Excitation of Sodium Atoms Attached to Helium Nanodroplets: The 3p

Jan 12, 2015 - Francesco Ancilotto , Manuel Barranco , François Coppens , Jussi Eloranta , Nadine Halberstadt , Alberto Hernando , David Mateo , Mart...
0 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/JPCA

Excitation of Sodium Atoms Attached to Helium Nanodroplets: The 3p ← 3s Transition Revisited Evgeniy Loginov,†,∥ Alberto Hernando,‡ J. Alberto Beswick,§ Nadine Halberstadt,§ and Marcel Drabbels*,† †

Laboratory of Molecular Physical Chemistry and ‡Laboratory of Theoretical Physical Chemistry, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland § Laboratoire des Collisions, Agrégats, Réactivité, IRSAMC, CNRS and Université Toulouse 3 Paul Sabatier, 31062 Toulouse, France ABSTRACT: The dynamics of Na atoms on the surface of helium nanodroplets following excitation via the 3p ← 3s transition has been investigated using state-specific ion-based detection of the products. Excitation of the system to the 3p 2Π states is found to lead to the desorption of both bare Na and NaHe exciplexes. The associated speed distributions point to an impulsive desorption process for Na products and a thermally driven process for the NaHe exciplexes. In contrast, excitation of the 3p 2Σ state leads exclusively to the impulsive desorption of Na atoms. In this case, the desorption is accompanied by a helium-induced relaxation process, as evidenced by the large fraction of detected Na 2P1/2 atoms. The relaxation process is thought to be related to a crossing between the 2Π1/2 and 2Σ potential energy curves at large distance.

■

INTRODUCTION Helium nanodroplets are fascinating quantum systems that are nowadays routinely used as a spectroscopic matrix. Many of the droplet properties have been investigated using atoms and molecules as nanoscopic probes.1−4 Alkali atoms play a special role in this context, since they are one of the few species known to reside on the surface of the droplets.5,6 As a result, the spectroscopy of the np 2P ← ns 2S transitions of alkali atoms attached to helium nanodroplets has attracted considerable theoretical and experimental interest.6−29 The np 2P ← ns 2S excitation spectra can be successfully reproduced using the so-called pseudodiatomic model.6,18 In this model, the internal degrees of freedom of the helium droplet are ignored, and the system is treated as a diatomic molecule in which the helium droplet plays the role of the second atom. Recently, spectra involving transitions to higher excited states of the alkali atoms have also been recorded.30−37 The diatomic model has been found to progressively fail to reproduce spectra for higher excited states, as polarization effects and helium-induced configuration interactions, which become increasingly important, are not taken into account.32,38 Spectroscopic studies of the np 2P ← ns 2S transitions have revealed that the excited atoms desorb from the droplets, either as bare atoms or as small alkali−helium exciplexes.6−9 The heavy alkalis Rb and Cs form an exception, as they remain attached to the helium droplet when excited close to the gas phase D1 transition.35,39 Time-resolved experiments have established the time scale for desorption and the exciplex formation process to be in the subnanosecond range.7−12 The exciplex formation has been addressed by a variety of theoretical methods of different complexity,25−27 but can be qualitatively described by a simple one-dimensional tunneling model that takes into account the © XXXX American Chemical Society

NaHe pair potentials and the energy required to remove a helium atom from the droplet surface.7 This model was recently successfully invoked to explain the exciplex formation after excitation of higher excited states.36,40 The desorption process of excited alkali atoms has been addressed by different theoretical methods.26,27 A recent combined experimental and theoretical study on the desorption dynamics of 4s excited Na revealed that the desorption of the excited atoms is a direct process in which the energy is partitioned between the helium droplet and the alkali atom.30 This allows the desorption process to be accurately described by an impulsive model analogous to the photodissociation of molecules. Studies involving higher excited states and other atomic systems have confirmed the validity of the impulsive model.36,37,40,41 In the present work we address the 3p ← 3s transition of sodium attached to helium droplets. This system has already been extensively studied in the past using laser-induced fluorescence (LIF) and beam depletion detection techniques.6−9,42 The spectrum can be fairly well reproduced by the pseudodiatomic model,6,18 although more sophisticated methods give a slightly better agreement with experiment.28,43 It is interesting to note that the spectrum can also be reproduced using line shape theory for collisional processes.44 The NaHe exciplexes formation has been extensively studied and can be well described by the one-dimensional tunneling model.6−9 In the present investigation we use an ion-based detection technique. Special Issue: Jean-Michel Mestdagh Festschrift Received: November 28, 2014 Revised: January 12, 2015

A

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A This has the advantage that excitation spectra can be recorded corresponding to specific products, and even specific quantum states. Moreover, in combination with ion imaging techniques, the speed distributions of the desorbed species can be determined in a state-specific fashion. As we will show, this new information requires an extension of the pseudodiatomic model, indicating that the dynamics of the system is more complex than generally assumed.

■

EXPERIMENTAL SECTION The experimental setup has been described in detail before.45,46 In brief, helium droplets are formed by expanding high-purity 4 He gas at a pressure of 30 bar into vacuum through a 5 μm orifice cooled to cryogenic temperatures by a closed cycle refrigerator. By varying the temperature of the nozzle between 11 and 20 K, the average droplet size can be varied from 1700 to 20000 helium atoms.47 After passing a skimmer, the droplets pick up sodium atoms as they pass through an oven holding sodium metal. The temperature of the oven is adjusted to ensure that the droplets on average pick up less than one Na atom. Via a differential pumping stage, the doped droplets enter a vacuum chamber holding a velocity map imaging setup.48 At the center of the setup, the Na-doped droplets are excited by crossing the droplet beam perpendicular to the output of a Nd:YAG pumped dye laser. The laser system is operated at a repetition frequency of 20 Hz and provides radiation with a pulse duration of 10 ns and a line width of less than 0.1 cm−1. The pulse energy is reduced to less than 20 μJ using neutral density filters to minimize saturation effects. Following their excitation, the sodium atoms are ionized by the absorption of an additional photon provided by another dye laser operating at a wavelength of approximately 400 nm. The ions or electrons are accelerated and projected onto a position sensitive detector consisting of a pair of microchannel plates and a phosphor screen. The light emitted by the phosphor screen is imaged onto a high-resolution CCD camera that is read out every laser shot. By gating the detector, images corresponding to a specific mass or mass range can be recorded. The individual images are analyzed online, and the centroids of the ion impacts are determined. The velocity distributions are determined by performing an inverse Abel transform on the image constructed from the accumulated centroids.49 Spectra are recorded by monitoring the number of impacts on the detector as a function of laser frequency. To record quantum state specific images or spectra, the sodium atoms are not ionized by the 400 nm laser pulse but excited to high Rydberg states in the presence of a weak electric field. Typically 2 μs after excitation, the voltages applied to the electrodes are increased to the values appropriate for velocity map imaging. The Rydberg atoms are field ionized, and the resulting ions are imaged onto the detector. With the settings used in these experiments a spectral resolution of 5 cm−1 is attained, sufficient to record state-specific spectra and velocity map images of Na 3p atoms.45

■

Figure 1. 3p 2P1/2,3/2 ← 3s 2S1/2 excitation spectra of NaHeN for droplets with mean radius of 41 Å recorded by monitoring bare Na+, NaHe+, NaHe2+and all products (upper panel). Excitation spectra recorded with the state-selective detection of Na atoms in the 3p 2P1/2 and 3p 2P3/2 states (lower panel).

Inspection of the spectra reported in Figure 1 reveals that the overall excitation spectrum consists of two contributions. The low frequency part is mainly due to NaHe and NaHe2, while the high frequency part originates almost exclusively from bare sodium. This observation nicely confirms the interpretation of the laser-induced fluorescence spectra.9 Following previous work, we tentatively assign the low frequency part, corresponding to NaHe and NaHe2 products, to the 3p 2Π1/2 ← 3s 2Σ and 3p 2Π3/2 ← 3s 2Σ transitions, while the high frequency part, corresponding to Na products, is assigned to the 3p 2Σ ← 3s 2Σ transition.6,18 Here the states are labeled nlΛΩ where n and l are the principal quantum number and orbital angular momentum of the correlating state of the free atom, Λ is the projection of the orbital angular momentum onto the axis defined by the sodium atom and the center of the helium droplet, and Ω is the projection of the total electronic angular momentum onto this axis. In agreement with previous studies, we find that the Na excitation spectrum shifts toward higher frequencies with increasing droplet size, while the NaHe and NaHe2 spectra slightly broaden.6 In contrast, the spectral width of the resonances observed in the present study is larger than that observed in previous studies. In addition, no partially resolved structure is observed in the NaHe and NaHe2 excitation spectra corresponding to the 3p 2Π1/2 ← 3s 2Σ and 3p 2Π3/2 ← 3s 2Σ transitions. This can be attributed to a mild saturation of the transitions at the laser fluence of 0.7 mJ/cm2 used to record these spectra, leading to a broadening of the spectra. Closer inspection of the Na excitation spectrum reveals a small “bump” around 16965 cm−1, corresponding to the maximum of the NaHe excitation spectrum. As this “bump” is absent in the LIF spectra, it very likely results from dissociative ionization of the NaHe and NaHe2 exciplexes. Information on possible relaxation processes can be obtained by recording state-specific excitation spectra. Spectra recorded using state-selective detection of desorbed Na atoms in 2P1/2 or 2P3/2 states are shown in Figure 1. Both spectra have the same overall shape, but they differ by their intensities and peak positions. A comparison reveals that the 2P3/2 excitation spectrum is shifted by approximately 20 cm−1 to higher frequencies with respect to the 2P1/2 spectrum, while its intensity is lower by a

RESULTS

Excitation Spectra. Excitation spectra corresponding to the 3p ← 3s transition of sodium on helium nanodroplets recorded by monitoring the Na+, NaHe+, NaHe2+, and overall ion yield are presented in Figure 1. The spectra were recorded by scanning the frequency of the excitation laser while keeping the frequency of the ionizing laser fixed at 25157 cm−1. Although NaHe3+ and NaHe4+ ions could be detected, vide inf ra, the signal levels were too low to record the corresponding excitation spectra. B

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A factor of 3. The fact that the “bump” is missing in these spectra supports the hypothesis that it results from dissociative ionization of the NaHe and NaHe2 exciplexes. As we will discuss below, the similarity of the two state-resolved spectra cannot be accounted for by the version of the pseudodiatomic model usually applied and points to a shortcoming of that simple version. Time-of-Flight Mass Spectra. The time-of-flight mass spectrum recorded after excitation at 17007 cm−1 is shown in Figure 2. It reveals not only the presence of Na, NaHe, and

of light emission in bulk helium has been explained by fast nonradiative relaxation of the excited sodium atom to the ground state.53 In analogy, we tentatively propose that the large NaHen exciplexes (n > 4) decay nonradiatively to the ground state, which then leads to the disintegration of the complex. It should be noted that the failure to observe NaHen exciplexes (n > 4) in the present experiment could potentially also indicate that the complex formation time exceeds the time scale for desorption from the droplet. However, in view of the fluorescence spectra recorded in dense helium gas, we deem this explanation less likely. Photoelectron and Zero Electron Kinetic Energy (ZEKE) Spectra. The excitation spectra provide information on the products and their state distribution. Additional information can be obtained by photoelectron spectroscopy. To achieve high energy resolution, photoelectron images were recorded using a photon energy of 25157 cm−1, which excites the system just above the ionization threshold. Figure 3 shows photoelectron images recorded following excitation of sodium-doped helium droplets at 16995 cm−1, corresponding to the maximum product yield, and at 17118 cm−1 corresponding to the maximum Na atom yield. The image obtained at 16995 cm−1 reveals two contributions in the photoelectron yield visible as two rings. In contrast, the image corresponding to 17118 cm−1 excitation shows only a single ring. The corresponding photoelectron spectra are clearly different and reflect the composition of the desorbed fragments as revealed by the excitation spectra. The photoelectron spectrum recorded following 17118 cm−1 excitation is dominated by the peak corresponding to a binding energy of 24450 cm−1 that can be unambiguously assigned to gas phase Na(3p) atoms.55 This observation is consistent with the excitation spectra, which reveal that the main products at this excitation energy are bare sodium atoms. The limited resolution of the spectrometer does not allow for resolving the two possible spin−orbit states of Na(3p), which are separated by 17 cm−1.55 The photoelectron spectrum following 16995 cm−1 excitation reveals two additional peaks centered at a binding energy of 24 600 and 24 750 cm−1, the former being the most intense. According to the spectra presented in Figure 1, excitation near 16995 cm−1 leads mainly to the formation of NaHe products, although appreciable amounts of Na atoms and NaHe2 complexes are also formed. Based on the intensities, we assign the peak at a binding energy of 24600 cm−1 to NaHe and that at 24750 cm−1 to NaHe2. This assignment is supported by the droplet size dependence of the photoelectron spectra, which shows an increasing intensity of the 24750 cm−1 peak with increasing droplet size, in agreement with the TOF mass spectra discussed above (see Figure 2). To confirm the proposed assignment, mass resolved photoionization spectra have been recorded by fixing the frequency of the excitation laser to 16995 cm−1 and scanning the ionization laser. The resulting spectra for NaHe and NaHe2 are reported in the lower panel of Figure 3. Comparison of the spectra with the corresponding photoelectron spectrum reveals that the onset of the NaHe and NaHe2 signals coincides with the photoelectron peaks tentatively assigned to NaHe and NaHe2, thereby confirming their assignment. The peaks in photoelectron spectra corresponding to NaHe complexes are somewhat broader than the experimental resolution, suggesting the presence of unresolved rovibrational structure. In order to confirm this hypothesis, ZEKE spectra of the products have been recorded with a resolution of 5 cm−1 following excitation of the system at 17000 cm−1. The ZEKE spectrum shown in Figure 4 reveals that the broad features in the

Figure 2. Time-of-flight mass spectrum recorded following 17007 cm−1 excitation of NaHeN with a mean radius of 41 Å (upper panel). Relative product abundance after the excitation of NaHeN at 17007 cm−1 for different mean droplet sizes (lower panel).

NaHe2, but also of NaHe3 and NaHe4 exciplexes. Analysis of the time-of-flight mass spectra reveals that the relative intensity of bare Na decreases with increasing droplet size, while that of NaHe remains constant and that of the NaHe2 and larger exciplexes increases (see Figure 2). This variation mainly reflects the change of the NaHen exciplex distribution with droplet size; the variation of the absorption spectrum contributes to a lesser extent. The exciplex formation is thought to be a local process, and as such reflects the change in the surface properties. The sodium atoms are known to be located in a dimple at the surface of the helium droplet.5,6 This dimple structure is calculated to become more pronounced with increasing droplet size, thereby enhancing the amount of helium in close proximity of the sodium atom for larger droplets.50 This is expected to lead to a more efficient exciplex formation. Another remarkable characteristic of the time-of-flight mass spectrum is the absence of NaHen exciplexes with n > 4. This result is in line with the work of Enomoto et al., who recorded the emission spectra of excited Na in cold helium gas.51 In that study, emission of NeHen exciplexes was observed up to n = 4 only. This is remarkable given that the first He solvation shell around the excited sodium atom has been calculated to contain 5 or more helium atoms.23,52,53 The present results therefore suggest that the larger exciplexes are unstable on the time scale of the experiment. The fact that no NaHen exciplexes with n > 4 are detected is likely closely related to the failure to detect fluorescence of excited Na atoms in liquid helium.54 The absence C

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 4. ZEKE spectrum of NaHeN with a mean radius of 41 Å recorded following excitation at 17000 cm−1 (upper panel). ZEKE spectrum calculated as the Franck−Condon factors between the NaHe+ 2Σ potential56 and the NaHe 3p 2Π potential of Pascale57 (middle panel) and Dell’Angelo et al.23 (lower panel).

transitions overlap, a detailed analysis and assignment of the ZEKE spectrum is not feasible. To extract information on the vibrational state distribution, we simulate the ZEKE spectrum based on the NaHe and Na+He pair potentials.31 For Na+He we use the ab initio potential of Soldan et al.56 which was calculated at the CCSD[T]/aug-cc-pVQZ level of theory. For 3p NaHe we use the widely used Pascale pseudopotentials57 and the recent ab initio potentials of Dell’Angelo et al. that have been calculated at the CASSCF-MRCI level of theory.23 The ZEKE spectrum is calculated as the Franck−Condon factors between the vibrational energy levels corresponding to the Na+He X 1Σ and NaHe 3p A 2Π potentials using the LEVEL 8.0 program of Le Roy.58 The calculated spectra are displayed in Figure 4 together with the experimental ZEKE spectrum corresponding to NaHe. The spectrum calculated with the Pascale pseudopotential clearly yields the best agreement with experiment. This is rather surprising given the age of this potential57 and the high level of theory used in the ab initio calculations by Dell’Angelo.23 Both simulations indicate that the NaHe spectral features close to the atomic transition correspond to Δv = −1 transitions, whereas those at higher frequencies correspond to Δv = 0 transitions. The good agreement between the calculated spectrum based on the Pascale potential and the experimental spectrum leads us to conclude that the desorbed NaHe exciplexes mainly populate the lowest four vibrational levels. Since the intensities of the transitions in the ZEKE spectrum depend on many, mostly unknown factors the relative populations cannot be reliably extracted. The conclusion, however, that mainly the v = 0−3 vibrational levels are populated is in agreement with laserinduced fluorescence studies.9 Speed Distributions. More insight into the desorption of the excited Na atoms and the formation of NaHen complexes can be obtained from the velocity distributions of the desorbed species. Figure 5 displays velocity map images of Na 2P1/2, Na 2P3/2, NaHe, and NaHe2. The images of bare Na atoms were recorded using state-selective detection after excitation at 17094 cm−1.

Figure 3. Photoelectron images and corresponding spectra recorded following 16995 and 17118 cm−1 excitation of NaHeN with a mean radius of 41 Å (top panel). The ionization frequency is 25157 cm−1. Photoelectron spectra recorded following excitation at 16995 cm−1 for two different droplet sizes (middle panel). Photoionization spectra for NaHe and NaHe2 following excitation at 16995 cm−1 (bottom panel).

photoelectron spectrum consist of many narrow overlapping transitions. The sharp intense line at 24488 cm−1 corresponds to the ZEKE transition of gas phase Na atoms in 3p 2P1/2 state. The transition frequency is approximately 5 cm−1 red-shifted with respect to the accepted ionization frequency.55 This small discrepancy can be attributed to the lowering of the ionization threshold by the pulsed electric field of 0.6 V/cm used to record the spectrum. The ZEKE transition of Na 3p 2P3/2 is observed at 24471 cm−1 and is a factor of 5 weaker than that of the Na 3p 2 P1/2, in agreement with the state-resolved excitation spectra. All other sharp lines observed in the ZEKE spectrum belong to rovibrational ZEKE transitions of the NaHe exciplexes. The high density of transitions indicates that the NaHe exciplexes are not only vibrationally but also rotationally excited. Since most of the D

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

However, the speed distribution of the 2P3/2 atoms is slightly narrower, while the most probable speed is slightly higher, 155 m/s for Na 2P3/2 vs 135 m/s for Na 2P1/2. The anisotropy parameters are found to vary almost linearly with increasing product speed, reaching a value of β = 1.6 for the highest speeds. The anisotropy parameter for the 3p 2P1/2 state is systematically smaller than for the 3p 2P3/2 state. It is important to note here that no such speed dependence of the anisotropy parameter has been found when the sodium atom is excited to the 4s, 3d, or 4p state.30,32,40 Like for other systems, the mean kinetic energy of the Na products, ⟨Ekin⟩, calculated from the speed distributions, scales linearly with the excitation frequency.30,32,37,40,41 As can be seen in Figure 6, the

Figure 5. Velocity map ion images of desorbed products recorded following 17094 cm−1 excitation of Na attached to helium droplets with a mean radius of 41 Å (top panel). The polarization of the laser is vertical. The corresponding speed distributions and anisotropy parameters, β, of Na (middle panel) and NaHe and NaHe2 exciplexes (bottom panel). Indicated are fits to a Maxwell−Boltzmann distribution yielding a temperature of 28 K.

Figure 6. Mean kinetic energies and corresponding mean anisotropy parameters of desorbed Na atoms in 3p 2P1/2 and 3p 2P3/2 states (upper panel) and of NaHe and NaHe2 exciplexes (lower panel) after excitation at different frequencies. The two vertical dotted lines indicate the energies of the free atom. The solid lines are linear fits to the data points.

They demonstrate a prominent angular anisotropy with the maximum intensity in the direction parallel to the laser polarization. This anisotropy is more pronounced for Na 3p 2 P3/2 than for Na 3p 2P1/2. To allow for a quantitative analysis, the velocity distributions of the products are extracted from the images. The corresponding speed distributions and anisotropy parameters are reported in Figure 5 The anisotropy parameter, β, is determined by fitting the normalized angular intensity distribution I(θKE) of the desorbed products to the standard expression: 1 I(θKE) = [1 + βP2(cos θKE)] (1) 4π

slopes for the two spin−orbit states are slightly different. Also the mean anisotropy parameters show a different frequency dependence. Both approach the limiting value of ⟨β⟩ = 1.6 at the highest excitation energies. However, the mean anisotropy parameter for the 2P3/2 state remains positive over the whole range of energies, while that for the 2P1/2 state becomes negative at low excitation energies. In contrast to bare Na, the images of NaHe and NaHe2 complexes are isotropic. Analysis of the images reveals that the anisotropy parameter does not vary with speed and is close to zero. Also, the speed distributions of the NaHe and NaHe2 products are notably different from those of the bare Na atoms. In contrast to the speed distribution of the Na products, which are fairly well described by Gaussian distributions, those of NaHe and NaHe2 are best described by a Maxwell−Boltzmann distribution corresponding to a temperature of 28 K. The difference between the Na and NaHen products becomes even more obvious when varying the excitation frequency (see Figure 6).

where θKE is the angle between the velocity vector of the desorbed atom and polarization of the light at a given kinetic energy and P2(cos θKE) is the second Legendre polynomial.59 The speed distributions of the 3p 2P3/2 and 3p 2P1/2 sodium products are quite similar as they both have a pronounced limit at about 250 m/s. E

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

the helium droplet is reduced to a one-dimensional potential that is calculated as the sum of NaHe pair potentials. In the case of the 3p state of sodium having nonzero orbital angular momentum, this gives rise to two effective potential energy curves of Σ and Π symmetry. If spin−orbit interaction is taken into account, the degeneracy of the Π states is lifted, and three states result. Of these, the 2Σ1/2 and 2Π3/2 states correlate to the 3p 2P3/2 state of the free sodium atom, while the 2Π1/2 state correlates to the 3p 2 P1/2 state (see Figure 2 in ref 7). Within the pseudodiatomic model, the low frequency part of the spectrum that gives rise to NaHe complex formation corresponds to the 3p 2Π1/2 ← 3s 2Σ1/2 and 3p 2Π3/2 ← 3s 2Σ1/2 transitions, while the high frequency part yielding bare sodium atoms corresponds to the 3p 2Σ1/2 ← 3s 2 Σ1/2 transition.18,43 One therefore expects that the sodium atoms resulting from excitation to the 3p 2Σ1/2 state reside exclusively in the 3p 2P3/2 state. However, the state-selective excitation spectra reveal that excitation of the 3p 2Σ1/2 ← 3s 2Σ1/2 transition yields almost 3 times more Na 3p 2P1/2 than Na 3p 2 P3/2. This unexpected large yield of 3p 2P1/2 atoms is confirmed by the high resolution ZEKE spectra. This raises the question of what mechanism produces the 2P1/2 sodium atoms. The simplest explanation would be that the Na 2P3/2 relaxes to the 2P1/2 state due to the interaction with the helium. However, the fact that the state selective spectra are not identical but rather displaced with respect to each other questions this explanation. The velocity distributions of the desorbed atoms can provide more insight into the underlying process. A recent study on the desorption dynamics of sodium atoms from helium droplets following excitation to the 4s state revealed a linear dependence of the desorbed atom’s mean kinetic energy on excitation energy.30 This dependence could be explained by an impulsive model according to which the mean kinetic energy of the desorbed atom is given by

Whereas the mean kinetic energy and anisotropy parameter of the desorbed Na atoms reveal a strong dependence on excitation frequency, they remain nearly constant at ⟨Ekin⟩ = 28 cm−1 and ⟨β⟩ = 0, respectively, for the NaHen complexes. These observations indicate that fundamentally different processes are underlying the desorption of atoms and complexes from the droplets.

■

DISCUSSION Exciplex Formation. The formation of NaHe exciplexes following excitation of sodium atoms on the surface of helium droplets has been discussed by Reho et al.7,9 They argued that an excited sodium atom remains temporarily bound to the droplet due to the presence of a shallow minimum in the potential describing the interaction of the excited Na atom with the helium droplet. The formation of the NaHe exciplexes then proceeds by binding of a helium atom in the surface region of the droplet to the excited sodium atom. This process can be described by a 1-dimensional tunneling process though a barrier on the potential energy surfaces constructed by folding the NaHe pair potential with the He−HeN interaction potential.7 From these potential curves it follows that exciplex formation can only occur after excitation to the Π states since the resulting Σ potential is repulsive at short internuclear distances.9 The present results appear to be in agreement with this model. Exciplex formation is only observed following excitation via spectral features assigned to the 2Π ← 2Σ transitions, and not when exciting via the 2Σ ← 2Σ transition. The velocity distributions of the desorbing Na and NaHe exciplexes are found to be quite different. In contrast to the velocity distributions of Na, those of the NaHe exciplexes are isotropic and can be described by a Maxwell−Boltzmann distribution independent of excitation energy. These observations indicate that the desorption of the NaHe exciplexes from the droplets is not driven by an impulsive process, like the desorption of the Na atoms, but rather by a thermal process.60 As suggested by Reho et al., and supported by recent time-resolved pump−probe experiments,12 the desorption is likely related to the vibrational relaxation of exciplexes formed on the surface of the helium droplet. Indeed, the theoretical NaHe 3p 2Π pair potential is calculated to support vibrational energy levels up to v = 6. As complexes are most efficiently formed in the highest vibrational states, the detection of NaHe products in low vibrational states v = 0−3 by ZEKE spectroscopy strongly supports the hypothesis that vibrational relaxation is the driving force for the desorption of NaHe exciplexes from the droplets. It should be noted that the characteristics of the NaHe velocity distributions reported here differ significantly from those found for NaHe complexes formed after excitation via the 3d ← 3s transition.40 In that case, the distributions are very similar to those observed for Na atoms leaving the droplets by an impulsive process. Also RbHe exciplexes formed after excitation via the 6p ← 5s transition reveal speed distribution characteristic of an impulsive process.37 This suggests that trapping of the excited atom on the surface of the droplet is not a requirement for the formation of exciplexes; they can also form directly upon excitation. Relaxation. The 3p ← 3s excitation spectrum of sodium atoms attached to helium nanodroplets has been successfully reproduced in the past using the so-called pseudodiatomic model.6,18 In this model, the internal degrees of freedom of the helium droplet are ignored, and the system is treated as a diatomic molecule in which the helium droplet plays the role of the second atom. The interaction between the sodium atom and

⟨E kin⟩ = η[hν − E0]

(2)

where hν is the photon energy, E0 is an energy offset, and η is a proportionality constant. Within the impulsive model, the proportionality constant, η, is related to the mass of the sodium atom, mNa, and the effective mass of the helium interacting with the excited sodium atom, meff, according to meff η= meff + mNa (3) Recent studies on other systems have confirmed the validity of this model.37,40,41 The present results for the Na atoms are also in line with this simple model. The proportionality constant, effective helium mass and the energy offset derived from the data are listed in Table 1. The proportionality constant, η, is Table 1. Fraction of Available Energy Converted into Kinetic Energy of the Sodium Atom, η, Energy Offset, E0 (cm−1), and Effective Mass, meff (amu) state 2

P1/2 2 P3/2

E0

η

meff

16986(2) 16990(2)

0.193(2) 0.221(2)

5.5 6.5

clearly different for the 2P1/2 and 2P3/2 atoms, suggesting that their interactions with the helium droplet are different. This in turn implies that the 2P1/2 state becomes populated while the Na atom is still in close proximity to the droplet. In contrast to the proportionality constant, the energy offset E0 is nearly identical for both spin−orbit states. Within the F

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A impulsive model, the energy offset can be related to the internal energy of the desorbed atom, Eint, and the binding energy of the ground state sodium atom to the surface of the droplet, Ebind, according to41 E0 = E int − E bind

(4)

The binding energy of a ground state sodium atom obviously does not depend on the quantum state of the desorbed atom. The fact that the same energy offset E0 is found for both Na products, leads us to conclude that initially only a single state is populated. Because the excited 2Σ1/2 states correlates to the 2P3/2 state of the free atom, one expects the internal energy to correspond to that of Na 2P3/2. With this assumption the binding energy of the ground state atom is found to be 17 ± 2 cm−1, in excellent agreement with the value of 18 cm−1 determined from LIF studies.9 The speed distributions of the desorbed sodium atoms thus suggest that the 2P1/2 state becomes populated by relaxation of Na atoms initially excited to states correlating to the 2 P3/2 state in the free atom. Additional information is provided by the angular distributions of the desorbed products. According to the impulsive model the angular distribution of the desorbed atoms is related to the symmetry of the state that is excited.30 The anisotropy parameter takes a value of −1 for a perpendicular and +2 for a parallel transition. As the system has a 3s Σ ground state, a value of β = −1 (+2) signifies excitation to a Π (Σ) state. The images for the Na products reveal that the anisotropy parameter varies with the speed of the desorbed atom and that only for the highest speeds a value close to the limiting value for the 3p 2Σ ← 3s 2Σ transition of +2 is reached (see Figure 5). This indicates that the sodium atoms do not result exclusively from excitation to the Σ state, but also from the Π states. The variation of the mean anisotropy parameter as a function of excitation frequency (see Figure 6) supports this assumption. Indeed, the anisotropy parameter is close to +2 at high excitation energies where mainly the 2Σ state contributes to the absorption spectrum, while a smaller value is found for lower excitation energies where the 2Π states contributes. In the case where two channels contribute, the anisotropy parameter of the desorbed atoms can be expressed as β = 2cΣ − cΠ

Figure 7. Decomposition of the Na excitation spectra into the 2Π and 2Σ contributions (upper three panels) and the reconstructed 3p 2Π ← 3s 2Σ absorption spectrum (lowest panel). The green line indicates the fraction of excited atom leaving the droplet as bare Na.

be reconstructed (see Figure 7), and the fraction of atoms that desorbs from the droplets as bare Na can be determined. As can be seen in Figure 7, this fraction depends strongly on the excitation frequency. At low frequencies most of the atoms form NaHe complexes while at high frequencies approximately half of the excited atoms leave the droplets as bare Na. It should be noted that due to the dissociative ionization of NaHe complexes, vide supra, the fraction of desorbing sodium atoms is overestimated in the lowest frequency region. These results suggest that fast atoms originating from excitation at the blue side of the spectrum desorb directly via an impulsive process. By contrast, slow atoms resulting from the excitation at the red side of the spectrum remain attached to the droplet and go on to form NaHe complexes, which later desorb from the droplets via a thermal process. Time resolved measurements have revealed that the formation time of the NaHe complexes is wavelength dependent, being slower at the lowest excitation energies.9 In agreement with experiment, the one-dimensional tunneling model predicts that the NaHe formation rate for excitation to the 2Π1/2 state is almost an order of magnitude smaller than for excitation to the 2Π3/2 state. The decomposition of the state specific Na+ spectra reveals that, following excitation of the 2Π states, the absolute Na 2P1/2 yield is ∼5 times larger than the Na 2P3/2 yield. This result agrees within a factor of 2 with the difference in the NaHe formation rates calculated by the tunneling model. Part of this discrepancy can be attributed to the difference in ionization cross section for Na 2P1/2 and 2P3/2, which equal 2.16 Mb and 3.74 Mb, respectively.61 Thus, while the observations for the 3p 2Π ← 3s 2Σ transitions can be described with the existing models, this is

(5)

where cΣ and cΠ are the relative contributions of the 2Σ and 2Π states to the absorption spectrum. Realizing that cΣ + cΠ = 1, the Na+ yield spectra reported in Figure 1 can be decomposed into their 2Σ and 2Π contributions using the mean anisotropy parameters determined by the imaging experiments and reported in Figure 6. The resulting decomposed spectra for the P1/2 and P3/2 products are shown in Figure 7. Analysis reveals that the 2Σ contribution to the spectra is identical for both product states. In contrast, the 2Π contribution for the 2P3/2 products is shifted by ∼17 cm−1 toward higher energy compared to that of the 2P1/2 products, while its relative contribution to the spectrum is 50% smaller. Because the state-specific spectra involving the 2Π state are shifted by the spin−orbit splitting of sodium, we assign the 2 P1/2 and 2P3/2 spectra to the 3p 2Π1/2 ← 3s 2Σ1/2 and 3p 2Π3/2 ← 3s 2Σ1/2 transitions, respectively. These above findings imply that upon excitation of the 2Π states not all Na atoms go on to form complexes but that some desorb from the droplets as bare Na. To determine the fraction of these atoms, we have decomposed the total Na+ yield spectrum shown in the upper panel Figure 1 into the 2Σ and 2Π components. By combining the 2Π Na+ spectrum with the NaHe+ and NaHe2+ spectra, the 3p 2Π ← 3s 2Σ absorption spectrum can G

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A not the case for the 3p 2Σ ← 3s 2Σ transition. The fact that the majority of the Na atoms are found to populate the 2P1/2 state signifies the existence of an unidentified relaxation process.

amplitudes at total energy E = Eg + hνi, with Eg being the ground state energy of the Na@HeN, are defined as

■

Mq(j)(Ωi , Ω, E) ≡ ⟨X2 Σ1/2 , Ωi|μq |Ψ(Ωj , E)δΩ, Ωi − q⟩

THEORY AND MODEL The pseudodiatomic model has been successful in reproducing most of the fluorescence excitation spectra of alkali-doped helium droplets. Here we apply it to shed light on some important observations made using state specific detection of the ejected sodium atom. The experiments reveal that the anisotropy parameter β for the Na products switches from zero or a slightly negative value to a value of ∼1.6, close to 2, when increasing the photon energy. This implies that the excitation at the Franck−Condon region evolves from 2Π to 2Σ. However, as stated above, the 2Σ state correlates adiabatically to 2P3/2 fragments, whereas the experimental results show 3 times more 2 P1/2 than 2P3/2 fragments in the higher energy region of the spectrum. Hence, some relaxation has to occur along the dissociation pathway in order to explain this high proportion of 2 P1/2 fragments. If it were collisional relaxation from 2P3/2 to 2P1/2 the angular distribution would be washed out and the anisotropy parameter would tend to zero. We therefore explore another possibility, that of a crossing between the 2Π1/2 and 2Σ1/2 potential curves in the long-range region due to the existence of a well for the 2Σ curve in addition to that for the 2Π curve. Theoretical Method. We consider the photodetachment process NaHeN + hνi → (NaHeN )* → Na*(j) + HeN (1S0)

where μq are the spherical tensorial components of the electric dipole operator in the body-fixed molecular frame (x, y, z) with z pointing along R, the HeN center-of-mass to Na vector. In eq 7, Ωi = ±1/2 and Ω = ±3/2, ±1/2 are the quantum numbers associated with the electronic angular momentum components on the body-fixed z-axis. The |Ψ(j,E) Ω ⟩ states are linear combinations of the asymptotic atomic states |j,Ω⟩ with energy Ej, |Ψ(Ωj , E)⟩ =

β (1/2)(E) =

∑ ψj(′Ωj ,E)(R)|j′, Ω⟩ (8)

j′

ψ(j,E) j′,Ω (R)

where are continuum wave functions solutions of the coupled equations at total energy E. Due to the selection rule (Ω = Ωi − q) in eq 7, only the following amplitudes can be nonzero: M(3/2) (±1/2, ±1/2, E), 0 (3/2) M(3/2) ±1 (±1/2, ∓1/2, E), and M∓1 (±1/2, ±3/2, E) for j = 3/2 fragments, M(1/2) (±1/2, ±1/2, E) and M(1/2) 0 ±1 (±1/2, ∓1/2, E) for j = 1/2 fragments. Note that M(3/2) ∓1 (±1/2, ±3/2, E) corresponds to 2Π3/2 excitation leading to 2P3/2 fragments. If spin−orbit coupling is neglected (adiabatic correlation), M(3/2) ±1 (±1/2, ∓1/2, (3/2) E) = M(1/2) (±1/2, ±1/2, E) = 0, and M (±1/2, ±1/2, E) 0 0 corresponds to 2Σ1/2 excitation leading to 2P3/2 fragments, while 2 M(1/2) ±1 (±1/2, ∓1/2, E) corresponds to Π1/2 excitation leading to 2 P1/2 fragments. However, in the general case where no approximation is made, spin−orbit coupling can produce Na 2P1/2 fragments from 2Σ1/2 excitation as M(1/2) (±1/2, ±1/2, E) ≠ 0, 0 or Na(2P3/2, Ω = 1/2) fragments from 2Π1/2 excitation because M(3/2) ±1 (±1/2, ∓1/2, E) ≠ 0. The final state selected absorption cross sections σ(3/2)(E) and (1/2) σ (E) for the production of Na 2P3/2 and Na 2P1/2 atoms, respectively, are given by

(6)

in which a sodium atom bound to a HeN pseudoatom is photodetached by a photon of frequency νi producing an excited Na* atom with fine structure electronic angular momentum quantum number j = 1/2 or 3/2. The system is initially in Hund’s case (a) |X 2Σ1/2⟩ state corresponding to a ground state Na(2S1/2) bound to a HeN(1S0) cluster. The excited states accessible from the ground state via electric-dipole transitions in the energy region of interest are |A 2Π1/2⟩, |A′ 2Π3/2⟩, and |B 2Σ1/2⟩. These states can be coupled by non-Born−Oppenheimer, Coriolis, and spin−orbit interactions. We use the same method as in ref 29 to calculate the product state specific excitation spectra. The photodetachment β (3/2)(E) =

(7)

σ (3/2)(E) ∝ 2[|M 0(3/2)(1/2, 1/2, E)|2 + |M1(3/2)(1/2, − 1/2, E)|2 2 + |M −(3/2) 1 (1/2, 3/2, E)| ] σ (1/2)(E) ∝ 2[|M 0(1/2)(1/2, 1/2, E)|2 + |M1(1/2)(1/2, − 1/2, E)|2 ]

(9)

and the anisotropy parameters for their angular distributions by62,63

2 2 |M 0(3/2)(1/2, 1/2, E)|2 − |M1(3/2)(1/2, − 1/2, E)|2 − |M −(3/2) 1 (1/2, 3/2, E)| 2 |M 0(3/2)(1/2, 1/2, E)|2 + |M1(3/2)(1/2, − 1/2, E)|2 + |M −(3/2) 1 (1/2, 3/2, E)|

2 |M 0(1/2)(1/2, 1/2, E)|2 − |M1(1/2)(1/2, − 1/2, E)|2 |M 0(1/2)(1/2, 1/2, E)|2 + |M1(1/2)(1/2, − 1/2, E)|2

Computational Details. The Na−HeN (N = 1000) interaction potentials were obtained as in ref 29. First the helium density was determined at each HeN−Na distance for the ground state using a density functional theory (DFT) description of the helium as applied in refs 64 and 65 to interpret experiments on solvation of alkali earth complexes in helium droplets.65,66 The Na−He ground pair state potential was taken from Patil.67 Next the Π and Σ excited state potential energy curves were obtained within the diatomics in molecules (DIM) approach by averaging the corresponding matrix elements over the ground state helium density. For the required excited state NaHe pair potentials,

(10)

we have used three different sets of potentials: the well-known pseudopotentials of Pascale,57 the recent model potentials of Mullamphy et al.,68 and the ab initio potentials of Allouche and co-workers.69 The latter are very similar to those of Dell’Angelo et al.23 but have been calculated for larger internuclear distances. The three sets of potentials mainly differ in terms of the well depth for the Π state and the long-range behavior of the Σ state. The ground state initial level (X 2Σ1/2, v = 0) was determined by finite difference integration followed by Numerov integration. The quantum coupled channel equations for the electronically excited states were solved using the De Vogelaere algorithm,70,71 H

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A including spin−orbit coupling between the Π and Σ curves, giving the |Ψ(j,E) Ω ⟩ in eq 8 and the photodetachment amplitudes M(j) q (Ωi,Ω, E) defined in eq 7. The state-selected spectra are obtained from the corresponding absorption cross sections σ(3/2)(E) and σ(1/2)(E) given in eqs 9 and the anisotropy parameters β(1/2)(E) and β(3/2)(E) from eqs 10. The Coupling Model. Figure 8 shows the state-resolved absorption spectra obtained using the three different Na−He

this energy region is due to a mixing of the 2Σ1/2 and 2Π1/2 curves by the spin−orbit interaction and as such depends critically on the finer details of the Na−He pair potentials. Although the spin−orbit interaction can give rise to Na 2P1/2 products, it obviously cannot account for the experimental observation that the majority of the products are Na 2P1/2 atoms. We therefore conclude that another process is responsible for the formation of the Na 2P1/2 products. It is unlikely related to collisional relaxation, as this process tends to wash out the angular distribution of the products. This is confirmed by the calculated anisotropy parameters for the 2P1/2 and 2P3/2 fragments reported in Figure 8, which show the same behavior as the experiment. The anisotropy parameters increase from −1 to 2 with increasing excitation energy, as expected when switching from Π to Σ excitation. To account for the formation of Na 2P1/2 products, we consider the possibility of a crossing or a near-crossing between the Σ and the Π curves in the outgoing region away from the Franck−Condon region. This crossing is made possible by the existence of an attractive well for both the Π and the Σ orientation of the sodium p orbital. Based on the NaHe pair potentials, one at first might only expect a well for the Π orientation. However, because averaging over many Na−He interactions where the Na−He axis is at an angle smaller than 90° incorporates a significant contribution from the (attractive) Π interaction, the Σ potential also has a well. This well can be of the same order of magnitude as the Π well but at larger distances. As illustrated in the upper panel of Figure 9, the 2Σ1/2 and 2 Π1/2 model potentials based on the NaHe pair potentials of Mullamphy et al.68 cross at certain distances. For the sake of

Figure 8. Calculated energy dependence of the state-specific absorption cross sections (solid lines) and anisotropy parameters (dashed lines) for Na@He1000 based on the NaHe pair potentials of Mullamphy et al.68 (upper panel), Pascale57 (middle panel), and Allouche et al.69 (lower panel). The zero for energy is defined as the spin-free dissociation limit He1000 + Na 2P.

interaction potentials. The calculated spectra are clearly too narrow compared to the experimental spectrum. Part of this disagreement is related to saturation broadening of the experimental spectra. Another factor is the size of the simulated droplet, which contains only 1000 atoms while the experimental spectrum is averaged over a wide distribution of droplet sizes. Lastly, helium density fluctuations, which have been found to contribute significantly to transition widths, are not taken into account.43 In agreement with experiment, the Π part of the absorption spectra reveals a shift equal to the atomic spin−orbit splitting, ΔSO, between the spectra corresponding to Na(2P1/2) and Na(2P3/2) fragments. This is because the 2Π3/2 and 2Π1/2 potential curves, leading to 2P 3/2 and 2P 1/2 fragments, respectively, are parallel in the Franck−Condon region but have dissociation thresholds that differ by ΔSO. The excitation spectrum yielding 2P3/2 fragments reveals almost equal intensity for the 2Π3/2 and 2Σ1/2 contributions. In contrast, the spectrum giving rise to 2P1/2 products corresponds mainly to excitation of the 2Π1/2 state. From these results it becomes obvious that excitation of the system in the 2Σ region of the spectrum leads primarily to 2P3/2 fragments. Depending on the choice of Na−He pair potentials, the relative yield of 2P1/2 fragments varies from almost zero, to up to 10%. The appearance of 2P1/2 fragments in

Figure 9. Potential energy curves for Na@He1000 as a function of the Na−He1000 center-of-mass distance. The diagonal part of the spin−orbit coupling has been added to the 2Π and 2Σ curves. The wave function of the ground electronic state is drawn to indicate the Franck−Condon region (dashed line). Model potentials (upper panel), Na@He1000 interaction potentials based on the NaHe pair potentials of Mullamphy et al.68 using a ground state helium density optimized for each position of the Na atom (middle panel), and potentials based on the same pair potentials but calculated using the helium density corresponding to the minimum energy ground state configuration (lower panel). I

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A demonstration, the well depths of the potentials in this figure have been artificially enlarged. In addition, the diagonal part of the spin−orbit coupling has been added to the Π and Σ curves in order to discuss the dynamics in terms of the Landau−Zener model.72 If the Landau−Zener parameters corresponding to the first crossing (around 26 Å) give conditions that are close to a diabatic passage, the 2Σ1/2 excitation (red curve) remains on the red curve. For the model potentials shown in the upper panel of Figure 9 we find that after excitation at the maximum of the 2Σ1/2 absorption, the probability to follow the 2Σ1/2 curve diabatically through the first crossing amounts to 72%. The slopes of the potential energy curves at the second crossing are smaller, leading to an adiabatic passage in this case. Indeed, for this crossing we find a 99.96% probability to remain on the adiabatic (lower) curve, leading to Na 2P1/2 products. Combining these two results and integrating over the 2Σ1/2 absorption profile we find that excitation of the 2Σ1/2 results in a Na 2P1/2 product formation yield of 67%, comparable with our experimental findings. Whereas the mechanism described above is able to account for the experimental observations, calculations based on the three NaHe pair potentials do not yield a large proportion of 2P1/2 fragments. This is due to the fact that the Σ wells calculated with the above-mentioned pair potentials are not very deep. As an example, Figure 9 shows the interaction potentials based on the NaHe pair potentials of Mullamphy et al.68 as a function of the distance between the Na atom and the center-of-mass of the helium droplet. It should be noted here that the radius of a pure He1000 droplet according to the liquid drop model corresponds to 22.2 Å. As a result of the limited well depth, the Σ and Π curves do not cross when the diagonal part of the spin−orbit coupling is added. The absence of a crossing for the 2Σ1/2 and 2Π1/2 potentials does not necessarily imply that curve crossings are not responsible for the large proportion of the Na 2P1/2 products observed experimentally. It may well be that for larger droplets like those used in the experiments which have deeper potential wells, a crossing between the energy curves does result. Furthermore, the Σ well depth depends critically on the longrange part of the NaHe pair potential, which is inherently difficult to calculate for weakly interacting systems like NaHe. A small correction to the pair potentials could lead to a significant increase in well depth. In addition, one should consider the possibility that a curve crossing develops dynamically due to the rearrangement of the helium density during the evolution of the system. This mechanism has been suggested before in order to explain the efficient relaxation of high excited states.40 Although this possibility cannot be addressed with the present static calculations, we find that the helium density configuration plays an important role. This is exemplified by the two lower panels of Figure 9. Both sets of potentials have been calculated based on the NaHe pair potentials of Mullamphy et al.,68 but they differ in the way the helium density has been determined. Like in the calculation of the state-specific absorption spectra, the potential curves in the middle panel have been determined using a ground state helium configuration optimized at each position of the Na atom. In contrast, the potential curves in the lower panel have been calculated using the helium density profile corresponding to the equilibrium configuration. The resulting sets of potential curves are clearly very different, suggesting that curve crossings could potentially occur during the evolution of the system. However, a confirmation of the proposed relaxation mechanism will have to await dynamical calculations like those that have been performed for other systems.30,37,73,74

Article

■

CONCLUSION

■

AUTHOR INFORMATION

In this study we have revisited the 3p ← 3s transition of Na on the surface of helium droplets using a mass and state-selective detection technique. By combining spectroscopy with velocity map imaging, we have gained unique insight into the dynamics of the excited system. We found that excitation via the 3p 2Π ← 3s 2 Σ transitions leads to the formation of NaHe exciplexes as well as bare Na products. The relative intensities of the 2P1/2 and 2P3/2 Na products as determined from state-specific spectra are in line with the predictions of the one-dimensional tunneling model put forward to describe the NaHe exciplex formation rate.7 The speed distributions of the desorbed Na atoms are indicative of a direct desorption process, and their dependence on excitation energy can be well described by an impulsive model.30 By contrast, the speed distributions of the NaHe exciplexes are independent of excitation energy and hint toward a thermally driven desorption process. The analysis of the internal state distribution of the NaHe products suggests that vibrational relaxation of the exciplex likely leads to their desorption from the droplets. Excitation via the 3p 2Σ ← 3s 2Σ transition has been found to yield exclusively Na products. The speed distribution of the atoms point to an impulsive desorption process. Stateresolved excitation spectra indicate that excitation of the 3p 2Σ state, which correlates to the 2P3/2 state in the free atom, leads to unexpected large amounts of Na 2P1/2. Theoretical considerations suggest that the formation of Na 2P1/2 is due to the existence of an efficient relaxation pathway resulting from curve crossings between the 2Σ and 2Π1/2 potential energy curves in the exit channel.

Corresponding Author

*E-mail: Marcel.Drabbels@epfl.ch. Present Address ∥

SICPA SA, 1000 Lausanne, Switzerland.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

We are grateful to G. Guillon, A. Viel, A. Allouche, M. AubertFrécon, G. Peach, and I. B. Whittingham for providing the Na−He potential energy curves. We would like to acknowledge the funding by the Swiss National Science Foundation (Grants 200020-112193 and 200021_146598), the ANR (project ANR08-BLAN-0146-01), and the CALMIP computer center (grant 2014-P1039).

(1) Grebenev, S.; Toennies, J. P.; Vilesov, A. F. Superfluidity within a Small Helium-4 Cluster: The Microscopic Andronikashvili Experiment. Science 1998, 279, 2083−2086. (2) Hartmann, M.; Mielke, F.; Toennies, J. P.; Vilesov, A. F.; Benedek, G. Direct Observation of Elementary Excitations in Superfluid He Droplets. Phys. Rev. Lett. 1996, 76, 4560−4563. (3) Brauer, N. B.; Smolarek, S.; Loginov, E.; Mateo, D.; Hernando, A.; Pi, M.; Barranco, M.; Buma, W. J.; Drabbels, M. Critical Landau Velocity in Helium Nanodroplets. Phys. Rev. Lett. 2013, 111, 153002. (4) Gomez, L. F.; et al. Helium Superfluidity. Shapes and Vorticities of Superfluid Helium Nanodroplets. Science 2014, 345, 906−909. (5) Ancilotto, F.; Lerner, P. B.; Cole, M. W. Phyiscs of Solvation. J. Low. Temp. Phys. 1995, 101, 1123−1146.

J

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

(27) Takayanagi, T.; Shiga, M. Theoretical Study on Photoexcitation Dynamics of the K Atom Attached to Helium Clusters and the Solvation Structures of K*He−N Exciplexes. Phys. Chem. Chem. Phys. 2004, 6, 3241−3247. (28) Nakayama, A.; Yamashita, K. Path Integral Monte Carlo Study on the Structure and Absorption Spectra of Alkali Atoms (Li, Na, K) Attached to Superfluid Helium Clusters. J. Chem. Phys. 2001, 114, 780− 791. (29) Hernando, A.; Beswick, J. A.; Halberstadt, N. Communication: Angular Momentum Alignment and Fluorescence Polarization of Alkali Atoms Photodetached from Helium Nanodroplets. J. Chem. Phys. 2013, 139, 221102. (30) Hernando, A.; Barranco, M.; Pi, M.; Loginov, E.; Langlet, M.; Drabbels, M. Desorption of Alkali Atoms from 4He Nanodroplets. Phys. Chem. Chem. Phys. 2012, 14, 3996−4010. (31) Loginov, E.; Drabbels, M. Unusual Rydberg System Consisting of a Positively Charged Helium Nanodroplet with an Orbiting Electron. Phys. Rev. Lett. 2011, 106, 083401. (32) Loginov, E.; Callegari, C.; Ancilotto, F.; Drabbels, M. Spectroscopy on Rydberg States of Sodium Atoms on the Surface of Helium Nanodroplets. J. Phys. Chem. A 2011, 115, 6779−6788. (33) Lackner, F.; Krois, G.; Ernst, W. E. Rydberg-Ritz Analysis and Quantum Defects for Rb and Cs Atoms on Helium Nanodroplets. Mol. Phys. 2013, 111, 2118−2125. (34) Lackner, F.; Krois, G.; Koch, M.; Ernst, W. E. Rubidium on Helium Droplets: Analysis of an Exotic Rydberg Complex for n* < 20 and 0 ≤ l ≤ 3. J. Phys. Chem. Lett. 2012, 3, 1404−1408. (35) Theisen, M.; Lackner, F.; Ernst, W. E. Cs Atoms on Helium Nanodroplets and the Immersion of Cs+ into the Nanodroplet. J. Chem. Phys. 2011, 135, 074306. (36) Fechner, L.; Gruner, B.; Sieg, A.; Callegari, C.; Ancilotto, F.; Stienkemeier, F.; Mudrich, M. Photoionization and Imaging Spectroscopy of Rubidium Atoms Attached to Helium Nanodroplets. Phys. Chem. Chem. Phys. 2012, 14, 3843−3851. (37) von Vangerow, J.; Sieg, A.; Stienkemeier, F.; Mudrich, M.; Leal, A.; Mateo, D.; Hernando, A.; Barranco, M.; Pi, M. Desorption Dynamics of Heavy Alkali Metal Atoms (Rb, Cs) off the Surface of Helium Nanodroplets. J. Phys. Chem. A 2014, 118, 6604−6614. (38) Callegari, C.; Ancilotto, F. Perturbation Method to Calculate the Interaction Potentials and Electronic Excitation Spectra of Atoms in He Nanodroplets. J. Phys. Chem. A 2011, 115, 6789−6796. (39) Aubock, G.; Nagl, J.; Callegari, C.; Ernst, W. E. Electron Spin Pumping of Rb Atoms on He Nanodroplets via Nondestructive Optical Excitation. Phys. Rev. Lett. 2008, 101, 035301. (40) Loginov, E.; Drabbels, M. Dynamics of Excited Sodium Atoms Attached to Helium Nanodroplets. J. Phys. Chem. A 2014, 118, 2738− 2748. (41) Loginov, E.; Drabbels, M. Spectroscopy and Dynamics of BariumDoped Helium Nanodroplets. J. Chem. Phys. 2012, 136, 154302. (42) Stienkemeier, F.; Wewer, M.; Meier, F.; Lutz, H. O. Langmuir− Taylor Surface Ionization of Alkali (Li, Na, K) and Alkaline Earth (Ca, Sr, Ba) Atoms Attached to Helium Droplets. Rev. Sci. Instrum. 2000, 71, 3480−3484. (43) Hernando, A.; Barranco, M.; Mayol, R.; Pi, M.; Ancilotto, F.; Bunermann, O.; Stienkemeier, F. Absorption Spectrum of Na Atoms Attached to Helium Nanodroplets. J. Low Temp. Phys. 2010, 158, 105− 111. (44) Allard, N. F.; Nakayama, A.; Spiegelman, F.; Kielkopf, J. F.; Stienkemeier, F. Absorption Spectra of Na Atoms in Dense He. Eur. Phys. J. D 2013, 67, 52. (45) Loginov, E.; Drabbels, M. Excited State Dynamics of Ag Atoms in Helium Nanodroplets. J. Phys. Chem. A 2007, 111, 7504−7515. (46) Braun, A.; Drabbels, M. Photodissociation of Alkyl Iodides in Helium Nanodroplets. I. Kinetic Energy Transfer. J. Chem. Phys. 2007, 127, 114303. (47) Lewerenz, M.; Schilling, B.; Toennies, J. P. A New Scattering Deflection Methode for Determining and Selecting the Sizes of Large Liquid Helium Clusters of 4He. Chem. Phys. Lett. 1993, 206, 381−387.

(6) Stienkemeier, F.; Higgins, J.; Callegari, C.; Kanorsky, S. I.; Ernst, W. E.; Scoles, G. Spectroscopy of Alkali Atoms (Li, Na, K) Attached to Large Helium Clusters. Z. Phys. D: At., Mol. Clusters 1996, 38, 253−263. (7) Reho, J.; Higgins, J.; Lehmann, K. K.; Scoles, G. Alkali-Helium Exciplex Formation on the Surface of Helium Nanodroplets. II. A TimeResolved Study. J. Chem. Phys. 2000, 113, 9694−9701. (8) Reho, J.; Higgins, J.; Callegari, C.; Lehmann, K. K.; Scoles, G. Alkali-Helium Exciplex Formation on the Surface of Helium Nanodroplets. I. Dispersed Emission Spectroscopy. J. Chem. Phys. 2000, 113, 9686−9693. (9) Reho, J.; Callegari, C.; Higgins, J.; Ernst, W. E.; Lehmann, K. K.; Scoles, G. Spin-Orbit Effects in the Formation of the Na−He Excimer on the Surface of He Clusters. Faraday Discuss. 1997, 108, 161−174. (10) Droppelmann, G.; Bunermann, O.; Schulz, C. P.; Stienkemeier, F. Formation Times of RbHe Exciplexes on the Surface of Superfluid Versus Normal Fluid Helium Nanodroplets. Phys. Rev. Lett. 2004, 93, 023402. (11) Schulz, C. P.; Claas, P.; Stienkemeier, F. Formation of K*He Exciplexes on the Surface of Helium Nanodroplets Studied in Real Time. Phys. Rev. Lett. 2001, 87, 153401. (12) Giese, C.; Mullins, T.; Gruner, B.; Weidemuller, M.; Stienkemeier, F.; Mudrich, M. Formation and Relaxation of RbHe Exciplexes on He Nanodroplets Studied by Femtosecond Pump and Picosecond Probe Spectroscopy. J. Chem. Phys. 2012, 137, 244307. (13) Callegari, C.; Higgins, F.; Stienkemeier, F.; Scoles, G. Beam Depletion Spectroscopy of Alkali Atoms (Li, Na, K) Attached to Highly Quantum Clusters. J. Phys. Chem. A 1998, 102, 95−101. (14) Stienkemeier, F.; Higgins, J.; Ernst, W. E.; Scoles, G. Spectroscopy of Alkali Atoms and Molecules Attached to Liquid He Clusters. Z. Phys. B: Condens. Matter 1995, 98, 413−416. (15) Nagl, J.; Aubock, G.; Callegari, C.; Ernst, W. E. Magnetic Dichroism of Potassium Atoms on the Surface of Helium Nanodroplets. Phys. Rev. Lett. 2007, 98, 075301. (16) Bruhl, F. R.; Trasca, R. A.; Ernst, W. E. Rb−He Exciplex Formation on Helium Nanodroplets. J. Chem. Phys. 2001, 115, 10220− 10224. (17) Mudrich, M.; Stienkemeier, F.; Droppelmann, G.; Claas, P.; Schulz, C. P. Quantum Interference Spectroscopy of Rubidium− Helium Exciplexes Formed on Helium Nanodroplets. Phys. Rev. Lett. 2008, 100, 023401. (18) Bunermann, O.; Droppelmann, G.; Hernando, A.; Mayol, R.; Stienkemeier, F. Unraveling the Absorption Spectra of Alkali Metal Atoms Attached to Helium Nanodroplets. J. Phys. Chem. A 2007, 111, 12684−12694. (19) Mayol, R.; Ancilotto, F.; Barranco, M.; Bunermann, O.; Pi, M.; Stienkemeier, F. Alkali Atoms Attached to He-3 Nanodroplets. J. Low Temp. Phys. 2005, 138, 229−234. (20) Stienkemeier, F.; Bunermann, O.; Mayol, R.; Ancilotto, F.; Barranco, M.; Pi, M. Surface Location of Sodium Atoms Attached to He3 Nanodroplets. Phys. Rev. B: Condens. Matter 2004, 70, 214508. (21) Bunermann, O.; Mudrich, M.; Weidemuller, M.; Stienkemeier, F. Spectroscopy of Cs Attached to Helium Nanodroplets. J. Chem. Phys. 2004, 121, 8880−8886. (22) Stienkemeier, F.; Meier, F.; Hägele, A.; Lutz, H. O.; Schreiber, E.; Schulz, C. P.; Hertel, I. V. Coherence and Relaxation in PotassiumDoped Helium Droplets Studied by Femtosecond Pump−Probe Spectroscopy. Phys. Rev. Lett. 1999, 83, 2320−2323. (23) Dell’Angelo, D.; Guillon, G.; Viel, A. Excited Li and Na in He−N: Influence of the Dimer Potential Energy Curves. J. Chem. Phys. 2012, 136, 114308. (24) Leino, M.; Viel, A.; Zillich, R. E. Electronically Excited Rubidium Atom in a Helium Cluster or Film. J. Chem. Phys. 2008, 129, 184308. (25) Leino, M.; Viel, A.; Zillich, R. E. Electronically Excited Rubidium Atom in Helium Clusters and Films. II. Second Excited State and Absorption Spectrum. J. Chem. Phys. 2011, 134, 024316. (26) Pacheco, A. B.; Thorndyke, B.; Reyes, A.; Micha, D. A. Quantum Dynamics of an Excited Alkali Atom in a Noble Gas Cluster: Lithium Attached to a Helium Cluster. J. Chem. Phys. 2007, 127, 244504. K

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A (48) Eppink, A. T. J. B.; Parker, D. H. Velocity Map Imaging of Ions and Electrons Using Electrostatic Lenses: Application in Photoelectron and Photofragment Ion Imaging of Molecular Oxygen. Rev. Sci. Instrum. 1997, 68, 3477−3484. (49) Vrakking, M. J. J. An Iterative Procedure for the Inversion of TwoDimensional Ion/Photoelectron Imaging Experiments. Rev. Sci. Instrum. 2001, 72, 4084−4089. (50) Hauser, A. W.; Gruber, T.; Filatov, M.; Ernst, W. E. Shifts in the Esr Spectra of Alkali-Metal Atoms (Li, Na, K, Rb) on Helium Nanodroplets. ChemPhysChem 2013, 14, 716−722. (51) Enomoto, K.; Hirano, K.; Kumakura, M.; Takahashi, Y.; Yabuzaki, T. Emission Spectra of Alkali-Metal (K,Na,Li)−He Exciplexes in Cold Helium Gas. Phys. Rev. A: At. Mol. Opt. Phys. 2004, 69, 012501. (52) Kanorsky, S.; Weis, A.; Arndt, M.; Dziewior, R.; Hansch, T. W. Pressure Shift of Atomic Resonance Lines in Liquid and Solid Helium. Z. Phys. B: Condens. Matter 1995, 98, 371−376. (53) Dupont-Roc, J. Excited P-States of Alkali Atoms in LiquidHelium. Z. Phys. B: Condens. Matter 1995, 98, 383−386. (54) Takahashi, Y.; Sano, K.; Kinoshita, T.; Yabuzaki, T. Spectroscopy of Alkali Atoms and Moleules in Superfluid Helium. Phys. Rev. Lett. 1993, 71, 1035. (55) Kramida, A.; Ralchenko, Y.; Reader, J.; NIST ASD Team (2012). NIST Atomic Spectra Database (version 5.0); National Institute of Standards and Technology: Gaithersburg, MD, 2012; available: http:// physics.nist.gov/asd. (56) Soldan, P.; Lee, E. P. F.; Wright, T. G. Interatomic Potentials for the Na+−Rg Complexes (Rg = He, Ne and Ar). Mol. Phys. 1999, 97, 139−149. (57) Pascale, J. Use of L-Dependent Pseudopotentials in the Study of Alkali-Metal-Atom-He Systems - The Adiabatic Molecular Potentials. Phys. Rev. A: At. Mol. Opt. Phys. 1983, 28, 632−644. (58) Le Roy, R. J. LEVEL 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels; University of Waterloo Chemical Physics Research Report CP-663(2007); see http://leroy.uwaterloo.ca/programs. (59) Zare, R. N. Photoejection Dynamics. Molecular Photochemistry 1972, 44, 1−37. (60) Braun, A.; Drabbels, M. Photodissociation of Alkyl Iodides in Helium Nanodroplets. III. Recombination. J. Chem. Phys. 2007, 127, 114305. (61) Amin, N.; Mahmood, S.; Anwar-ul-Haq, M.; Riaz, M.; Baig, M. A. Measurement of the Photoionization Cross-Section of the 3p 2P1/2,3/2 Excited Levels of Sodium. Eur. Phys. J. D 2006, 37, 23−28. (62) Beswick, J. A.; Glassmaujean, M.; Roncero, O. On the Orientation of Molecular Photofragments Produced in Highly Excited Rotational States. J. Chem. Phys. 1992, 96, 7514−7527. (63) Siebbeles, L. D. A.; Glassmaujean, M.; Vasyutinskii, O. S.; Beswick, J. A.; Roncero, O. Vector Properties in Photodissociation Quantum Treatment of the Correlation between the Spatial Anisotropy and the Angular-Momentum Polarization of the Fragments. J. Chem. Phys. 1994, 100, 3610−3623. (64) Douberly, G. E.; Stiles, P. L.; Miller, R. E.; Schmied, R.; Lehmann, K. K. (HCN)(M)−M−N (M = K, Ca, Sr): Vibrational Excitation Induced Solvation and Desolvation of Dopants in and on Helium Nanodroplets. J. Phys. Chem. A 2010, 114, 3391−3402. (65) Hernando, A.; Masson, A.; Briant, M.; Mestdagh, J. M.; Gaveau, M. A.; Halberstadt, N. Fluorescence Emission of Ca-Atom from Photodissociated Ca2 in Ar Doped Helium Droplets. II. Theoretical. J. Chem. Phys. 2012, 137, 184311. (66) Masson, A.; Briant, M.; Hernando, A.; Halberstadt, N.; Mestdagh, J. M.; Gaveau, M. A. Fluorescence Emission of Ca-Atom from Photodissociated Ca2 in Ar-Doped Helium Droplets. I. Experimental. J. Chem. Phys. 2012, 137, 184310. (67) Patil, S. H. Adiabatic Potentials for Alkali Inert-Gas Systems in the Ground-State. J. Chem. Phys. 1991, 94, 8089−8095. (68) Mullamphy, D. F. T.; Peach, G.; Venturi, V.; Whittingham, I. B.; Gibson, S. J. Collisional Broadening of Alkali Doublets by Helium Perturbers. J. Phys. B: At., Mol. Opt. Phys. 2007, 40, 1141−1152.

(69) Allouche, A. R.; Alioua, K.; Bouledroua, M.; Aubert-Frecon, M. Ab Initio Potential Energy Curves and Transition Dipole Moments for the Interaction of a Ground State He with Na(3s−3p). Chem. Phys. 2009, 355, 85−89. (70) Launay, J. M. Body-Fixed Formulation of Rotational Excitation Exact and Centrifugal Decoupling Results for Co−He. J. Phys. B: At., Mol. Opt. Phys. 1976, 9, 1823−1838. (71) Lester, W. A., Jr. Calculation of Cross Sections for Rotational Excitation of Diatomic Molecules by Heavy Particle Impact: Solution of the Close-Coupled Equations. Methods in Computational Physics 1971, 10, 211−241. (72) Tannor, D. J. Introduction to Quantum Mechanics: A TimeDependent Perspective; University Science Books: Sausalito, CA, 2007. (73) Mateo, D.; Hernando, A.; Barranco, M.; Loginov, E.; Drabbels, M.; Pi, M. Translational Dynamics of Photoexcited Atoms in He-4 Nanodroplets: The Case of Silver. Phys. Chem. Chem. Phys. 2013, 15, 18388−18400. (74) Mateo, D.; Leal, A.; Hernando, A.; Barranco, M.; Pi, M.; Cargnoni, F.; Mella, M.; Zhang, X. H.; Drabbels, M. Communication: Nucleation of Quantized Vortex Rings in He-4 Nanodroplets. J. Chem. Phys. 2014, 140, 131101.

L

DOI: 10.1021/jp511885t J. Phys. Chem. A XXXX, XXX, XXX−XXX