Dynamics of Excited Sodium Atoms Attached to Helium Nanodroplets

Article pubs.acs.org/JPCA

Dynamics of Excited Sodium Atoms Attached to Helium Nanodroplets Evgeniy Loginov† and Marcel Drabbels* Laboratoire de Chimie Physique Moléculaire, Ecole polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland ABSTRACT: The dynamics of laser-excited sodium atoms at the surface of helium nanodroplets has been investigated as a function of quantum state. For all cases, excitation of the system leads to desorption of the sodium atom from the droplet surface. The mean kinetic energy of the desorbed atoms scales linearly with excitation frequency, indicative of an impulsive desorption process. The energy partitioning between the helium and the desorbing sodium atom depends on the quantum state and appears to be related to the size and shape of the electron orbital. The speed distributions of desorbed NaHe exciplexes point toward a direct formation process of an exciplex with no internal energy. Photoelectron spectroscopy reveals an increasing importance of helium-induced relaxation with increasing quantum state, which is tentatively attributed to curve crossing between different NaHeN interaction potentials during the desorption process.

1. INTRODUCTION Helium nanodroplets are fascinating quantum systems that are nowadays routinely used as matrix for spectroscopic studies.1−4 Many of the droplets’ properties have been elucidated using atomic and molecular probes.5−7 Alkali atoms play a special role in this, as they are one of the few species known to reside on the surface of the droplets and thus able to probe the boundary region.8,9 Consequently, the np 2P ← ns 2S transitions of alkali atoms attached to helium nanodroplets have attracted the interest of theoreticians and experimentalist alike.9−31 Recently the spectroscopy of higher excited states has been explored.32−42 From these studies some general trends could be identified. The spectra involving states with low and intermediate principal quantum number are characterized by broad resonances that are blue-shifted with respect to the corresponding atomic resonances, reflecting the repulsive interaction of the excited valence electron of the atom with the helium. The spectra can be successfully reproduced using the so-called pseudodiatomic model, in which 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.9,21 The interaction between the alkali atom and the helium droplet is reduced to a one-dimensional potential calculated as the sum of alkali−He pair potentials. This simple model progressively fails to reproduce the experimental spectra involving higher excited states as helium-induced configuration interactions are not taken into account.34,43 For states with large principal quantum number where the mean radius of the electron orbit is comparable or larger than the size of the droplet, the interaction of the valence electron with the helium decreases and a Rydberg-like system results.33,36 © 2014 American Chemical Society

While the role of the excited state on the spectrum is now fairly well understood, its influence on the ensuing dynamics is still largely unexplored. Experiments concentrating on the np 2P ← ns 2S transitions have found that the excited atoms desorb from the droplets on a picosecond time scale, either as bare atoms or as alkali-helium exciplexes.10−15 The heavy alkalis Rb and Cs are an exception, they remain attached to the helium droplet when excited close to the gas phase D1 transition.37,44 Only recently the desorption dynamics and the exciplex formation involving higher excited states was investigated.38,45 A combined experimental and theoretical study revealed that the desorption of the excited atoms is a direct, rather than a statistical, process in which the energy is partitioned between the helium droplet and the alkali atom.45 This allows the desorption process to be accurately described by an impulsive model, analogous to the dissociation of molecules. Another study revealed that the exciplexes formation and desorption is a direct process and that the helium induces relaxation of the excited atoms.38 Similar processes have been identified in experiments on barium atoms which are also located at the surface of helium droplets.46 In order to establish how the different processes depend on the excited state we have investigated the dynamics of Na atoms located on helium nanodroplets as a function of the excitation energy. The dynamics of the 4s state has been reported recently.45 Here we discuss the result for states ranging from the 3d state all the way up to high Rydberg states close to the ionization threshold. Received: December 13, 2013 Revised: March 27, 2014 Published: March 27, 2014 2738

dx.doi.org/10.1021/jp4121996 | J. Phys. Chem. A 2014, 118, 2738−2748

The Journal of Physical Chemistry A

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Here the states are labeled as nlΛ, where Λ is the projection of the electron’s orbital angular momentum onto the axis defined by the sodium atom and the center of the helium droplet and n and l are the principal quantum number and orbital angular momentum of the correlating atomic state, respectively. In order to determine whether helium induces relaxation of the 3d excited atoms during the desorption process, photoelectron spectra have been recorded. Following excitation of the system at 29400 cm−1, absorption of an additional photon leads to the ionization of the excited products. The resulting photoelectron spectrum is presented in Figure 2. The two

2. EXPERIMENTAL SECTION The experimental setup has been described in detail before.47,48 Helium droplets are formed by expanding 4He gas at a pressure of 30 bar into vacuum through a 5 μm orifice cooled to cryogenic temperatures by a closed cycle refrigerator. After passing a skimmer, the droplets pick up sodium atoms as they traverse sodium vapor formed by heating sodium metal. The temperature of the oven holding the metal 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 velocity map imaging setup. At the center of the setup, the sodiumdoped droplets are excited by crossing the droplet beam perpendicularly with the fundamental or frequency-doubled 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 ranges from 4 mJ for the frequency-doubled and up 50 mJ for the fundamental output of the dye laser. For most transitions investigated, the laser beam is focused slightly to yield an estimated spot size of 0.5 mm diameter at the excitation region. Following excitation, the excited alkali atoms are ionized by the absorption of an additional photon. The ions, or alternatively the electrons, are 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 highresolution CCD camera. The individual images are analyzed online and the centroids of the ion/electron impacts are determined. The velocity distributions of the ions/electrons are determined by performing an inverse Abel transform on the images constructed from the accumulated centroids. Ion images can be recorded at a specific mass or masses by gating the front of the detector at the arrival time of the ions of interest. 3. RESULTS AND DISCUSSION 3d State. The spectrum corresponding to the 3d ← 3s transition has been found to share many of the characteristics of the 3p ← 3s transition and is reproduced in Figure 1.9,12,34 At low frequencies the spectrum is characterized by the formation of NaHe and NaHe2 exciplexes, while at high frequencies mainly Na products are observed. The corresponding spectra have been tentatively assigned to the 3d Π ←3s Σ and 3d Σ ← 3s Σ transitions for the NaHe and Na products, respectively.34

Figure 2. Photoelectron spectra, plotted as internal energy of the sodium atom, recorded after excitation of the NaHeN system to various states. The stick spectrum represents the calculated photoelectron spectrum in the absence of helium-induced relaxation.

peaks in the spectrum are readily assigned to Na 3d and Na 3p. Unfortunately, the resolution does not allow resolving the spectra corresponding to the individual Na, NaHe, and NaHe2 products. It should be noted that no evidence is found for excited sodium atoms remaining attached to the helium droplets. When interpreting the photoelectron spectrum care has to be taken to attribute the presence of the Na 3p peak to helium-induced relaxation, as the signal levels do not necessarily reflect the relative population of the various states. We therefore have simulated the photoelectron spectrum in the absence of helium-induced relaxation, using an approach similar

Figure 1. Mean kinetic energy and anisotropy parameter of Na and NaHe products as a function of excitation frequency. The solid lines are linear fits to the data points. The vertical dotted line indicates the energy of the sodium 3d state. The shaded areas correspond to the Na (blue) and NaHe (red) excitation spectra. 2739



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to that used for excitation to the 4s state.45 The simulations take into account the radiative decay of the various excited states during the laser pulse, as well as the state specific ionization cross sections.49−51 The result of the model calculations is represented by the stick spectrum shown in Figure 2 and clearly deviates from the experimental spectrum. This discrepancy might indicate that the helium environment induces a fast relaxation of the 3d excited sodium to the 3p state. However, it cannot be excluded that exciplexes, which constitute 55% of the products at this excitation frequency, are responsible for this difference, since these might have different radiative lifetimes and ionization cross sections than bare atoms. Additional information on the desorption process and exciplex formation can be provided by the velocity distributions of the desorbed products. Figure 3 displays velocity map images

the speed distribution, is slightly positive at low excitation frequencies and approaches zero at higher frequencies. The mean kinetic energy of desorbed sodium has been fitted to the following expression: Ekin ̅ (Na) = η[hν − E0]

(2)

where hν is the photon energy, E0 an energy offset, and η the proportionality constant describing the fraction of available energy converted into kinetic energy of the sodium atom. The linear dependence of the atom’s mean kinetic energy on excitation energy has been explained before by an impulsive model.45 In this model the problem is reduced to a pseudopolyatomic description in which the sodium atom is considered to be bound to the helium droplet via a single helium moiety. The available energy is initially partitioned between the kinetic energies of the sodium atom and this helium moiety. The kinetic energy is subsequently partitioned between the translation and internal degrees of freedom of the helium droplet. According to the impulsive model the energy offset can be related to the internal energy of the desorbed atom, Eint(Na), and the binding energy of the ground state sodium atom to the surface of the droplet, Ebind, via E0 = Eint (Na) − Ebind

(3)

The proportionality constant η is given by meff η= meff + mNa

(4)

where mNa is the mass of the sodium atom and mef f is the effective mass of the helium moiety interacting with the excited atom. The results for excitation of the Na atom to the 3d state are in line with this simple model. The effective helium mass and energy offset obtained from the fit are listed in Table 1. Table 1. Proportionality Constant, η, Energy Offset, E0 (cm−1), Effective Mass meff (Number of Helium Atoms), and mean electron orbit radius, ⟨re⟩ (Å), for Different Quantum States

Figure 3. Ion images of Na and NaHe products recorded following excitation to the 3d state at 29400 cm−1 (left) and the corresponding speed distributions and angular anisotropy parameters (right).

of Na and NaHe, recorded after excitation at 29400 cm−1. The images for both products are quite similar and reveal almost isotropic angular distributions. To allow for a quantitative analysis, the velocity distributions of the products have been extracted. The corresponding speed distributions and anisotropy parameters are reported in Figure 3. The anisotropy parameters, β, have been determined by fitting the angular intensity distribution I(θKE) of the desorbed products to the standard expression: 1 I(θKE) = [1 + βP2(cos θKE)] (1) 4π

a

state

η

E0

meff

⟨re⟩

3p1/2a 3p3/2a 4sb 3d 3d NaHe 4p 5s 4d 5p

0.193(2) 0.221(2) 0.516(4) 0.27(2) 0.14(1) 0.406(6) 0.56(2) 0.47(2) 0.48(3)

16986(2) 16990(2) 25743(4) 29164(40) 28637(43) 30209(25) 32908(47) 34608(23) 34809(100)

1.4 1.7 6.1 2.1 1.1 3.9 7.3 5.1 5.3

3.1 3.1 5.6 5.5 5.5 7.3 10.6 11.0 13.1

Reference 55. bReference 45.

From this analysis one finds that the excited sodium atom interacts effectively with approximately two helium atoms. This value is notably smaller than found for excitation of Na to the 4s state. This difference is thought to be related to the size of the electronic orbitals, vide inf ra. The binding energy of the ground state Na atom to the helium droplet can be determined from the excess energy, E0 = 29164 ± 40 cm−1. Taking for the energy of the Na 3d state, Eint(Na) = 29173 cm−1, we find a Na(3s)−HeN binding energy of Ebind = 9 ± 40 cm−1, consistent with the calculated value of 13 cm−1.53 According to the impulsive model the angular distribution of the desorbed atoms

where θKE 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.52 As suggested by the images, the speed and angular distributions of the two products are slightly different. To characterize the variation of the velocity distributions with excitation energy the mean kinetic energy E̅kin is plotted in Figure 1 for selected excitation frequencies. Analogous to other systems,45,46 we find that the mean kinetic energy of the desorbed Na increases linearly with excitation energy. Furthermore, we find that the mean anisotropy parameter, ⟨β⟩, determined by averaging over 2740



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to the potential of the 3d Π state, that corresponding to the 3d Σ state exhibits a large barrier of ∼1000 cm−1, see inset Figure 4. This barrier effectively inhibits the formation of NaHe exciplexes. In contrast, vertical excitation from the ground state of the system to the 3d Π state, indicated by the vertical dotted line in Figure 4, leads to a direct formation of a NaHe exciplex. According to this model the complexes are formed with substantial internal energy, as they are created at energies ∼30 cm−1 below the dissociation threshold. The overall repulsive interaction of the exciplex with the helium droplet is expected to lead to a prompt desorption of the NaHe exciplex from the surface. Although the above does explain the exciplex formation, it cannot fully account for the experimental observations. While the model predicts the formation of a highly excited NaHe exciplex, the experiment seems to indicate otherwise. As pointed out above, the energy offset, E0, for the NaHe exciplex is ∼500 cm−1 below that of a free Na 3d atom. This we interpret as that the exciplex is formed in the vibrational ground state. On the basis of the weak He−HeN interaction strength,10 one expects that the overall interaction of the NaHe exciplex is quite similar to that of a Na atom with the droplet. Hence, one expects very similar proportionality constants, η, for Na and NaHe. Also this is not observed. The energy transfer to the helium droplet is significantly larger for NaHe than for Na, as expressed by the smaller proportionally constant. Clearly, a more sophisticated description of the exciplex formation process is required to account for these observations. We refrain from speculating about such a mechanism without the support of realistic simulations of this process. 4p State. Excitation spectra of the 4p ← 3s transitions have been reported before and are reproduced in Figure 5.34 In contrast to the 3p ← 3s transition mainly Na atoms are detected as products.12 Using the angular distributions of the desorbed Na atoms, more specifically the variation of the mean angular anisotropy parameter with excitation energy as shown in Figure 5, it has been possible to disentangle the contributions of the 4p Π and Σ states. As these results have already been extensively discussed,34 we here only report on the variation of the mean kinetic energy with excitation frequency, see Figure 5. The behavior is similar to that found for excitation to the 3d state, except that the energy offset, E0, and the slope, η, are different, see Table 1. This reflects the difference in internal energy of the sodium atom leaving the droplet and its interaction with the helium droplet. While the photoelectron spectrum recorded for the excitation to the 3d state provided indications of a possible helium-induced relaxation process, no evidence for this is found for the 4p state. The photoelectron spectrum shown in Figure 2 recorded following excitation via the 4p Σ ← 3s Σ transition at 32000 cm−1, is dominated by a single peak, corresponding to the 4p state of free Na. In agreement with our model simulations, a weak peak with a relative intensity of 1% is observed for the 3p state. 5s State. One would expect that the dynamics following excitation to the 5s state is similar to that of the 4s state, especially since the spectrum can be well reproduced using the diatomic model. However, the photoelectron spectra shown in Figure 2 recorded at the maximum of the 5s ← 3s absorption band, i.e., 34200 cm−1, reveals many peaks. The presence of sodium atoms in these many excited states suggests that the helium induces fast relaxation of the Na atom after excitation. This assumption is confirmed by our model calculations of the

is related to the symmetry of the states involved. 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. At low frequencies ⟨β⟩ is slightly positive, implying that the 3d Σ ← 3s Σ transition has a somewhat larger contribution to this part of the spectrum than the 3d Π ← 3s Σ transition. It is interesting to note that this is opposite to what was concluded based on the Na and NaHe yields.34 For now we do not have a conclusive explanation for this observation. The mean kinetic energy of the NaHe exciplex is also found to scale linearly with excitation energy. Following the impulsive model, one finds that the excited NaHe exciplex interacts with approximately one helium atom. The difference in the number of interacting helium atoms for Na and NaHe equals exactly one, suggesting that one of the interacting helium atoms binds to the Na to form the NaHe exciplex. Additional information on the exciplex formation process is provided by the energy offset. For NaHe we find E0 = 28638 cm−1, i.e. more than 500 cm−1 below the energy of the 3d state of Na. As the binding energy of NaHe to a helium droplet is thought to be quite similar to that of Na, this result suggests that the internal energy of the NaHe exciplex is ∼500 cm−1 less than that of free Na 3d. This energy difference is close to the calculated binding energy of the Na(3d)He exciplex,54 suggesting that the exciplex is formed in the vibrational ground state. Exciplex formation was first observed by Reho et al. in their study on the 3p ← 3s transition of Na and was interpreted by a 1-dimensional tunneling model based on the NaHe pair potentials and the energy required to remove a helium atom from the droplet surface.11,12 This model was later successfully invoked to account for RbHe exciplex formation.19,38 The 1dimensional NaHe−HeN interaction potentials have been constructed following the procedure by Reho et al. which calls for a folding of the NaHe pair potential with the He−HeN interaction potential.10 For this we have used the NaHe pair potentials for the 3d state of Pascale,54 which have been found to accurately reproduce the 3d ← 3s exaction spectrum of sodium atoms attached to helium droplets,34 and have assumed a value of 6 Å for the distance between the Na atom and the droplet surface. The resulting potential energy curves for the different symmetry states are displayed in Figure 4. In contrast

Figure 4. NaHe−HeN interaction potentials (solid lines and inset) and the NaHe pair potentials (dashed lines) correlating to the 3d state of the sodium atom. The vertical dotted line corresponds to the equilibrium distance of the ground state sodium atom with respect to the droplet surface. 2741



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distribution going out to speeds of 1500 m/s that is largely independent of excitation frequency, and a narrow distribution with a sharp cutoff at high velocities that varies strongly with excitation frequency. The two channels are characterized by different angular distributions. For the broad distribution the anisotropy parameter increases with increasing speed from a slightly negative value to β ≈ 1.7. In contrast, the narrow distribution is characterized by a speed independent anisotropy parameter of β ≈ 1.3. This observation suggests that the sharp distribution corresponds to excitation of an almost pure Σ state, whereas the broad structure corresponds to excitation of a mixed state. Having two overlapping contributions it becomes difficult to accurately determine the frequency dependence of the mean kinetic energy of these distributions. We therefore report in Figure 5 the kinetic energy corresponding to the sharp onset in the speed distributions for different excitation energies. Like for the other excited states a linear dependence is found. The energy offset found from a linear fit to the data gives a value slightly below the energy of the 5s state; see Table 1. The small discrepancy can be attributed to the fact that in this graph the energetic cutoff, and not the average kinetic energy is reported. In combination with an anisotropy parameter of β ≈ 1.3, this leads us to conclude that the sharp distribution corresponds to 5s excited atoms. An unambiguous assignment of the broad speed distribution is not possible. However, based on the photoelectron spectrum we tentatively assign it to Na atoms populating the 3d state. 4d State. The spectrum of the 4d ← 3s transition has been decomposed into the 4d Π ← 3s Σ at low frequency, yielding mainly NaHe and NaHe2 exciplexes and the 4d Σ ← 3s Σ transition at high frequency yielding mainly bare Na atoms,34 see Figure 5. The photoelectron spectrum recorded following excitation at 35200 cm−1, close to the maximum of the 4d Σ ← 3s Σ transition, reveals population of several atomic states; see Figure 2. The broad signal around 20000 cm−1 internal energy is due to background electrons. The calculated photoelectron spectrum in which helium-induced relaxation is not taken into account does not reveal any signal corresponding to the 3d state, implying that this state is populated due to the interaction of the Na atoms with the helium. It should be noted here that the photoelectron spectrum reveals no population of the 5s state, suggesting that relaxation does not proceed via the 5s state. The presence of the relaxation channel is reflected in the speed distributions of the desorbed atoms. While the speed distributions of the NaHe and NaHe2 exciplexes recorded at the maximum of the 4d Π ← 3s Σ transition are characterized by a single Gaussian like distribution, that of the Na atoms contains two overlapping contributions, one narrow and one broad; see Figure 7. The angular distributions of the exciplexes are characterized by slightly negative, speed independent anisotropy parameters, in agreement with the assignment of the spectrum. The speed distributions of the Na products depend strongly on the excitation frequency. At low frequencies the speed distribution is dominated by a broad component, but its relative contribution decreases quickly at higher excitation energies, see Figure 7. The mean anisotropy parameter of the broad distribution is approximately zero, independent of excitation frequency. In contrast, that of the narrow distribution varies across the absorption band from positive to negative to zero, see Figure 5. This behavior reflects the increasing contribution of the 4f Π ← 3s Σ, and 4f Σ ← 3s Σ transitions at higher energies.34 The narrow component of the speed

Figure 5. Kinetic energy of the desorbed sodium atoms and mean value of the anisotropy parameter as a function of the excitation frequency. The solid lines are linear fits to the data points. The vertical dashed lines correspond to the energy of the indicated states of Na. The shaded areas correspond to the Na (blue) and NaHe (red) excitation spectra.

photoelectron spectrum shown in Figure 2 which reveal that in the absence of helium-induced relaxation no 3d Na atoms should be observed. It should be noted that the broad signal below 20000 cm−1 internal energy is due to background electrons created by scattered light and not to atoms attached to helium droplets. The velocity distributions of the desorbed atoms are quite different than those found for the lower lying states. Whereas for the lower states the speed distribution can be well represented by a single Gaussian-like distribution, this is not the case for excitation to the 5s state, see Figure 6. The speed distributions appear to consist of two contributions, a broad

Figure 6. Speed distribution of sodium atoms and speed dependence of the anisotropy parameter following excitation at two different frequencies within the 5s ← 3s absorption band. 2742



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High Rydberg States. As the principal quantum number of the excited state increases, the interaction of the atom with the helium changes. This is not only reflected in the excitation spectra but also in the dynamics. For low principal quantum numbers the strong repulsive interaction of the Rydberg electron with the helium results in spectra that are blue-shifted with respect to the gas phase.34,36,40 At the same time it leads to the desorption of the excited atoms with large kinetic energies.45 For high values of n, where the radius of the Rydberg electron becomes larger than the droplet size, the interaction of the sodium atom with the helium is dominated by the attractive interaction of the ionic core with the helium. As a result, the spectra are red-shift with respect to the gas phase and form a Rydberg series that converges to the vertical ionization threshold of the alkali doped helium droplet.33,36,40 The spectrum recorded using one-photon excitation has been found to resemble the np ← 3s Rydberg series of the free atom, apart from a splitting into Σ and Π symmetry states.33 Alike, the two-photon excitation spectrum of NaHeN recorded monitoring the NaHe+ yield shown in Figure 8 resembles the

Figure 7. Speed distribution of sodium atoms following excitation at three different frequencies within the 4d ← 3s absorption band (upper panel). Speed distributions of Na, NaHe, and NaHe2 products following excitation at 34686 cm−1 (lower panel).

distribution shows a strong dependence on excitation frequency, in contrasts to the broad component. Its kinetic energy as determined from the peak maximum is found to scale linearly with excitation frequency, see Figure 5. A linear fit to the data yields an excess close to that of the 4d state, see Table 1, which we take as evidence that this component of the speed distribution corresponds to 4d excited Na atoms. Like for excitation to the 5s state, we assign, based on the photoelectron spectrum, the broad speed distribution to 3d excited sodium atoms. The speed distributions of the NaHe and NaHe2 exciplexes have only been recorded at a single excitation frequency, making it difficult to determine the exciplex formation process. The angular distributions of the desorbed exciplexes are slightly negative, while the speed distributions are similar to those of the desorbing Na(4d) atoms. These two observations leads us to conclude that the exciplexes do not desorb form the droplet by a thermal process but rather by an impulsive process as is found for the 3d state. Intermediate States. With increasing excitation energy helium-induced relaxation is expected to become more important. Indeed, the photoelectron spectrum recorded at an excitation energy of 36680 cm−1 shown in Figure 2, corresponding to excitation of the nominal 5p Σ state, reveals only population of the 4d state, indicating an extremely efficient relaxation induced by the helium. This fast relaxation is also reflected in the speed distribution of the desorbed atoms. The mean kinetic energy shows a similar frequency dependence as found for excitation to states correlating to 4d atoms; see Table 1. In addition, the energy offset is close to the energy of the 4d state of free sodium, suggesting that the sodium desorbs from the helium droplet as a 4d excited atom. These observations imply that in this particular case the helium-induced relaxation is much faster than the desorption process. The spectrum in the region of 37000−37500 cm −1 corresponds to several overlapping transitions, 5p Π/6s Σ/5d Π.34 The photoelectron spectrum recorded at an excitation energy of 37015 cm−1, i.e., at the red side of the spectral feature, is dominated by Na(4d) atoms, see Figure 1, indicative of an efficient relaxation pathway. The speed distributions of the desorbed atoms are bimodal, reflecting the contribution of the various states.

Figure 8. Excitation spectrum close to the ionization threshold for sodium-doped droplets with a mean radius of 41 Å recorded by detecting NaHe+ following one- and two-photon absorption.

atomic spectrum characterized by the selection rule Δl = 0, ± 2. The spectrum is dominated by nd ← 3s transition, while at low frequencies also ns ← 3s transitions contribute. Since for 2photon excitation ΔΛ = 0 transitions have the highest intensities, only states of Σ symmetry are observed within the present signal-to-noise ratio. The two-photon spectrum has been analyzed using the analogue of the Rydberg formula: En = IT − R/(n − dl)2,where En is the energy of the level with the principal quantum number n, IT the ionization threshold of the Na-doped helium droplet, R the Rydberg constant, and dl the ldependent quantum defect. In agreement with the analysis of the one-photon spectrum, a reduction of the ionization threshold by 125 cm−1 is found for droplets with a mean radius of 41 Å.33 The lowering of the ionization threshold of species in or on helium droplets has been attributed to polarization effects.33,56 For the quantum defect of the ns states we find d0 = 1.10 ± 0.02, which is slightly smaller than that of the free atom, d0 = 1.37.57 This reduction can be explained by the helium-induced configuration interaction with atomic p states. This mechanism has been invoked before to explain the quantum defect for the Na np Σ states, which was found to be larger than that of the free atom,33 and for Cs atoms on helium droplets.40 For the nd states a value of d2= −0.058 ± 0.005 is 2743



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obtained. This negative value can evidently not be attributed to configuration mixing. Rather it signifies the effective screening of the nucleus by the surrounding helium. This is confirmed by the droplets size dependence of the spectra. The ionization threshold and quantum defect for the nd states derived from the spectra are plotted in Figure 9 as a function of mean droplet

Figure 9. Droplet size dependence of the ionization threshold and l = 2 quantum defect as determined from two-photon excitation spectra.

radius. The variation of the ionization threshold is in perfect agreement with the results found for one-photon excitation to np states.33 The quantum defect for the d states shows an almost linear decrease with droplet radius, in agreement with an increased shielding of the core by larger droplets. It should be noted that a similar explanation has been offered for the reduced quantum defects observed for Rb attached to helium droplets.36 Conservation of energy dictates that sodium atoms that desorb from the droplets following excitation to a red-shifted high n Rydberg states must undergo relaxation. This is indeed observed, as can be seen in Figure 10, which shows photoelectron spectra recorded at selected red-shifted transitions via 2-photon excitation. It should be noted that high background signals prevented recording photoelectron spectra via 1-photon excitation. The photoelectron spectrum reveals that the desorbed atoms populate almost exclusively states with n ≤ 7. The high intensities for the nd states reflect the large ionization cross sections for these states compared to ns and np states.50,51 Another striking feature in the photoelectron spectrum is the presence of 3d excited atoms at the highest excitation energies. The energy onset for populating the 3d state is found to coincide with the onset for the formation of NaHe3 and NaHe4 exciplexes.33 To highlight the correlation, the relative intensity of the 3d state in the photoelectron spectra is plotted as a function of excitation energy in Figure 11 together with the relative NaHe3 and NaHe4 yields. This strongly suggests that these exciplexes are formed around a Na(3d) atom. Experiments on barium atoms attached to helium droplets have revealed that the change of interaction between Rydberg atoms and the helium is also reflected in the speed distributions of the desorbed atoms.46 Higher excitation energies yield slower atoms, reflecting the increasing attractive interaction between the atom and the helium droplet with increasing principal quantum number. Despite the mass difference, one expects a similar behavior for Rydberg states of sodium-doped

Figure 10. Photoelectron spectra, plotted as internal energy of Na, following two-photon excitation at selected energies close to the ionization threshold. The vertical lines indicate the energies of the various Na states.

droplets. Rather unexpectedly, the speed distributions of the desorbed sodium atoms are largely independent of excitation energy in this spectral range. The distributions all peak around 700 m/s and are rather wide, see Figure 11. Consequently, also the mean kinetic energy is largely independent of excitation energy, see Figure 12. In contrast to barium, excitation of sodium leads to very efficient exciplex formation. The speed distributions of the NaHen (n = 1−4) exciplexes are all quite similar and in contrast to bare Na, show a strong dependence on excitation frequency, see Figure 11. At relatively low excitation frequencies these are characterized by a broad distribution similar to that found for Na atoms. As the frequency increases, a slow component with a central speed of ∼150 m/s appears and gains intensity. At excitation frequencies close to the ionization threshold the speed distributions are almost fully determined by this slow component. This behavior is reflected in the mean kinetic energies of the exciplexes which are found to decrease strongly with increasing excitation frequency, see Figure 12. It should be noted that these trends are independent whether the system is excited by 1- or 2photon absorption. Remarkably, the appearance of the slow speed component coincides with the onset of the formation of NaHe3 and NaHe4 exciplexes and the appearance of 3d sodium atoms in the photoelectron spectrum, see Figure 12. The slow component can be well described by a Maxwell−Boltzmann distribution corresponding to a translational temperature of 30 K. Similar temperatures have been found before for species resulting from evaporative like processes.58 On the basis of the observed correlations and the speed distribution, we propose 2744



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level dynamical calculations are required to confirm this hypothesis.

4. REMARKS The experimental results reveal that the desorption dynamics following the excitation of sodium atoms on the surface of helium nanodroplets depend strongly on the excited state. However, for all states we find that the atoms do not remain attached to the droplets but desorb either as bare atoms or as NaHen exciplexes. In general, we observe that the dynamics become more complex with increasing energy. This complexity is mainly related to relaxation of the excited atoms induced by the helium. The relaxation of excited sodium atoms by the interaction with rare gases, and helium in particular, has been extensively studied in the past.59 Relaxation by helium gas has been found to be insignificant for states with low principle quantum numbers, efficient relaxation has been only observed for high Rydberg states. For the nd states, l-mixing between nearly degenerate states provides the most efficient relaxation pathway.60 In contrast, for ns states, quenching is the main relaxation mechanism. This is much less efficient than l-mixing due to the large energy gaps between the states.61 The relaxation in this case depends critically on the presence of curve crossings or avoided crossings of the NaHe pair potentials.62 In this context it is not obvious why the helium environment induces fast relaxation of the sodium atoms when excited to specific low-lying states. The NaHeN interaction potentials for the lowest states, see Figure 8 of ref 34, reveal no curve crossings that could for example explain the fast 5s to 3d relaxation channel. Also the fact that the helium environment induces mixing of atomic states cannot explain the observed relaxation pathways. For example the 4p state reveals no relaxation, although it contains a 20% mixture of the 3d state. On the other hand, the 5s state shows strong relaxation to the 3d state, but contains only a 1% contribution of the 3d state. Obviously another mechanism is responsible for the observed relaxation processes. As mentioned above, the calculated NaHeN interaction potentials reveal no obvious crossings or avoided crossings.34,43 However, one should realize that these potential curves have been calculated assuming a frozen helium density profile corresponding to that of the ground state sodium atom. While this assumption is justified for the excitation process, it is not necessarily so for the ensuing dynamics which occur on a much longer time scale. As simulations of the desorption process for the 4s state have convincingly shown, the helium density changes significantly after excitation of the sodium atom.45 As a result of this changing helium density, the interaction of the excited atom with the helium will evolve in time and thus also the corresponding the NaHeN potentials calculated within the frozen helium density approximation will evolve in time. Although the NaHeN potentials do not cross at the time of excitation, they might well do so for other helium configurations at some later times. Depending on the position of the excited sodium atom with respect to the curve crossing, it might relax to another state. In such a case, the system would evolve according to the interaction of the relaxed atom with the helium. This process could explain why excitation to the 6s Σ state yields 4d sodium atoms that have speed distributions similar to those found following direct excitation to the 4d state. It should be realized that such a relaxation mechanism is expected to be least efficient for states with low principle

Figure 11. Speed distributions of Na and NaHe2 products following one-photon excitation at selected energies close to the ionization threshold. The green line is the result of a fit to a Maxwell−Boltzmann distribution yielding a temperature of 30 K.

Figure 12. Mean kinetic energy of Na and NaHen exciplexes (upper panel), relative intensity of 3d state in the photoelectron spectrum (middle panel) and relative NaHe3 and NaHe4 yields (lower panel) at selected energies close to the ionization threshold.

that the slow speed component corresponds to Na(3d)He3 and Na(3d)He4 exciplexes that evaporate from the droplet after relaxation of the excited Na atom to the 3d state. Clearly, high 2745



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resulting from atomic s states, those resulting from p and d states are directional, pointing along the axis defined by the atom and the center of mass of the helium droplet. As a result of their directionality, they will interact less with helium atoms located off axis compared to the isotropic Σ orbitals resulting from s states. Hence, the effective number of interacting helium atoms is possibly smaller for the p and d atomic states than for the s states. In order to confirm this simple geometrical argumentation, simulations of the desorption dynamics of other states than the 4s are called for.45

quantum number. These state have strong repulsive interactions with the helium, leading to a fast desorption of the excited atom. Since the rearrangement of the helium occurs on a slightly longer time scale, the atoms might already have left the droplet before a crossing of the potential curves occurs. For states with high principal quantum number, the interaction between the Na atom and the helium is less repulsive or maybe even attractive, leading to a slower desorption or even to solvation of the atom. At the same time, the energy levels are closely spaced, which enhances the probability of curve crossings. As a result, one expects relaxation to become more and more likely as one approaches the ionization limit. Clearly, detailed theoretical calculations that include the dynamical evolution of the systems are required to corroborate this hypothesis. With the recent development of time-dependent density functional methods to simulate the helium environment, such calculations might soon come within reach.7,45,63,64 Even though the relaxation process is not fully understood and plays an important role for many excited states, one can observe systematics in the mean kinetic energy of the desorbed atoms. According to the impulsive model used to describe the desorption of Na(4s) and Li(3s) excited atoms, the mean kinetic energy depends linearly on the excitation frequency.45 The proportionality constant can be related to the effective mass of the helium moiety interacting with the excited atoms. These constants and the corresponding effective masses reported in Table 1 show a distinct variation with principal quantum number and angular momentum. This provides an opportunity to get a better insight into the properties that determine the energy partitioning between the helium droplet and the desorbing atom. Theoretical simulations of the desorption process have revealed that excitation of sodium, in this case to the 4s state, launches density waves into the helium droplets.45 These waves start at the droplet surfaces, indicating that they result from the displacement of a limited number of helium atoms. It is these helium atoms that are thought to be related to the effective helium mass in the impulsive model. In this simple picture one might consider that the number of helium atoms is related to the shape and size of the excited electron orbital. To a first approximation the mean radius of the electron orbit is given by ⟨re⟩ =

5. CONCLUSION We have investigated the dynamics of laser excited sodium atoms at the surface of helium nanodroplets. To establish a relation between the dynamics and the excitation energy a wide variety of states have been excited, ranging from the 3d state all the way up to high Rydberg states close to the ionization threshold. Excitation in all cases leads to desorption of the sodium atom from the droplet surface. Helium-induced relaxation already occurs for low lying states and becomes more prominent with increasing quantum state. Most remarkable is the relaxation observed following the excitation of high Rydberg states close to the ionization threshold which gives rise to the formation of Na(3d)He3 and Na(3d)He4 exciplexes. We tentatively attribute the efficient relaxation processes to curve crossings between the different NaHeN interaction potentials during the evolution of system. In the absence of relaxation, the mean kinetic energy of the desorbed atoms scales linearly with excitation frequency, indicative of an impulsive desorption process. The fraction of available energy converted into kinetic energy of the sodium atom depends on the quantum state and appears to be most efficient for isotropic electron orbitals and to scale with the radius of the electron orbit for a given angular momentum. Excitation to the 3d state leads to an efficient formation of NaHe exciplexes. The corresponding speed distributions point to a direct formation of these exciplex with no internal energy.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (M.D.) Marcel.Drabbels@epfl.ch.

a0 [3n*2 − l(l + 1)] 2

Present Address †

SICPA SA, 1000 Lausanne, Switzerland

where n* designates the effective principle quantum number which takes into account the l-dependent quantum defect δl, n*=n − δl and a0 is the Bohr radius.59 On the basis of this expression one expects that the number of interacting helium atoms increases with principle quantum number n for a given value of l. Such a dependence is indeed observed experimentally, see Table 1. However, the simple picture fails if one considers the angular momentum dependence for a given n. Taking into account the quantum defect for the various l states, one finds that the electron radius is smallest for s (l = 0) states, followed by p (l = 1) and d (l = 2) states; see Table 1. Experimentally we find that the number of interacting helium atoms is largest for s states, not smallest. Clearly, the size of the orbital is not the only determining factor. Likely, also its shape plays a role. When considering the shape of the orbitals one has to take into account its orientation with respect to the helium droplet. Analysis of the excitation spectra within the diatomic model indicates that the repulsive interaction of the excited atoms results mainly from Σ states.34 In contrast to Σ orbitals

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was made possible by the financial support of the Swiss National Science Foundation through Grant Nos. 200020-112193 and 200020-140396.

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REFERENCES

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Dynamics of Excited Sodium Atoms Attached to Helium Nanodroplets

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