Dissociative ionization of the H 2 O molecule induced by medium energy singly charged projectiles
S. T. S. Kovács, P. Herczku, Z. Juhász, L. Sarkadi, L. Gulyás, B. Sulik
aa r X i v : . [ phy s i c s . a t o m - ph ] J un Dissociative ionization of the H O molecule induced by mediumenergy singly charged projectiles
S. T. S. Kov´acs, ∗ P. Herczku, Z. Juh´asz, L. Sarkadi, L. Guly´as, and B. Sulik
Institute for Nuclear Research, Hungarian Academy of Sciences (MTA Atomki),P.O. Box 51, H-4001 Debrecen, Hungary (Dated: September 7, 2018)
Abstract
We report on the fragmentation of the water molecule by 1 MeV H + , He + and 650 keV N + ion impact. The fragment-ion energy spectra were measured by an electrostatic spectrometer atdifferent observation angles. The obtained double-differential fragmentation cross sections for N + is found to be more than an order of magnitude higher, than that for H + . The relative ratios ofthe fragmentation channels are also different for the three projectiles. Additional fragmentationchannels were observed in the spectra for He + and for N + impact, which are missing in the caseof H + . From the analysis of the kinetic energy of the fragments, the maximum observed degree ofionization was found to be q max = 3, 4, and 5 for H + , He + and N + impact, respectively. Absolutemultiple ionization cross sections have been determined. They are compared with the predictions ofthe classical trajectory Monte Carlo and continuum-distorted-wave eikonal-initial-state theories. Atlower degrees of ionization, theories provide reasonable agreement with experiment. The systematicoverestimation of the cross section by the theories towards higher degrees of ionization indicatesthe failure of the independent particle model. PACS numbers: 34.50.Gb, 34.10.+xKeywords: molecular collisions, molecular fragmentation, ionization, multiple ionization, CTMC, CDW-EIS ∗ Electronic address: [email protected] . INTRODUCTION The dissociation of small few-atomic molecules has been extensively studied by the impactof various types of projectiles, such as photons [1–3], electrons [4, 5], protons [6–8], andmultiply charged ions [9–13]. Molecular fragmentation by ion impact is a rather complexprocess, which is highly interesting in different areas from astrophysics to cancer therapy.In these fields the most interesting impact energy region is the surrounding of the so calledBragg peak, where the energy transfer to the medium maximizes [14–16]. The equilibriumcharge state of the projectile ions in the distal region of the Bragg peak is usually closeto unity in a wide kinetic energy range, e.g., heavier ions are strongly screened there [17].In spite of their relevance, systematic studies in the Bragg-peak region with dressed-ionprojectiles are rather scarce. In one of those works Montenegro et al. [14] found that thefragmentation yield does not follow the steep decrease of the linear energy transfer (LET)at the low-energy side of the Bragg peak. The dissociation yield has been found practicallyconstant down to very low projectile energies.The fragmentation pattern of a target molecule is determined by the velocity, chargestate and structure of the projectile [10] and the open fragmentation channels taking placein the reaction [9]. By the collision, the target molecule may fall to several possible ex-cited and ionized states. Some of those states of the transient (=precursor) molecular ionwill initiate dissociation into the open fragmentation channels. Multiple vacancy states areparticularly dissociative. Multiple electron removal from the target molecule can happene.g., by direct multiple ionization, by transfer-ionization or by single ionization followed bysecondary processes. Scully [18] et al. showed that the role of secondary Auger-processesis non-negligible in producing multiply charged molecular ions even in the case of electronimpact. The emitted fragments can be neutral or charged particles in excited or groundstates [7]. There are also two or three-step fragmentation processes [7, 10, 19], i.e. sequen-tial dissociations such as H O → OH + +H + → O + +H + +H . Note that a fragmentationchannel is usually characterized by the charge states of the precursor ion and the fragments,without specifying their electronic, vibrational or rotational states. Accordingly, the samechannel notation may be used for a set of sub-channels with different kinetic energy release(KER) values.The kinetic energy release is typically low for ion-neutral breakups. For few-atomic2olecules, it is often only a few tenths of eV, and the upper limit is around 5 eV. Forbreakups involving at least two positive ions the region of KER extends up to much higherenergies, it is between cca. 3 and 100 eV [19]. The higher KER for the latter case is due tothe Coulomb repulsion between the charged fragments, which increases with the charge stateof the transient molecular ion (Coulomb explosion) [11, 20]. For the accurate determinationof the KER distribution one has to take into account the electronic excitation of the transientmolecular ion and the emergent fragments [20, 21], as well as the rotational and vibrationaldegrees of freedom of the precursor molecular ion [11, 12]. The several possible excited statesof the precursor molecular ion and the emergent fragments result in a spread of the kineticenergies of the fragments originating from the same dissociation channel. Furthermore, thekinetic energy distribution for a certain fragmentation channel may differ in the case of one-, two- or three-step processes [7, 19]. As a result, the fragment energy spectra are rathercomplex.In most of the experiments, the dissociation pattern of water was studied thoroughly onlyfor the low charge state transient molecular ion (H O q + , where q et al. [2] studied the dissociation of the H O molecularion in details, induced by XUV photons from H O + ions. They devoted special attentionto the excited states of the initial molecular ion and the emitted fragments, and their effecton the KER distribution. Higher ionization states of the water molecule were observed incollisions with slow, highly charged ions (HCI) [12, 13, 24–26], where the dominant ionizationprocess is multiple electron capture. Here the degree of target ionization strongly dependson the initial charge of the projectile: The maximal degree of target ionization was foundto be q = 4 , , and 8 by different groups utilizing Ne [13], Ar [12] and Xe [26],respectively. Recently Wolff and co-workers [36] observed higher degrees of ionization of thewater molecule ( q = 4 ,
5) by the impact of MeV energy ions.For heavier ions only relatively few works [14, 36] cover both the charge state and en-ergy ranges, which are typical for the close surrounding and the distal region of the Braggpeak. In the present work we concentrate on this relevant but less investigated area. Westudy the emission of fragments from the multiple ionization of water, while bombarding itwith medium-energy, single charged atomic-ion projectiles. These projectiles mostly inter-act with the target molecule by weak, screened Coulomb potential, therefore direct singleionization is the dominant process. Classical and quantum mechanical calculations confirm3hat in such collision systems, the electron emission spectrum is dominated by electrons fromsingle ionization [27]. However, in close collisions, the perturbation strength for ”dressed”projectiles may approach that for bare projectiles. This is due to the rapidly decreasingscreening effect of the projectile electrons towards smaller impact parameters. In such closecollisions the effective charge exceeds the ionic charge for a short time period [28], and thetarget feels strong perturbation. Such collision events can produce remarkable double, andmultiple ionization yields even for neutral atom impact [29]. Though their contributionsmay remain low compared with single ionization, they are responsible for the productionof the majority of the fragments. The connection between the primary ionization and thesubsequent molecular fragmentation has been subject of numerous studies for lower degreesof ionization [7, 10, 26]. As the degree of ionization becomes higher with increasing pertur-bation, several new fragmentation channels open. Thus, fragmentation measurements offera sensitive method for studying multiple ionization of molecules.In this work we measured double differential fragment-ion emission spectra for the gasphase H O molecule by the impact of H + , He + and N + ions. From the spectra we determinedabsolute cross sections for the individual fragmentation channels. The latter procedure isbased on extensive earlier studies performed by several research groups [2, 10–13, 15, 22–26], in which the overwhelming majority of the fragmentation channels have been identifiedand their KER data have been determined, dominantly for H + , He q + and HCI projectiles.From the cross sections determined for the individual fragmentation channels we deducedthe multiple ionization cross sections for the target molecule. The experimental results areanalysed by comparing them with the predictions of the continuum-distorted-wave eikonal-initial-state (CDW-EIS) and the classical trajectory Monre Carlo (CTMC) theories. II. EXPERIMENT
The fragmentation of the H O molecule was investigated in a standard crossed beamexperiment in Atomki, Debrecen [27]. Beams of H + , He + and N + were provided by a 5 MVVdG accelerator with energies 1 MeV/u, 250 keV/u and 46 keV/u respectively.The ion beams were guided through a 15 ◦ deflector chamber in order to keep the chargestate of the ions well defined. After the deflector chamber two pairs of electrostatic steererswere mounted in the beamline, as fine-tuning elements. Collimation of the ion beam was4erformed by a four-jawed slit placed 120 cm distance from the entrance of the experimentalchamber, and a somewhat larger aperture between the four-jawed slit and the chamber.During beam tuning a precisely aligned additional aperture was temporarily placed justafter the entrance of the experimental chamber. This aperture was removed during themeasurements. The beam current was measured by a two-staged differential Faraday-cup.A double-layer magnetic shielding reduced the magnetic field to a few mG in the scatteringchamber.A jet of H O vapour was led into the experimental chamber through a 1 mm diameternozzle. A pressure regulator with an automatically operated needle valve ensured constantbuffer pressure and continuous gas flow regulation. The container of the pre-purified, carbon-free liquid water was attached to the entrance of this pressure regulating system. Dissolvedgases were carefully pumped out. The target gas density in the collision volume was 2 × cm − . The continuous background pressure was around 9 × − mbar and 1 × − mbarwithout and with target gas inlet respectively.The cylindrical scattering chamber of 1000 mm diameter was equipped with rotatablerings. Charged fragments ejected from the collisions were energy analysed by a single stageenergy dispersive electrostatic spectrometer fixed on one of the rings. The experimentalgeometry allowed us to measure the angular distribution of the fragments from 20 ◦ to 160 ◦ relative to the incident ion beam. In order to avoid recombinations caused by the backgroundgases, we used a small, compact spectrometer, close to the collision region. The pass lengthfrom the collision center to the channeltron detector was less than 10 cm. The base energyresolution of the spectrometer was 3%.Fragment ion energy spectra at different observation angles were taken from 0 . η = 0 . ± .
08) was taken from the literature [31].The statistical error was estimated less than 20% for H + impact, and far below 10%for He + and N + projectiles in the main, structured region of the spectra (typically in the3 −
15 eV, 3 −
30 eV and 3 −
50 eV energy range for proton, helium and nitrogen ionimpact, respectively). The systematic error was estimated around 25% in these energy5egions, mostly due to the uncertainty of the detection efficiency. Thus the overall accuracyof the cross section data in the structured region is ≤ −
50% here. At higherenergies, near the end of the spectra, the overall uncertainty also increases due to theincreasing statistical error.
III. THEORETICAL CONSIDERATIONS
In a previous work [27] we studied the present collision systems by measuring andanalysing the energy spectra of the emitted electrons. There the electron emission crosssections were compared with the results of CDW-EIS and CTMC calculations, extended totreat molecular orbitals and screened potentials for describing the electron emission frommolecules impacted by dressed projectiles. The details of the theories can be found inRefs. [27, 32–34]. The models were applied at the level of the independent particle approx-imation. In the present work we use the same models to describe multiple ionization ofthe H O molecule, leading to molecule fragmentation. For the treatment of the multiplevacancy production in the framework of the independent particle model (IPM), the impactparameter formulation is used. For a specific molecular orbital (MO) the calculations yieldimpact-parameter dependent single-electron probabilities for ionization, p i ( b ) and electroncapture, p c ( b ). We note that for molecules, the impact parameter is a vector in the plane,which is perpendicular to the projectile trajectory. Moreover, the probabilities are not onlyimpact-parameter, but also orientation dependent.The multiple vacancy production, when n electrons are ejected, and m are captured to theprojectile from the initial number of electrons N on a specific MO is given by the followingmultinomial expression: P i n c m = (cid:18) Nn (cid:19)(cid:18) N − nm (cid:19) p ni p mc (1 − p i − p c ) N − ( n + m ) (1)For a molecule having Q MOs, the probability of multiple vacancy creation is aproduct of the contributions of the individual MOs. The probability of creating the( n , n , ..., n Q ; m , m , ..., m Q ) vacancy configuration is given by6 i n ,n , ... nQ c m ,m , ... mQ = Q Y k =1 (cid:18) N k n k (cid:19)(cid:18) N k − n k m k (cid:19) × p n k ik p m k ck (1 − p ik − p ck ) N k − ( n k + m k ) (2)where k = 1 , ..., Q ; N k is the number of the electrons on the k th MO; p ik , and p ck are theionization, and capture probabilities from the k th MO, respectively; n k is the number ofejected and m k is the number of captured electrons from orbital k . IV. RESULTS AND DISCUSSIONS
The fragment ion energy spectra measured in the present work (see Fig. 1) exhibitsignificant differences for the three projectiles. The fragment ion emission is found to beisotropic, except a high energy tail of the spectra around 90 ◦ observation angle, which is dueto binary collisions between the projectile and one of the target nuclei. Therefore, in Fig.1 we show spectra taken at just one particular observation angle (45 ◦ ). The cross sectionincreases with the atomic number of the projectile. It is two orders of magnitude higherfor N + than that for H + impact at all energies. The structure of the spectra also changessignificantly with the atomic number of the projectile.For the identification of the measured fragmentation channels and fragment energies weleant on the KERs and individual fragment energies given in Refs. [2, 10–13, 35]. Thesevalues are summarised in Table I. In these studies the fragmentation pattern of the H Omolecule was investigated by the impact of different projectiles. Pedersen et al. [2] studiedthe fragmentation of the H O molecular ions by XUV photons in coincident measurements.Special attention was put on the different excited states of the precursor molecular ions andfragments, and their effect on the measured spectra. Alvarado et al. [10] studied thefragmentation of water molecules induced by singly charged ion bombardment. Using time-of-flight technique, they measured the energy distribution of the fragments originating fromthe single, double and triple ionization of the molecule. Fragments from the higher ionizationstates of the H O molecule were observed in collisions of water with slow HCIs by differentgroups [11–13]. In a recent work Wolff et al. [36] studied the fragmentation pattern ofwater by different ion projectiles (H + , Li ... , C + and C ). Their fragmentation channelidentification was based on a combination of Coulomb explosion and CTMC calculations(CE-CTMC) in reasonable agreement with their experimental results.7
10 10010 -22 -21 -20 -19 -18 -17 DDC S ( c m / e V / s r) Energy/Charge (eV)
FIG. 1: Absolute double differential fragmentation cross section spectra for H O molecule measuredat 45 ◦ observation angle. Open triangles stand for H + impact, open circles for He + , and full squaresfor N + projectile. The enhanced high energy tail above 15 eV, which appears for He + and N + projectiles, is due to multiple ionization ( q >
3) processes.
We detected only one of the fragments from each dissociation events. However, thefragmentation channels could be well identified in the measured spectra using the informationfound in the above-mentioned works. From the tabulated KER values in Table I, one canestimate the kinetic energy of the individual fragments for ion-pair breakups by taking intoaccount that the kinetic energies are inversely proportional to the mass of the fragments.Assuming that the neutrals carry a negligible amount of KER [19], this estimation can beextended to ion-pair + neutral breakups, too.The identified fragmentation channels are shown in Fig. 2. The unresolved hump below3 eV reflects mostly heavy fragments (O q + ; OH q + ) from ion-pair and ion-triplet breakups.A small amount of low energy H + ions from ion-neutral breakups (single ionization of water)may also contribute to this region. In the case of ion-pair and ion-triplet breakups protonfragments produce a structured region above ca. 3 eV. According to Fig. 2, the doubleionized water molecule dissociates mostly into two fragments. Protons form the OH + +H + channel produce an almost flat region from ca. 3 eV to 7 eV, and a more structuredpart between 7 and 12 eV. It contains several overlapping peaks, which belong to differentexcitation states of the transient H O molecular ion and the emergent OH + fragments.Similar conclusions were drawn for the overlapping peaks in Refs. [2, 10, 11]. We note here8hat Refs. [2, 12, 13] predict a slight contribution of ion-pair + neutral channels to thisenergy region. The three-, four- and five-fold ionized molecules dominantly dissociate intoion-triplets [10]. Protons from these highly ionized ( q >
2) transient molecular ions appearabove 15 eV.A further analysis of the spectra in Fig. 1 revealed that the proton fragment peaks aboveca. 15 eV, appearing only for He + and N + projectiles, belong to the fragmentation channelswhich are due to the four- and five-fold ionization of the water molecule. In parallel withthese proton peaks, the relative yield of the heavy fragments ( < q max = 3, 4, and 5 for H + , He + and N + impact respectively.The fragmentation spectrum for N + impact observed in the present work is very similarto those reported in Refs. [13, 25] measured by slow highly charged ions (see Fig. 3b inRef. [13]). At first sight the perturbation exerted by the single charged nitrogen projectileseems to be surprisingly strong. The strong multiple ionization capability of the dressedN + projectile can be attributed to the reduced screening of the projectile nucleus by itselectrons in close collisions, i.e., at small N-O impact parameters, where multiple ionizationis dominant. Accordingly, the effective charge for multiple ionization may exceed the ioniccharge significantly.For a quantitative analysis of the measured fragmentation patterns the spectra weredecomposed to contributions from particular fragmentation channels. The fit curves togetherwith the measured data are shown in Fig. 3. The fit is based on the data listed in Table I andon our channel identification (Fig. 2). The region of heavy fragments ( < . + projectile an additional peak around 58 eV wasnecessary to insert at the end of the spectrum. This peak is likely to be due to fragmentsfrom the highly excited, five-fold ionized H O * molecule. Data about the FWHM valuesare scarce in the literature. The few FWHM values for the individual channels presentedin Table I have large uncertainties. Nevertheless, for charged particle impact, these FWHMvalues are roughly proportional to the mean channel energies. Therefore, to resolve the9 ABLE I: Summary of the literature data used in the present analysis. The last column refers to the identification number of the peak, whichstands for the fragmentation channel in Fig. 3 and Table II. The same number with different lowercase letters represent the components ofone ”collector” peak during the fit.
Projectile Method Fragmentation channel KER (eV) FWHM (eV) H + energy (eV) H + FWHM (eV) Ref. No. Peak No.6-23 keV H + ; He + ; He TOF H O + → OH + H + − − ± . − [10] 46-23 keV H + ; XUV TOF; coinc H O → OH + + H + . ± . − . ± . − [2, 10] 56-23 keV He + ; XUV TOF; coinc H O → OH + + H + . ± . − . ± . ∼ a He II PIPICO H O → OH + + H + . ± . − ∼ . − [35] 6 b XUV, He II ion spect H O → O + + H + + H . ± . − − [13, 35] 6 c TOF; coinc H O → OH + + H + . ± − . ± ∼ a XUV coinc H O → OH + + H + ± − − − [2] 7 b XUV coinc H O → OH + + H + . − − − [2] 8XUV coinc H O → OH + + H + . − − − [2] 96-23 keV H + ; He + TOF H O → O + + H + + H . − . ± ∼
15 [10] 106-23 keV He TOF H O → O + + H + + H + − . ± . ∼
15 [10] 11 a
20 keV HCI TOF, ion spect H O → O + + H + + H + ∼ − ± . ∼
15 [11–13] 11 b TOF H O → O + H + + H ∼ − ± . ∼
23 [10] 13 a
20 keV HCI ion spect H O → O + H + + H − − ± − [12, 13] 13 b O → O + H + + H + ∼ ∼ − − [11] 1420 keV HCI ion spect H O → O + H + + H − − ± − [13] 15100-125 keV HCI TOF H O → O + H + + H + ∼ ∼ − − [11] 16
10 10002x10 -18 -18 -18 -18 O +H + +H O +H + +H + O +H + +H + O +H + +H O + +H + +H + OH + +H + DDC S ( c m / e V / s r) Energy/Charge (eV) O q+ ; OH q+ OH +H + O + +H + +H Degree of ionization: q=2+ q=3+ q=4+ q=5+
FIG. 2: Absolute double-differential fragmentation cross section spectra of the H O molecule in-duced by 650 keV N + impact. The presented spectrum was measured at 45 ◦ observation angle. Theidentified fragmentation channels and the regions of the different ionization degrees are indicated. problem of the incomplete knowledge of the FWHM data, we assumed that the widths ofthe peaks are proportional to their energy centers. The initial value of the proportionalityfactor was set to 0.4. In an iterative fitting procedure this factor was allowed to vary in arange between 0.2 and 0.4. In a small extent we allowed also slight changes (max. 5%) ofthe peak centers. Finally the same set of the FWHM and energy center values were used tofit the spectra for all the three projectiles. The results of the fit are shown in Fig. 3 and inTable II.We note that the fitted curves in the 4 −
12 eV energy region may contain slight contri-butions of fragmentation channels different from the identified components of the OH + +H + channel. According to the published experimental data, the H O → O + + H + + H [12, 13, 35] channel also provides a small yield between 5 and 6 eV. Calculated data in Ref.[2] suggest that the H O → O + H + + H + fragmentation channel may also contribute tothe 4 −
12 eV region, but it has not been detected in any experimental work. As the articlesreport only small yields for these channels, the questioned energy region is attributed to theOH + +H + fragmentation channel in our work, characterized by slightly different KER values(see Table I).The mean energies of the fragmentation channels of three-, four- and five-fold ionization11 ABLE II: The obtained cross sections ( σ ) of the individual fragmentation channels for the three projectiles. They are the results of thefit presented in Fig. 3. The energy center and FWHM values are the same for all projectiles. The uncertainties includes only the statisticalerrors and the estimated uncertainties of the fit. Peak No. Fragmentation channel Center (eV) FWHM (eV) σ H + (cm ) σ He + (cm ) σ N + (cm )1 Heavy (OH q+ ; O q+ ) 0 .
89 0 .
35 2 . ± . × − . ± . × − . ± . × − q+ ; O q+ ) 1 .
25 0 .
65 8 . ± . × − . ± . × − . ± . × − q+ ; O q+ ) 1 .
83 0 .
74 4 . ± . × − . ± . × − . ± . × − O + → OH + H + .
54 1 .
23 8 . ± . × − . ± . × − . ± . × − O → OH + + H + .
87 1 .
68 1 . ± . × − . ± . × − . ± . × − O → OH + + H + .
46 2 .
45 1 . ± . × − . ± . × − . ± . × − O → OH + + H + .
63 2 .
83 9 . ± . × − . ± . × − . ± . × − O → OH + + H + .
89 3 .
50 3 . ± . × − . ± . × − . ± . × − O → OH + + H + .
94 4 .
22 2 . ± . × − . ± . × − . ± . × −
10 H O → O + + H + + H .
93 5 .
33 2 . ± . × − . ± . × − . ± . × −
11 H O → O + + H + + H + .
83 6 .
11 8 . ± . × − . ± . × − . ± . × −
12 H O → ? 23 .
24 5 .
30 1 . ± . × − . ± . × − . ± . × −
13 H O → O + H + + H .
30 6 .
59 9 . ± . × − . ± . × − . ± . × −
14 H O → O + H + + H + .
52 8 . − . ± . × − . ± . × −
15 H O → O + H + + H .
36 12 . − . ± . × − . ± . × −
16 H O → O + H + + H + .
58 10 . − − . ± . × −
17 H O → O + H + + H .
22 11 . − − . ± . × − IG. 3: Fragment ion spectra of H O induced by H + (a), He + (b), and N + (c) projectiles (symbols).The peaks represent Gaussian fit for the fragmentation channels listed in Table 1 and Table 2.Channel positions are indicated by vertical lines with numbers. fall above 17 eV. They agree well with those of calculated by the nCTMC model of Wolff et al. [36]. Their channels denoted by e-h in Ref. [36] can be identified with our channelsNo. 13-16 in Table II, respectively. At lower energies the number of peaks in Ref. [36]is significantly smaller, though they can be identified with some of the peaks found inthe present fittings. The reason is that many of the considered channels, taken from theliterature, belong to excited states of the ionized precursor molecule, while no excitation isincluded in the model of Wolff et al. [36]. Nevertheless, their predicted energy positions aresurprisingly good for the ground state of the precursor molecule ion.13 IG. 4: The σ N + /σ He + ratios for the individual fragmentation channels (the colours of the linesare the same as the colours of the Gaussians in Fig. 3). The ratios are presented only from theOH + +H + channel. The sequence of the lines is almost the same as the sequence of the energycenters of the Gaussians. The ionization degree of the H O molecule and the O-fragments areindicated.
The analysis of the obtained cross sections, presented in Table II shows that the highestenergy fragmentation channels have almost two orders of magnitude lower yield than thedouble ionization channels for all projectiles. The highest-energy proton fragments belongto the fragmentation channels of O + H + + H , O + H + + H and O + H + + H forH + , He + and N + impact respectively.Further analysis was made via the σ N + /σ He + ratios of the individual fragmentation chan-nels (Fig. 4). It is expected that this ratio is increasing with higher degrees of ionization.Indeed, the ratios form groups according to the degree of ionization of the molecule, andsubgroups according to the degree of ionization of the oxygen atom. As expected, the ra-tio is an almost monotonic function of the energy of the proton fragment. It is seen thatthe multiple ionization efficiency of the N + projectile relative to that of He + dramaticallyincreases with the degree of ionization.From the results of the fit we deduced the multiple ionization cross sections of the watermolecule as sums of the partial cross sections of the corresponding individual fragmenta-tion channels. Single ionization cross sections could not been determined with the presentmethod. The main reason is that the non-dissociative single ionization events can not be14etected by our method at all. Another reason is that in the 0 . − + fragments originating from single ionization. Moreover the kinetic energy ofsome of the fragments from ion-neutral breakups falls below our detection limit (0 . O molecule may easily happen by removing both electronsfrom one of the O-H bonds. Accordingly, there is a rather large probability that one of thechemical bonds breaks, while the other remains unharmed. This can be the reason for therelatively large yield of the OH + +H + channel. For higher degrees of ionization both O-Hbonds are likely to be affected. Therefore, the probability of ion-pair breakups becomesnegligible, and the molecule prefer to dissociate into three parts.The experimentally obtained multiple ionization cross sections (CS) are compared tothose calculated by the CTMC and CDW-EIS method. Multiple ionization data producedby the two theoretical methods are also compared with each-other. The detailed descriptionof the models is given in Refs. [27, 29, 32–34]. We found in our previous study [27] thatCTMC provided good agreement with the measured double differential electron emissioncross sections for all the present collision systems. The results of the CDW-EIS calculationsalso reproduced the experimental double differential electron emission cross sections for H + and He + projectile, but they shown significant deviations for N + impact. In the presentwork, we concentrate on the total probabilities and cross sections for ionization and electroncapture. At this level, both theories predict that electron emission is dominated by singleionization.In the following we analyse the multiple target vacancy production for water predictedby the two theories within the framework of the independent particle model (IPM). Fora descriptive presentation we derive orientation-averaged P i n c m ( b ) values (see Eq. (1)) for n -fold ionization and simultaneous m -fold electron capture as a function of a scalar impactparameter b . This way, we can demonstrate and compare the approximate impact parameterdependence of the multiple vacancy creation probabilities. In Fig. 5, we present CTMCresults for n -fold ionization (a) and for singe-electron capture + ( n − bP i n ,c ( b ) and bP i n − c ( b ) curves for H + impact on H O are plotted in Fig. 5aand Fig. 5b respectively. The impact parameter dependence of the same processes for N + impact is shown in Fig. 6. In the figures, the impact parameter is ”measured” from thenucleus of the oxygen atom. Note that the areas under the bP ( b ) curves are proportional to15 IG. 5: Ionization (a), and single capture + ionization (b) probabilities as function of the impactparameter for the H + + H O collision system. The number of vacancies produced in the targetmolecule, n is indicated at the curves. the cross sections of the particular processes.According to the CTMC results for H + impact, single ionization is dominant in the fullimpact parameter region. The yields of higher degrees of ionization become more significantin narrower regions of smaller impact parameters (see Fig. 5a). They remain much belowthe single ionization yield everywhere. The maximum of the calculated bP ( b ) curves de-creases about three orders of magnitude from single- to five-fold ionization. Single capture+ ionization is limited to a small impact parameter range, and its contribution to vacancyproduction is negligible at all degrees of ionization. The shape of the bP i n − c ( b ) curves fordifferent n -s are very similar to each other. (See Fig. 5b).16 IG. 6: Ionization (a), and single capture + ionization (b) probabilities as function of the impactparameter for the N + + H O collision system. The number of vacancies produced in the targetmolecule, n is indicated at the curves. The relevant impact parameter region for ionization is much larger for N + than that for H + projectile (See Fig. 6a). Single ionization is also dominant here in the whole 1 − a.u. impactparameter region with a maximum around 3 a.u. . The multiple ionization curves for N + impact extend to impact parameter ranges that are twice as large as those for proton impact.Similarly to H + impact, increasing degrees of ionization have smaller yields in graduallynarrower windows at smaller impact parameters. However, the decrease of the yields ismuch weaker here: the maximum of the curve is only about one order of magnitude smallerfor five-fold than for single ionization. In contrary to H + impact, multiple ionization curvesexceed that for singe ionization at small impact parameters (below 2 a.u. ). It shows thatthe effective perturbation strength increases towards smaller impact parameters. Moreover,it indicates that this is due to the screened potential of a Z = 7 central charge, which goes17 IG. 7: Pure ionization (i n c ) and single capture + ionization (i n − c ) cross sections for H + (a),and for N + (b) projectiles. Pure ionization is presented as full circles for CTMC and full trianglesfor CDW-EIS calculations. Capture + ionization process is presented by open circles and opentriangles for CTMC and CDW-EIS respectively. The lines are for guide the eye. far above the ionic potential at small distances. This behaviour is even more pronouncedfor the single capture + ionization process, as it is seen in Fig. 6b.The calculated multiple vacancy production cross sections for H + and N + impact areshown in Fig 7. According to the CTMC calculations the target ionization cross section forH + impact decreases more than three orders of magnitude from single to five-fold ioniza-tion. Cross sections calculated by CDW-EIS for single, double, and triple ionization are alsopresented in Fig 7a. They decrease faster with increasing degree of ionization than those ob-tained by the CTMC method. According to both theories the electron capture contributionto the vacancy production is negligible for the H + projectile. The yield of single-electron18apture + ionization events remains at least two orders of magnitude lower than that ofpure ionization leading to the same number of vacancies.For N + impact, the absolute cross sections are significantly larger, and their relativeyields are strongly different from those of H + impact. The decrease of the cross section withincreasing number of vacancies is much slower here, only one order of magnitude from singleto five-fold ionization. Moreover, the role of electron capture is not negligible for N + impact.With increasing degree of target ionization the cross sections of the two processes approacheach other. The cross section for single-capture + four-fold ionization even exceeds that ofpure five-fold ionization (See Fig. 7b).In Figure 8, the experimentally determined multiple ionization cross sections are com-pared with those obtained by CDW-EIS and CTMC calculations. For double vacancy pro-duction, CDW-EIS provides a good agreement with experiment for both H + and He + impactat 1 MeV projectile energy. Moreover, there is a reasonably good agreement with CDW-EISfor the triple vacancy yields too. This quantum treatment seems to perform better thanCTMC at high impact velocities and small perturbations, as it is seen for H + impact.We could not measure single ionization in the present experiment directly. Neverthe-less, we note that we have experimental information about it. In our earlier work [27] wemeasured the electron emission from the same collision systems, and determined absolutedouble differential cross sections for it. Those data have been compared with the resultsof both CDW-EIS an CTMC calculations at the level of double differential spectra. Goodagreement was found with CDW-EIS results for H + and He + impact, and with CTMCresults for all the three projectiles (H + , He + and N + ).Therefore, we may also consider thetheoretical predictions for single ionization as ”semi-experimental” values.For He + the CDW-EIS results also agree well with the measured multiple target ionizationcross sections (See Fig. 8 (b)). The agreement is as good as for proton impact in the caseof double and triple ionization. However, the experimental four-fold ionization cross sectionis far below the prediction of the theory. A slight five-fold ionization cross section is alsopredicted but it was not found in the measurements. For the slowest N + projectile, theCTMC results practically coincide with the experiment up to triple ionization (See Fig.8 (c)). For four-fold ionization, there is a slight deviation. Only the five-fold ionizationcross section is overestimated significantly. Since we compare absolute cross sections, thisagreement is remarkable. 19 IG. 8: Multiple ionization cross section as function of the ionization degree of the target for H + (a), He + (b) and N + (c) bombardment. The theoretical predictions for the different ionizationdegrees are also shown. A closer inspection of Figure 8 shows a general tendency, namely that the measuredmultiple target ionization cross sections decrease faster with the degree of ionization thanthe calculated data. It is true for both theoretical models. While for double target ionizationboth calculations provide reasonable agreement with experiment, they both tend to graduallyoverestimate the experimental data towards higher ionization degrees. At four-fold and20ve-fold ionization this tendency becomes very strong. This increasing deviation of thecalculated data from the experiment can be attributed to the limitations of IPM. The roleof electron correlation in electron emission increases with the degree of ionization. When asingle ionization probability is calculated with the first ionization potential as parameter,IPM is expected to overestimate the multiple electron removal from the target.Our data show that this overestimation is stronger if the perturbation is weak, andbecomes less significant with strong perturbation. While for H + , He + projectiles the theoriesoverestimate the cross section for n = 3, and dramatically overestimate it for n = 4, for N + impact the agreement is perfect for n = 3 and still reasonable for n = 4. It breaks downonly at n = 5. This finding suggests that the importance of electron correlation may dependon the ratio of a mean correlation energy to a mean energy transfer characteristic for thecollision. V. SUMMARY AND CONCLUSIONS
We studied the fragmentation of H O molecules by the impact of 1 MeV energy H + , He + ,and 0.65 MeV energy N + projectiles. Single charged ions in this energy region are relevantfor studying ion + H O collisions in the distal region of the Bragg peak. The energy andangular distribution of the emerging fragments were measured by a single stage, parallel-plate type, electrostatic spectrometer in a standard, crossed beam experiment. Absolutedouble differential fragmentation cross sections of water were obtained for the three collisionsystems. The fragment energy spectra were fitted by Gaussian functions, and absolutecross sections for the particular fragmentation channels have been determined. From thosechannel yields we deduced the multiple ionization cross sections for the water molecule, andcompared them with those calculated by CTMC and CDW-EIS methods.The identification of the particular fragmentation channels is based on their experimentalKER values published in the literature. We found that up to five-fold ionization, the listof the fragmentation channels is close to complete. Moreover, we confirmed that a recenttheoretical approach [36] provided correct identification and reasonable KER values for animportant fraction of the fragmentation channels.We found that the fragment ion emission was isotropic for all projectiles. The differentialfragmentation cross section for N + is more than four times larger than that for He + , and21lmost two order of magnitude higher than that of H + in the entire fragment energy region.This strong variation of the yields is attributed to the increasing perturbation strengthof the slower and slower projectile ions from H + to N + . Besides the absolute differencesbetween the cross sections, the relative ratios of the individual fragmentation channels arealso different for the three projectiles, and additional channels appear for He + and evenmore for N + impact towards the high energy end of the spectra. The presence of thesefragmentation channels indicate that the maximum ionization degree increases from H + toN + . It was found to be q max = 3, q max = 4, and q max = 5 for H + , He + and N + impactrespectively.The fragmentation cross section spectrum for N + impact is very similar to those obtainedby slow HCIs. This similarity indicates that the perturbation strength for the N + projectilecan approach those for HCIs. This is partially due to the increase of the effective projectilecharge in close collisions with the oxygen atom of the target. The dominance of low impactparameter events in the production of multiple ionized H O q + molecular ions ( q = 2 , ... + impact, the non-perturbativecharacter of the classical CTMC method gains importance. At this strong perturbation, theagreement between CTMC and experiment is remarkably good up to triple, and it remainsreasonable even for four-fold ionization.Towards higher ionization states both theories systematically more and more overestimatethe experimental cross sections. We attribute it to the limitations of the independent particlemodel, namely the neglect of electron correlation within the IPM framework. In addition,we found that the overestimation is stronger if the perturbation is weak, and becomes lesssignificant with strong perturbation. For N + impact the agreement with experiment holds upto four-fold ionization. This finding suggests that the importance of electron correlation maydepend on the ratio of a mean correlation energy to a mean energy transfer characteristicfor the collision.In conclusion, we studied the distal (i.e., the low energy) part of the Bragg peak in ion -water molecule collisions both experimentally and theoretically. We found that our CDW-22IS and CTMC models are able to provide quantitative account for the multiple ionizationof the target molecule in a wide range of the perturbation strength. Quantum calculations(CDW-EIS) proved to be more accurate for weak perturbations, while the non-perturbativeCTMC method provided excellent agreement with experiment for violent collisions. We alsogained information about the relative importance of electron correlation for weak and strongperturbations. We expect that a combined application of the tested theoretical methodswill provide a satisfactory level of quantitative description in this focal region of differentapplications. VI. ACKNOWLEDGEMENTS
This work has been supported by the Hungarian Scientific Research Foundation (OTKAGrant No.: K109440), and by the National Information Infrastructure Program (NIIF). Theauthors thank the VdG-5 accelerator stuff for the careful operation.23
1] M. N. Piancastelli, A. Hempelmann, F. Heiser, O. Gessner, A. Rdel, and U. Becker, Phys.Rev. A , 300 (1999).[2] H. B. Pedersen, C. Domesle, L. Lammich, S. Dziarzhytski, N. Guerassimova, R. Treusch, L. S.Harbo, O. Heber, B. Jordon-Thaden, T. Arion, M. Frstel, M. Stier, U. Hergenhahn, A. Wolf,Phys. Rev. A , 013402 (2013).[3] G. Dujardin, D. Winkoun, S. Leach, Phys. Rev. A , 3027 (1985).[4] A. L. F. de Barros, J. Lecointre, H. Luna, M. B. Shah, E. C. Montenegro, Phys. Rev. A ,012716 (2009).[5] F. Fr´emont , C. Leclercq, A. Hajaji, A. Naja, P. Lemennais, S. Boulbain, V. Broquin, J.-Y.Chesnel, Phys. Rev. A , 042702 (2005).[6] H. Luna, A. L. F. de Barros, J. A. Wyer, S. W. J. Scully, J. Lecointre, P. M. Y. Garcia, G.M. Sigaud, A. C. F. Santos, V. Senthil, M. B. Shah, C. J. Latimer, and E. C. Montenegro,Phys. Rev. A , 042711 (2007).[7] H. Luna, E. G. Cavalcanti, J. Nickles, G. M. Sigaud, E. C. Montenegro, J. Phys. B , 4717(2003).[8] I. Ben-Itzhak, K. D. Carnes, D. T. Johnson, P. J. Norris, and O. L. Weaver, Phys. Rev. A ,881 (1994).[9] P. M. Y. Gracia, G. M. Sigaud, H. Luna, M. B. Shah, Phys. Rev. A , 052708 (2008).[10] F. Alvarado, R. Hoekstra, T. Schlath¨olter, J. Phys. B , 4085 (2005).[11] U. Werner, K. Beckord, J. Becker, H. O. Folkerts, H. O. Lutz, Nucl. Instrum. Methods Phys.Res., Sect. B , 385 (1995)[12] J. Rajput, C. P. Safvan, Phys. Rev. A , 052704 (2011).[13] P. Sobocinski, Z. D. Pesic, R. Hellhammer, D. Klein, B. Sulik, J-Y Chesnel, N. Stolterfoht, J.Phys. B , 927 (2006).[14] E. C. Montenegro, M. B. Shah, H. Luna, S. W. J. Scully, A. L. F. de Barros, J. A. Wyer, J.Lecointre, Phys. Rev. Lett. , 213201 (2007).[15] H. Luna and E. C. Montenegro, Phys. Rev. Lett. , 043201 (2005).[16] D. Schardt. T. Elssser, D. Schulz-Ertner, Rev. Mod. Phys. , 383 (2010).[17] H. Paul and A. Schinner, At. Data Nucl. Data Tables, , 377 (2003).
18] S. W. J. Scully, J. A. Wyer, V. Senthil, M. B. Shah, Phys. Rev. A. , 040701 (2006).[19] I. Ben-Itzhak, K. D. Carnes, S. G. Ginther, D. T. Johnson, P. J. Norris, O. L. Weaver, Phys.Rev. A. , 3748 (1993).[20] U. Werner, J. Becker, T. Farr, H. O. Lutz, Nucl. Instrum. Methods Phys. Res., Sect. B ,298 (1997)[21] M. Tarisien, L. Adoui, F. Frmont, D. Lelivre, L. Guillaume, J.-Y. Chesnel, H. Zhang, A.Dubois, D. Mathur, S. Kumar, M. Krushnamurthy, A. Cassimi, J. Phys. B , L11 (2000).[22] B. Seredyuk, R. W. McCullough, H. Tawara, H. B. Gilbody, D. Bodewits, R. Hoekstra, A. G.G. M. Tielens, P. Sobocinski, D. Pesic, R. Hellhammer, B. Sulik, N. Stolterfoht, O. Abu-Haija,E. Y. Kamber, Phys. Rev. A. , 022705 (2005).[23] P. Sobocinski, Z. D. Pesic, R. Hellhammer, N. Stolterfoht, B. Sulik, S. Legendre, J-Y Chesnel,J. Phys. B , 4295 (2005).[24] Z. D. Pesi´c , J-Y Chesnel, R. Hellhammer, B. Sulik, N. Stolterfoht, J. Phys. B , 1405 (2004).[25] Z. D. Pesi´c , R. Hellhammer, B. Sulik, N. Stolterfoht, J. Phys. B , 235202 (2009).[26] G. H. Olivera, C. Caraby, P. Jardin, A. Cassimi, L. Adoui, B. Gervais, Phys. Med. Biol. ,2347 (1998).[27] S. T. S. Kov´acs , P. Herczku, Z. Juh´asz, L. Sarkadi, L. Guly´as, B. Sulik, Phys. Rev. A. ,012704 (2016).[28] ´A. K¨ov´er, Gy. Szab´o, D. Ber´enyi, D. Varga, I. K´ad´ar, S. Ricz, J. V´egh, Phys. Lett. , 71(1982).[29] L. Sarkadi, P. Herczku, S. T. S. Kov´acs, ´A. K¨ov´er, Phys. Rev. A. , 062705 (2013).[30] E. Lattouf, Z. Juh´asz, J.-Y. Chesnel, S. T. S. Kov´acs, E. Bene, P. Herczku, B. A. Huber, A.M´ery, J.-C. Poully, J. Rangama, and B. Sulik, Phys. Rev. A. , 062721 (2014).[31] E. W. Kuipers and A. L. Boers, Nucl. Instrum. Methods Phys. Res. B29 , 567 (1987).[32] L. Sarkadi, Phys. Rev. A. , 062704 (2015).[33] L. Guly´as, I. T´oth and L. Nagy, J. Phys. B , 075201 (2013).[34] L. Guly´as, S. Egri, H. Ghavaminia and A. Igarashi, Phys. Rev. A , 032704 (2016).[35] P. J. Richardson, J. H. D Eland, P. G. Fournier, D. L. Cooper, J. Chem. Phys. , 3189(1986).[36] W. Wolff, H. Luna, R. Schuch, N. D. Cariatore, S. Otranto, Phys. Rev. A , 022712 (2016)., 022712 (2016).