel plate detector to record flight times.Measuring electrons and ions in coincidence allows us toextract from the data both ion mass spectra and mass-correlated velocity-map photoelectron images. The latterare transformed into PES and angular distributions usingstandard Abel inversion programs [27, 28].The narrow-band synchrotron radiation ( E/ ∆ E (cid:38) ) is varied between 21 and 66 eV in this study. All pho-ton energy dependent ion and electron spectra are nor-malized to the light intensity which is monitored by a cal-ibrated photodiode. Note that a non-negligible amountof second and third order radiation is present at the lowerend of the tuning range hν (cid:46)
20 eV. The pulse repetitionrate is 500 MHz and the peak intensity in the interactionregion is estimated to I ∼
15 W m − .An additional beam dump chamber is attached to theend of the apparatus which contains a channel electronmultiplier mounted directly in the path of the He dropletbeam. It is used for measuring the yield of metastable Heatoms and droplets excited by the synchrotron radiation. III. RESULTS AND DISCUSSION
In this work we focus on ion mass-correlated photo-electron spectroscopy of pure He nanodroplets irradiatedby EUV radiation at variable photon energies hν < E i, He up to hν (cid:38) × E i, He . Let us start the discussion of ex-perimental results by presenting typical ion mass spectra.The dependence of electron and ion yields on the exper-imental parameters (photon energy hν , He droplet size N ) will be discussed subsequently. Finally, the ion mass-correlated PES and angular distributions at variable hν will be presented. A. Ion yield spectra
Fig. 1 compares typical mass spectra recorded at hν =25 eV (a) and at hν = 23 . hν = 25 eV (a) the Heatoms in the droplets are directly ionized (regime (iii)),whereas at hν = 23 .
01 x 1 0 I o n m a s s - t o - c h a r g e r a t i o m / z b ) 2 3 . 8 e V H O + H e +2 H O + H e +3 H e +2 Ion signal [arb. u.] a ) 2 5 e VH e + FIG. 1. Difference mass spectra of ionized (a) and autoion-izing (b) He nanodroplets. The He expansion conditions are p = 50 bar and T = 23 K ( N = 1900). nantly excited into the droplet equivalent of the 1s3p Pand 1s4p P atomic He level out of which they decay byautoionization and other processes (regime (ii)). The Hedroplet beam source is operated at He expansion condi-tions of p = 50 bar and T = 23 K. The correspondingmean He droplet size amounts to N = 1900 [26].At photon energies hν > E i, He (Fig. 1 (a)), the high-est mass peaks in the spectra are those of He + and He +2 .Note that He +2 is even more abundant than He + , in con-trast to earlier electron impact and synchrotron experi-ments [2, 6, 17, 29]. This may be due to the long flightdistance from the nozzle up to the ionization region of71 cm in our experiment, which results in a highly colli-mated droplet beam where the content of free He atomsaccompanying the droplet beam is suppressed. The effi-cient formation of He +2 ions agrees with the establishednotion that the initially created He + positive hole mi-grates within the He droplets and localizes by forming aHe +2 ion. The binding energy liberated by forming theHe +2 molecule as well as by forming a tightly bound shellof He atoms around the ion (‘snowball’) subsequently in-duces droplet fragmentation and the ejection of bare He +2 .Higher He + n cluster ion masses are also present with lowerintensities in the entire mass range shown. The H O + signal stems from water molecules picked up by the Hedroplets from the residual gas which are ionized by chargetransfer ionization.At photon energies hν < E i, He (Fig. 1 (b)), the He + signal nearly completely vanishes as expected due to en- Signal [arb. units] E i , H e a ) e - b ) H e +2 P h o t o n e n e r g y [ e V ] c ) m e t a s t a b l e
FIG. 2. Photon energy dependence of the yield of photoelec-trons (a), He +2 ions and metastable atoms and droplets (c).The vertical dashed lines indicate He atomic level energies. ergy conservation. However, at hν = 23 . +2 and small He + n cluster ions and ultraslow photoelec-trons [6, 9, 13, 15]. This explains the high He +2 yield ascompared to all other masses.The dependence of the characteristic ionization signalson the photon energy hν is studied by recording the elec-tron and He +2 ion signals for varying hν . The result-ing spectra are depicted in Fig. 2. The He expansionconditions are set to p = 50 bar and T = 21 K corre-sponding to a mean droplet size of N = 2900. Differentvertical scales are used for the three panels (a)-(c). Theyield of metastable atoms and droplets shown in (c) isrecorded in the ‘chopper open’ position using a singlechannel electron multiplier mounted into the He dropletbeam. It therefore contains contributions from both theHe droplet beam as well as from atomic He effusing intothe detection chamber. Note that we cannot strictly ex-clude contributions to the signal from EUV fluorescencelight reaching the electron multiplier.The broad band structure in Fig. 2 (a) and (b) at pho-ton energies 23 ≤ hν ≤ . hν . This indicates the partialpresence of large He + n cluster ions with n >
100 whichfall beyond the detection range of our setup [6]. Thepeaked structures around 21 .
8, 23 .
1, 23 . . P, 1s3p P, 1s4p P,and highly excited Rydberg levels of atomic He. At hν > . T = 17 and 27 K the overall He +2 countrate slightly changes with a maximum at T = 21 K butthe structure of the spectrum remains nearly constant.Surprisingly, we find a weak broad maximum in the He +2 signal around hν = 21 . P excitation band of He droplets. Since this bandlies below E i, He by about 3 eV, which is more than thebinding energy of He +2 , autoionization of singly exciteddroplets is impossible. As we will discuss below, we at-tribute this feature to multiply excited He droplets thatdecay by a Penning-like process in which one He ∗ exci-tation relaxes to the ground state whereas the other He ∗ is ionized.The signal measured using the ion detector intercept-ing the droplet beam at the end of the beam line showssharp peaks corresponding to atomic lines as well as onebroad maximum around hν = 21 . P, n=2,3, . . . reflect the detectionof metastable atomic states of He populated by radiativedecay of the P states excited in the atomic He part of thebeam [30]. We attribute the broad peak at hν = 21 . P droplet excitation which decays by relax-ation into the metastable 1s2s S state of He atoms or intothe lowest Σ + u,g state of He ∗ excited dimers. The lat-ter either remain weakly bound to the droplet surface ordesorb off the droplets due to vibrational relaxation [2].Note that the relaxation of the 1s2p P droplet excitationinto 1s2s S and even lower-lying levels of He ∗ and He ∗ was previously observed for doped droplets [16, 31]. B. Photoelectron imaging
In order to obtain more detailed information aboutthe dynamics of He droplet ionization in the differentregimes (i)-(iii) we record photoelectron images in co-incidence with the most abundant ions He + and He +2 .Fig. 3 gives an overview of such images recorded at var-ious photon energies hν . In these images, the polariza-tion vector of the synchrotron radiation is oriented verti-cally in the image plane as indicated by the arrow in (a).The electron distribution measured in coincidence withHe + at hν = 25 eV (a) shows an anisotropic ring-shapedstructure which matches the characteristic angular dis-tribution of a p-wave, as expected for direct one-photonionization out of the He 1s-orbital. The electrons cor-relating to He +2 emitted at the same photon energy (b)feature a similar ring-shaped distribution which has thesame radius but is more isotropic. The angular distribu-tions of directly emitted electrons recorded in correlationwith He +2 and He +3 are analyzed further below. FIG. 3. Raw velocity map images of photoelectrons from Hedroplets in correlation with He + (a), (c), (e) and to He +2 (b),(d), (f) irradiated at photon energies hν = 21 .
6, 24, 25 eV.The arrow in (a) indicates the direction of the polarizationvector of the EUV radiation.
At the photon energy hν = 24 eV, that is in regime (ii),the electron signal correlating to He + nearly vanishes,whereas that correlating to He +2 concentrates in a smallcentral spot indicating very low electron kinetic energy.As mentioned above, nearly zero kinetic energy electronshave been observed in many experiments with pure anddoped He droplets [7, 8, 13, 16, 31, 32]. They appearmost prominently when hν is tuned slightly below E i, He and droplet autoionization becomes an important decaychannel.Surprisingly, at hν = 21 . P band, significantelectron signals correlating to both He + and He +2 are re-covered. The two images feature extended isotropic cir-cular structures of nearly equal size. As discussed belowin more detail, we attribute these electrons to the decayof multiply excited He droplets by Penning-like ioniza-tion. a. Mass-correlated photoelectron spectra
First, we examine the PES which we obtain by inverseAbel transformation and angular integration of the pho-toelectron images recorded in regime (iii). The spectrashown in Fig. 4 are recorded at hν = 25 eV for differentHe droplet sizes by varying the nozzle temperature T (cid:1) (cid:16) (cid:26) (cid:1) (cid:8) (cid:13) (cid:17) (cid:4) (cid:1) N (cid:14) (cid:11) (cid:12) (cid:7) (cid:7)(cid:1) (cid:16) (cid:26) (cid:1) (cid:9) (cid:8) (cid:17) (cid:4) (cid:1) N (cid:14) (cid:9) (cid:13) (cid:7) (cid:7)(cid:1) (cid:16) (cid:26) (cid:1) (cid:9) (cid:10) (cid:17) (cid:4) (cid:1) N (cid:14) (cid:8) (cid:13) (cid:7) (cid:7)(cid:1) (cid:1) (cid:31)" (cid:28) (cid:5) ! " $ (cid:23) (cid:31)(cid:1) (cid:27) (cid:29)% (cid:1)(cid:1) (cid:23) (cid:2) (cid:1) (cid:16) (cid:26) + (cid:19) (cid:1)(cid:21)( (cid:22) (cid:1)(cid:1)(cid:18) (cid:26) %(cid:26) $(cid:30) (cid:23) (cid:1)(cid:26) %(cid:1)(cid:23) (cid:31)(cid:6)(cid:1)(cid:1)(cid:26) & (cid:1) (cid:27) (cid:29)% (cid:24) (cid:2) (cid:1) (cid:16) (cid:26) (cid:3)(cid:9) Electron signal [arb. units] (cid:15) (cid:31)(cid:26) (cid:25) % $ " ! (cid:1) (cid:30) (cid:29)! (cid:26) % (cid:29)(cid:25) (cid:1) (cid:26) ! (cid:26) $ (cid:28) ’ (cid:1) (cid:21) (cid:26) (cid:20) (cid:22) (cid:25) (cid:2) (cid:1) (cid:16) (cid:26) (cid:3)(cid:10)
FIG. 4. Photoelectron spectra measured in coincidence withHe + (a), He +2 (b), and He +3 ions (c) at hν = 25 eV for differ-ent He droplet sizes. The He + spectrum (a) is modeled by alog-normal distribution (dashed line). The dashed line in (b)represents the convolution of the fit function in (a) and a log-normal distribution that accounts for the pure He +2 spectrum.The inset in b) compares the resulting nearest-neighbor dis-tribution for pairs of He atoms with an ab initio calculationby Peterka et al. [8]. as indicated in the legend. The spectra correlating toHe + (Fig. 4 (a)) are obtained from the background-subtracted (‘chopper closed’) electron images of thefull signal (‘chopper open’) so as to discriminate theelectrons correlated with the He droplet beam. Thedashed line represents the result of fitting the averageof the experimental curves by a log-normal distributionfunction, which is and empirical function that wellreproduces the measured peak shape. The maximum ispeaked at 0.39(2) eV which matches the excess energy hν − E i, He = 0 .
41 eV in the direct ionization of Heatoms. The width of the spectral feature of He + reflectsthe energy resolution of the spectrometer and matchesthe width measured for atomic He from backgroundgas. Thus, within the experimental uncertainties, we seeno significant influence of the presence of He dropletson the PES. This suggests that the He + atomic ionsstem from the atomic component that accompanies thedroplet beam. Possibly, there is a contribution from Heatoms located at the outer surface of the droplets wherethe He density is too low to cause significant line shifts and to induce charge migration and He +2 formation [5].As discussed in the following section, the high degreeof anisotropy of the He + -correlated photoelectrons(Figs. 5, 6) further supports this interpretation.The peak in the PES correlating to He +2 (Fig. 4 (b)),however, is slightly shifted and significantly broadenedtowards higher kinetic energies. The spectrum of He +3 (c) is even more extended towards higher electron ener-gies than that of He +2 . In the previous work, Peterkaet al. [8] have measured and analyzed the total PESrecorded without ion mass correlation. The presence ofa shoulder extending to higher energies was interpretedusing a simple model based on the assumption that ion-ization occurs vertically for pairs of closely spaced Heatoms in the droplet, thereby accessing the attractivepotential region of the cationic He +2 core. The result-ing photoelectrons have higher kinetic energy than thoseof atomic He [8]. The shape of this shoulder was simu-lated by a Franck-Condon model based on the He andHe +2 difference potential and the distribution of He-Heinteratomic distances for the nearest He-He atom pairs(‘nearest neighbor’) obtained from path integral MonteCarlo calculations.We adopt the same model in order to infer the distri-bution nn ( r ) of distances r for nearest He-He atom pairswhich we identify as precursors for He +2 formation. Notethat this model of vertical transitions from He-He pairsinto bound levels of He +2 does not contradict the con-cept of creating He + charges that migrate through thedroplets before localizing by forming deeply bound He +2 .Due to the presence of one or more additional He atomsclose to the respective He-He pair the total interactionpotential is extended to a double-well or multiple-wellpotential where the heights of the barriers depend on thedistances between the three or more atoms. For suffi-ciently close spacing and excitation of high-lying levelsabove the barriers, the charge is therefore delocalized.Localization then occurs due to vibrational relaxationinto one potential well which prevents further hoppingover or tunneling through a barrier. Thus, the low-energyedge of the He +2 peak (Fig. 4 (b)) is associated with He +2 formed after charge migration, whereas the high-energytail is identified with direct formation of deeply boundHe +2 .The model curve shown as a dashed line in Fig. 4 (b)is obtained by fitting the convolution of the fit func-tion of the He + peak (dashed line Fig. 4 (a)) with alog-normal distribution function f He +2 ( E e ). This func-tion is chosen empirically to describe the characteristicline shape of the He +2 component. From that distribu-tion we obtain nn ( r ) by mapping the energy distribu-tion f He +2 onto the shifted difference potential ∆ V = V He +2 − V He + hν − E i,He [33, 34] using the transformation nn ( r ) = f He +2 (∆ V ( r )) d ∆ V ( r ) /dr where hν = 25 eV.The result is shown as a solid line in the inset of Fig. 4(b). It only slightly deviates from the original calculation(dashed line) in that its maximum is slightly shifted to FIG. 5. Raw velocity map images of photoelectrons fromionized He droplets at hν = 35 eV recorded in coincidencewith He + (a), He +2 (b), and He +3 (c) ions. a shorter He-He distance r = 2 . R = 3 . +2 ionsare formed in regions of varying density inside or at thesurface of the droplets the shown nn ( r ) distribution is adensity average for the present experimental conditions. b. Mass-correlated photoelectron angular dis-tributions
Next, we discuss the angular distributionsof photoelectrons correlating to He + , He +2 and He +3 inmore detail. To this end we record photoelectron im-ages at variable hν up to 50 eV for droplet sizes rang-ing from N = 1200 to 5600. Typical raw photoelectronimages recorded at hν = 35 eV are depicted in Fig. 5. As for hν = 25 eV (Fig. 3 (a), (b)), we note a reducedanisotropy of the photoelectron distributions correlatingto the molecular ions He +2 and He +3 (Fig. 5 (b), (c)).From the images, we infer the average anisotropy param-eter β by fitting the angular dependence of the signalintensity I ( θ ) in the inverse Abel transformed images us-ing the standard expression I ( θ ) ∝ βP (cos θ ) [35].The resulting values of β are compiled in Fig. 6 (a)for variable hν and in Fig. 6 (b) for variable T (dropletsize). While for electrons correlating to He + we find aconstant value β = 2 . +2 and He +3 theanisotropy parameter is reduced to β = 0 . hν and T . This seems to indicate that He +2 and He +3 alsomerely stem from the He and He molecular compo-nents which accompany the He droplet beam. However,the fact that the photoelectron distributions measured incoincidence with dopant ions generated by charge trans-fer ionization [16] strongly resemble those of He +2 suggeststhat He +2 do stem from droplets. The reduced anisotropyis probably due to scattering of the outgoing photoelec-tron from the He droplets. We rather believe that theprobed range of droplet sizes in not sufficiently broadto see a significant influence of a changing average Hedensity on the photoelectron distribution. A better un-derstanding of the photoelectron angular distributionsand spectra requires further experimental and theoret-ical efforts. In particular, the comparison with PES ofmass-selected He as recently studied [36] would give in-teresting new insight into the effect of the He droplet onthe photoelectron distributions. c. Penning ionization
So far we have examinedthe photoelectron distributions of He nanodroplets in theregime (iii) of direct ionization. However, the photonenergy dependent ion yield measurements (Fig. 2) andphotoelectron images (Fig. 3) have revealed weak ioniza-tion signals even at hν = 21 . + dopant ions are detected as a result of a Penningprocess where the He ∗ excitation energy is transferred tothe dopant [16]. However, since we measure the photo-electrons in coincidence with He + we do not expect anyinfluence of the presence of dopants on the He ionizationsignals. In particular, the PES measured in coincidencewith Na + ions, discussed in our previous paper [16], sig-nificantly differ from those correlating to He + and He +2 .Thus, a false mass-correlation of the latter electrons isexcluded.The PES recorded in coincidence with He + and He +2 are depicted in Fig. 7 for two different He droplet sizes N = 7000 ((a) and (c)) and N = 800 ((b) and (d)). In allmeasurements we distinguish 3 components in the PES.A sharp peak at electron energies E e = 2 × hν − E i, He =18 . b ) H e +2 Anisotropy parameter (cid:1)
N o z z l e t e m p e r a t u r e [ K ] b ) P h o t o n e n e r g y [ e V ]
Anisotropy parameter (cid:1)
H e + H e +2 H e +3 a ) a ) H e + FIG. 6. Anisotropy parameters β inferred from the photo-electron images correlating to He + , He +2 , and He +3 ions as afunction of hν (a) and as a function of nozzle temperature inthe range T = 18-25 K corresponding to N = 5600-1200 (b).In (a) N = 4500 and in (b) hν = 25 eV. order radiation which have undergone an inelastic colli-sion with a surrounding He atoms, as discussed in the lastpart of this section. This peak is the dominant featurein the spectra recorded for small He droplets N = 800(Fig. 7 (b) and (d)). In addition, the spectra recorded forlarge droplets (Fig. 7 (a) and (c)) exhibit a pronouncedpeak shifted to lower electron energies E e ≈
16 eV. Thebroad structure at low energies around E e = 7 eV, whichis also present in the spectra from the effusive back-ground, is attributed to background signal presumablyfrom scattered photons and from false coincidences.These spectra closely resemble the ones measured incoincidence with rare-gas or alkali metal dopant ions [16,31]. In those experiments, the peaked structures simi-lar to the ones visible in Fig. 7 between hν = 15 and20 eV were assigned to electrons produced by ionizationof dopants X in a Penning-like processHe ∗ [He N ] + X → He[He N ] + X + + e − , (1)where the droplet-induced relaxation of He ∗ into lower-lying levels such as 1s2s S was likely to precede Penningionization [16, 31]. In the present case of He + corre-lated PES, we take the presence of components shifted E l e c t r o n k i n e t i c e n e r g y c ) H e + , 1 7 Kd ) H e + , 2 7 K S + 2 s SH e *2 + H e *2 h v - E i,H e P + 2 p P2 s S + 2 s S S + 2 s S Probability [arb. units]
E l e c t r o n k i n e t i c e n e r g y b ) H e + , 2 7 K O p e n C l o s e d h v - E i,H e P + 2 p P2 s S + 2 s S a ) H e + , 1 7 K FIG. 7. Photoelectron spectra measured in coincidence withHe + (a), (b) and to He +2 ions (c), (d) at hν = 21 . p = 50 bar and T = 17 K ( N = 7000)(a), (c) and T = 27 K ( N = 800) (b), (d). The vertical linesindicate electron energies expected for the relaxation of twoexcited He atoms into various 1s2p-levels or into the lowestexcited state of He +2 . Labels “Open” and “Closed” refer todata recorded in the open and closed positions of the dropletbeam chopper. to lower energies E e < × hν − E i, He as an indication fora Penning-like reaction involving two He ∗ excitations inthe same droplet as given by Eq. (1), for X =He ∗ . Thisprocess has been discussed in the context of reduced EUVfluorescence emission observed when resonantly excitinglarge He droplets ( N > ) [11].The probability for double excitation of a He nan-odroplet P = P by the interaction with one syn-chrotron pulse can be estimated from the probabilityof single excitation, P = N σ a ∆ tI/ ( ehν ) ∼ × − ,where I is the light intensity. Here, we assume an ab-sorption cross section σ a ≈
25 Mb of one He atom in adroplet containing N atoms, ∆ t ≈
130 ps is the pulselength, and e and h denote the elementary charge andPlanck’s constant, respectively. When assuming that afraction of excited He droplets relaxes into metastablestates with life times τ exceeding the pulse repetitionperiod T = 2 ns, P is replaced by P t tr /T ≈ P ,where t tr ≈ µ s denotes the transit time of the dropletsthrough the focus of the synchrotron beam. For thosedroplets we obtain P ≈ × − , which yields a signalcount rate S = P N HeN /t tr ∼ . − . Here, the num-ber of He droplets in the focal volume N HeN amounts to N HeN = n HeN dw ≈ × , where n HeN = 10 cm − stands for the number density of He droplets, d = 4 mm isthe diameter of the droplet beam, and w = 400 µ m is thefocus diameter. This estimate approximately matchesthe count rate measured experimentally. The rapidincrease of the Penning signal with increasing dropletsize N can be rationalized by the quadratic dependence S ∼ N . Note, however, that this estimate relies onthe population of metastable excitations which leads toan accumulation of excitations in one droplet over manylight pulses. In contrast to that, He droplets that aremultiply excited by single intense ultrashort light pulsesas available from free-electron lasers will autoionize by adifferent mechanism akin to interatomic Coulombic de-cay [37, 38].Thus, the Penning ionization process appears to bevery efficient relative to the decay of He ∗ or He ∗ exci-tations by spontaneous relaxation or by desorption offthe droplet surface. This interpretation is supported bythe results of earlier experiments studying the dynam-ics of excitations in bulk superfluid He and on molecularbeam studies of He ∗ -He ∗ Penning collisions. In super-fluid He the lifetimes of He ∗ in 1s2s S and of He ∗ ex-cimers in their lowest state a Σ + u ( v = 0) were measuredto be about 15 µ s and 13 s, respectively [39, 40]. How-ever, upon producing multiple excitations in bulk He theHe ∗ excimer population was found to decay due to binaryPenning ionization collisions with a rate coefficient risingup to 2 × − cm /s at He temperatures 1 . ∗ excimers this corre-sponds to a decay time of about 1 . ∗ move freely inside the He droplets as in superfluid He.Note that the crossover from diffusive to ballistic mo-tion of He ∗ in superfluid He was observed only recentlyin the temperature range between 100 and 200 mK, closeto the He droplet temperature [41]. The Penning colli-sion rate for He ∗ can be estimated using the known crosssection σ He ∗ ≈
300 ˚A from molecular beam scatteringexperiments [42]. Assuming a mean relative velocity ofthe He ∗ atoms of 60 m/s the rate coefficient amounts toabout 1 . × − cm /s and the Penning collision timeis 1 . ∗ or He ∗ excitations maybe enhanced by the simultaneous migration of the twoexcitations towards the droplet surface due to repulsiveHe-He ∗ interaction [3, 15, 16] while polarization forcessteer them towards each other as in the case of chargemigration [44].The vertical dashed lines at 15 ≤ E e ≤ . ∗ in various electronic levels as denoted inthe legend. Other asymmetric combinations of excitedstates such as He ∗ (1s2p P)+He ∗ (1s2s S) are also possi-ble but omitted in Fig. 7 for the sake of clarity. Penningionization of the directly excited 1s2p P droplet stateyields an electron energy E e = 2 × hν − E i, He (blue dashedline) whereas Penning ionization following the relaxationof He ∗ into atomic levels 1s2p P, 1s2s S, 1s2s S dimin-ishes the Penning electron energy (light dashed lines).At He expansion conditions where small droplets ( N = 800) are formed (Fig. 7 (b) and (d)), the PES are domi-nated by direct ionization or by Penning ionization of theunrelaxed He droplet state, which we cannot distinguish.For larger He droplets N (cid:38) ∗ that have relaxed into 1s2s S andlower-lying levels prior to ionization becomes more pro-nounced. This can be rationalized by the longer migra-tion distances covered by the two He ∗ excitations in largedroplets in order to come close and react. The fact thatthe PES recorded in coincidence with He +2 significantlydiffer from the ones of He + points at a process wherefirst He ∗ excited dimers form and then the Penning re-action occurs. The conceivable alternative process, He +2 dimer ion formation after Penning ionization of He ∗ [2],would result in identical PES. The small shift of the Pen-ning peak to lower energies in Fig. 7 (c) indicates thatPenning ionization involves He ∗ in various vibronic levelsthat reach down to even lower energies than the atomictriplet states (vertical dashed line at E e ≈
11 eV). Giventhe low statistics of our data and the limited energy res-olution of the spectra we cannot infer more details aboutthis ionization mechanism. d. Inelastic photoelectron-helium collisions
Finally, we present PES measured at high photonenergies hν >
46 eV. To the best of our knowledge,no experiments with He nanodroplets at such elevatedphoton energies have been reported to date. Fig. 8(a) depicts typical PES correlating to He + and He +2 recorded at hν = 50 eV. The corresponding raw imagefor He +2 is shown as an inset. While the photoelectrondistribution correlating to He +2 is significantly moreisotropic than that of He + (Fig. 6), the PES are nearlyidentical at these high photon energies. In addition tothe highest peak from directly emitted electrons withenergy hν − E i, He = 25 .
41 eV a second peak appears atenergy E E − loss = hν − E i, He − E s s,p ≈ E s s,p stands for the energies of all levels of the 1s2sand 1s2p configurations of He atoms ( S, S, P, P)which can be excited by electron impact but remainunresolved in the PES. This low-energy feature is presentat the reduced energy E E − loss in all measured spectrawhere hν >
46 eV, as shown in Fig. 8 (b). It is dueto the loss of kinetic energy of the photoelectrons byinelastic collisions with surrounding He atoms as theypass through the droplets in a process of the type e − ( E kin ) + He(1s ) → He ∗ + e − ( E kin − E E − loss ) . This interpretation is supported by a vanishinganisotropy parameter β = 0 . β = 1 . P inel for such collisions can be esti-mated using the well-known inelastic scattering cross sec-tions σ inel [45], P inel = σ inel ρ He N R He N . Here, ρ He N =0 . − denotes the density of He droplets [46] and h (cid:2) (cid:1) - E i - S , Ph (cid:2) (cid:1) - 2 E i Signal [arb. units] a ) h (cid:2) (cid:1) - E i H e + H e +2 P e a k ( 1 ) P e a k ( 2 ) h n - E i h n - E i - E ( 2 s S ) h n - E i - E ( 2 s S ) h n - E i - E ( 2 p P ) h n - E i - E ( 2 p P )
Peak position [eV]
P h o t o n e n e r g y [ e V ] b ) FIG. 8. (a) Photoelectron spectra recorded in coincidencewith He + (shaded area) and He +2 (solid line) at hν = 50 eV( p = 50 bar, T = 23 K). Peak 1 corresponds to electronscreated directly by ionization of He atoms or He dimers inthe droplets. Peak 2 stems from electrons that lost energyby inelastic collisions with surrounding He atoms. The in-set depicts the photoelectron image correlating to He +2 . (b)Dependence of the peak positions on hν . The dashed linesdepict the energies of photoelectrons emitted directly (black)or after energy-loss by inelastic collisions (colored) when con-sidering the He atomic ionization energy E i, He and the levelenergies of the 1s2s , S and 1s2p , P atomic levels. R He N = (3 N/ (4 πρ He N )) / = 32 ˚A is the droplet radiusfor a mean droplet size N = 2900. For hν = 50 eV we ob-tain P inel ≈
6% when summing over all the relevant chan-nels, which roughly matches the ratio of areas of peaks (2)and (1) amounting to about 20%. When estimating theprobability of ionizing He by collisions with photoemittedelectrons in the same way, we find P ion ≈ + atomic ions, forwhich we measure a very pronounced anisotropy of thecoincident electron distribution, stem from the atomic Hecomponent accompanying the He droplet beam. IV. CONCLUSION
Using velocity-map imaging photoelectron-photoioncoincidence (VMI-PEPICO) measurements we have in-vestigated the photoionization dynamics of pure He nan-odroplets in the regimes of direct ionization and autoion-ization. We present photoelectron distributions mea-sured in coincidence with the most abundant ion massesHe + , He +2 , and He +3 in a wide range of photon energies.The He +2 mass-correlated photoelectron spectra are inter-preted in terms of contributions from ionized He dropletsthat relax to form He +2 and from vertically ionized pairsof nearest neighboring He atoms. The highly anisotropicphotoelectron angular distributions recorded in coinci-dence with He + indicate that overwhelmingly free Heatoms accompanying the droplet beam contribute to theHe + signal. In contrast, angular distributions of He +2 andHe +3 display significantly reduced anisotropy, presumablydue to scattering of the outgoing photoelectron from theHe droplet.In the regime of pure droplet excitation we measureionization signals which indicate multiple excitation ofthe droplets that decay by Penning-like ionization evenin the range of small droplets ( N (cid:46) ACKNOWLEDGMENTS
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