Decays of excited silver cluster anions Ag n , n=4 to 7 , in DESIREE
E. K. Anderson, M. Kamińska, K. C. Chartkunchand, G. Eklund, M. Gatchell, K. Hansen, H. Zettergren, H. Cederquist, H. T. Schmidt
DDecays of excited silver cluster anions Ag − n , n = 4 to , in DESIREE E. K. Anderson, ∗ M. Kami´nska,
1, 2
K. C. Chartkunchand, G. Eklund, M. Gatchell,
1, 3
K. Hansen,
4, 5
H. Zettergren, H. Cederquist, and H. T. Schmidt Department of Physics, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden Institute of Physics, Jan Kochanowski University, 25-369 Kielce, Poland Institute for Ion Physics and Applied Physics, University of Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria Center for Joint Quantum Studies and Department of Physics,Tianjin University, 92 Weijin Road, Tianjin 300072, China Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden (Dated: October 5, 2018)Spontaneous decays of small, hot silver cluster anions Ag − n n = 4 − ∼ − )and cryogenic (13 K) operation of DESIREE. The yield of neutral particles from stored beams ofAg − and Ag − anions were measured for 100 milliseconds and were found to follow single power lawbehaviour with millisecond time scale exponential cut-offs. The Ag − and Ag − anions were storedfor 60 seconds and the observed decays show two-component power law behaviors. We presentcalculations of the rate constants for electron detachment from, and fragmentation of Ag − and Ag − .In these calculations, we assume that the internal energy distribution of the clusters are flat and withthis we reproduce the early steep parts of the experimentally measured decay curves for Ag − andAg − , which extends to tens and hundreds of milliseconds, respectively. The fact that the calculationsreproduce the early slopes of Ag − and Ag − , which differ for the two cases, suggests that it is thechanges in fragmentation rates with internal cluster energies of Ag − and Ag − rather than conditionsin the ion source that determines this behavior. Comparisons with the measurements stronglysuggest that the neutral particles detected in these time domains originate from Ag − → Ag − + Agand Ag − → Ag − + Ag fragmentation processes. I. INTRODUCTION
Access to mass-selected clusters of different sizes allowthe study of how physical and chemical properties changewhen going from small systems with just a few atoms tosystems with tens, hundreds or thousands of atoms, andto bulk matter. Small clusters are particularly interestingto study in this context as their various properties are ex-pected to depend strongly on the number of atoms theycontain. Here, spontaneous and/or photo-induced decaysof various sorts may be used to probe the energetics andstructural properties of these systems. Internal excita-tion energies in, for example, charged metal clusters candissipate via different types of processes, including radia-tive cooling. Often several decay channels are open andmay contribute to the decay on different time scales. Ob-servations of electron detachment and/or fragmentationcan then reveal features of photo-emission processes.The development of cryogenic electrostatic ion beamstorage devices [1–6] has made it possible to store ionsfor extended periods of time and to investigate relax-ation processes on time scales ranging from microsecondsto hours. Electrostatic ion storage devices have no up-per mass limit, which facilitates the storage of heavy keVion beams as demonstrated by the first electrostatic stor-age ring for atomic, molecular, and cluster physics – theELISA ring in Aarhus [7]. ELISA is operated at room ∗ [email protected] temperature with a residual gas pressure of 10 − − − mbar (molecular number density ∼ cm − ), yieldingtypical ion beam storage times on the order of seconds.Cryogenic operation vastly improves ion beam storage ca-pabilities as it lowers the residual gas pressure by ordersof magnitude. Number densities between 10 and 10 percm [2, 4, 8] have been reported to give 1/e ion beam stor-age lifetimes of minutes and up to almost an hour [4, 8, 9].Equally important, cryogenic operation may allow thestored ions to approach thermal equilibrium with the de-vice at temperatures down to a few kelvin [1, 2, 4–6, 10].In 2001, Hansen et al. [11] reported on the spontaneousdecay of internally hot metal cluster anions in ELISA.It was found that the production rate of neutrals leav-ing the ring varied with time t after injection as t − δ where | δ | <
1. This power law decay is caused by abroad distribution of decay constants, most often pro-duced by a close-to-uniform distribution of internal exci-tation energies of the stored ions [11]. Since then, powerlaw decays have been reported for many different types ofcharged polyatomic systems including metal clusters [12–16], fullerenes [17, 18], small carbon and hydrocarbonmolecules [19–21], biomolecules [22–24], Polycyclic Aro-matic Hydrocarbons (PAHs) [25, 26], and SF − [27, 28].In many of these cases, deviations from a pure t − de-cay have been observed. These deviations are most fre-quently observed for systems consisting of a few atomsonly and are discussed in terms of their specific propertiessuch as heat capacities [19], available decay channels [29],densities of final states [28] and the shape of the internal a r X i v : . [ phy s i c s . a t m - c l u s ] M a y MCP e- Glassplate Neutrals Injection FIG. 1. A schematic of one of the DESIREE ion storagerings. Size-selected silver cluster anions, Ag − n , n = 4 – 7, wereinjected and stored in the ring at 10 keV. The neutral parti-cles from spontaneous decay (fragmentation and/or electrondetachment) of the excited clusters were counted by a detec-tor system consisting of a glass plate with a gold-titaniumfilm emitting secondary electrons and a micro-channel plate(MCP) detector. energy distribution [26].In a pioneering study, Hansen et al. [11] reported powerlaw decay behavior extending to milliseconds for Ag − n ( n = 4 – 9), with radiative cooling being significant ontime scales of tens of milliseconds for clusters with n = 4,6, and 8. The Ag − anion, however, followed a power lawin their whole measurement window of 50 ms [11].In this paper we present experimental studies of thespontaneous decay of small, internally hot silver clusteranions (Ag − n , n = 4 – 7) as a function of storage timefor up to 60 seconds in one of the DESIREE ion beamstorage rings. Furthermore, we present calculations ofvibrational autodetachment and fragmentation rates forthe Ag − and Ag − clusters and discuss these in light ofthe present experimental results. II. EXPERIMENTAL APPARATUS ANDMETHODS
A detailed description of the DESIREE ion beam stor-age rings can be found elsewhere [1, 2, 9], so only anoutline of the salient features will be given here. Sil-ver anions were produced using a Source of NegativeIons by Cesium Sputtering (SNICS II) [30] with a sil-ver cathode. This type of ion source is known to producea range of cluster sizes with broad internal energy distri-butions [31]. The Ag − n ions were accelerated to 10 keVand mass-selected using a 90 ◦ analyzing magnet and in-jected into one of the ion storage rings of DESIREE, asshown in Fig. 1. A chopped ion bunch of tens of microsec-onds duration, filling up half the ring upon injection, wasstored and neutral particles were counted by means of adetector mounted along the line-of-sight of one of thestraight sections of the ring. The detector assembly con-sists of a gold-titanium coated glass plate, a triple-stackmicro-channel plate (MCP) and a resistive anode encoder(RAE). When neutral keV particles impinge on the glassplate, secondary electrons are emitted and acceleratedtowards the MCP for detection as indicated in Fig. 1.Two sources of background need to be considered: de- Time [ms] N e u t r a l Y i e l d [ A r b . U n it s ] Time [ms] N e u t r a l Y i e l d [ A r b . U n it s ] injection beam dumpdetector bg FIG. 2. Yield of neutrals produced by a 10 keV Ag − beamrecorded as a function of time after injection. The inset showsthe raw data for the first 2 ms (the first 15 turns can be seen)where the length of a single ion bunch corresponds to half aturn in the ring at injection. In the main figure, each point onthe curve is a sum of the counts within a single turn. For thisparticular data set the measurement time window was chosento be 120 ms. The removal of the remaining ions (the beamdump), and the detector dark counts are indicated. tector dark counts and counts generated by neutrals dueto collisions with the residual gas [2]. The detector darkcount rate was measured between injections, with no ionsin the ring, and subtracted from the rates measured af-ter ion injection. Due to the extremely low residual gasdensity, the signal from residual gas collisions gives onlya very small contribution in relation to the high neu-tral rates from spontaneously decaying hot clusters andis only visible after the initial decays discussed here haveoccurred, after seconds of storage or longer.Measurements of neutral yields due to the stored clus-ters were performed by accumulating data over manyion-injection-and-storage cycles. Each measurement cy-cle started with injection of a mass-selected ion bunch,followed by storage of this beam for a pre-set time win-dow, removal (dumping) of the stored beam, and mea-surement of the detector dark count background rate asshown in the example in Fig. 2. The storage time win-dows ranged from 100 ms to 60 s depending on the clusterion. A. Ion beam storage capability as measured withAg − The silver monomer anion, Ag − , has only onebound state (4 d s S ) with a binding energy of1.30447(2) eV [32]. We used a laser-probing technique tomeasure the storage lifetime of the Ag − beam to gaugethe general storage conditions for ions including the clus- Time [s] L a s e r I ndu ce d N e u t r a l Y i e l d [ A r b . U n it s ] Duty Cycle of Probing Laser [%] Γ e ff × [ s - ] Ag − + h ν → Ag + e − λ = 632 nm Γ Γ = 1624 ±
65 s
FIG. 3. Recorded neutral yield from photodetachment of sil-ver monomer anions, Ag − , at λ = 632 nm as a function oftime with a 5% laser duty cycle. The solid line is a fit to thedata with the sum of a single exponential function and a con-stant due to the detector dark counts. The inset shows themeasured effective decay rate, Γ eff , as a function of laser dutycycle. The lifetime of the Ag − beam is inversely proportionalto the decay rate, Γ, obtained by extrapolating the measuredΓ eff to zero duty cycle. ter ions of interest here. These measurements show thatthe ion storage time is orders of magnitude longer thanthe typical cluster decay times we are investigating here.A mechanical shutter was used to chop a continuouswave 632 nm (1.99 eV) laser beam into pulses for theAg − storage measurement. This pulse train producedneutral Ag atoms via photodetachment proportional tothe number of Ag − ions in the ring as a function of timeafter injection. The laser duty cycle was varied for suc-cessive measurements. The laser and ion beams trav-elled in opposing directions in a collinear configurationin the straight section of the ring. In this configuration,the laser first passed through the glass plate in front ofthe detector and then interacted with the Ag − beam.The neutral Ag atoms from the photodetachment processwere registered by the MCP. The neutral yield recordedwith a laser duty cycle of 5% is shown in Fig. 3.The measured effective decay rate Γ eff contains con-tributions from laser-induced photodetachment losses.Therefore the effective decay rate, Γ eff , was measuredas a function of laser duty cycle as shown in the inset inFig. 3. By extrapolating to zero laser duty cycle, a de-cay rate, Γ, gave a storage lifetime of 1 / Γ = 1624 ±
65 sfor 10 keV Ag − ions. Furthermore, the ion beam storagetime is expected to increase with cluster size for fixedstorage energy, as applied here, and thus ion beam lossdue to residual gas collisions during the first 60 seconds(the maximum cluster decay measuring time) of storageis negligibly small.
426 428 430 432 434 436
Mass [amu] I on B ea m C u rr e n t [ n A ] i = 0 1 32 4 Ag i Ag i FIG. 4. Recorded mass spectra for the Ag − anions (open cir-cles). The peak label i indicates the number of Ag atoms inthe clusters. The abundances of the masses were determinedfrom gaussian fits to the peaks (dashed lines) and were foundto agree with those expected from the natural abundanceswithin a per cent.
B. Are there hydrogenated silver cluster anions inthe Ag − beams? Silver has two naturally occurring isotopes of mass 107and 109 amu with close to equal abundances, so there are n +1 possible isotopologues for Ag − n . A mass spectrum forAg − , generated by scanning the analyzing magnet andmeasuring the ion current on a Faraday cup located afterthe magnet, is shown in Fig. 4. The relations betweenthe ion beam currents at masses 428, 430, 432, 434, and436 amu agree to within a per cent of those expectedfrom the natural abundances. We found the measuredtime dependences of the neutral yields due to stored Ag − beams with different masses (428, 430, and 436 amu) tobe the same within the experimental uncertainty.Contamination of, for example, the Ag − beam byAg H − ions, could potentially contribute to the mea-sured neutral yields. However, Fig. 4 shows well sep-arated peaks for the different masses of the Ag − clusters,suggesting there is no or very little contamination of theion beams with Ag H − . This was further investigatedby means of a measurement of the Ag − cluster wherethe mass of the ions was chosen (by a slight shift of thesetting of the analyzing magnet) to be on the high massshoulder of the main peak, where we expect larger rela-tive contributions to the ion beam from Ag H − , if at allpresent. By comparing to a measurement of the time de-pendence of the neutral yield where the analyzing magnetwas set to the center of the Ag − mass peak, we concludedthat Ag n H − contaminations were sufficiently small to beneglected. C. Measurements with Ag − – Ag − : Time windowsand cluster currents The neutral yield from Ag − and Ag − clusters weremeasured using several time windows of up to 60 s. Theemission of neutral particles from Ag − and Ag − weremeasured for only a single 100 ms time window. A lowion current of a few pA was used for the shortest mea-surement time window of 100 ms; using a low currentprevents saturation of the detector and effectively elimi-nates the effects of beam losses due to ion-ion interac-tions [2]. Higher currents of a few nA were used forlonger time windows in cases where the signal rates permolecule were much lower. The different data sets werethen combined using an overlapping time region wherethe data sets are unaffected by saturation. In the resultspresented in Figs. 5 and 8 we have added data from manyinjections. The first few points in each figure are the ac-cumulated counts from individual turns of the ion bunchin the ring. Data for all later times are sorted into timebins increasing linearly in width with time so that thesedata points are equidistant on a logarithmic scale. III. MODELLING THE DECAY OF EXCITEDCLUSTER ANIONS
An excited silver cluster anion, (Ag − n ) ∗ , can decay viathe following channels,(Ag − n ) ∗ → Ag n + e − electron detachmentAg − n − m + Ag m fragmentation † Ag − n + hv radiative cooling † m = 1 , ..., n − µ s or longer), will proceed viavibrational autodetachment (VAD) where vibrational en-ergy is transferred to the electron. Radiative cooling pro-cesses lower the internal energy of the ion, which remainsstored in the ring, with reduced probabilities for frag-mentation or electron detachment. The time-dependenttotal neutralization rate, R ( t ) following the injection ofa bunch of N non-interacting ions with an initial distri-bution g ( E ) of internal excitation energies E is R ( t ) = N (cid:90) ∞ g ( E ) k neutral ( E ) e − k tot ( E ) t d E. (1)Here, the neutral particle production rate constant, k neutral ( E ) = k VAD ( E ) + k frag ( E ), and the total decayrate constant, k tot ( E ) = k neutral ( E ) + k rad ( E ) are ex-pressed in terms of the rates for vibrational autodetach-ment ( k VAD ), fragmentation ( k frag ), and radiative cooling( k rad ). In Eq. 1, we assume that a single photon emis-sion event effectively gives k neutral = 0 s − for all latertimes. The radiative cooling rate, k rad , is expected tovary much more slowly with E than k neutral ( E ) and maythen be treated as a constant.As mentioned above, the time dependence of R ( t ) is inmany cases simple and can be characterized through R ( t ) ∝ t − δ (2)where δ can be positive or negative and is often small [15,22, 33].A strict t − behavior follows from Eq. 1 provided k tot is a sufficiently rapidly increasing function of E and pro-vided that g ( E ) does not change significantly with E overthe (narrow) range of internal energies involved. Then,for k rad ( E ) << k tot ( E ) the function k tot ( E ) te − k tot ( E ) t ( ≈ k neutral ( E ) te − k tot ( E ) t ) is strongly peaked at its max-imum value at E = E max and R ( t ) is proportional to g ( E max ) /t (to see this think of k neutral ( E ) te − k tot ( E ) t asa delta function at E = E max and do the integral inEq. 1). Since k tot ( E ) increases strongly with increasing E , the initial distribution g ( E ) is depleted from the highenergy side. That is, ions with higher internal energydecay first. As a consequence E max decreases with timebut when g ( E ) is constant, the value of g ( E max ) does notchange with time yielding the t − power law [11]. Forlarge systems, such as amino acids, the absolute value of δ has typically been found to be smaller than 0.1 [22].For small systems | δ | values of up to 1 have been re-ported [14, 16, 28, 33].Radiative cooling will lower the internal energies ofthe stored ions. These photon emission processes willnot produce neutrals but may quench the power law de-cay at times t approaching a characteristic time τ , when k rad ( E ) is no longer insignificant compared to k tot ( E ).The neutralization rate including radiative cooling pro-cesses, provided that k neutral is effectively negligible afterthe emission of the photon, is given by [16] R ( t ) ∝ t − δ e − t/τ , (3)where τ is the characteristic photon emission time.To enable quantitative comparisons with our experi-mental data we calculate the rate constants for electrondetachment and fragmentation processes based on de-tailed balance considerations. The calculated rate con-stants and a constant value of g ( E ) will then be usedin Eq. 1 to calculate the total rates for neutral particleproduction.The rate constant for electron detachment is taken tobe [34, 35] k VAD ( E, ε ) = 2 m e π (cid:126) εσ L ( ε ) ρ (0) ( E − E a − ε ) ρ ( − ) ( E ) , (4)where E is the internal excitation energy, ε the kineticenergy of the emitted electron, σ L ( ε ) is the Langevincross section for electron attachment to the neutral sil-ver cluster, m e is the mass of the electron, and E a isthe electron affinity of the corresponding neutral cluster. ρ (0) and ρ ( − ) are the vibrational level densities of theAg n product (with internal energy, E − E a − ε ) and ofthe initial Ag − n state (with internal energy E ), respec-tively. The factor of 2 is due to the spin degeneracy ofthe emitted electron. The level densities can be deter-mined using the Beyer-Swinehart algorithm [36] wherevibrational frequencies, electron affinities and dissocia-tion thresholds are required as input.In analogy with Eq. 4 we express the rate constant, k frag ( E, ε ), for a fragmentation process in which the clus-ter parent anion (Ag − n ) emits a neutral silver monomeror dimer as k frag ( E, ε ) = γµπ (cid:126) εσ c ρ ( d ) ( E − E D − ε ) ρ ( p ) ( E ) . (5)Here, E is again the excitation energy of the parent ion( p ), ε is the sum of the kinetic energy release and any in-ternal excitation energy of the emitted particle, E D is thedissociation energy for the given fragmentation channeland µ the reduced mass of the two fragments, and σ c isthe cross section for the reverse process where the parentsystem is formed from the fragments. The level densitiesof the parent ( p ) and daughter ( d ) systems are ρ ( p ) and ρ ( d ) with internal energies E and E − E D − ε , respectively.The degeneracy of the emitted fragment is denoted by γ .The summed electron detachment and fragmentationrates are k VAD ( E ) = (cid:90) k VAD ( E, ε ) d ε and k frag ( E ) = (cid:90) k frag ( E, ε ) d ε , (6)respectively. IV. RESULTS AND DISCUSSIONA. Ag − and Ag − : Experimental data The measured neutral particle yields from the storedAg − and Ag − anion beams are shown as functions of timein log-log plots in Fig. 5. At short times, steep linear be-havior appears in both plots corresponding to power laws t − δ with large values of | δ | . In both cases (Ag − andAg − ), this changes to a less steep slope over time rangesof a few tens or hundreds of milliseconds. Finally, thecurves bend down until reaching levels that slowly de-crease. The latter are slow decays of the stored ion beamsdue to residual-gas collisions (see Section II A). Simi-lar behavior (i.e. different exponents in different timeranges) have been reported for the spontaneous decayfrom small copper cluster anions of size n = 3 – 6 [14, 16].A fitted function of the form R ( t ) = at − δ + bt − δ e − t/τ + C (7)is shown together with the experimental data in Fig. 5.The first term in Eq. 7 is a power law and the second term an exponentially quenched power law (as in Eq. 3). Theconstant C is the contribution from residual gas collisions- the decay of the beam is very slow (see Section II A).The parameters δ , δ and τ used to fit Eq. 7 to theexperimental data are listed in Fig. 5. Two-componentpower laws may indicate that two different classes of Ag − n ions are simultaneously stored in the ring.In previous studies of small silver clusters [11] an ex-ponential cut-off with a characteristic time of τ = 5 mswas reported for Ag − and was then ascribed to radiativecooling [11]. We do not see an exponential cut-off in thistime range in the present data for Ag − . We do, how-ever, observe a characteristic exponential cut-off time of τ = 1 . − . This is consistent with the measurements presentedhere, where an exponential cut-off with a characteristictime of τ = 0 .
35 s is deduced. The present character-istic times are of the same order of magnitude as thosefound for small copper clusters stored in DESIREE [16]( τ = 0 .
83 s for Cu − and τ = 0 .
18 s for Cu − ). B. Ag − and Ag − : Rate calculations andcomparisons We calculate the rates for electron detachment and forfragmentation through emission of neutral monomers andneutral dimers separately for both cluster sizes followingthe procedures outlined in Section III. Rotational excita-tions are neglected in these calculations.Several parameters are required in each case and forthe detachment processes we first calculate σ L ( ε ), theLangevin electron capture cross section for both clus-ter sizes using a polarizability of 15 . . This valuewas taken from reference [14] where it was extrapolatedfrom experimental data for Cu − . The Langevin crosssection assumes unit sticking probability and the calcu-lated rate constant for vibrational autodetachment (seeEq. 4) will thus serve as an upper limit within the presentmodel. For the fragmentation processes a geometric valueof σ c =1 ˚A was used for the formation cross section (seeEq. 5).The harmonic vibrational frequencies, electron affini-ties and dissociation thresholds needed for the level den-sities were calculated by means of density functional the-ory (DFT) at the B3LYP/LANL2DZ level of theory. Theresulting electron affinities for Ag and Ag were thenfound to be 1 .
72 eV and 2 .
01 eV respectively. The dissoci-ation thresholds for monomer and dimer loss were calcu-lated to be 1 .
08 eV and 1 .
43 eV respectively for Ag − and1 .
66 eV and 1 .
20 eV respectively for Ag − . A degeneracyof γ = 2 was used when calculating the fragmentationrates from Eq. 5. Atomic silver has a spin-1/2 groundstate, so the degeneracy value for monomer emission is calc calc FIG. 5. Neutral particle yield from stored beams of Ag − andAg − as a function of time after the ions are formed in thesource. The solid black lines are curves described by Eq. 7with parameter values as indicated. The grey lines are thecalculated neutral emission rates R calc ( t ) with no radiativecooling included ( k rad = 0 s − ) and where rotational excita-tions are neglected.
2. For dimer emission the spin degeneracy could be 1or 3 depending on whether the dimer is in a singlet ortriplet state. Here we use a rough average value of 2.The radiative decay rate, k rad was set to zero.In Fig. 6, we show calculated rates for electron detach-ment via VAD and fragmentation of Ag − and Ag − . Thegrey shaded areas in the plots indicate rates that corre-spond to the detection time window of the present ionbeam storage experiment. The total neutralization ratesfor Ag − and Ag − resulting from the calculated data inFig. 6 are shown as grey lines in Fig. 5.The rate constants calculated for Ag − (upper panelFig. 6) indicate that monomer loss (i.e. fragmentation)is the dominant process at all times where we have adecay signal in the experiment and that all neutrals de-tected in the measurement are silver atoms from this dis-sociation process. For Ag − the calculations (lower panelFig. 6) indicate that fragmentation through dimer loss FIG. 6. The calculated rate constants for Ag − and Ag − for vi-brational autodetachment (VAD) and fragmentation resultingin the loss of a neutral monomer or neutral dimer as functionsof the internal vibrational energies of the parent anions. Inthese calculations rotational excitations are neglected. Thegrey shaded area shows the rate constants that correspond tothe experimental time window. is the only process contributing to the measured yieldof neutrals. The corresponding calculated neutral rates(using the method described in Section III and shownin Fig. 5) reproduce the surprisingly steep slopes at earlytimes in both cases (Ag − and Ag − ), but fall far below themeasured rate at later times. As the initial strong devia-tions from t − are reproduced in the calculations, whichassume constant values for the initial internal energy dis-tributions g ( E ), specific initial conditions are likely not the cause of these deviations. Furthermore, as was ar-gued in Section III and in several earlier studies of thepower-law decay phenomenon [11], t − follows from sim-ple arguments when g ( E ) is assumed constant and when k tot ( E ) te − k tot ( E ) t is assumed to be a delta function. Thisindicates that the large δ values for early times may beconnected to the explicit energy dependence of the decayrate. C. Ag − and Ag − : High- J contributions? While the model works relatively well for short timesit appears that ensembles of more slowly decaying clus-ters are present in the stored Ag − and Ag − beams andthat these could dominate the neutralisation signals onlong time scales. This other class could be moleculesin high rotational states as discussed in a recent studyof Cu − n [16]. There, electron detachment was the low-est energy decay channel for low J , while fragmentationwas energetically more favourable at higher J . It wasthen speculated that this could be related to the two-component shape of the decay curve for some of the smallcopper clusters [16].For Ag − and Ag − , the threshold energy for fragmen-tation is lower than the threshold energy for electron de-tachment for much wider ranges of angular momenta. ForAg − , this is illustrated in Fig. 7, where the minimum ex-citation energies needed for, fragmentation and electrondetachment are shown as functions of J ( J + 1). Theseenergies were calculated by means of density functionaltheory (DFT) for stable structural isomers. The Ag − iso-mers have rhombic, Y-shaped and linear forms and theenergies of their vibrational ground states as a functionof J ( J + 1) are shown as solid blue lines in Fig. 7. Therelevant electron detachment limits (solid black lines) lieabove the two lowest fragmentation limits (red dashedlines) over the whole range of J values covered in Fig 7.Unlike the situation for the copper clusters, the dominat-ing decay mechanism is the same irrespective of the valueof the total angular momentum quantum number withincertain bounds. This, however, does not exclude the pos-sibility that ions with very different values of J can decaythrough fragmentation on very different time scales andthat the slow components that are not described by thepresent model could be due to clusters with high valuesof J . D. Ag − and Ag − The neutral particle yields from Ag − and Ag − ions areshown as functions of time in Fig. 8. The decay curves forboth these cluster ions show similar behavior, a power lawat early times followed by an exponential drop-off at latertimes. This shape is indicative of an ensemble of clusteranions with a broad internal energy distribution wherethe decay is dominated by electron detachment and/orfragmentation at early times, whilst at later times theneutral particle emission yield is quenched by e.g. radia-tive cooling processes. Eq. 3 describes this behavior andwas used to fit the experimental data to obtain the ex-ponential cut off times of τ = 23 ± τ = 110 ±
60 msfor the Ag − and Ag − anions respectively. The lattervalue agrees well with the previously reported value of ∼
100 ms for Ag − , while the former value is dramaticallylonger than the ∼ − in the previousstudy [11]. For these more complex systems (with many Ag + Ag Ag + Ag
2- 2 + e - + e - Ag + Ag
J (J+ J E t o t = E e l + E v i b + B J ( J + ) [ e V ]
316 4470
FIG. 7. Yrast plot for Ag − . Shown are the calculated relativeexcitation energies (blue lines) and corresponding electron de-tachment limits (black lines) as functions of J ( J +1), where J is the rotational angular momentum quantum number. Thelowest energy fragmentation channels (dashed red lines) arecalculated for J = 0. In principle these dashed lines shouldhave small non zero slopes as the rotational barrier height in-creases with J . Full dynamics simulations would be requiredto properly describe this for all geometries, which is beyondthe scope of this work. Rotations along the axis with thesmallest value of B were assumed to give lower limits to theexcitation energies. The excited vibrational states, which willextend from the lowest state for each structure, are not indi-cated. possible isomers and dissociation channels) we have notattempted to make any model calculations. V. SUMMARY AND CONCLUSIONS
In this work we have presented measurements of thedecays of small internally hot Ag − n n = 4 − − and Ag − anion beams follow t − δ behaviorwith large | δ | values at early times but follow less steeppower laws at later times. These experimental obser-vations prompted calculations of the rate constants forvibrational detachment and fragmentation of rotationalground state Ag − and Ag − . These detailed-balance cal-culations strongly suggest that fragmentation dominatesthe decays of Ag − and Ag − through the emission of neu-tral monomers and dimers, respectively. The calculatedneutral yields reproduce the measured steep slopes. Sincethe calculations use a constant value for the initial energydistribution we ascribe the large | δ | values to inherentproperties of the specific clusters rather than to the ionsource conditions. Whilst the calculated neutral rates re-produce the early times of the experimental yields theydeviate at later times indicating that there are ensem-bles of more slowly decaying clusters in the Ag − andAg − beams. The origin of the two-component structuresin the Ag − and Ag − data are not yet clear but couldpossibly be connected to ions with low and high angu-lar momenta. The Ag − and Ag − decay curves are found FIG. 8. Neutral particle yield from stored beams of silverclusters Ag − and Ag − as a function of time. to follow single power laws with exponential cut offs of23 ± ±
60 ms respectively.In future experimental campaigns we plan to performcoincidence measurements between neutral and chargedfragments in order to conclusively determine if fragmen-tation or electron detachment dominate in the decay ofsmall metal clusters.
ACKNOWLEDGEMENTS
This work was performed at the Swedish National In-frastructure, DESIREE (Swedish Research Council con-tract No. 2017-00621). It was further supported bythe Swedish Research Council (grant numbers 2014-4501,2015-04990, 2016-04181, 2016-06625). M. K. acknowl-edges financial support from the Mobility Plus Program(Project No. 1302/MOB/IV/2015/0) funded by the Pol-ish Ministry of Science and Higher Education. [1] R. D. Thomas, H. T. Schmidt, G. Andler, M. Bj¨orkhage,M. Blom, L. Br¨annholm, E. B¨ackstr¨om, H. Danared,S. Das, N. Haag, P. Halld´en, F. Hellberg, A. I. S. Holm,H. A. B. Johansson, A. K¨allberg, G. K¨allersj¨o, M. Lars-son, S. Leontein, L. Liljeby, P. L¨ofgren, B. Malm, S. Man-nervik, M. Masuda, D. Misra, A. Orb´an, A. Pa´al, P. Rein-hed, K.-G. Rensfelt, S. Ros´en, K. Schmidt, F. Seitz,A. Simonsson, J. Weimer, H. Zettergren, and H. Ced-erquist, Review of Scientific Instruments , 065112(2011).[2] H. T. Schmidt, R. D. Thomas, M. Gatchell, S. Ros´en,P. Reinhed, P. L¨ofgren, L. Br¨annholm, M. Blom,M. Bj¨orkhage, E. B¨ackstr¨om, J. D. Alexander, S. Leon-tein, D. Hanstorp, H. Zettergren, L. Liljeby, A. K¨allberg,A. Simonsson, F. Hellberg, S. Mannervik, M. Larsson,W. D. Geppert, K. G. Rensfelt, H. Danared, A. Pa´al,M. Masuda, P. Halld´en, G. Andler, M. H. Stockett,T. Chen, G. K¨allersj¨o, J. Weimer, K. Hansen, H. Hart-man, and H. Cederquist, Review of Scientific Instru-ments , 055115 (2013).[3] P. Reinhed, A. Orb´an, J. Werner, S. Ros´en, R. D.Thomas, I. Kashperka, H. A. B. Johansson, D. Misra,L. Br¨annholm, M. Bj¨orkhage, H. Cederquist, and H. T. Schmidt, Phys. Rev. Lett. , 213002 (2009).[4] M. Lange, M. Froese, S. Menk, J. Varju, R. Bastert,K. Blaum, J. R. C. L´opez-Urrutia, F. Fellenberger,M. Grieser, R. von Hahn, O. Heber, K.-U. K¨uhnel,F. Laux, D. A. Orlov, M. L. Rappaport, R. Repnow,C. D. Schr¨oter, D. Schwalm, A. Shornikov, T. Sieber,Y. Toker, J. Ullrich, A. Wolf, and D. Zajfman, Reviewof Scientific Instruments , 055105 (2010).[5] R. von Hahn, F. Berg, K. Blaum, J. C. Lopez-Urrutia,F. Fellenberger, M. Froese, M. Grieser, C. Krantz, K.-U.K¨uhnel, M. Lange, S. Menk, F. Laux, D. Orlov, R. Rep-now, C. Schr¨oter, A. Shornikov, T. Sieber, J. Ullrich,A. Wolf, M. Rappaport, and D. Zajfman, Nuclear In-struments and Methods in Physics Research Section B:Beam Interactions with Materials and Atoms , 2871(2011).[6] Y. Nakano, Y. Enomoto, T. Masunaga, S. Menk,P. Bertier, and T. Azuma, Review of Scientific Instru-ments , 033110 (2017).[7] S. P. Møller, Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers,Detectors and Associated Equipment , 281 (1997). [8] R. von Hahn, A. Becker, F. Berg, K. Blaum, C. Breit-enfeldt, H. Fadil, F. Fellenberger, M. Froese, S. George,J. G¨ock, M. Grieser, F. Grussie, E. A. Guerin, O. Heber,P. Herwig, J. Karthein, C. Krantz, H. Kreckel, M. Lange,F. Laux, S. Lohmann, S. Menk, C. Meyer, P. M.Mishra, O. Novotn´y, A. P. O’Connor, D. A. Orlov,M. L. Rappaport, R. Repnow, S. Saurabh, S. Schippers,C. D. Schr¨oter, D. Schwalm, L. Schweikhard, T. Sieber,A. Shornikov, K. Spruck, S. S. Kumar, J. Ullrich, X. Ur-bain, S. Vogel, P. Wilhelm, A. Wolf, and D. Zajfman,Review of Scientific Instruments , 063115 (2016).[9] E. B¨ackstr¨om, D. Hanstorp, O. M. Hole, M. Kaminska,R. F. Nascimento, M. Blom, M. Bj¨orkhage, A. K¨allberg,P. L¨ofgren, P. Reinhed, S. Ros´en, A. Simonsson, R. D.Thomas, S. Mannervik, H. T. Schmidt, and H. Ced-erquist, Phys. Rev. Lett. , 143003 (2015).[10] H. T. Schmidt, G. Eklund, K. C. Chartkunchand, E. K.Anderson, M. Kami´nska, N. de Ruette, R. D. Thomas,M. K. Kristiansson, M. Gatchell, P. Reinhed, S. Ros´en,A. Simonsson, A. K¨allberg, P. L¨ofgren, S. Mannervik,H. Zettergren, and H. Cederquist, Phys. Rev. Lett. ,073001 (2017).[11] K. Hansen, J. U. Andersen, P. Hvelplund, S. P. Møller,U. V. Pedersen, and V. V. Petrunin, Phys. Rev. Lett. , 123401 (2001).[12] B. Kafle, O. Aviv, V. Chandrasekaran, O. Heber, M. L.Rappaport, H. Rubinstein, D. Schwalm, D. Strasser, andD. Zajfman, Phys. Rev. A , 052503 (2015).[13] Y. Toker, O. Aviv, M. Eritt, M. L. Rappaport, O. Heber,D. Schwalm, and D. Zajfman, Phys. Rev. A , 053201(2007).[14] C. Breitenfeldt, K. Blaum, M. W. Froese,S. George, G. Guzm´an-Ram´ırez, M. Lange, S. Menk,L. Schweikhard, and A. Wolf, Phys. Rev. A , 033407(2016).[15] J. Fedor, K. Hansen, J. U. Andersen, and P. Hvelplund,Phys. Rev. Lett. , 113201 (2005).[16] K. Hansen, M. H. Stockett, M. Kaminska, R. F. Nasci-mento, E. K. Anderson, M. Gatchell, K. C. Chartkun-chand, G. Eklund, H. Zettergren, H. T. Schmidt, andH. Cederquist, Phys. Rev. A , 022511 (2017).[17] J. U. Andersen, C. Gottrup, K. Hansen, P. Hvelplund,and M. O. Larsson, Eur. Phys. J. D , 189 (2001).[18] S. Tomita, J. U. Andersen, H. Cederquist, B. Concina,O. Echt, J. S. Forster, K. Hansen, B. A. Huber,P. Hvelplund, J. Jensen, B. Liu, B. Manil, L. Mau-noury, S. B. Nielsen, J. Rangama, H. T. Schmidt, andH. Zettergren, The Journal of Chemical Physics ,024310 (2006).[19] M. Goto, A. E. K. Sund´en, H. Shiromaru, J. Matsumoto,H. Tanuma, T. Azuma, and K. Hansen, The Journal ofChemical Physics , 054306 (2013).[20] H. Shiromaru, T. Furukawa, G. Ito, N. Kono, H. Tanuma,J. Matsumoto, M. Goto, T. Majima, A. E. K. Sund´en, K. Najafian, M. S. Pettersson, B. Dynefors, K. Hansen,and T. Azuma, Journal of Physics: Conference Series , 012035 (2015).[21] K. Najafian, M. S. Pettersson, B. Dynefors, H. Shi-romaru, J. Matsumoto, H. Tanuma, T. Furukawa,T. Azuma, and K. Hansen, The Journal of ChemicalPhysics , 104311 (2014).[22] J. U. Andersen, H. Cederquist, J. S. Forster, B. A. Huber,P. Hvelplund, J. Jensen, B. Liu, B. Manil, L. Maunoury,S. Brøndsted Nielsen, U. V. Pedersen, H. T. Schmidt,S. Tomita, and H. Zettergren, The European Physi-cal Journal D - Atomic, Molecular, Optical and PlasmaPhysics , 139 (2003).[23] J. U. Andersen, H. Cederquist, J. S. Forster, B. A. Huber,P. Hvelplund, J. Jensen, B. Liu, B. Manil, L. Maunoury,S. Brondsted Nielsen, U. V. Pedersen, J. Rangama, H. T.Schmidt, S. Tomita, and H. Zettergren, Phys. Chem.Chem. Phys. , 2676 (2004).[24] S. B. Nielsen, J. U. Andersen, P. Hvelplund, B. Liu, andS. Tomita, Journal of Physics B: Atomic, Molecular andOptical Physics , R25 (2004).[25] S. Martin, J. Bernard, R. Br´edy, B. Concina, C. Joblin,M. Ji, C. Ortega, and L. Chen, Phys. Rev. Lett. ,063003 (2013).[26] M. Ji, R. Br´edy, L. Chen, J. Bernard, B. Concina,G. Montagne, A. Cassimi, and S. Martin, PhysicaScripta , 014091 (2013).[27] J. Rajput, L. Lammich, and L. H. Andersen, Phys. Rev.Lett. , 153001 (2008).[28] S. Menk, S. Das, K. Blaum, M. W. Froese, M. Lange,M. Mukherjee, R. Repnow, D. Schwalm, R. von Hahn,and A. Wolf, Phys. Rev. A , 022502 (2014).[29] O. Aviv, Y. Toker, D. Strasser, M. L. Rappaport,O. Heber, D. Schwalm, and D. Zajfman, Phys. Rev. A , 023201 (2011).[30] U. National Electrostatic Corp., “Source of negative ionsby cesium sputtering - SNICS II,” (2017).[31] A. Wucher and B. J. Garrison, The Journal of ChemicalPhysics , 5999 (1996).[32] R. C. Bilodeau, M. Scheer, and H. K. Haugen, Journalof Physics B: Atomic, Molecular and Optical Physics ,3885 (1998).[33] M. W. Froese, K. Blaum, F. Fellenberger, M. Grieser,M. Lange, F. Laux, S. Menk, D. A. Orlov, R. Repnow,T. Sieber, Y. Toker, R. von Hahn, and A. Wolf, Phys.Rev. A , 023202 (2011).[34] V. Weisskopf, Phys. Rev. , 295 (1937).[35] K. Hansen, Statistical physics of nanoparticles in the gasphase , Springer Series on Atomic, Optical, and PlasmaPhysics, Vol. 73 (Springer Dordrecht, 2013).[36] T. Beyer and D. F. Swinehart, Commun. ACM16