Desorption Dynamics of Heavy Alkali Metal Atoms (Rb, Cs) off the Surface of Helium Nanodroplets
J. von Vangerow, A. Sieg, F. Stienkemeier, M. Mudrich, A. Leal, D. Mateo, A. Hernando, M. Barranco, M. Pi
DDesorption Dynamics of Heavy Alkali Metal Atoms(Rb, Cs) off the Surface of Helium Nanodroplets
J. von Vangerow, † A. Sieg, † F. Stienkemeier, † M. Mudrich, ∗ , † A. Leal, ‡ D.Mateo, ‡ , ¶ A. Hernando, § M. Barranco, ‡ and M. Pi ‡ Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany, Departament ECM,Facultat de Física and IN UB, Universitat de Barcelona, 08028 Barcelona, Spain, Department ofChemistry and Biochemistry, California State University at Northridge, 18111 Nordhoff St.,Northridge, CA 91330, USA, and Laboratoire de Chimie Physique Moléculaire, Swiss FederalInstitute of Technology Lausanne (EPFL), 1015 Lausanne, Switzerland
E-mail: [email protected]
Abstract
We present a combined ion imaging and density functional theory study of the dynamicsof the desorption process of rubidium and cesium atoms off the surface of helium nanodropletsupon excitation of the perturbed 6 s and 7 s states, respectively. Both experimental and theo-retical results are well represented by the pseudodiatomic model for effective masses of thehelium droplet in the desorption reaction of m eff / m He ≈
10 (Rb) and 13 (Cs). Deviations fromthis model are found for Rb excited to the 6 p state. Photoelectron spectra indicate that the ∗ To whom correspondence should be addressed † Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany ‡ Departament ECM, Facultat de Física and IN UB, Universitat de Barcelona, 08028 Barcelona, Spain ¶ Department of Chemistry and Biochemistry, California State University at Northridge, 18111 Nordhoff St.,Northridge, CA 91330, USA § Laboratoire de Chimie Physique Moléculaire, Swiss Federal Institute of Technology Lausanne (EPFL), 1015Lausanne, Switzerland a r X i v : . [ phy s i c s . a t m - c l u s ] J un opant-droplet interaction induces relaxation into low-lying electronic states of the desorbedatoms in the course of the ejection process. Introduction
Helium nanodroplets are fascinating many-body quantum systems which feature unique propertiessuch as an extremely low internal temperature (0.38 K), nanoscopic superfluidity, and the ability toefficiently cool and aggregate embedded species (dopants). Therefore, He nanodroplets are widelyused as nearly ideal spectroscopic matrices for high resolution spectroscopy of isolated atoms,molecules, and clusters.
While most studies so far pertain to the structure and time-independent spectroscopy of dopedHe nanodroplets, the dynamics initiated by laser-excitation or ionization of either the dopants or thedroplets themselves moves into the focus of current research. A limited number of time-resolvedexperiments has been carried out with pure and doped He droplets using femtosecond pump-probe techniques. Likewise, theoretical models of pure and doped He nanodroplets have mostlybeen restricted to static structure and to excitation spectrum calculations.
Only recently, thedevelopment of time-dependent density functional theory (TDDFT) methods applicable to micro-scopic superfluids has opened the way to a time-dependent description of doped He dropletsin a range of sizes comparable to those used in the experiment.
Dopants consisting of alkali (Ak) metal atoms or molecules are particularly interesting due totheir weak attractive interaction with He droplets which results in their location in shallow dimplestates at the droplet surface.
Upon electronic excitation, Ak atoms tend to desorb off theHe droplet as a consequence of the repulsive interaction caused by the overlap of their extendedelectronic orbitals with the surrounding He.
The only known exceptions are Rb and Cs atomsexcited to their lowest excited states.
The dynamics of the desorption process of excited Ak atoms off the surface of He droplets hasbeen recently studied in detail experimentally using the velocity-map imaging technique applied2o Li, Na and Rb atoms, and theoretically using TDDFT for Li and Na.
The calculated Hedroplet response following the dopant excitation process from ns to ( n + ) s states was found tobe quite complex involving different types of density waves propagating through the droplet whilethe Ak dopant is ejected within a few picoseconds. In spite of this, the experiments show thatthe kinetic energy of the desorbed atom depends linearly on the excitation energy of the dopant.This conspicuous result, also reproduced by the TDDFT simulations, gives further support to thepseudodiatomic model which has already been successfully applied to interpreting the absorptionspectra as well as the ion velocity distributions.
According to this model, the dynamics of theexcited AkHe N complex follows that of a dissociating diatomic molecule where He N plays therole of one single atom in this pseudo-diatom. The part of the He droplet that effectively interactswith the Ak atom was found to have an effective mass m eff ≈
15 and m eff ≈
25 amu for Li and Na,respectively. In the present work, we extend previous ion imaging and TDDFT studies to the heaviest stableAk metal atoms Rb and Cs. We again find linear dependences of the ion kinetic energies uponlaser photon energy in both experiment and theory. From these we infer the effective mass of theinteracting He droplet for the desorption of Rb and Cs excited to the perturbed 6 s and 7 s states,respectively.While most excited Ak atoms interact repulsively with a He nanodroplet as a whole, someexcited states experience local attraction with one or a few He atoms. Therefore, as the excited Akatom is expelled from the droplet surface, a bound AkHe molecule or in some cases small AkHe n , n = , These so called ‘exciplexes’ are characterized by havingbound vibronic states as long as the complex is electronically excited. Upon spontaneous decayinto the electronic ground state the exciplex decomposes. For such excited states of the Ak atom,the desorption dynamics may be expected to deviate from that described by the simple dissociatingpseudo-diatom model.In our previous experiment on Rb-doped He droplets excited into the 6 p Π state, the ion kineticenergy distributions indicated that desorption of excited Rb atoms and RbHe exciplexes proceeds3long the repulsive pseudodiatomic potential which correlates to the closest-lying excited 6 p stateof the free Rb atom. However, the photoelectron spectra clearly revealed that a large fraction of thedesorbed Rb atoms have electronically relaxed into lower-lying levels. The photoelectron spectracontained components of the 6 p state and of lower-lying levels (4 d and 5 p / ). Previously, droplet-induced relaxation of excited Rb atoms was only observed within the 5 p / , / fine-structure doublet. For Rb and Cs injected into bulk superfluid He fast relaxation of the low-est excited p / state into the p / and probably to the s / ground state was found to proceedwithin ∼
30 ps. For Na-doped He nanodroplets, droplet-induced electronic relaxation was first observed onlyfor higher-lying excitations with principal quantum numbers n >
6, where the dopant-droplet in-teraction induces significant mixing of electronic configurations. In a more recent study, even forthe 3 d , 5 s and 4 d -states the authors found indications for droplet-induced decay into lower-lyinglevels. Interestingly, the presence of the relaxation channels was also visible in the speed distri-butions of the desorbed atoms, which contained multiple components. High-lying Rydberg stateswere found to completely relax into levels n ≤
7. Based on these observations, the authors sug-gested that droplet-induced relaxation proceeds via level-crossings of the pseudodiatomic potentialcurves which occur while the local He droplet environment of the excited Na dopant dynamicallyrearranges. Efficient He droplet-induced electronic relaxation was also observed for barium andfor the transition metal atoms silver, chromium and copper, which are submerged in thedroplet interior.Note, however, that the light Ak metals Li and Na were not found to electronically relax bydroplet interactions when excited into the lowest excited s -states (orbital angular momentum (cid:96) = In contrast, in the present study on Rb and Cs atoms in their lowest excited s -states wedetect exclusively relaxed electronic levels in the photoelectron spectra. We discuss the apparentdiscrepancy between the ion and electron measurements in terms of the desorption dynamics andelectron energetics. 4 xperimental The experiments presented here are performed using the same setup as described previously. In short, a continuous beam of He nanodroplets with a mean size ranging from 200 to 17000 Heatoms per droplet is generated by varying the temperature T of a cryogenic nozzle with a diameterof 5 µ m. An adjacent vacuum chamber contains a vapor cell filled with bulk metallic Rb orCs heated to 85 ◦ C and 70 ◦ C, respectively. In the detector chamber further downstream, the Hedroplet beam intersects a dye laser beam (Sirah Cobra, pulse length 10 ns, pulse energy 10 µ J,repetition rate 1 kHz) at right angles in the center of a velocity map imaging (VMI) spectrometer.The laser is linearly polarized along the direction of the He droplet beam, which is perpendicularto the symmetry axis of the VMI spectrometer. We record single events per image frame forwhich the coordinates are determined using the centroid method. Velocity-map photoelectron andphotoion images are transformed into kinetic energy distributions using standard Abel inversionprograms.
Theoretical approach
In order to model the absorption spectra as well as the dynamic response of the excited doped Hedroplets we describe the doped He droplets within the Density Functional Theory (DFT) frame-work. The basic ingredients of our approach are described in detail in Refs.
Let us just recallthat we have used the Born-Oppenheimer approximation to factorize the electronic and nuclearwavefunctions, the Franck-Condon approximation which assumes that the atomic nuclei do notchange their positions or momenta during the electronic transition, and the diatomics-in-moleculesapproximation (pseudodiatomic model). We have first obtained the structure of the Rb-droplet and Cs-droplet complexes in the groundstate. Throughout this work we have used the Orsay-Trento (OT) density functional neglectingthe backflow term. The Rb-He and Cs-He ground state pair potentials V X have been taken fromRef. Due to the large mass of Rb and Cs compared to that of He, we describe them as classical5articles in the dynamics while their effect in the statics is incorporated as an external field actingupon the droplet. Accordingly, the energy of the system is written as E [ ρ ] = (cid:90) d r ¯ h m He (cid:12)(cid:12) ∇ (cid:112) ρ ( r ) (cid:12)(cid:12) + E He [ ρ ( r )]+ (cid:90) d r ρ ( r ) V X ( | r Ak − r | ) , (1)where E He is the OT potential energy density per unit volume, Ak represents either the Rb or Csatom, and ρ is the He particle density. Upon variation, one obtains the Euler-Lagrange equationthat has to be solved to determine the equilibrium density ρ ( r ) of the droplet and the location ofthe dopant Rb or Cs atom r Ak . Schematically, δδ ρ (cid:18) ¯ h m He (cid:12)(cid:12) ∇ √ ρ (cid:12)(cid:12) + E He (cid:19) + V X = µ , (2)where µ is the chemical potential of the He droplet that throughout this paper is made of N = This will be useful fordetermining the mean kinetic energy of the ejected Ak atom as a function of the excess excitationenergy.Equation ( ?? ) has been solved in cartesian coordinates using a spatial grid of 0.4 Å and a 200 × ×
250 points mesh. The derivatives have been calculated with 13-point formulas. Extensiveuse of fast-Fourier techniques has been made to efficiently calculate the energy density and dopant-droplet interaction potentials.
The dynamics is triggered by the sudden substitution of the Ak-He ground state pair potentialby the excited one. Within TDDFT, we represent the He droplet by a complex effective wavefunc-tion Ψ He ( r , t ) such that ρ ( r , t ) = | Ψ He ( r , t ) | . The position of the Ak atom r Ak ( t ) obeys Newton’sequation. For excitations involving two s states, the evolution equations derived in Ref. adopt a6imple form, namely i ¯ h ∂∂ t Ψ He = (cid:20) − ¯ h m He ∇ + δ E He δ ρ ( r ) + V ns ( r − r Ak ) (cid:21) Ψ He m Ak ¨ r Ak = − ∇ r Ak (cid:20) (cid:90) d r ρ ( r ) V ns ( r − r Ak ) (cid:21) . (3)In the above equations, V ns with n = ( ) is the 6 s ( s ) excited Rb(Cs)-He pair potential. Theinitial configuration to solve Eqs. (3) is the static dopant-droplet configuration, either at equilibriumor with the dopant sitting in another position around the surface dimple, Ψ ( r , t = ) = (cid:112) ρ ( r ) , r Ak ( t = ) = r Ak . The initial velocity of the Ak dopant is set to zero.Equations (3) have been solved using the same grid as for the static problem and a time stepof 0.5 fs. We have used a predictor-corrector method fed by a few time steps obtained by afourth-order Runge-Kutta algorithm. Photoions
In this work we focus on the ns Σ → ( n + ) s Σ transitions of the RbHe N and CsHe N pseudo-diatoms,where n = , The ionic potential is obtained byintegration of the Rb + -He pair potential over the He density distribution corresponding to theRb ground state configuration, which we assume to be frozen. Since the Ak-He interaction in theexcited ( n + ) s Σ states is purely repulsive, the excited Ak atoms detach from the He droplets asneat atoms. Subsequent ionization by the absorption of a second photon from the same nanosecondlaser pulse yields atomic ions which we detect with the VMI spectrometer.Using these potentials, we have obtained the Rb and Cs absorption spectra by calculatingwave functions and Franck-Condon factors for the pseudodiatomic transitions using R. LeRoy’sprogram BCONT 2.2 . The results are depicted in Fig. 2. We have also calculated the Rb 5 s Σ → D i s t a n c e f r o m t h e d r o p l e t s u r f a c e ( Å )
R b + Wave number (1000 cm-1) S P S S R b + e - H e N R b
Figure 1: Sketch of the excitation and ionization scheme of Rb attached to He nanodroplets. Uponexcitation of the RbHe N complex to a repulsive pseudodiatomic potential, the Rb atom departsfrom the droplet surface and is ionized by a second photon from the same laser pulse.8 - 1 )( c )( a ) 6 P S L a s e r w a v e n u m b e r ( c m - 1 ) FCF (arb. u.) DFT (arb. u.) P S Ion signal (arb. u.)
R b ( d )( b )
C s
Figure 2: Simulated (a, b) and measured (c, d) photoionization spectra of He nanodroplets dopedwith Rb and Cs. The filled curves in (a, b) show Franck-Condon calculations based on Rb-He N andCs-He N pseudodiatomic potentials; the blue lines show the Rb 6 s Σ (a) and Cs 7 s Σ (b) absorptionprofiles obtained from the present atomic-like DFT sampling method.6 s Σ and Cs 6 s Σ → s Σ absorption band contours by employing the atomic-like DFT samplingmethod described in Ref., shown in that figure as blue lines. The vertical dashed lines indicatethe atomic transitions.Both experimental and theoretical absorption spectra are characterized by broad bands whichare blue-shifted with respect to the free atomic transitions. The blue-shift of the transitions of Rbattached to He droplets results from the fact that all excited pseudodiatomic potentials are repulsivewhereas the ground state is slightly attractive (Fig. 1). The widths of the absorption contoursreflect the width of the ground state wave function which is mapped onto the excited repulsivepotential upon excitation. While the calculated Franck-Condon profile of the Rb 6 p Π transitionand the experimental spectrum is satisfactory, the Franck-Condon profile of the 6 s Σ transition isslightly red-shifted with respect to the experimental contour, whereas the DFT result is blue-shifted(Fig. 2 a and c). The photoionization spectrum of Cs (Fig. 2 d) features a maximum in the range ∼
18 300-19 000 cm − associated with the 7 s Σ transition. The corresponding DFT calculation(Fig. 2 b) yields a peak centered at 19 635 cm − , which is again significantly blue-shifted. The9FT calculation thus overestimates the atomic shift, being unclear which part of the disagreementhas to be attributed to deficiencies of the model and which to inaccuracies of the excited Ak-Hepair potentials we are using. Note that a broad Rb + ion signal level which features a step around 20 700 cm − is measuredaround the 6 s Σ feature, as previously observed in photoion and laser-induced fluorescence spec-tra around the 6 p Π transition. This contribution may be due to photoionization of Rb dimerswhich fragment into Rb + . In particular, at wave numbers below 20 700 and above 21 000 cm − we observe significant Rb + signals in the tof mass spectrum which could be due to resonance-enhanced ionization via the 2 Σ u and via the 2 Σ u , 2 Π u , or 3 Π g states of Rb , respectively. The dynamics of the laser-induced desorption process of Rb and Cs atoms is studied by record-ing velocity-map ion images. Fig. 3 (a) and (b) displays the raw and inverted Rb + ion images takenupon excitation to the 6 s Σ state of the RbHe N complex at the laser wave number ¯ ν =
20 800 cm − .The image features a circular intensity distribution with a pronounced anisotropy of the angulardependence. The intensity maxima are directed along the polarization axis of the laser (yellowarrow), as expected for the parallel 5 s Σ → s Σ transition. The velocity-map ion images of Csrecorded at the 6 s Σ → s Σ transition around ¯ ν =
18 700 cm − closely resemble those for Rb. Inthe measurements of Rb excited to the 5 p Π state around ¯ ν =
24 100 cm − , the opposite anisotropyis observed as expected for a perpendicular Σ → Π transition in the frame of the pseudodiatomicmodel. From these images we infer the ion kinetic energy distributions (KED) by applying inverseAbel transformation and angular integration. Typical examples of such KED for excitation aroundthe maximum of the 6 s Σ band are depicted in Fig. 3. Similarly to the previous measurements withLi and Na, the KED consist of well-resolved maxima of widths ∼
70 meV which shift towardhigher kinetic energies as the photon energy increases.Figure 4 presents a compilation of the results of the analysis of the ion images recorded aroundthe Rb 6 s Σ band as a function of the laser wave number. The total Rb + ion counts [black squaresin a)] reproduce the photoionization spectrum (red diamonds) with some systematic deviation at10
10 20 30 40 50 -1 -1 P r obab ili t y ( a r b . u . ) -1 Rb + kinetic energy (meV) (b) (a) (c) Figure 3: Top: Raw (a) and inverse Abel transformed (b) velocity-map Rb + ion images recordedwhen exciting Rb atoms attached to He nanodroplets on the transition 5 s Σ → s Σ at the laserwave number ¯ ν =
20 800 cm − . The laser polarization direction is indicated by the vertical arrow.Bottom: Rb + ion kinetic energy distributions inferred from ion images recorded at the indicatedlaser wave numbers. 11 . 0 20 . 0 40 . 0 60 . 0 80 . 1 00 . 1 22 23 34 4 2 0 6 0 0 2 0 8 0 0 2 1 0 0 0 2 1 2 0 0 2 1 4 0 00 . 00 . 51 . 01 . 52 . 0 L a s e r w a v e n u m b e r ( c m - 1 ) Counts per frame a ) b b ) Rb+ KER (meV) c )
Figure 4: (a) Total Rb + ion counts and tof peak intensity (red), (b) Rb + mean kinetic energies, (c)anisotropy parameters β inferred from ion images recorded at various laser wavelengths aroundthe maximum of the Rb 6 s Σ absorption band. 12ave numbers >
20 850 cm − of unknown origin. The mean values of the KED inferred fromthe images, shown in Fig. 4 (b), nearly linearly increases with laser wave number. In addition,Fig. 4 (c) shows the variation of the anisotropy parameter β within a 4 sigma range around theKED intensity maximum inferred from the angular distributions I ( θ ) by fitting to the generalexpression for the probability distribution of one-photon transitions I ( θ ) ∝ + β P ( cos θ ) . Forlaser wave numbers close to the maximum of the 6 s Σ absorption band (20700-21100 cm − ) weobtain beta=1.9(3). Within the experimental error this is consistent with the value β = Σ − Σ transition. In this case the angulardistribution of dissociation products takes the form I ( θ ) ∝ cos θ .This result nicely confirms the validity of the pseudodiatomic model and the assignment of thespectral band to the parallel 5 s Σ → s Σ transition. However, in the wings of the absorption peak wefind the anisotropy of the angular ion distribution to be significantly reduced. This may be due tothe contribution of fragment ions from Rb dimers which are present to a small extent in the dropletbeam. Besides, it is conceivable that dynamic deformations of the local He droplet environmentduring the departure of the Rb atom induce perturbations of the electronic configuration of theexcited Rb atom which are not accounted for in the pseudodiatomic picture.In order to obtain more detailed insight into this process, we have simulated the ejection ofa Rb atom from the nominal 6 s state and of a Cs atom from the nominal 7 s state using TDDFTcalculations. The velocities and positions as a function of time for Rb and Cs ejected from theequilibrium position at the surface dimple are shown in Fig. 5. It can be seen that the Cs atomreaches an asymptotic velocity of ∼
230 m/s after a time evolution of ∼ .
25 ps. By this time, theCs atom is ∼ ∼
350 m/s, ∼ ∼ . V e l o c i t y 0 1 2 3 4 5 024681 0 ( b ) C s P o s i t i o n
Position of Cs atom (Å)
T i m e ( p s )
Velocity of desorbing Rb / Cs atom (m/s)
V e l o c i t y ( a ) R b 024681 01 21 41 6 P o s i t i o n
Position of Rb atom (Å)
Figure 5: (Color online) Velocity (solid line, left scale) and displacement from its equilibriumlocation at the surface dimple (dashed line, right scale) of the desorbing Rb (a) and Cs (b) atomsas a function of time after excitation of the 6 s Σ state.14inear density waves are excited in the droplet which take a large part of the energy deposited inthe system upon photo excitation, the desorption dynamics is rather insensitive to them.
01 02 03 04 05 06 0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 001 02 03 04 05 06 0 ( a ) R b
E x p e r i m e n t T h e o r y L i n e a r f i t e x p . L i n e a r f i t t h e o r y ( b ) C s
Mean ion kinetic energy (meV)
E x c e s s e n e r g y h (cid:2) (cid:1) - E ( ) ( m e V ) Figure 6: Mean kinetic energies of desorbed Rb (a) and Cs (b) atoms upon excitation to the 6 s Σ and 7 s Σ states, respectively. Straight lines: linear fits to the theoretical and experimental data.Detailed information about the kinematics of the desorption process can be gained from thekinetic energies of the desorbing dopants as a function of the excess excitation energy (differencebetween photon energy and internal energy of the free Rb or Cs atom in the 5 s and 6 s states). The results are shown in Fig. 6 and compared to the experimental mean kinetic energies. Thecalculated points have been obtained by starting the dynamic simulation from different positionsof the Ak obtained by a constrained minimization of the total energy of the Ak-He N complex as15ndicated in Sec. III.For both Rb and Cs dopants, the kinetic energy displays a linear dependence on the excessexcitation energy. This dependence indicates that in spite of its apparent complexity, the ejectionprocess is well represented by the pseudodiatomic model. Indeed, imposing the energy andlinear momentum conservation in the instantaneous ejection of the Ak atom from the droplet oneobtains E kin = η ( ¯ h ω − ¯ h ω ) . (4)Here, ω denotes the laser frequency and ω is the atomic transition frequency. Within this model,the value of the slope η is related to the mass m eff of the part of the He droplet that effectivelyinteracts with the Ak atom by η = m eff m eff + m Ak = ⇒ m eff = η − η m Ak . (5)By fitting the experimental and simulation data to the expression Eq. ( ?? ) one obtains a theoreticalvalue m eff ∼ . . m eff ∼ . . are collected in Table 1 and plotted in Fig. 7. One observesan increase of m eff with the mass of the Ak atom, as indicated by Eq. ( ?? ), although the prefactor η / ( − η ) has the opposite behavior.The conspicuous dependence of the effective mass of the helium droplet m eff on the Ak dopantmass m Ak is expected to be mainly determined by two effects. On the one hand, the geometricstructure of the excited Ak-droplet system is different for each species due to slight variationsof the ground state equilibrium configuration (radius of the surface dimple, distance of the Akatom from the surface) as well as due to a varying mean radius of the excited Ak atom orbital r e .On the other hand, the kinematics of the dissociation process induces an Ak mass-dependence,irrespective of the differing geometric initial conditions.16 C sR bN a
E x p e r i m e n t a l D F T G e o m e t r i c K i n e m a t i c
Effective helium mass (amu)
A l k a l i d o p a n t m a s s ( a m u )
L i
Figure 7: Experimental, theoretical and estimated values of the effective mass of the He droplet inthe desorption process of various alkali species excited to their first excited s -states.17he geometric effect is estimated by computing the geometrical overlap of the electron orbit ofthe excited Ak atom with the adjacent He atoms of the dimple. Based on the He dimple parametersspecified in Ref. and on values for the mean orbital radius (cid:104) r e (cid:105) we calculate the number of Heatoms in the overlap volume V eff of the excited Ak orbit and He dimple surface, N He , eff = V eff ρ eff .Here, ρ eff is taken as half the bulk value ρ He = . − which roughly matches the average Hedensity within the overlap volume due to its location dimple surface where the density smoothlyfalls off. The mean orbital radius is approximated by (cid:104) r e (cid:105) = a ( n − δ l ) , (6)where a is the Bohr radius and δ l is the quantum defect of the Ak excited state. The correspondingvalues of (cid:104) r e (cid:105) and N He , eff are added to Table 1 and to Fig. 7.The kinematic effect of the varying mass of the desorbing Ak atom is probed by solving theclassical equations of motion of the Ak atom being repelled off a linear chain of effective, mutu-ally non-interacting He atoms, each containing the mass of 7 He atoms which roughly equals thenumber of He atoms in the first surface layer next to the Ak dopant. The initial spacing betweenthe He “layersÂt’Ât’ is taken as the average distance between He atoms in the droplets, 3 . The distance between the Ak atom and the fist He “layerÂt’Ât’ is held fixed at 5 . V Ak − He ( d ) = . ( − d / − ) (in atomic units) is used for all Akspecies. The trajectories of the Ak atoms closely follow those shown in Fig. 5 and the trajectoriesof the He layers show that mostly the first He layer participates in the desorption dynamics. Ac-cordingly, the effective mass of the He droplet (approximated by the linear chain of atoms with themass of the He layers) only slightly exceeds the mass of the first He layer, 28 amu, see the solidline in Fig. 7.While the He effective mass in this simple kinematic model matches the experimental and DFTvalues for Rb, the variation as a function of Ak dopant mass is not sufficiently well reproduced(Fig. 7). The simple estimate based on the geometric Ak-He orbital overlap, however, shows a18trong variation of the effective mass in surprisingly good agreement with the experimental values.We therefore conclude that the difference in the number of interacting He atoms for the differentAk species is likely related to the difference in the dimple structure and excited electron orbit ratherthan to the kinematics of the desorption process.The detailed picture of the dynamics of the He droplet upon excitation of the Ak atom isobtained from the DFT calculations. Fig. 8 shows the evolution of the CsHe and RbHe complexes after the Ak atom has been excited. It can be seen the dramatic changes in the dropletdensity caused by the excitation and subsequent ejection of the dopant.Figure 9 shows the evolution of the He cross-sectional density profiles of a He dropletdoped with a Rb and a Cs atom for the first 5 ps. Initially, the droplet extends along the z symmetryaxis from about 0 to 44 Å, and the Ak atom is located in a dimple at the droplet surface (near z = ( n + ) s state causes the dimple first to deepen due to the highlyrepulsive Ak-He interaction in the ( n + ) s Σ state. The associated compression of the He dropletlasts up to ∼ z =
42 Å) isunperturbed and at rest, indicating that during these first ps the energy deposited in the dropletgoes to its internal excitation and not to its center-of-mass motion.Figures 8 and 9 reveal that the excitation of the Cs and Rb atoms launches highly non-lineardensity waves into the droplet. In the case of Rb, the first perturbation front, labeled as 1, movesat ∼
900 m/s. This perturbation generates carrier waves with a phase velocity of ∼
430 m/s,modulated by supersonic envelope fronts with growing intensity. The ones with highest intensity,labeled as 2, have a group velocity of ∼
700 m/s. Next, a high intensity wave appears traveling at ∼
410 m/s (labeled as 3), which generates secondary waves propagating backwards. In the case ofCs, the velocities of the fronts are 880 m/s, 675 m/s, and 410 m/s, respectively. A similar behaviorwas found in Ref. for Na and Li atoms.As an extension of our previous ion imaging measurements at the Rb 6 p Π band we analyzehere the mean ion kinetic energy as a function of the excess energy. Since in the 6 p Π configuration19igure 8: Evolution of the He density distributions of the CsHe (left column) and RbHe (right column) systems after excitation to their ( n + ) s Σ states. (Multimedia view)20igure 9: Evolution of the He density profile of the AkHe system along the symmetry axis.Three supersonic wave fronts are identified and labeled by 1 to 3. Equidensity lines correspondingto 0.5 and 0.1 times the He saturation density, 0.0218 Å − , representing the surface region of thedroplet, are shown in white. 21 h (cid:2) (cid:1) - E ( ) ( m e V )E x c e s s e n e r g y h (cid:2) (cid:1) - E ( ) ( m e V ) Mean ion kinetic energy (meV)
R b + R b H e + R b P - 2 0 - 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 Figure 10: Experimental mean kinetic energies of Rb atoms and of RbHe exciplexes ejected out ofHe droplets upon excitation of the 6 p Π state of the RbHe N complex. The lines are linear fits to thedata. 22he Rb-He pair potential along the internuclear axis is attractive, RbHe exciplexes are formedwith roughly 40% relative abundance. Therefore, we record ion images for Rb + and RbHe + ions separately and extract the mean ion kinetic energies for each of the two species.Figure 10 shows that the data points lie on a straight line that surprisingly intercepts the abscissaat a finite value of the excess energy of about −
22 meV. Using Eq. ( ?? ), from the slope of the line η one obtains m eff = . m eff = . s Σ state.The fact that the extrapolation of the 6 p Π experimental data to zero kinetic energy yields a finiteenergy shift at zero kinetic energy, at variance with the extrapolation of the 6 s Σ data, discloses anintrinsic limitation of the method used to analyze the results. The pseudodiatomic approximation,even if appropriate for the description of a direct dissociation via a purely repulsive state, does notaccount for other effects which are present in the dissociation kinematics of the ( n + ) p excitation.In the case of the 6 p Π state of Rb, the dopant-He interaction contains both repulsive and attractivecontributions, the latter inducing the formation of exciplexes. It is conceivable that the bindingenergy of the RbHe exciplex may be converted into additional translational energy upon desorptionof RbHe. This interpretation has recently been invoked to rationalize the negative excess energyoffset measured for NaHe exciplexes formed upon excitation of Na into the droplet-perturbed3 d state. The binding energy of RbHe in the 6 p Π state amounts to about 8 meV, which doesnot account for the observed energy shift alone. Additional internal energy may be released intotranslational motion of the desorbing Rb by droplet-induced relaxation of population from theupper 6 p / into the lower 6 p / spin-orbit state of Rb. In that case, the excess energy axis wouldbe down-shifted as represented by the horizontal top scale of Fig. 10 provided the droplet effectivemass is the same ( m eff = . + ions are actually produced by23issociative ionization of RbHe, the latter being the dominant product of the desorption reaction.Thus, it seems that the pseudodiatomic model no longer strictly applies when the internal de-grees of freedom of the constituent atom are involved in the dynamics. Note that for the case of thedesorption of sodium (Na) atoms excited to the 3 p state deviations from the pseudodiatomic modelwere also observed. However, in contrast to the Rb case discussed here, a positive value for theabscissa intercept was found. TDDFT studies of Ak atoms ejected from the ( n + ) p excited statescould help elucidate this open issue, but improved Ak-He pair potentials have to be previouslyobtained. Photoelectrons
Complementary information about the dynamics following laser excitation of Ak atoms attachedto He nanodroplets is obtained from imaging photoelectrons. In the experiment, velocity-mapphotoelectron images are obtained by simply reversing the polarity of the voltages applied to therepeller and extractor electrodes. A typical raw and inverse Abel transformed image recordedat the laser wave number ¯ ν =
21 400 cm − is depicted in the upper and lower half of Fig. 11 (a),respectively. The image clearly contains three separated ring structures, indicating that ionizationoccurs out of three Rb atomic orbitals. The faint ring structure between the two inner rings inthe low half of Fig. 11 (a) is an artifact of the inverse Abel tranformation caused by the limitedstatistics. As for the ion images, we again convert the electron images into angular distributionsand electron kinetic energy spectra. The latter are shown in Fig. 11 (b) for Rb and in (c) for Cs.Surprisingly, all the photoelectron spectra recorded within the Rb 6 s Σ band reveal contributionsof the Rb 5 p / , 5 p / and 4 d atomic levels. No electron signal associated with the 6 s state isdetected within the noise level, although the 6 s state is the dominant atomic component of theoriginally excited 6 s Σ state of the RbHe N complex. The same holds for Cs excited to the 7 s Σ state. Only one peak is present in the spectrum due to ionization out of the Cs 5 d state. The 6 p states, which are probably populated as in the Rb case, are not detected because of insufficient24 a) Rb Figure 11: (a) Raw (upper half) and Abel inverted photoelectron image (lower half) of Rb + ionsrecorded with Rb-doped He nanodroplets excited into the 6 s Σ state at the laser wave number ¯ ν =
21 400 cm − . (b) and (c) Photoelectron spectra of Rb and Cs inferred from images recorded at thelaser wave numbers 21 400 cm − and 18 700 cm − , respectively. The vertical bars represent therelative populations in the respective atomic states.25hoton energy for one-photon ionization of the 6 p states.This result is at odds with the previous measurements of Li and Na excited to ( n + ) s statesand to our previous photoelectron spectra recorded at the Rb 6 p Π band where on resonance thedominant photoelectron signals came from the correlating atomic 6 p state. The lower lying 4 d and 5 p / , / states became particularly apparent for off-resonant excitation. In the present case,however, the absence of the Rb 6 s and Cs 7 s photoelectron signals is probably due to the partic-ularly small photoionization cross sections of about 0 .
01 Mb which result from Cooper minimaclose to the laser wave numbers used in the experiment.
For comparison, the detected stateshave photoionization cross sections >
10 Mb.
In the case of Na attached to He nanodroplets, the appearance of lower-lying atomic states wasattributed to the short radiative life time of the excited level as compared to the laser pulse length. In the Rb and Cs cases, however, as for the Rb 6 p Π state previously studied, the lifetimes of thefree Rb and Cs atoms in the 6 s and 7 s states ( ∼
50 ns ) by far exceed the laser pulse length(9 ns). Moreover, the appearance of the 4 d state of Rb and of the 5 d state of Cs cannot be explainedby spontaneous radiative decay due to selection rules. Merely the Rb 5 p photoelectron signalmay contain a contribution from radiative decay. Therefore, we attribute the population of lower-lying electronic states to He droplet-induced relaxation. Whether this relaxation mechanism ispredominantly non-radiative or whether the dopant-droplet interaction induces fast radiative decayeven at nominally forbidden transitions cannot be determined from theses measurements.The vertical bars in Fig. 11 (b) and (c) depict the relative populations of the detected states asinferred from the peak integrals weighted by the photoionization cross sections. The correspondingvalues of the undetected Rb 6 s and Cs 7 s -states reflect the noise level and can only be consideredas upper bounds. Thus, while the populations of the Rb 6 s and Cs 7 s states and of the lower lyingstates (Rb 5 s and Cs 6 s , 6 p ) are undetermined, the Rb 5 p / and 4 d states are nearly equally popu-lated. When assuming that the Rb 5 p level is populated purely by radiative decay, this populationcorresponds to a fraction of about 13% of the original 6 s population whereas the 5 p / state ispopulated only by 7%. However, the fact that the measured population of the 5 p / state only26mounts to about 8% of the 5 p / population indicates that an additional droplet-induced decayprocess is active. In the case of Cs only the 5 d state is detected so no quantitative comparison withother states can be made.The detection of photoelectrons exclusively out of relaxed states seems to contradict the resultsfrom ion imaging which clearly demonstrate that desorption proceeds according to the pseudo-diatomic model for a fixed ( n + ) s Σ electronic configuration. For Na excited into the droplet-perturbed states 5 s and 4 d , the presence of relaxation channels was also observed in the speeddistributions of the desorbed atoms. A broad, nearly laser wavelength independent componentextending out to velocities ∼ ∼
270 meV) was assigned to atoms havingundergone relaxation to the lower 3 d -level. However, in the present experiments on Rb and Cs inthe ( n + ) s -state, no such broad component of the ion distributions is observed (see Fig. 3). Therange of kinetic energies observed (Fig. 6) matches well the values expected for dissociation toproceed along the Rb and Cs ( n + ) s Σ potentials, see Fig. 1.Furthermore, we have considered the possibility that the photoelectron peaks from relaxedstates could be associated with Rb + and Cs + dimer ions. However, the relative yield of dimersfalls far below the proportion of photoelectrons in relaxed states. Besides, the dependence of thesignal intensity of the relaxed electrons on the Rb and Cs vapor pressure in the doping cells clearlyindicates that these electrons correlate to Rb + and Cs + atomic ions. In addition, the possiblecorrelation of these electrons with large ion masses, resulting from unfragmented ion-doped Hedroplets, was probed by performing dedicated time-of-flight measurements using a different detec-tion unit. The measured proportion of large cluster ions to Rb + again stayed well behind that ofrelaxed electrons to (undetected) electrons out of the Rb 6 s -state. However, due to the uncertaintyin determining the relative detection efficiency for large ions, this possibility cannot strictly beruled out.Thus, our observations seem to imply that electronic relaxation occurs with some time delaywith respect to the strong repulsive interaction which accelerates the dopant atom away from thedroplet surface. He induced electronic couplings may be facilitated by the formation of a com-27ressed shell of He atoms around the dopant in the course of desorption ( t = s Σ band. The slight shift to higher wave numbers of thespectral feature measured by detecting electrons with respect to ions [Fig. 12 (a)] likely resultsfrom contributions of ionized Rb in the electron measurement.The relative yields of photoelectrons out of the relaxed states 4 d , 5 p / , and 5 p / are depictedin Fig. 12 (b). Similarly to our previous measurements around the Rb 6 p Π state, the relative pop-ulations of the lowest detected levels increase as the laser is detuned below the droplet resonance.This change in relative populations likely reflects the variation of the monomer to dimer ratio.Changing relaxation rates into the various target electronic states of Rb due to droplet interactionsmay also contribute.The anisotropy parameters β and β , which characterize the angular distribution of emittedelectrons by two-photon ionization, are depicted in Fig. 12 (c) and (d). The values of β remainnearly constant within the accuracy of the measurement over the excitation spectrum. The β values for the 5 p states are roughly consistent with zero for all laser wave numbers. This indicatesvanishing alignment of the electron orbitals as previously found for Rb 6 p Π excitation. However,the 4 d orbital appears to retain a certain degree of orbital alignment when exciting on the blue sideof the Rb 6 s Σ band. Likely, this is due to faster desorption when exciting further up on the repulsivebranch of the Rb-He N potential. Summary
We have studied the desorption dynamics of the heavy alkali metal atoms Rb and Cs off the sur-face of He nanodroplets, initiated by excitation to the perturbed 6 s and 7 s states, respectively. As28 . 00 . 51 . 01 . 50 . 00 . 51 . 00 . 00 . 51 . 0 Counts per frame
R b + x 1 0 e - a )b ) 5 p e - o u t o f 4 d e - o u t o f 4 d5 p c ) 5 p e - o u t o f 4 dd ) b b L a s e r w a v e n u m b e r ( c m - 1 ) Figure 12: Total photoion signal and photoelectron counts (a), relative abundances of electrons outof different atomic states (b), and anisotropy parameters β (c) and β (d) inferred from electronimages recorded a various laser wavelengths around the maximum of the Rb 6 s Σ absorption band.29or Li and Na adatoms, the calculations reveal a complex response of the helium droplet to theimpulsive perturbation induced by the excitation of the Rb and Cs adatoms. We find significantlocal deformations of the droplets and three distinct types of non-linear density waves which prop-agate through the droplets at different speeds. Nevertheless, both the measured and theoreticallycalculated mean kinetic energies of the desorbed atoms, which are in excellent agreement, canbe modeled as a simple pseudodiatomic direct photodissociation reaction driven by a highly re-pulsive interaction. We find values of the effective mass of the He droplet interacting with Rband Cs of about 10 and 13 He atoms, respectively. Deviations from this simple model are foundexperimentally for the desorption dynamics of Rb on helium droplets excited to the 6 p state.The photoelectron spectra measured upon excitation to the perturbed 6 s and 7 s states evidencesignificant electronic relaxation of the desorbed Rb and Cs atoms into lower-lying states, at vari-ance with analogous measurements using the light alkali species Li and Na attached to He droplets.While the ion and electron measurements appear to be contradictory, possible correlations of theobserved electrons with other ion signals can largely be ruled out.This puzzling issue will be further studied by measuring photoelectron spectra with femtosec-ond time-resolution in pump-probe experiments. Further theoretical work in this direction is alsoplanned. Acknowledgement
The authors gratefully acknowledge support by DGI, Spain (FEDER) under Grants No. FIS2011-28617-C02-01, by Generalitat de Catalunya (2009SGR1289), and by the Deutsche Forschungsge-meinschaft. AL has been supported by the ME (Spain) FPI program, Grant No. BES-2012-057439.Animated views (mpeg-files) of the evolution of the helium density distributions upon exci-tation of rubidium and cesium adatoms are available as Supporting Information. This material isavailable free of charge via the Internet at http://pubs.acs.org.30 eferences (1) Stienkemeier, F.; Vilesov, A. F. Electronic spectroscopy in He droplets.
J. Chem. Phys. , , 10119–10137.(2) Toennies, J. P.; Vilesov, A. F. Superfluid helium droplets: A uniquely cold nanomatrix formolecules and molecular complexes. Angew. Chem. Int. Ed. , , 2622–2648.(3) Stienkemeier, F.; Lehmann, K. K. Spectroscopy and dynamics in helium nanodroplets. J.Phys. B: At. Mol. Opt. Phys. , , R127 – R166.(4) Barranco, M.; Guardiola, R.; Hernández, S.; Mayol, R.; Navarro, J.; Pi, M. Helium Nan-odroplets: an Overview. J. Low Temp. Phys. , , 1–81.(5) Kornilov, O.; Bünermann, O.; Haxton, D. J.; Leone, S. R.; Neumark, D. M.; Gessner, O. Fem-tosecond Photoelectron Imaging of Transient Electronic States and Rydberg Atom Emissionfrom Electronically Excited He Droplets. J. Phys. Chem. A , , 7891–7900.(6) Bünermann, O.; Kornilov, O.; Haxton, D. J.; Leone, S. R.; Neumark, D. M.; Gessner, O. Ul-trafast probing of ejection dynamics of Rydberg atoms and molecular fragments from elec-tronically excited helium nanodroplets. J. Chem. Phys. , , 214302.(7) Droppelmann, G.; Bünermann, O.; Schulz, C. P.; Stienkemeier, F. Formation Times of RbHeExciplexes on the Surface of Superfluid versus Normal Fluid Helium Nanodroplets. Phys.Rev. Lett. , , 023402.(8) Döppner, T.; Fennel, T.; Diederich, T.; Tiggesbäumker, J.; Meiwes-Broer, K. H. Control-ling the Coulomb Explosion of Silver Clusters by Femtosecond Dual-Pulse Laser Excitation. Phys. Rev. Lett. , , 013401.(9) Claas, P.; Droppelmann, G.; Schulz, C. P.; Mudrich, M.; Stienkemeier, F. Wave packet dy-namics of potassium dimers attached to helium nanodroplets. J. Phys. B , , S1151.3110) Przystawik, A.; Göde, S.; Döppner, T.; Tiggesbäumker, J.; Meiwes-Broer, K.-H. Light in-duced collapse of metastable magnesium complexes formed in helium nanodroplets. Phys.Rev. A , , 021202.(11) Mudrich, M.; Heister, P.; Hippler, T.; Giese, C.; Dulieu, O.; Stienkemeier, F. Spectroscopyof triplet states of Rb by femtosecond pump-probe photoionization of doped helium nan-odroplets. Phys. Rev. A , , 042512.(12) Pentlehner, D.; Nielsen, J. H.; Slenczka, A.; Mølmer, K.; Stapelfeldt, H. Impulsive LaserInduced Alignment of Molecules Dissolved in Helium Nanodroplets. Phys. Rev. Lett. , , 093002.(13) Pentlehner, D.; Nielsen, J. H.; Christiansen, L.; Slenczka, A.; Stapelfeldt, H. Laser-inducedadiabatic alignment of molecules dissolved in helium nanodroplets. Phys. Rev. A , ,063401.(14) Göde, S.; Irsig, R.; Tiggesbäumker, J.; Meiwes-Broer, K.-H. Time-resolved studies on thecollapse of magnesium atom foam in helium nanodroplets. New J. Phys. , , 015026.(15) Whaley, K. B. Structure and dynamics of quantum clusters. Int. Rev. Phys. Chem. , ,41–84.(16) Kwon, Y.; Huang, P.; Patel, M. V.; Blume, D.; Whaley, K. B. Quantum solvation and molec-ular rotations in superfluid helium clusters. J. Chem. Phys. , , 6469–6501.(17) Chin, S. A.; Krotscheck, E. Systematics of pure and doped He clusters.
Phys. Rev. B , , 10405–10428.(18) Krotscheck, E.; Zillich, R. Dynamics of He droplets.
J. Chem. Phys. , , 10161–10174.(19) Giacomazzi, L.; Toigo, F.; Ancilotto, F. Dynamics of liquid He in confined geometries fromtime-dependent density functional calculations.
Phys. Rev. B , , 104501.3220) Lehtovaara, L.; Kiljunen, T.; Eloranta, J. Efficient numerical method for simulating static anddynamic properties of superfluid helium. J. Comput. Phys. , , 194.(21) Mateo, D.; Jin, D.; Barranco, M.; Pi, M. Excited electron-bubble states in superfluid He: Atime-dependent density functional approach.
J. Chem. Phys. , , 044507.(22) Hernando, A.; Barranco, M.; Pi, M.; Loginov, E.; Langlet, M.; Drabbels, M. Desorption ofalkali atoms from He nanodroplets.
Phys. Chem. Chem. Phys. , , 3996–4010.(23) Mateo, D.; Hernando, A.; Barranco, M.; Loginov, E.; Drabbels, M.; Pi, M. Translationaldynamics of photoexcited atoms in He nanodroplets: the case of silver.
Phys. Chem. Chem.Phys. , , 18388–18400.(24) Mateo, D.; Leal, A.; Hernando, A.; Barranco, M.; Pi, M.; Cargnoni, F.; Mella, M.; Zhang, X.;Drabbels, M. Communication: Nucleation of quantized vortex rings in 4He nanodroplets. J.Chem. Phys. , , 131101.(25) Dalfovo, F. Atomic and molecular impurities in He clusters.
Z. Phys. D , , 61–66.(26) Ancilotto, F.; DeToffol, G.; Toigo, F. Sodium dimers on the surface of liquid He.
Phys. Rev.B , , 16125–16129.(27) Stienkemeier, F.; Ernst, W. E.; Higgins, J.; Scoles, G. On the use of liquid helium clusterbeams for the preparation and spectroscopy of the triplet states of alkli dimers and otherweakly bound complexes. J. Chem. Phys. , , 615–617.(28) Reho, J.; Higgins, J.; Callegari, C.; Lehmann, K. K.; Scoles, G. Alkali-helium exciplex for-mation on the surface of helium nanodroplets. I. Dispersed emission spectroscopy. J. Chem.Phys. , , 9686–9693.(29) Schulz, C. P.; Claas, P.; Stienkemeier, F. Formation of K ∗ He exciplexes on the surface ofhelium nanodroplets studied in real time.
Phys. Rev. Lett. , , 153401.3330) Callegari, C.; Ancilotto, F. Perturbation Method to Calculate the Interaction Potentials andElectronic Excitation Spectra of Atoms in He Nanodroplets. J. Phys. Chem. A , ,6789–6796.(31) Auböck, G.; Nagl, J.; Callegari, C.; Ernst, W. E. Electron Spin Pumping of Rb Atoms on HeNanodroplets via Nondestructive Optical Excitation. Phys. Rev. Lett. , , 035301.(32) Theisen, M.; Lackner, F.; Ernst, W. E. Rb and Cs Oligomers in Different Spin Configurationson Helium Nanodroplets. , , 7005–7009.(33) Fechner, L.; Grüner, B.; Sieg, A.; Callegari, C.; Ancilotto, F.; Stienkemeier, F.; Mu-drich, M. Photoionization and imaging spectroscopy of rubidium atoms attached to heliumnanodroplets. Phys. Chem. Chem. Phys. , , 3843 –â ˘A ¸S 3851.(34) Stienkemeier, F.; Higgins, J.; Callegari, C.; Kanorsky, S. I.; Ernst, W. E.; Scoles, G. Spec-troscopy of alkali atoms (Li, Na, K) attached to large helium clusters. Z. Phys. D , ,253–263.(35) Bünermann, O.; Droppelmann, G.; Hernando, A.; Mayol, R.; Stienkemeier, F. Unraveling theAbsorption Spectra of Alkali Metal Atoms Attached to Helium Nanodroplets. J. Phys. Chem.A , , 12684 – 12694.(36) Loginov, E.; Callegari, C.; Ancilotto, F.; Drabbels, M. Spectroscopy on Rydberg States ofSodium Atoms on the Surface of Helium Nanodroplets. J. Phys. Chem. A , , 6779–6788.(37) Lackner, F.; Krois, G.; Theisen, M.; Koch, M.; Ernst, W. E. Spectroscopy of nS, nP, andnD Rydberg series of Cs atoms on helium nanodroplets. Phys. Chem. Chem. Phys. , ,18781–18788.(38) Busch, G. E.; Wilson, K. R. Triatomic Photofragment Spectra. II. Angular Distributions fromNO Photodissociation.
J. Chem. Phys. , , 3638–3654.3439) Reho, J.; Callegari, C.; Higgins, J.; Ernst, W. E.; Lehmann, K. K.; Scoles, G. Spin-orbit ef-fects in the formation of the Na-He excimer on the surface of He clusters. Faraday Discussion , , 161–174.(40) Brühl, F. R.; Trasca, R. A.; Ernst, W. E. Rb–He exciplex formation on helium nanodroplets. J. Chem. Phys. , , 10220–10224.(41) Mudrich, M.; Droppelmann, G.; Claas, P.; Schulz, C.; Stienkemeier, F. Quantum interferencespectroscopy of RbHe exciplexes formed on helium nanodroplets. Phys. Rev. Lett. , ,023401.(42) Giese, C.; Mullins, T.; Grüner, B.; Weidemüller, M.; Stienkemeier, F.; Mudrich, M. Forma-tion and relaxation of RbHe exciplexes on He nanodroplets studied by femtosecond pumpand picosecond probe spectroscopy. J. Chem. Phys. , , 244307.(43) Takahashi, Y.; Sano, K.; Kinoshita, T.; Yabuzaki, T. Spectroscopy of alkali atoms andmolecules in superfluid helium. Phys. Rev. Lett. , , 1035–1038.(44) Loginov, E.; Drabbels, M. Dynamics of Excited Sodium Atoms Attached to Helium Nan-odroplets. J. Phys. Chem. A , , 2738–2748.(45) Loginov, E.; Drabbels, M. Spectroscopy and dynamics of barium-doped helium nanodroplets. J. Chem. Phys. , , 154302.(46) Loginov, E.; Drabbels, M. Excited State Dynamics of Ag Atoms in Helium Nanodropletsâ ˘A˘a. J. Phys. Chem. A , , 7504–7515.(47) Kautsch, A.; Koch, M.; Ernst, W. E. Electronic Relaxation after Resonant Laser Excitationof Cr in Superfluid Helium Nanodroplets. J. Phys. Chem. A , , 9621–9625.(48) Lindebner, F.; Kautsch, A.; Koch, M.; Ernst, W. E. Laser ionization and spectroscopy of Cuin superfluid helium nanodroplets. Int. J. Mass Spectrom. ,
365 - 366 , 255 – 259.3549) Vrakking, M. J. J. An iterative procedure for the inversion of two-dimensionalion/photoelectron imaging experiments.
Rev. Sci. Instr. , , 4084.(50) Garcia, G. A.; Nahon, L.; Powis, I. Two-dimensional charged particle image inversion usinga polar basis function expansion. Rev. Sci. Instrum. , , 4989–4996.(51) Ellison, F. O. A Method of Diatomics in Molecules. I. General Theory and Application toH O. J. Am. Chem. Soc. , , 3540.(52) Dalfovo, F.; Lastri, A.; Pricaupenko, L.; Stringari, S.; Treiner, J. Structural and dynamicalproperties of superfluid helium. Phys. Rev. B , , 1193.(53) Patil, S. H. Adiabatic potentials for alkali-inert gas systems in the ground state. J. Chem.Phys. , , 8089–8095.(54) Pascale, J. Use of l -dependent preudopotemtials in the study of alkali-metal-atom-He sys-tems. The adiabatic molecular potentials. Phys. Rev. A , , 632–644.(55) Ralston, A.; Wilf, H. S. Mathematical methods for digital computers ; John Wiley and Sons,New York, 1960.(56) Koutselos, A. D.; Mason, E. A.; Viehland, L. A. Interaction universality and scaling lawsfor interaction potentials between closedâ ˘A ˇRshell atoms and ions.
J. Chem. Phys. , ,7125–7136.(57) LeRoy, R. J.; Kraemer, G. T. BCONT 2.2. Computer Program for Calculating Absorp-tion Coefficients, Emission Intensities or (Golden Rule) Predissociation Rates. The sourcecode and manual for this program may be obtained from “Computer ProgramsÂt’Ât’ linkat http://leroy.uwaterloo.ca. University of Waterloo Chemical Physics Research Report CP-650R , 2004.(58) Mateo, D.; Hernando, A.; Barranco, M.; Mayol, R.; Pi, M. Absorption spectrum of atomicimpurities in isotopic mixtures of liquid helium. Phys. Rev. B , , 174505.3659) Pifrader, A.; Allard, O.; Auböck, G.; Callegari, C.; Ernst, W. E.; Huber, R.; Ancilotto, F.One- and two-photon spectroscopy of highly excited states of alkali-metal atoms on heliumnanodroplets. J. Chem. Phys. , , 164502.(60) Lozeille, J.; Fioretti, A.; Gabbanini, C.; Huang, Y.; Pechkis, H.; Wang, D.; Gould, P.;Eyler, E.; Stwalley, W.; Aymar, M.; Dulieu, O. Detection by two-photon ionization and mag-netic trapping of cold Rb triplet state molecules. Eur. Phys. J. D , , 261 –â ˘A ¸S 269.(61) Zare, R. N. Photoejection Dynamics. Mol. Photochem. , , 1.(62) Ancilotto, F.; Cheng, E.; Cole, M. W.; Toigo, F. The binding of alkali atoms to the surfacesof liquid helium and hydrogen. Z. Phys. D , , 323–329.(63) Gallagher, T. Rydberg Atoms ; Cambridge University Press: Cambridge, U.K., 1994.(64) Peterka, D. S.; Kim, J. H.; Wang, C. C.; Poisson, L.; Neumark, D. M. Photoionization Dy-namics of Pure Helium Droplets.
J. Phys. Chem. A , , 7449 – 7459.(65) Loginov, E. Photoexcitation and Photoionization Dynamics of Doped Liquid Helium-4 Nan-odroplets. Ph.D. thesis, École Polytechnique Fédérale de Lausanne, 2008.(66) Moskvin, Y. V. Photoionization of atoms and recombination of ions in the vapors of alkalimetals. Opt. Spectrosc. , , 316 – 318.(67) Lahiri, J.; Manson, S. T. Oscillator-strength distributions for discrete and continuum transi-tions of excited states of cesium. Phys. Rev. A , , 3151–3165.(68) Aymar, M.; Robaux, O.; Wane, S. Central-field calculations of photoionisation cross sectionsof excited states of Rb and Sr + and analysis of photoionisation cross sections of excited alkaliatoms using quantum defect theory. J. Phys. B , , 993 – 1007.(69) Heavens, O. Radiative Transition Probabilities of the Lower Excited States of the Alkai Met-als. J. Opt. Soc. Am. , , 1058–1061.3770) Reid, K. L. Photoelectron angular distributions. Annu. Rev. Phys. Chem. , , 397 â ˘A ¸S424. 38able 1: Characteristics of the experimental and theoretical kinetic energy distributions of thedesorbed alkali atoms, see text for details. All masses are given in amu.Ak m Ak (exp) η (exp) η (th) m eff (exp) m eff (th) (cid:104) r e (cid:105) (Å) m effeff