Unusual charge exchange by swift heavy ions at solid surfaces
UUnusual charge exchange by swift heavy ions at solidsurfaces
Tapan Nandi, Prashant Sharma, Pravin Kumar
Inter University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi - 110067, INDIA
Abstract
We have employed x-ray spectroscopy to probe the charge changing processonly in the bulk of the foil when swift heavy ions pass through it. In contrast, theelectromagnetic methods take into account integral effect of the charge changingprocess in the bulk as well as the charge exchange phenomenon at the surfaceof the foil. Thus, the difference between the mean charge states so measuredfrom the two methods disentangles the charge exchange phenomenon at the sur-face from the charge changing process in the bulk and, provides opportunitiesto refine the understanding of ion-surface interactions. Very surprisingly, upto tens of electrons per event participate in the charge exchange phenomenonduring swift heavy ion-surface interactions. This finding has been validatedwith a series of experiments using several ions (z = 22-35) in the energy rangeof 1.5-3.0 MeV/u and also verified theoretically with Fermi-gas model. Inter-estingly, such unusual charge exchange phenomenon could play significant rolein x-ray emission of many astrophysical environments, infrared emission bandsfrom range of environments in galaxies, accelerator physics, ion energy losses insolids, heavy ion cancer treatments, inner shell ionization by heavy ions, andsurface modifications in nano scale.The charge exchange (CX) phenomenon, i.e., non-radiative electron capture(NRC) and radiative electron capture (REC), is very important aspect of ion-
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Present address: Faculty of Physics, Weizmann InstituteofScience, Rehovot 7610001, Israel, [email protected] (Prashant Sharma )
Preprint submitted to ..... May 14, 2019 a r X i v : . [ phy s i c s . a t o m - ph ] M a y tom (gas) as well as ion-solid collisions. The number of electrons captured bythe projectiles in ion-atom collisions is dictated by its charge state as well as tar-get nuclear charge. However, the capture process in ion-solid collisions is inde-pendent of target nuclear charge owing to dangling electrons at the solid surface.Irrespective of initial charge state, slow highly charged ions ( v p < v , v p =ion ve-locity and v =Bohr velocity) tend to acquire neutrality after passage through athin foil [1]. Furthermore, the relative contribution of the electron capture pro-cess in the bulk and at foil surface remains unaccounted. In order to investigateonly the surface contribution, the scattering of multi charged slow ions incidenton a metal surface at glancing angles is considered [2]. Even though, highlycharged relativistic ions at normal incidence are found to capture several elec-trons after passage through a thin foil [3], the net electron capture contributionat the exit surface remains still unknown. To deduce it experimentally, a cleardistinction between charge states of the incident and emerging ions is necessaryand hence, multi-electron heavy ions are preferred as projectiles. This, in turn,enables us to distinguish ion-surface interactions at the entrance and exit sur-faces. In this letter, a clear evidence of the net electron capture contribution atthe exit surface is showcased with the multi-electron, swift heavy ions (SHI).At intermediate energies ( v p > v ), the x-ray spectra of highly charged ionsin post foil interactions account for charge states much higher [4,5] than thatmeasured usually by electromagnetic methods [6]. The two methods are distin-guishable in terms of the distance between source and detector. This distancefor beam-foil spectroscopy is of the order of mm, whereas the detector is placeda few meters away from the source for electromagnetic methods. To analyze thecharge state of the multi-electron projectile ions right at the beam-foil interac-tion region, the x-ray spectroscopy method [7,8] is utilized. Several electronsfrom the entrance surface are captured by the projectile ions in their high Ryd-berg states, which are re-ionized along with ionization of the projectile ions athigh frequency, ion-solid collisions in the bulk. The higher charge state of theemerging ions so formed undergo multi-electron capture (MEC) processes in thehigh Rydberg states at the exit surface of the foil [9]. The high Rydberg states2re long lived and therefore, the signature of their existence is hardly traceablein x-ray spectra recorded for ion-solid collision region. The REC process doesnot undergo any excitation mechanism and thus, is instantaneous, producing nolifetime structure. Also, REC structure is distinguishable from primary x-raypeaks. Therefore, the ions undergone to REC process further experience the in-teraction with the exit surface to capture the electrons in high Rydberg states.Hence, the primary peak in the x-ray spectra recorded during the ion-solid col-lisions demonstrate the charge changing processes only in the bulk. Whereas,the electromagnetic methods [6] measure integral effect of the charge changingprocess in the bulk as well as the charge exchange phenomenon at the surfaceof the foil. Therefore, the difference between the mean charge state measuredonly in bulk ( q bm ) and, in both the bulk and exit surface ( q tm ), can shed light onthe CX at the exit surface.Interestingly, an improved empirical formula constructed from a large setof experimental charge-state distributions analyzed by electromagnetic meth-ods [10] shows good agreement with experimentally measured integral effect incharge change of the projectile ions. To the best of our knowledge, no theoryhas been developed until now to quantify the charge changing process in thebulk owing to the scarcity of the measurements [11]. Recently, an extensivelyused x-ray spectroscopy technique [8], which rescues all challenges, has beenemployed to determine the q bm for several ions ( z = 22-35) in the energy rangeof 1.5-3.0 MeV/u. With great surprise, we notice that simple Fermi-gas modelexplains entire data set very well. This development enables us to assess theo-retically the CX contribution only at the exit surface.Several ion-solid collision experiments were carried out using 15 UD tandemaccelerator at IUAC. The energetic ion beams of Ti, V, Fe, Ni, Cu,and Br (current ≈ α x-ray emissions to determine the q bm of the projectile ions. For this purpose,3idely used experimental technique [7,12,13] is employed and its details is givenelsewhere [8]. During experiments, the pressure in the vacuum chamber wasmaintained around 1 × Torr. Two germanium ultra-low-energy detectors(GUL0055 and GUL0035, Canberra Inc., with a 25 m thick Be entrance window,resolution 150 eV at 5.9 keV, and constant detector efficiency in the range of 5to 20 keV) were placed at right angle to the beam axis. While, the target foilholder was kept at 45 ◦ to the beam axis and a set of collimators were used torestrict the scattered x-rays recorded by the detector. Hence, only the promptx rays are allowed to enter into the detectors through thin mylar windows of 6 µ m thickness. The Doppler broadening is maximum for this geometry, whereasthe first-order Doppler shift is zero and, depending on the beam energies, thesecond-order shift appears at the fourth or fifth decimal place confirming therequirement of no further corrections. The detectors were calibrated with dif-ferent radioactive sources like Fe, Co, and
Am before as well as afterthe experiments to check the systematic errors in the spectra and no significantdeviations were noticed. The NRC processes at the exit of the target surface in-volve high Rydberg states and do not influence the prompt x-ray spectra at all.Thereby, in contrast to the conventional electromagnetic methods accounted foraggregated effects of charge changing processes in the bulk as well as the chargeexchange phenomenon in the exit surface, the present x-ray technique showcasesan account for the charge changing processes only in the bulk.A series of ion-solid collision experiments were carried out with various ionspecies and taking the advantage of analysis made in our earlier studies [8,13,14],the mean charge state of the projectile ions in the bulk of the carbon foil wasmeasured from the centroid of the K α x-ray peaks. The fitting error in the cen-troid energy is found to be less than 1%. The amorphous carbon foils used in allexperiments showed excellent electrical conductivity and could be approximatedto the metal behaving like an electron gas at high temperature and pressure. Inthese beam-foil experiments, the swift ions interact with bulk Fermi electrons(velocity ≈ v F ) [15]. Further, the impact of interaction depends upon the beam4 .4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.01820222426283032 Cu (F) Cu (E) Br (F) Br (E) Fe (F) Fe (E) Ni (F) Ni (E) Ti (F) Ti (E) V (F) V (E) M e a n c h a r g e s t a t e ( q m ) Beam Energy (MeV/u)
Figure 1: Comparison of experimentally governed (empty symbols) and theoretically esti-mated (filled symbols) q bm s for various projectile ions as a function of beam energies. TheFermi-gas model was used for theoretical estimations. The projectile ions are specified withtheir elemental symbols. E and F in the parentheses represent the experiment and Fermi-gasmodel, respectively. The uncertainties are within the symbol size. Beam Energy (MeV/u) M e a n c h a r g e s t a t e ( q m ) Figure 2: Comparison of the q bm and q tm as measured by x-ray spectroscopy (present work)and electromagnetic techniques, respectively. The Cu beam of various energies was allowedto pass through a carbon foil. The uncertainties are within the symbol size. velocity ( v p ) as well and the q bm , which is related with two velocities as: q bm = z p (1 − v F v p ) . (1)Where z P is the nuclear charge of the projectile ions and v F =2.61 × m/secfor amorphous carbon foil [16]. The theoretical values of q bm using equation(1) along with experimental values are depicted in Fig. 1. The theoreticalpredictions match well with the experiments and, agreement improves further5
20 40 60 80 10001020304050607080 Fermi Schiwietz [13] Fermi - SchiwietzAtomic number (Z) M e a n c h a r g e s t a t e ( q m ) N u m b er o f e l ec t r o n s c a p t u re d (a) (b) Fermi Schiwietz [13] Fermi - SchiwietzBeam Energy (MeV/u) M e a n c h a r g e s t a t e ( q m ) N u m b er o f e l ec t r o n s c a p t u re d Figure 3: Theoretical values of q bm from Fermi-gas model and q tm from improved Schiwietzformula as a function of (a) atomic number up to uranium with constant beam energy of 1MeV/u and (b) beam energies (1-110 MeV/u) for U ions. The difference between the q bm and q tm representing a direct measure of the charge exchange at the exit surface of the foil( N ec ) is also shown. The analysis shows that as high as 37 electrons are captured from theexit surface by 1 MeV/u U ion and this number decreases with energy; reduces to nearlyzero for energies >
80 MeV/u. for beam energies > v p > v F and equilibrium foil thickness, for which a number ofcollisions take place and the projectile charge attains a kind of saturation.We also made an attempt to compare the q bm with q tm . As q tm can be ei-ther measured by electromagnetic methods or estimated accurately using an6 igure 4: The illustration of a five-stage model (see text) based on the charge changingprocess in the bulk and charge exchange phenomenon at foil surfaces during the passage ofprojectile ions. improved formula [10], a case study of the copper beam on account of meancharge state using various approaches is summarized in Fig. 2. The measured q bm values are in well accord with the predictions of Fermi-gas model and q tm values [6] follow Schiwietz formula [10]. The difference between q bm and q tm givesa direct measure of the charge exchange at the exit surface of the foil ( N ec ) ig-noring the effect of autoionization at the moment.The energy loss by SHI is mostly in the bulk and only a small fraction ofit takes place at the exit surface [18]. The loss in both regions depends onthe charge state of the ion in the bulk [19,20], which is far different from itsvalue during incidence as well as emergence of ions. This behaviour is well ex-plained by the Fermi-gas model and hence finds wide applications in importantresearch fields, for example, calculations of stopping power [19,21] and inner-shell ionization in solids [22]. Also, this information is useful in calculation ofthe biologically effective dose not only in the target region but also in the entireirradiation volume during heavy ion cancer treatment [23].In Fig.3 (a) and (b), we have plotted q bm , q tm and N ec as a function of z p and beam energy (keeping one constant at a time), respectively. It can be seenthat N ec takes a significant figure for z p ≈
15 and increases with increase in z p up to the value of uranium. The analysis shows that up to 37 electrons arecaptured at the exit surface of the foil for uranium ions at 1 MeV/u and this7umber decreases rapidly with increasing the beam energy owing to reducedNRC cross-section. For example, N ec is only a few for 46.5 MeV/u, which isin good agreement with the experiment [3]. Large number of electrons can becaptured to the projectile ion if enough vacancies are available. This conditionprevails in the circular Rydberg states and after large-scale electron capture,the hallow ions are formed. In comparison to such hallow ion formation, thecapture of two or more electrons in low lying states is more complex because ofCoulomb screening and electron-electron correlations.Because of the fact that Auger rates are high for low z p , low for high z p ,and moderate for intermediate z p , the data points governed by Schiwietz for-mula are fitted well with two straight lines as shown in Fig.3(a). With similaranalogy, N ec reflects the variation of Auger and radiation decay rates with z P .In contrast, the q bm data fit well with a straight line implying that the chargechanging process in the bulk is independent of the decay modes because fastAuger transition is not possible at high frequency, ion-solid collisions.In astronomical environments, the CX is an important aspect of atomic col-lisions in gas phase [24]. Besides, it plays a significant role in ion-solid collisionsbecause of the existence of amorphous and crystalline silicates, refractory oxidesof magnesium, aluminum, silicon, and iron in the majority of O-rich envelopes,and, SiC in C-rich and AGB stars [25]. Further, amorphous organic solids,widely observed in a range of environments in the galaxies [26] are also heav-ily influenced by CX. Apart from this, CX is significant in basic and appliedphysics, viz., surface modification of solids by SHI at nano scales [27-30].As bulk and surface for gas targets are undefined, the concept of only meancharge state (q m ), which is analogous to q tm in solids, is introduced. Generally,the q tm in solid is expected to be higher than that in gas target [10] because ofthe high density. However, this fact is not true as in experiments, rather a bithigher value of q m is observed [31]. This effect is attributed to the CX at exitsurface in solids. Therefore, the surface contribution is extremely important indeciding the charge strippers for accelerators [32].Having charge exchange at the exit surface, the resulting ions have to elapse8 long while before they are counted in the detector placed at the focal plane.In this duration, the z p dependent auto-ionizing decay is highly probable. Asthe difference of q bm and q tm is also z p dependent, the net number of electronstransferred (net charge-exchange) as measured by the detector is governed bythe charge exchange as well as autoionization processes. The former lowersthe projectile charge state and the latter increases the same. Therefore, actualcharge exchange at the exit surface of the foil can be larger than the net chargeexchange, N ec = q bm - q tm , depending upon z p . For instance, Auger rates areso large for the light ions that all the excited states can be autoionized beforethey are detected. Hence, N ec ≈ z p ≈
15 and it increases with z p owing toincreasing radiative rates. The N ec for high z p , say, for Uranium, stands for thecharge exchange at the exit surface of the foil as the Auger rate is almost zero.The charge changing process in the bulk material and charge exchange phe-nomenon at the exit surface can be summarized in a five-stage model as shownin Fig. 4. In the first stage, the ions have to spend a long while before ap-proaching the target and hence, lie in the ground state. In the second stage,before entering to the target, the entrance surface electrons are polarized andpulled out by the projectile ions and finally, are placed into Rydberg states. Inthe third stage, such states will be re-ionized in the high-frequency collisionsinside the bulk. Here, many more electrons lying in the ground state are alsoionized enhancing the projectile charge state. Further, innershell vacancies arecreated in the high-frequency collisions and thus, the observation of K-x rays.In the fourth stage, as highly charged ions cross the exit surface, many electronscan be picked up and placed in the high lying states including the Rydberg andcircular Rydberg states. The properties of the states so formed can differ de-pending on z p . Up to z p = 15, Auger rates are many orders of magnitude higherthan radiative decay rates. For z p ≈
25, the Auger or radiative decay rates arecomparable. In contrast, for z p ≥
47, radiative decay rates are many ordersof magnitude higher than Auger rates and the high lying states so formed aretermed as circular Rydberg states, possessing highest magnetic quantum num-ber as observed in several experiments [9,33]. These states undergo neither9uger transition nor fast radiative decay because of restriction on the dipoleselection rules ∆ l = ±
1. They decay only through a cascading chain and takea considerable time to relax into the ground states. The decay through chainalso continues during flight between source and detector. If time taken by theprojectile ions to reach to the detector is more than the cascading time, i.e., T ( n, l ) > (cid:80) τ ( n, l ), where τ ( n, l ) is the lifetime of the circular Rydberg statewith quantum numbers n and l , the ground state is achieved. Otherwise, thestate lies somewhere in the middle of the cascading chain as shown in the fifthstage of the model. Whatsoever, the ionic state of projectile remains intact asseen by the electromagnetic analyzer.To conclude, the electromagnetic methods for charge state analysis providean integral measure of the charge changing processes in the bulk and chargeexchange phenomenon at the exit surface of the foil. However, disentanglingthese two contributions are essential for many applications, e.g., x-ray emis-sion of many astrophysical objects, the infrared emission bands from range ofenvironments in the galaxies, accelerator physics, ion energy losses in solids,cancer therapy and ionization by heavy ions, and the surface modifications innano scales. Accordingly, we have employed the x-ray spectroscopy techniqueto measure the mean charge states of swift heavy ions evolved due to the chargechanging process only in the bulk of the carbon foils. We find that the meancharge states so measured by the two methods are very different, because x-raytechnique takes account of q bm , whereas q tm is deduced by the electromagneticanalyzer; the q bm being higher than q tm . Theoretical prediction of q bm are madeusing a simple model assuming that the target electrons form a Fermi-gas, withwhich the swift heavy ions interact. For a series of measurements with severalions (z = 22-35) in the energy range 1.5-3.0 MeV/u, a very good agreement isseen between the present experiments and theory. The q tm s of the ions as mea-sured by electromagnetic methods are also evaluated accurately by an improvedformula. The q bm - q tm is a measure of the net charge exchange process responsi-ble at the exit surface of the foil. Very surprisingly, for 1 MeV/u uranium ions,up to tens of electrons per event participate in charge exchange process at the10urface of the carbon foils. Acknowledgement
We would like to acknowledge the co-operation and support received fromthe Pelletron accelerator staff and all colleagues of the atomic physics group,IUAC, New Delhi.