Direct inner-shell photoionization of Xe atoms embedded in helium nanodroplets
Ltaief Ben Ltaief, Mykola Shcherbinin, Suddhasattwa Mandal, Sivarama krishnan, Robert Richter, Thomas Pfeifer, Marcel Mudrich
DDirect inner-shell photoionization of Xe atoms embedded in helium nanodroplets
L. Ben Ltaief, M. Shcherbinin, S. Mandal, S. Rama Krishnan, R. Richter, T. Pfeifer, and M. Mudrich
1, 3 Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark Indian Institute of Science Education and Research, Pune 411008, India Indian Institute of Technology Madras, Chennai 600036, India Elettra-Sincrotrone Trieste, Basovizza, 34149 Trieste, Italy Max-Planck-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany (Dated: June 16, 2020)We present the first measurements of photoelectron spectra of atomic clusters embedded in super-fluid helium (He) nanodroplets. Owing to the large absorption cross section of xenon (Xe) around100 eV photon energy (4d inner-shell ionization), direct dopant photoionization exceeds charge trans-fer ionization via the ionized He droplets. Despite the predominant creation of Xe and Xe bysubsequent Auger decay of free Xe atoms, for Xe embedded in He droplets only singly charged Xe + k , k = 1 , , + ion kinetic-energy distributions indicate Coulombexplosion of the ions due to electron transfer to the primary Auger ions from surrounding neutralatoms. The electron spectra correlated with Xe ions emitted from the He nanodroplets contain alow-energy feature and nearly unshifted Xe photolines. These results pave the way to extreme ultra-violet (XUV) and x-ray photoelectron spectroscopy of clusters and molecular complexes embeddedin He nanodroplets. I. INTRODUCTION
Helium (He) nanodroplets are widely used as an ul-tracold matrix for spectroscopy of embedded moleculesand nanostructures [1, 2]. The main benefits of He nan-odroplets are the high resolution of absorption spectra inthe infrared and visible spectral regions and the propertyof He droplets to efficiently form molecular aggregatesthat thermalize to the droplet temperature of 0.37 K.Performing spectroscopy at higher photon energies wherethe dopants or even the He droplets are directly ionizedisn’t straight forward, though; the strong interaction ofphotoions and electrons with the He droplet tends tomassively shift and broaden the electron spectral linesand to alter the fragmentation dynamics compared to thegas phase [3]. Therefore, only few photoelectron spectro-scopic studies of dopants have been reported, all of whichemployed resonant multi-photon ionization schemes [4–10].However, one-photon photoionization of doped He nan-odroplets has recently turned out to be a rewarding ap-proach for studying various types of fundamental cor-related electronic decay processes such as interatomicCoulombic decay (ICD) [11–15] and electron-transfer me-diated decay (ETMD) [16–18]. Although the photon en-ergy exceeded the dopant’s ionization energy E i in thosestudies, dopants were always ionized indirectly throughthe excited or ionized He. This is due to the large totalabsorption cross section of He nanodroplets containingthousands of He atoms ( ∼
25 Mbarn per He atom forthe dominant 1s2p P absorption resonance at the pho-ton energy hν = 21 . ∗ , and positive charges, He + , efficiently migrate through the He droplet to the dopant which is then ionized by transfer of energy or charge,respectively [15, 19–22]. Large differences in the Pen-ning ionization efficiency and the structure of the Pen-ning electron spectra were found for dopants (alkali met-als) attached to the surface of He nanodroplets comparedto those immersed in the droplet interior. This was ra-tionalized by the tendency of He ∗ to migrate toward thedroplet surface [23, 24], whereas He + remains in the bulkof the droplets [23, 25]. Using photoelectron-photoion co-incidence (PEPICO) detection, we have previously mea-sured high Penning ionization yields for alkali metals,whereas the efficiency of Penning ionization for heavierrare gas atoms was lower than that for charge transferionization [21]. The Penning ionization electron spectrawere found to feature either sharp lines reflecting the Heenergy levels and the dopants’ E i [15, 21], a broad distri-bution peaked at low energies [22], or a combination ofboth [20, 26].Here, we present the first experimental study wheredopant atoms attached to He nanodroplets are directlyphotoionized and electron and ion spectra are recorded.This is achieved using Xe as a dopant and setting hν ∼
100 eV where Xe features a pronounced maximum of the4d-shell ionization cross section, whereas the absorptioncross section of He is down by a factor ∼ /
20 comparedto the value near E He i . Photoions from free atoms inthe gas phase are mostly produced in doubly and triplycharged states as a result of normal or cascaded Augerdecay, respectively. In contrast, from doped He dropletsmostly singly charged Xe + as well as small Xe + n clustersare emitted. This points at efficient partial neutraliza-tion of highly charged cations in He nanodroplets by elec-tron transfer to the dopant photoion from neutral dopantatoms surrounding it. Electron spectra exhibit sharp un-shifted photolines from the embedded Xe clusters as well a r X i v : . [ phy s i c s . a t m - c l u s ] J un as a pronounced low-energy distribution indicative forelectron-He scattering and electron localization. II. EXPERIMENTAL
The experiments are performed using a He nan-odroplet apparatus combined with a velocity-map imag-ing photoelectron-photoion coincidence (VMI-PEPICO)spectrometer installed at the GasPhase beamline ofElettra-Sincrotrone Trieste, Italy. The apparatus hasbeen described in detail elsewhere [21, 27]. Briefly, abeam of He nanodroplets is produced by continuouslyexpanding pressurized He (50 bar) of high purity out ofa cold nozzle (14 K) with a diameter of 5 µ m into vac-uum, resulting in a mean droplet size of ¯ N He = 2 . × He atoms per droplet. The He droplets were doped withXe atoms by leaking Xe gas into a doping gas cell oflength 30 mm. The measurements presented in this pa-per were done at a Xe pressure in the doping cell of4 . × − mbar. This corresponds to a mean num-ber of 24 Xe dopants per He droplet. A mechanicalbeam chopper at the entrance of the doping chamber isused for discriminating droplet-beam correlated signalsfrom the background. In the detector chamber, the Hedroplet beam crosses the synchrotron beam at the centerof the VMI-PEPICO detector at right angles. By de-tecting either electrons or ions with the VMI detector incoincidence with the corresponding particles of oppositecharge on the TOF detector, we obtain either ion mass-correlated electron images or mass-selected ion images.Kinetic-energy distributions of electrons and ions are ob-tained by Abel inversion of the images [28]. The energyresolution of the electron spectra obtained in this way is∆ E/E = 6%.
III. RESULTS AND DISCUSSION
In our previous PEPICO study of Ar-doped He nan-odroplets it appeared that heavier rare gas atoms sol-vated in the droplet interior are inefficiently Penning ion-ized through excited He [21]. In contrast, Wang et al. had previously reported well-resolved Penning electronspectra of Kr and Xe indicating that Penning ionizationof Kr and Xe embedded in He nanodroplets is quite effi-cient [20].To resolve these conflicting findings, we record the to-tal electron yield of Xe-doped He nanodroplets in thewide photon energy range hν =20-160 eV. Those elec-trons emitted from Xe dopants embedded in He dropletsare extracted from the data by first subtracting from thetotal electron signal (chopper open) those electrons emit-ted by ionization of the background gas (chopper closed).Then, we subtract from the measurement done with Xedoping on a reference measurement where the Xe doping H e + H e *
X e
H e * P Electrons from Xe dopants (arb. u.)
P h o t o n e n e r g y ( e V )
Figure 1. Electron yield spectrum due to Xe atoms embed-ded in He nanodroplets as a function of the photon energy.The signal below the ionization energy of He (to the left ofthe break in the hν -axis) is due to indirect ionization of Xethrough excited and autoionized He, the part at hν >
70 eVis mostly due to direct photoionization of the Xe dopants. was turned off. The resulting electron yield spectrum isshown in Fig. 1.In the range hν < E He i , the electron yield closely fol-lows the absorption spectrum of pure He nanodroplets,which is dominated by the 1s2p P absorption resonanceof He nanodroplets peaked at hν = 21 . hν = 21 . hν > . hν >
70 eV, theyield of electrons is lower than that measured at the He1s2p P resonance but clearly shows a broad maximumcentered around hν ∼
100 eV. In this range of hν theelectron yield closely follows the absorption cross sectionof Xe atoms which is dominated by a maximum of the4d-subshell photoionization cross section, also called ‘gi-ant resonance’ [32, 33]. This is a clear indication thatnow the detected electrons are mostly emitted by theXe dopants. Photoionization of the He droplets followedby charge transfer ionization of the Xe dopants, whichis the dominant dopant-ionization mechanism near E He i ,contributes to a lesser extent. This is due to the large dif-ference in absorption cross sections of Xe (23.6 Mbarn)and He (0.52 Mbarn) at hν = 90 eV [34]. Given thedroplet size of about 2 . × He atoms and the esti-mated Xe dopant clusters size of 24 Xe atoms, we ob-tain a ratio of the efficiencies of direct photoionizationof embedded Xe vs. indirect charge transfer ionizationof about 7 assuming a charge transfer ionization prob-ability of the Xe cluster of 1 % [35, 36]. This valueis in good agreement with the signal contrast from on-resonant ( hν ∼
100 eV) Xe photoionization with respectto the off-resonant ( hν ∼
150 eV) background measuredhere (Fig. 1). Thus, we have demonstrated for the firsttime that direct one-photon ionization of dopants embed-ded in He nanodroplets is possible, at least at high XUVphoton energies hν (cid:29) E He i where He nanodroplets arenearly transparent.When Xe is 4d-subshell ionized, a cascaded Auger de-cay takes place resulting in multiply charged Xe ions [33].Fig 2 (c) shows typical mass spectra recorded for Xeatoms in the background gas (black line) and for Xe em-bedded in He nanodroplets (red line) at hν = 90 eV.Clearly, the dominant charge states from Auger decay areXe and Xe , whereas Xe + is hardly visible when nor-malizing the ion signal scale to the Xe peak. Note thatthe abundances of the highly charged Xe and Xe ionsare likely enhanced compared to Xe + and in particularto Xe +2 and Xe +3 due to a higher detection sensitivity. Incontrast, just below and above E He i (Fig 2 (a) and (b)),Xe + is by far the most abundant product. The small con-tribution of Xe in the mass spectrum at hν = 25 eVis likely due to one-photon double ionization of Xe bysecond-order synchrotron radiation which is quite abun-dant at that photon energy.The He droplet-correlated Xe + signal at hν = 19 eV
3. The fragmentation of thesesmall Xe dopant clusters is due to charge transfer ioniza-tion through the ionized He nanodroplets, as it has beendiscussed in Ref. [36].One main result of this work is that at hν = 90 eV,the He droplet-correlated Xe + mass spectrum (red linein Fig 2 (c)) again consists of small singly charged Xe + k clusters, although Xe ionization is mainly due to directXe 4d-ionization which predominantly creates Xe andXe . Thus, multiply charged ions in He nanodroplets N +2 ( a ) h n = 1 9 e V H e d r o p l e t c o r r e l a t e d B a c k g r o u n dX e + X e ( b ) h n = 2 5 e V X e + X e +3 X e +2 X e + Ion signal (arb. u.)
X e
X e ( c ) h n = 9 0 e V X e +2 X e +3 X e + I o n m a s s / c h a r g e ( a . u . )
Figure 2. Mass spectra of Xe-doped He nanodropletsrecorded at different photon energies. The ion signal corre-lated to the doped He nanodroplets (red line) is discriminatedfrom the background (black line) through a mechanical chop-per that interrupts the He nanodroplet beam. are very efficiently partly neutralized. Electron transferfrom neighboring neutral atoms to the highly chargedions can occur on a subfemtosecond time scale, i. e. faster than the Auger process [37]. Partial neutral-ization of doubly charged metals in He nanodropletscreated by electron-transfer mediated decay was ob-served previously [17]. Even pure Xe clusters irradiatedby soft and hard x-rays have recently been found toefficiently quench high charge states created by Augerionization [38, 39]. This was interpreted by electron-ionrecombination which is a common process in expandingnanoplasmas [38]. Here, we show that electron transferto multiply charged ions is highly efficient even in theabsence of a nanoplasma. Likely, in [38] also electrontransfer from neutral Xe contributed to the measuredhighly abundant Xe + signals [38]. In our experiment(Fig 2 (c)), where the He nanodroplets contain small Xeclusters, likely electron transfer between Xe atoms is themain mechanism. We note that even when we reducedthe number of doped Xe atoms down to the detectionlimit of Xe ions from He droplets in an attempt todope the He droplets by single Xe atoms, no Xe werepresent although the latter cannot be neutralized by Heas E Xe + i < E He i . The likely reason is that a multiplycharged cation is strongly bound to a He droplet byforming a so-called snowball complex [40] and thusevades its detection. Likewise, no experimental evidencefor charge transfer to the highly charged Xe fromsurrounding neutral He atoms was found in this work,although it would be energetically allowed. The possiblecharge transfer processes that can occur between Xeatoms embedded inside He nanodroplets are as follows:Xe n He N + hν → Xe n He N + e Aug + e ph → Xe n − k − He N + Xe + + Xe + k + e Aug + e ph , where k =1 , , n He N + hν → Xe n He N + 2 e Aug + e ph → Xe n − k − He N + Xe + Xe + k + 2 e Aug + e ph → Xe n − He N + Xe + + Xe + + Xe + + 2 e Aug + e ph .When we compare the Xe + k distribution measured bycharge transfer ionization (Fig 2 (b)) with the one byAuger ionization in conjunction with electron transfer(Fig 2 (c)), we note that the Xe + peak is higher andbroader in the latter case. This is likely due to Coulombexplosion of the two or three Xe + ions formed from Xe or Xe by electron transfer, respectively. When twoions are formed with substantial kinetic energy, they areless prone to being trapped by the He droplet and aretherefore detected with higher probability [14, 17].Further evidence for the formation of Xe + by Coulombexplosion is obtained from directly measuring the ion ki-netic energy by velocity-map imaging the Xe + on a po-sition sensitive detector in the ion-imaging mode. TheXe + and Xe +2 ion kinetic energy distributions inferredfrom ion images are displayed in Fig. 3 in comparisonwith the ion kinetic energy distributions for Xe andXe from free Xe atoms. The Xe + ion spectrum con-sists of a broad feature that peaks around 1.5 eV andextends up to 6.5 eV, whereas the Xe and Xe spec-tra both exhibit only a very narrow peak at 0 eV. Thewidth of these peaks reflects the experimental resolution.For Xe dimers, the bond length is R = 4 .
36 ˚A [41].Assuming instantaneous formation of an ion pair Xe + + Xe + by Auger decay and electron transfer, the ki-netic energy release (KER) due to Coulomb explosion X e / 1 5 0 f r o m X e a t o m s X e / 1 5 0 f r o m X e a t o m s X e +2 f r o m d r o p l e t s X e + f r o m d r o p l e t s Xe ion counts (cps)
I o n k i n e t i c e n e r g y ( e V )
Figure 3. Kinetic energy distributions of Xe + and Xe +2 ionscreated from Xe doped He droplets in comparison with Xe and Xe Auger ions from free Xe atoms. All ion spectra aremeasured at hν = 90 eV. according to the repulsive Coulomb potential e / (4 πε R )is estimated to 3.3 eV. Thus, each Xe + ion acquiresa kinetic energy of 1.7 eV, which is in good agree-ment with the maximum of the measured kinetic en-ergy distribution. For larger Xe clusters, the KER isexpected to be higher since the interatomic distance be-tween two nearest-neighbor atoms is slightly shorter asit approaches the bond length in bulk Xe, 4 .
26 ˚A [42].The tail in the kinetic energy distribution extendingup to 6.5 eV in the Xe + is likely due to Coulomb ex-plosion of three Xe + ions after creation of one Xe byAuger decay followed by electron charge transfer fromtwo neighboring Xe atoms. The kinetic energy of theXe + for the Coulomb explosion of a Xe trimer systemare expected to range between 3.3 eV and 4.5 eV de-pending on the initial configuration. Furthermore, whenCoulomb explosion occurs in a larger Xe k cluster whereone charge is localized on one Xe atom and the other islocalized on the remaining cluster Xe k − , the Xe + ac-quires a kinetic energy up to the full KER in the limitof a very large Xe + k − . This kinematic effect adds to theasymmetric broadening of the Xe + kinetic energy distri-bution towards higher energies.The Xe +2 ion spectrum shows a bimodal distributionwith a trailing edge (0.5-4 eV) that resembles the one ofthe Xe + ion spectrum (1-6 eV) but scaled down to lowerenergy. Again, this may be due to the kinematic effect,from which we expect a factor of 2 lower energy of Xe +2 than Xe + for the case that Coulomb explosion occursfrom the Xe +3 system. The peak at < . +2 spectrum might be related to a non-thermal ejectionprocess that occurs for vibrationally excited molecularions [43], assuming that part of the Coulomb exploding
061 21 80 . 00 . 51 . 0 0 3 6 9 1 2 1 5 1 8 2 1 2 4 2 70 . 0 00 . 0 50 . 1 0 ( b )( a )
X e
X e - 15 / 2 - 13 / 2
X e a t o m s X e + / X e + X e +2 / X e + X e +3 / X e + X e + X e +2 X e +3 Electron counts (cps)
E l e c t r o n k i n e t i c e n e r g y ( e V )X e d o p e d H e d r o p l e tX e d o p e d H e d r o p l e t( c ) Figure 4. Electron spectra recorded for Xe atoms (a) and forHe droplets doped with Xe atoms ((b) and (c)) at photon en-ergy hν = 90 eV. Black and red spectrum in (a) are recordedin coincidence with Xe and Xe , respectively. The spectradenoted in black, red and blue in (b) recorded in coincidencewith Xe + , Xe +2 and Xe +2 , respectively. The black, red andblue curves in (c) show electron spectra measured in doublecoincidence with Xe + /Xe + , Xe + /Xe +2 and Xe + /Xe +3 , respec-tively. The vertical dashed lines show the energy positions ofthe atomic 4d − / and 4d − / lines according to [44]. Xe +2 are fully decelerated by collisions with surroundingXe and He atoms in the droplets prior to ejection.Fig. 4 shows electron spectra for Xe atoms measured incoincidence with atomic Xe and Xe ions (panel (a))as well as those measured in coincidence with Xe + , Xe +2 and Xe +3 emitted from He droplets (panels (b) and (c)).The two energy-resolved 4d − / and 4d − / lines seen in theatomic PES spectra for Xe and Xe are also presentin the He droplet-correlated electron spectra (Panel (b)).This is another important result of this work. The low-energy part of the He droplet-correlated electron spectracontains a pronounced feature that resembles the low-energy Auger electron spectrum of the atomic Xe PESmeasured in coincidence with Xe . However, the frac-tion of electrons of low-kinetic energy vs. the photolinesis larger for the He droplet-correlated PES than for thecharge-state averaged atomic PES by a factor of 2.5. Thisimplies that in He droplets, part of the photoelectrons are slowed to low kinetic energies by electron-He scattering.Following inner shell ionization of Xe clusters insideHe droplets, ICD or ETMD driven by Auger decay couldbe competing processes to the local atomic Auger de-cay [45–48]. These processes typically generate slow elec-trons which may add to the low-energy part of the Hedroplet-correlated electron spectra observed here. Directexperimental evidence would be the detection of Xe in coincidence with Xe + . However, the Xe signal isquenched by the rapid charge transfer occurring in clus-ters quenches. Direct inner-shell ICD could also takeplace, but its observation is hampered by the low branch-ing ratio with respect to local Auger decay. Core-levelICD in rare gas dimers and clusters has recently beenfound to contribute by only 0.26-0.8 % of the local Augerdecay [49, 50].Overall the resulting electron spectra, which are char-acterized by sharp atomic peaks at high energy and abroad tail that rises towards zero-kinetic energy, have asimilar structure as previously measured Penning ioniza-tion electron spectra of dopants in He nanodroplets [20,26]. The presence of these two features in the spectramay be related to the dopants occupying different statesclose to the droplet surface or deep inside the droplets.Further evidence for the presence of sharp atomicpeaks in the He droplet-correlated Xe electron spectrais obtained from the electron spectra for electron-ion-ion triple coincidence events, shown in panel (c). In-terestingly, the 4d − / , / photolines in the electron-Xe + -Xe + triple-coincidence spectra as well as in the electron-Xe +2 , double-coincidence spectra are slightly shifted to-wards higher kinetic energies as compared to those of Xeatoms. Fig. 5 clearly shows this energy shift on an en-larged scale, which amounts to about 0.2 eV (4d − / ) and0.4 eV (4d − / ) for electrons measured in coincidence withXe + and to about 0.4 eV (4d − / ) and 0.7 eV (4d − / ) forelectrons measured in coincidence with Xe +2 . The redlines depict Lorentzian fit functions whose widths wereset to the resolution of our spectrometer. These energyshifts are consistent with the shifts of inner-shell levelsmeasured in highly resolved electron spectra of free Xeclusters [51, 52]. The latter exhibited well resolved peaksassigned to surface and bulk atoms that were shifted by0.8 and 1.2 eV, respectively, with respect to the freeatomic 4d − / and 4d − / photolines. Thus, within the lim-ited energy resolution of the current experiment, the Hedroplet environment does not seem to induce additionalshifts and broadening of the photolines of the embeddedXe clusters. The fact that the photolines measured in co-incidence with Xe + are nearly unshifted (Fig. 4 b)) mayindicate that Xe + atomic fragments tend to be emittedfrom 4d-ionized Xe or small Xe clusters whose inner-shell electron spectra are only weakly perturbed, whereaslarger Xe clusters, which feature more strongly perturbedelectron spectra, fragment more likely into Xe +2 and Xe +3 . Xe doped He droplets
X e + Electron counts (arb. u.)
E l e c t r o n k i n e t i c e n e r g y ( e V )4 d - 15 / 2 - 13 / 2
X e
X e +2 Xe atoms
Figure 5. Close-ups of the 4d − / and 4d − / photolinesin case of free Xe atoms and Xe clusters formed inside Henanodroplets and irradiated with an XUV photons of energy hν = 90 eV. The solid curves depicted in red are Lorentzianfit functions to determine the energy positions of the 4d − / and 4d − / photolines in each electron spectrum. IV. CONCLUSION
We have reported the first experimental evidence ofdirect one-photon ionization of dopants embedded in Henanodroplets. We exploit the large absorption cross sec-tion for 4d inner-shell ionization of Xe at a photon energyaround hν = 100 eV where He has a low absorption crosssection. For Xe clusters formed inside He nanodroplets,multiply charged Xe atoms created by Auger decay areefficiently partially neutralized into singly charged Xe + k , k = 1 , ,
3, clusters by electron transfer from surroundingneutral Xe and He atoms. Subsequent Coulomb explo-sion generates Xe + ions with up to 6.5 eV of kinetic en-ergy. The electron spectra of droplet-bound Xe clustersfeature both an enhanced low-energy component indica-tive for electron-He scattering, and nearly unshifted 4dphotolines.These results demonstrate that photoelectron spec-troscopy of clusters embedded in He nanodroplets in theXUV range is possible. Very likely, the same holds for x-rays, provided a sufficiently sensitive detection scheme isused that copes with the low target density. This pavesthe way to x-ray photoelectron spectroscopy (XPS) of unconventional atomic clusters and molecular complexes,which can form in He nanodroplets owing to their uniquequantum fluid properties [53–56]. Furthermore, the se-lective multiple ionization of dopants in He nanodropletsis an efficient mechanism for igniting a nanoplasma [57].Probing the dynamics of nanoplasmas by ultrashort XUVand x-ray pulses has attracted considerable attention inthe free-electron laser science community [39, 58–60]. ACKNOWLEDGEMENT
M.M. and L.B.L. acknowledge financial support byDeutsche Forschungsgemeinschaft (DFG, German Re-search Foundation, projects MU 2347/10-1 and BE6788/1-1) and by the Carlsberg Foundation. SRK thanksDST and MHRD, Govt of India, through the IMPRINTprogrammes, and the Max Planck Society. M.M. andS.R.K. gratefully acknowledge funding from the SPARCProgramme, MHRD, India. The research leading tothis result has been supported by the project CALIPSO-plus under grant agreement 730872 from the EU Frame-work Programme for Research and Innovation HORI-ZON 2020. [1] J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. , 2622 (2004).[2] F. Stienkemeier and K. Lehmann, Spectroscopy and dy-namics in helium nanodroplets, J. Phys. B , R127(2006).[3] M. Mudrich and F. Stienkemeier, Photoionisaton of pureand doped helium nanodroplets, Int. Rev. Phys. Chem. , 301 (2014).[4] P. Radcliffe, A. Przystawik, T. Diederich, T. D¨oppner,J. Tiggesb¨aumker, and K.-H. Meiwes-Broer, Excited-state relaxation of Ag clusters embedded in heliumdroplets, Phys. Rev. Lett. , 173403 (2004).[5] E. Loginov, D. Rossi, and M. Drabbels, Photoelectronspectroscopy of doped helium nanodroplets, Phys. Rev.Lett. , 163401 (2005).[6] E. Loginov and M. Drabbels, Excited state dynamics ofag atoms in helium nanodroplets, J. Phys. Chem. A ,7504 (2007).[7] E. Loginov, A. Braun, and M. Drabbels, A new sensitivedetection scheme for helium nanodroplet isolation spec-troscopy: application to benzene, Phys. Chem. Chem.Phys. , 6107 (2008).[8] L. Fechner, B. Gr¨uner, A. Sieg, C. Callegari, F. Ancilotto,F. Stienkemeier, and M. Mudrich, Photoionization andimaging spectroscopy of rubidium atoms attached to he-lium nanodroplets, Phys. Chem. Chem. Phys. , 3843(2012).[9] B. Thaler, S. Ranftl, P. Heim, S. Cesnik, L. Treiber,R. Meyer, A. W. Hauser, W. E. Ernst, and M. Koch,Femtosecond photoexcitation dynamics inside a quantumsolvent, Nature communications , 1 (2018). [10] N. Dozmorov, A. Baklanov, J. von Vangerow, F. Stienke-meier, J. Fordyce, and M. Mudrich, Quantum dynamicsof rb atoms desorbing off the surface of he nanodroplets,Phys. Rev. A , 043403 (2018).[11] L. S. Cederbaum, J. Zobeley, and F. Tarantelli, Giantintermolecular decay and fragmentation of clusters, Phys.Rev. Lett. , 4778 (1997).[12] M. Shcherbinin, A. C. LaForge, V. Sharma, M. Devetta,R. Richter, R. Moshammer, T. Pfeifer, and M. Mudrich,Interatomic coulombic decay in helium nanodroplets,Phys. Rev. A , 013407 (2017).[13] M. Kelbg, M. Zabel, B. Krebs, L. Kazak, K.-H. Meiwes-Broer, and J. Tiggesb¨aumker, Auger emission from thecoulomb explosion of helium nanoplasmas, J. Chem.Phys. , 204302 (2019).[14] A. LaForge, M. Shcherbinin, F. Stienkemeier, R. Richter,R. Moshammer, T. Pfeifer, and M. Mudrich, Highly ef-ficient double ionization of mixed alkali dimers by in-termolecular coulombic decay, Nature Physics , 247(2019).[15] L. Ben Ltaief, M. Shcherbinin, S. Mandal, S. Krish-nan, A. LaForge, R. Richter, S. Turchini, N. Zema,T. Pfeifer, E. Fasshauer, et al. , Charge exchange dom-inates long-range interatomic coulombic decay of excitedmetal-doped helium nanodroplets, J. Phys. Chem. Lett. , 6904 (2019).[16] J. Zobeley, R. Santra, and L. S. Cederbaum, Electronicdecay in weakly bound heteroclusters: Energy trans-fer versus electron transfer, J. Chem. Phys. , 5076(2001).[17] 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, Enhanced ionization of embedded clus-ters by electron-transfer-mediated decay in helium nan-odroplets, Phys. Rev. Lett. , 203001 (2016).[18] L. B. Ltaief, M. Shcherbinin, S. Krishnan, R. Richter,T. Pfeifer, M. Bauer, A. Ghosh, M. Mudrich,K. Gokhberg, A. Laforge, et al. , Electron transfer medi-ated decay of alkali dimers attached to he nanodroplets,Phys. Chem. Chem. Phys. (2020).[19] R. Fr¨ochtenicht, U. Henne, J. P. Toennies, A. Ding,M. Fieber-Erdmann, and T. Drewello, The photoioniza-tion of large pure and doped helium droplets, J. Chem.Phys. , 2548 (1996).[20] C. C. Wang, O. Kornilov, O. Gessner, J. H. Kim, D. S.Peterka, and D. M. Neumark, Photoelectron imaging ofhelium droplets doped with Xe and Kr atoms, J. Phys.Chem. , 9356 (2008).[21] 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, Charge transfer andpenning ionization of dopants in or on helium nan-odroplets exposed to euv radiation, J. Phys. Chem. A , 4394 (2013).[22] M. Shcherbinin, A. C. LaForge, M. Hanif, R. Richter,and M. Mudrich, Penning ionization of acene moleculesby helium nanodroplets, J. Phys. Chem. A , 1855(2018).[23] A. Scheidemann, B. Schilling, and J. P. Toennies,Anomalies in the reactions of he+ with sf6 embedded inlarge helium-4 clusters, J. Chem. Phys. , 2128 (1993). [24] M. Mudrich, A. LaForge, A. Ciavardini, P. O’Keeffe,C. Callegari, M. Coreno, A. Demidovich, M. Devetta,M. Di Fraia, M. Drabbels, et al. , Ultrafast relaxation ofphotoexcited superfluid he nanodroplets, Nature Com-munications (2020).[25] K. K. Lehmann and J. A. Northby, Potential of an ionicimpurity in a large he-4 cluster, Mol. Phys. , 639(1999).[26] S. Mandal, R. Gopal, M. Shcherbinin, A. D’Elia, H. Srini-vas, R. Richter, M. Coreno, B. Bapat, M. Mudrich, S. Kr-ishnan, and V. Sharma, Penning spectroscopy and struc-ture of acetylene oligomers in he nanodroplets, Phys.Chem. Chem. Phys. (2020).[27] 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, Extremeultraviolet ionization of pure he nanodroplets: Mass-correlated photoelectron imaging, penning ionization,and electron energy-loss spectra, J. Chem. Phys. ,084301 (2013).[28] B. Dick, Inverting ion images without abel inversion:maximum entropy reconstruction of velocity maps, Phys-ical Chemistry Chemical Physics , 570 (2014).[29] M. Joppien, R. Karnbach, and T. M¨oller, Electronic ex-citations in liquid-helium: The evolution from small clus-ters to large droplets, Phys. Rev. Lett. , 2654 (1993).[30] L. A. der Lan, P. Bartl, C. Leidlmair, H. Sch¨obel,R. Jochum, S. Denifl, T. D. M¨ark, A. M. Ellis, andP. Scheier, The submersion of sodium clusters in heliumnanodroplets: Identification of the surface → interiortransition, J. Chem. Phys. , 044309 (2011).[31] L. An der Lan, P. Bartl, C. Leidlmair, H. Sch¨obel,S. Denifl, T. D. M¨ark, A. M. Ellis, and P. Scheier, Sub-mersion of potassium clusters in helium nanodroplets,Phys. Rev. B , 115414 (2012).[32] D. L. Ederer, Photoionization of the 4d electrons inxenon, Phys. Rev. Lett. , 760 (1964).[33] U. Becker, D. Szostak, H. Kerkhoff, M. Kupsch,B. Langer, R. Wehlitz, A. Yagishita, and T. Hayaishi,Subshell photoionization of Xe between 40 and 1000 ev,Phys. Rev. A , 3902 (1989).[34] J. Samson and W. C. Stolte, Precision measurements ofthe total photoionization cross-sections of he, ne, ar, kr,and xe, Journal of electron spectroscopy and related phe-nomena , 265 (2002).[35] B. Callicoatt, D. Mar, A. Apkarian, and K. Janda,Charge transfer within he clusters, J. Chem. Phys. ,7872 (1996).[36] T. Ruchti, B. E. Callicoatt, and K. C. Janda, Chargetransfer and fragmentation of liquid helium dropletsdoped with xenon, Phys. Chem. Chem. Phys. , 4075(2000).[37] C. Gnodtke, U. Saalmann, and J. M. Rost, Ionizationand charge migration through strong internal fields inclusters exposed to intense x-ray pulses, Phys. Rev. A , 041201 (2009).[38] T. Oelze, B. Sch¨utte, M. M¨uller, J. P. M¨uller,M. Wieland, U. Fr¨uhling, M. Drescher, A. Al-Shemmary,T. Golz, N. Stojanovic, et al. , Correlated electronic de-cay in expanding clusters triggered by intense xuv pulsesfrom a free-electron-laser, Scientific reports , 1 (2017).[39] Y. Kumagai, H. Fukuzawa, K. Motomura, D. Iablonskyi,K. Nagaya, S.-i. Wada, Y. Ito, T. Takanashi, Y. Sakak- ibara, D. You, et al. , Following the birth of a nanoplasmaproduced by an ultrashort hard-x-ray laser in xenon clus-ters, Physical Review X , 031034 (2018).[40] K. Atkins, Ions in liquid helium, Phys. Rev. , 1339(1959).[41] K. Tang and J. Toennies, The van der waals potentialsbetween all the rare gas atoms from he to rn, The Journalof chemical physics , 4976 (2003).[42] A. Hermann and P. Schwerdtfeger, Complete basis setlimit second-order møller–plesset calculations for the fcclattices of neon, argon, krypton, and xenon, The Journalof chemical physics , 244508 (2009).[43] S. Smolarek, N. B. Brauer, W. J. Buma, andM. Drabbels, Ir spectroscopy of molecular ions by non-thermal ion ejection from helium nanodroplets, Journalof the American Chemical Society , 14086 (2010).[44] P. Lablanquie, S. Sheinerman, F. Penent, R. Hall, M. Ah-mad, T. Aoto, Y. Hikosaka, and K. Ito, Photoemission ofthreshold electrons in the vicinity of the xenon 4d hole:dynamics of auger decay, J. Phys. B: At. Mol. Opt. Phys. , 3265 (2002).[45] Y. Morishita, X.-J. Liu, N. Saito, T. Lischke, M. Kato,G. Pr¨umper, M. Oura, H. Yamaoka, Y. Tamenori,I. Suzuki, et al. , Experimental evidence of interatomiccoulombic decay from the auger final states in argondimers, Physical review letters , 243402 (2006).[46] K. Ueda, X.-J. Liu, G. Pr¨umper, H. Fukuzawa, Y. Mor-ishita, and N. Saito, Electron–ion coincidence momentumspectroscopy: Its application to ar dimer interatomic de-cay, Journal of electron spectroscopy and related phe-nomena , 113 (2007).[47] K. Ueda, H. Fukuzawa, X.-J. Liu, K. Sakai, G. Pr¨umper,Y. Morishita, N. Saito, I. Suzuki, K. Nagaya,H. Iwayama, et al. , Interatomic coulombic decay follow-ing the auger decay: Experimental evidence in rare-gasdimers, Journal of Electron Spectroscopy and RelatedPhenomena , 3 (2008).[48] K. Sakai, S. Stoychev, T. Ouchi, I. Higuchi, M. Sch¨offler,T. Mazza, H. Fukuzawa, K. Nagaya, M. Yao,Y. Tamenori, et al. , Electron-transfer-mediated decayand interatomic coulombic decay from the triply ion-ized states in argon dimers, Physical review letters ,033401 (2011).[49] L. Liu, P. c. v. Kolorenˇc, and K. Gokhberg, Efficiencyof core-level interatomic coulombic decay in rare-gasdimers, Phys. Rev. A , 033402 (2020). [50] A. Hans, C. K¨ustner-Wetekam, P. Schmidt, C. Ozga,X. Holzapfel, H. Otto, C. Zindel, C. Richter, L. S. Ceder-baum, A. Ehresmann, U. Hergenhahn, N. V. Kryzhevoi,and A. Knie, Core-level interatomic coulombic decay invan der waals clusters, Phys. Rev. Research , 012022(2020).[51] O. Bj¨orneholm, G. ¨Ohrwall, and M. Tchaplyguine, Freeclusters studied by core-level spectroscopies, Nucl. In-strum. Methods Phys. Res. A , 161 (2009).[52] M. Tchaplyguine, R. Marinho, M. Gisselbrecht, J. Schulz,N. M˚artensson, S. Sorensen, A. Naves de Brito, R. Feifel,G. ¨Ohrwall, M. Lundwall, et al. , The size of neutral freeclusters as manifested in the relative bulk-to-surface in-tensity in core level photoelectron spectroscopy, J. Chem.Phys. , 345 (2004).[53] J. Higgins, C. Callegari, J. Reho, F. Stienkemeier, W. E.Ernst, K. K. Lehmann, M. Gutowski, and G. Scoles, Pho-toinduced chemical dynamics of high-spin alkali trimers,Science , 629 (1996).[54] K. Nauta and R. E. Miller, Nonequilibrium self-assemblyof long chains of polar molecules in superfluid helium,Science , 1895 (1999).[55] K. Nauta and R. Miller, Formation of cyclic water hex-amer in liquid helium: The smallest piece of ice, Science , 293 (2000).[56] A. Przystawik, S. G¨ode, T. D¨oppner, J. Tiggesb¨aumker,and K.-H. Meiwes-Broer, Light-induced collapse ofmetastable magnesium complexes formed in helium nan-odroplets, Phys. Rev. A , 021202 (2008).[57] D. Schomas et al. , Ignition of a helium nanoplasma byx-ray multiple ionization of a heavy rare-gas core, arXivpreprint arXiv:2005.02944 (2020).[58] H. Wabnitz, L. Bittner, A. De Castro, R. D¨ohrmann,P. G¨urtler, T. Laarmann, W. Laasch, J. Schulz,A. Swiderski, K. von Haeften, et al. , Multiple ionizationof atom clusters by intense soft x-rays from a free-electronlaser, Nature , 482 (2002).[59] M. Hoener, C. Bostedt, H. Thomas, L. Landt, E. Erem-ina, H. Wabnitz, T. Laarmann, R. Treusch, A. De Castro,and T. M¨oller, Charge recombination in soft x-ray laserproduced nanoplasmas, J. Phys. B.[60] T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Fou-car, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp,B. Erk, et al. , Femtosecond and nanometre visualizationof structural dynamics in superheated nanoparticles, Na-ture photonics10