Inelastic processes in Na + − Ne, Ar and Ne + , Ar + − Na collisions in energy range 0.5−14 keV
aa r X i v : . [ phy s i c s . a t o m - ph ] O c t Inelastic processes in Na + − Ne, Ar and Ne + , Ar + − Na collisions in energyrange . − keV R. A. Lomsadze , M. R. Gochitashvili , R. Ya. Kezerashvili , Tbilisi State University, Tbilisi, 0128, Georgia New York City College of Technology, The City University of New York, Brooklyn, NY 11201, USA The Graduate School and University Center,The City University of New York, New York, NY 10016, USA (Dated: July 9, 2018)Absolute cross sections for charge-exchange, ionization and excitation in Na + − Ne and Na + − Arcollisions were measured in the ion energy range 0 . −
10 keV using a refined version of a capacitormethod, and collision and optical spectroscopy methods simultaneously in the same experimentalset-up. Ionization cross sections for Ne + − Na and Ar + − Na collisions are measured at the energiesof 2 −
14 keV using a crossed-beam spectroscopy method. The experimental data and the schematiccorrelation diagrams are used to analyze and determine the mechanisms for these processes. For thecharge-exchange process in Na + − Ar collisions two nonadiabatic regions are revealed and mecha-nisms responsible for these regions are explained. Structural peculiarity on the excitation functionfor the resonance lines of argon atoms in Na + − Ar collisions are observed and the possible mech-anisms of this phenomenon are explored. The measured ionization cross sections for Na + − Ne andNe + − Na collisions in conjunction with the Landau-Zener formula are used to determine the couplingmatrix element and transition probability in a region of pseudo-crossing of the potential curves.
PACS numbers: 34.80.Dp, 34.70.+e, 34.50.Fa, 32.80.Zb
I. INTRODUCTION
Studies of inelastic processes in slow ion–atom collisions yield extensive data in a quasimolecular mech-anism of interaction between the colliding particles. Molecular terms of the system of colliding particlesare used in the description of inelastic processes in ion–atom collisions. At present, such terms havebeen calculated for only a small number of simple systems, so that schematic correlation diagrams formolecular orbitals are widely used but provide only a qualitative explanation of the known features ofthese processes. However, theoretical calculations alone are insufficient for the complete understanding ofthe interaction picture due to complicated many–channel character of the processes under investigation.Moreover, because different mechanisms are active at various internuclear distances their study requiresseveral experimental techniques all working together to make a consistent interpretation possible.On the experimental side, for investigation of the molecular potential curves of a scattering system a setof differential cross sections for various channels following these potential curves are needed. However,due to the limited energy resolution of the differential scattering technique most often is problematican identification of the specific final states, and only possible a determination of two groups of levelscorresponding to one– and two–electron excitation. Thus, in order to infer the differential scatteringcross section which results when the system follows specified molecular potential curves on the incomingand outgoing portions of the trajectory, differential energy–loss spectra must be supplemented by crosssections for a photon emission and electron ejection as a function of the respective energies.Despite many experimental studies of the alkali ion–gas collisions, which have been carried out byvarious experimental methods [1–23] available data for the absolute cross section for the most inelasticprocesses are contradictory [1–3, 10, 13] and in some cases unreliable [4].The inelastic collision mechanism has been studied experimentally and theoretically for the systemsLi + –He and Li + –Ne in Refs. [8, 9, 18, 24, 25]. Double differential cross sections have also been measuredin Ref. [12].The results of the measurements of the excitation function for Na + –He and K + –He colliding pairsin arbitrary units are reported in Refs. [5] and [6]. A relative differential cross section for Na + –Ar ismeasured in Ref. [17]. The absolute values of the differential cross section at two fixed energies E = 200eV and E = 350 eV of Na + ions were determined by using the experimental integral cross sections and therepulsive potential deduced also experimentally are reported in Ref. [11]. Excitation processes in Cs + –Arcollisions were studied at laboratory collision energies of 0.2–1 keV by means of differential scatteringspectroscopy in Ref.[21]. Recently in Ref. [23] a comprehensive study of excitation mechanisms in Na + –He and K + –He collisions at ions energies range of 1.0–1.5 keV by differential scattering spectroscopy wasreported. Double differential cross sections were measured by detecting all scattering particles (Na + ,Na, K + , K, He + and He) over a wide range of center-of-mass scattering angles. A systematic studyof inelastic processes in K + –He collisions is presented in Ref. [22]. Absolute cross sections for chargeexchange, ionization, stripping, and excitation in K + –He collisions were measured in the ion energy range0.7–10 keV.For Na + –Ar collisions an energy spectrum of electrons ejected from autoionizing states of Ar atoms at E = 15 keV [15] have been briefly reported, but no results exist for lower energy collisions.The most comprehensive approach to study ion-atom collisions with closed electron shells has so farbeen carried out only for a Na + –Ne pair [16]. Though, measurements were performed at a limited energyinterval. Therefore, in our study attention will be focused on the extension of the energy interval from0.7 to 10 keV.In earlier publication [19] we have reported limited results for inelastic processes realized in Na + –Arcollisions. In the present study, the differential cross section as well as the energy loss spectrum forNa + –Ar collisions will be investigated additionally over a wide range of energy and scattering angles.To our mind the reason for a lack of systematic measurements and reliable data for alkali metal ionsand rare gas atoms collisions, and having not at all measurements for inert gas ions collisions with alkalimetal atoms are linked with experimental difficulties. Mainly, in the case of the alkali metal ions and raregas atoms collisions these difficulties related to collections and detections of secondary particles, while,in case of the rare gas ions and alkali metal atoms collisions mostly related to the preparation of alkalimetal atoms as a target.The lack of systematic absolute cross sections measurements for Na + − Ne and Ne + − Na colliding pairsmotivated the present detailed investigation of the primary mechanisms for these collision processes.The collision of a Na + ion beam with Ne and Ar atoms leads mainly to the following processes:Na + + Ne → Na + Ne + , (1) → Na + + Ne + + e, (2) → Na + + Ne ∗ , (3)and Na + + Ar → Na + Ar + , (4) → Na + + Ar + + e, (5) → Na + + Ar ∗ . (6)In the charge-exchange processes (1) and (4) the Na atom and Ne + or Ar + ion can be in the groundstates or in different excited states. The reactions (2) and (5) represent the ionization processes for thetarget atoms, that include different channels for the excitation of the Na + ion or/and Ne + (Ar + ) ion,as well as the excitation of autoionization states of the target atom that leads to its ionization. Theexcitation processes (3) and (6) include different channels for excitation of the Na + ion or/and Ne(Ar)atom.In collisions of Ne + and Ar + ions with a Na atom let’s consider only charge-exchange and ionizationprocesses: Ne + + Na → Ne + Na + , (7) → Ne + + Na + + e (8)Ar + + Na → Ar + Na + , (9) → Ar + + Na + + e, (10)The processes (7) and (9) represent the charge-exchange reactions when the Ne(Ar) atom and Na + ion can be in the ground state or in different excited states, while a result of the ionization reactions (8)and (10) includes different channels for the excitation of the Na + ion or/and Ne + (Ar + ) ion, as well asexcitation of autoionization states of the target atom that leads to its ionization.The simultaneous study of the processes (1) and (7), as well as (4) and (9), when productsof the reactions are in the ground states represent a fundamental interest because they are the re-versible processes. A symmetry of these processes arises from the concept of time reversal. Thesymmetry transformation that changes a physical system with a given sense of the time evolutioninto another with the opposite sense is called time reversal. The symmetry of these processes meansthat the probabilities for the processes Na + +Ne → Na( g.s. )+Ne + ( g.s. ) ( g.s. hereafter refers as theground state) and Na + +Ar → Na( g.s. )+Ar + ( g.s. ) are the same as the probabilities for the reversed pro-cesses Ne + +Na → Ne( g.s. )+Na + ( g.s ) and Ar + +Na → Ar( g.s. )+Na + ( g.s. ) . This reciprocity leads to theimportant principle of detailed balance that relates the cross section, for example, for the reactionNa + +Ne → Na( g.s. )+Ne + ( g.s. ) with that of the time-reversed reaction Ne + +Na → Ne( g.s )+Na + ( g.s. ) . Motivated by the CP violation found in the neutral kaon system [26], several tests of time reversal in-variance in low-energy nuclear physics have been performed in the weak, electromagnetic, and stronginteractions and were consistent with the time irreversibility [27]. Since an experimental test of the de-tailed balance and time irreversibility in the reactions AI+ p ⇆ Mg+ α [28] this problem still remainsessential and important [29]. The detailed balance and time irreversibility have been also studied in ki-netics [30]. In our best knowledge there is no studies of time irreversibility and detailed balance in atomiccollisions. The above mentioned processes are good candidates for the such test. However, experimentaldifficulties of identifications of the ground states of the charge-exchange products do not allow us toproceed accurate measurements. Though this task poses challenges, they are challenges we are ready toface.A simultaneous study of the ionization processes (2) and (8), as well as (5) and (10) also represent aparticular interest. A close attention to the reactions (2) and (8), and (5) and (10) shows the similarity ofthe reactions products. One of the objectives of this work is to show that in some cases (e.g. for Na + − Ne)the information extracted from the theoretical calculations can be obtained experimentally using a simpleapproach, namely by measuring a relative ionization cross section for Na + − Ne and Ne + − Na collidingpairs.Below we report the absolute total and differential cross sections for charge-exchange, ionization aswell as the excitation of the both the projectile and target particles and energy loss spectra in collisionsof Na + ions with Ne and Ar atoms, and Ne + and Ar + ions with a Na atom. In later case, the cross sectionof ionization will be reported for the first time.The remainder of this paper is organized in the following way. In Sec. II the experimental set-upsand procedures are described and four different experimental methods of measurements for collisionexperiments are presented. Here we introduce the procedures for measurements of the absolute total anddifferential cross sections for charge-exchange, ionization and excitation. Results of measurements for theprocesses (1)–(3), (4)–(6), (8), and (10), the comparison of our measurements with results of previousexperimental studies, and discussion of mechanisms for different processes occurring in Na + –Ar collisionare given in Sec.III. The method and procedure for estimation of some theoretical parameters (transitionprobability, matrix element) from our experimental results are reported in Sec. IV. Finally, in Sec.V wesummarize our investigations and present the conclusions. II. EXPERIMENTAL SET-UPS AND PROCEDURES
The basic experimental approaches used in the present experiments for measurements of total and dif-ferential cross sections of ionization, charge-exchange and excitation processes are the following: crossed-beam spectroscopy method, refined version of a capacitor method, collision and optical spectroscopymethods. The basic experimental set-up for measurements of the total and differential cross sectionsof ionization, charge-exchange and excitation processes in collisions between Na + ion and Ne and Aratoms was discussed previously in detail in Ref. [22], so the only brief description will be given here. Theuniqueness of our experimental approach [22] is that for colliding pairs Na + − Ne and Na + − Ar involvedin the above mentioned processes the quality of the beam as well as the experimental conditions alwaysremain identical because the experimental apparatus has three collision chambers. The latter allows touse a refined version of the capacitor method, collision spectroscopy method, and optical spectroscopymethod under the same “umbrella.” For the experimental measurements of the ionization cross section
FIG. 1: Schematic diagram of the experimental set-up for study of collisions of ions with alkali metal atoms. in collisions between Ne + and Ar + ions and an alkali–metal atom a new experimental set-up is developedusing a crossed–beam spectroscopy method. Details of the apparatus and description of the method arepresented below. A. Crossed–beam spectroscopy method
Measurements of the ionization in collision of ions with alkali–metal atoms are related to well known dif-ficulties: preparation of the target; determination of its density; protection of the surface of an ionizationchamber and insulators from desorption of a metallic vapor, etc. In the present study, for measurementsof the ionization cross section of alkali metal atoms, we are using the method of intersected beams. Thismethod of measurement of the ionization cross section has some advantage compared to other methods.Particularly, in the framework of the method, there is no need to avoid the scattering of an incident beam(as it is peculiar e.g. for a capacitor method) and secondary particles (recoil ions and electrons) on acollector, the emission of electrons from the surface of collectors, etc. The idea of crossed–beam methodwas suggested in Ref. [31], and used to study the ionization and charge transfer in proton–hydrogenatom collisions. Here this method is significantly elaborated and for the first time is used to investigatethe ionization of alkali metal atoms. A schematic drawing of the apparatus for the measurement of theionization cross section is shown in Fig. 1. The core part of the experimental set-up consists of the ionsource, magnetic mass-analyzer, ionization chamber, source of an atomic beam, system for collection oflight from the crossing beam region and spectrometer for analyzing of the radiation.A primary ion beam from a 30 MHz radiofrequency ion source, using permanent longitudinal magneticfield, passes through the single channel capillary formed by the collimating slit and enters into theionization chamber and is collected by an ion collector. An input of high-frequency power in dischargewas carried out by an inductive connection. The power needed to cause the discharge in the ion sourcewas about 150 W. The formation of a plasma pinch in the extraction region is possible by the Pyrex cupand stainless steel capillary. The extraction voltage is 1.0-2.5 keV and the density of the ion beam in theionization chamber (after passing the magnetic mass–analyzer and collimating slit) is about 0.1 mA/cm .A neutral atom beam emerged from an aperture and passed through a collimating slit and directedinto the interaction area of the ionization chamber. The atomic beam itself is formed by an extractionnozzle of an oven, where an alkali metal vapor is generated. A diameter of the nozzle is 0.6 mm, whilethe length of the channel is 6 mm. The oven is made from a tantalum with a massive cone which isscrewed on a crucible with the evaporated metal. The heating of the oven is performed by the currentof 1.8–2.0 A. The evaporated metal temperature is measured and controlled by the thermocouple that ismounted on the oven. At the exit from the oven at the distance of 10 mm from the nozzle the density ofthe sodium atoms beam compose 0.3 × –3 × cm − . The primary ion beam and the modulatedatomic beam cross each other perpendicularly at the interaction area of the ionization chamber that issurrounded by magnetic and electric fields. The magnetic field is created by the Helmholtz coils, while theuniform electric field is produced by the set of circular electrodes. Both fields are parallel to each other,opposite directed and perpendicular to the ion and the modulated atomic beams. The atomic beam thatis not shown in Fig. 1 is perpendicular to the drawing plane. The magnetic field allows determinationof the crossing beam region from where the electrons are collected onto the collector, while the uniformelectric field is needed for transporting these electrons towards the electron collector for the registration.Electrons formed in the ionization chamber, as a result of collision of the ionic and atomic beams arecollected by the collector of electrons. The electrons, those are produced mostly in the crossing region ofthe ion and atomic beams, due to the presence of transverse magnetic field can escape from the crossingregion just transversely with respect to the direction of the ion beam. The strength of the magnetic fieldaccounts 100-200 Oersted. This means that the shift towards the longitudinal direction does not exceed1 − λ = 585 . – 3s[1/2] ) excited by the proton at an energy of 10 keV. The cross section of this line is known [35],and the wave length of the line sufficiently close to the wave length of resonance lines of a Na doublet.As to the concentration of Ne atoms in the region of collection of the electrons, it could be measuredby a simple and reliable method – by measuring the pressure of neon in the collision chamber, using anionization manometric lamp, calibrated by a compression manometer of Macleod gauge.The sources of measurement uncertainties of the method are mostly related to the nature of the vapor–metallic target, impossibility of quick shutdown of the target, the increase of surface conductivity ofan insulator due to condensation of Na vapor, and the presence of heated elements in the ionizationchamber. All these uncertainties were minimized in our measurements. The resultant uncertainty of themeasurements is estimated as 15%, and is linked mainly with the measurement of the Ne pressure, theaccuracy of which is estimated as 7%. B. Refined version of a capacitor method
A beam of Na + ions from a surface-ionization ion source is accelerated and focused by an ion – opticssystem, which includes quadruple lenses and collimated slits [22]. After the beam passes through amagnetic mass spectrometer, it enters the collision chamber containing Ne and Ar gases. The pressurein the collision chamber when there is no a Ne or Ar target gas is kept at about 10 − Torr, while thetypical pressure under operation is 10 − Torr, which is low enough to ensure single–collision conditions.The charge–exchange and ionization cross sections were measured by a refined version of the capacitormethod [36]. In an earlier paper [4] the measurements were performed by the standard transfer electricfield method. It is the customary procedure to use one of the central electrodes as the measurementselectrode. We consider that such an approach is the reason for significant errors in measurements [4]because scattered primary ions may strike the electrodes used for measurements. To avoid this deficiencywe used a refined version of the transfer electric field method by shifting from the central electrode (astandard method) to the first electrode (towards the beam entrance side). In this case the defeat of theelectrodes by the scattered primary ions that affects the results of measurements is substantially reduced.Due to fringing effects at the edges of this electrode a system of auxiliary electrodes between the firstelectrode and the entrance slit were installed. These auxiliary electrodes create a uniform potential nearthe first electrode. The first electrode, the auxiliary electrodes, and the entrance slit are all positionedtogether as close as possible. This close arrangement limits the scattering region of the beam to theentrance side. The primary ions are detected by the Faraday cup. The particles (secondary positive ionsand free electrons) produced during collision are detected by a collector. The collector consists of tworows of plate electrodes that run parallel to the primary ion beam. A uniform transverse electric field,responsible for the extraction and collection of secondary particles, is created by the potentials appliedto the grids. This method yields direct measurements of the cross section σ + for the production of singlypositively charged ions and σ − for electrons as the primary beam passes through the gas under study.These measured quantities are related in an obvious way to the capture cross section σ c and the apparentionization cross section σ i and are determined as σ + = σ c + σ i , σ − = σ s + σ i . (11)In (11) σ s is the stripping cross section of the incident ion. The ionization cross section σ i is always largerthan the cross section for stripping σ s . For Na + − Ne collisions, the uncertainty in the measurements of charge–exchange and ionization crosssections are estimated to be 15%. This is determined primarily by the uncertainty in the measurementof the absolute values of the cross sections σ + and σ − and by the uncertainty in the measurement of atarget gas pressure in the collision chamber.For Na + − Ar collisions, the uncertainty in the measurements of the absolute values of the cross sections σ + and σ − is estimated to be 15% over the entire energy interval studied. This is determined primarily bythe uncertainty in the measurement of the target gas pressure in the collision chamber. The uncertaintyin the determination of the ionization cross section σ i , is estimated to be 15% over the energy range andit is determined by the error in the measurement of σ − . The uncertainty in the measurements of thecapture cross sections σ c at the energy less than 2 keV is estimated to be 15%, while at the energy 5 keVand above the uncertainty does not exceed 25%. For Na + − Ar collisions at the energy less than 2 keVthe cross section σ + is significantly larger than σ − . Accordingly, the error in the determination of thecapture cross section σ c in this energy region is related primarily by the error in the measurement of σ + . With increasing of the Na + beam energy the cross sections σ + and σ − becomes more nearly equal. As aresult the error in the determination of σ c increases. C. Collision spectroscopy method
The energy–loss spectra and differential scattering experiments have been performed with a collisionspectroscopy apparatus. Since the details of the apparatus have been given elsewhere [37], only a briefdescription will be given below.The primary beam extracted from the ion source was accelerated to the desired energy before beinganalyzed according to q / m ( q and m are the ion’s charge and mass, respectively). The analyzed ionbeam was then allowed to pass through the collision chamber by appropriately adjusting the slits priorto entering into a “box” type electrostatic analyzer. The energy resolution of this analyzer is ∆ E/E = 1/500. Automatic adjustments of the analyzer potentials gives the possibility for investigation of theenergy–loss spectra in the energy range of 0–100 eV. The differential cross section is measured by rotatingthe analyzer around the center of collisions over an angular range between 0 ◦ and 25 ◦ . The laboratoryangle is determined with respect to the primary ion beam axis with an accuracy of 0.2 ◦ .For the measurements of the charge–exchange differential cross section the charge component of scat-tered primary particles realized in the collision chamber is separated by the electric field and neutralparticles formed by electron–capture collisions are registered by the secondary electron multiplier. Sucha tool gives us the possibility to determine the total cross sections and to compare them with the resultsobtained by the refined version of the capacitor method [36]. In addition, the measured energy–loss spec-trum gives detailed information related to the intensity of inelastic processes realized in the excitation,charge–exchange and ionization processes. D. Optical spectroscopy method
The method used for the optical measurements have been described previously [38], therefore a briefdescription will be given here. The alkali metal ion beam leaving the surface–ionization ion source is firstaccelerated to a predetermined energy. It is then focused by the quadruple lenses and analyzed by the massspectrometer. The emerging ions passed through a differentially pumped collision chamber containingthe target gas at low pressure. The ion current is measured by the collector and the light emitted,as a result of the excitation of colliding particles, from the collision chamber is viewed perpendicularlyto the beam by a spectrometer. The spectral analysis of the radiation was performed in the vacuumultraviolet as well as in the visible spectral regions. The linear polarization of the emission in the visiblepart of the spectrum is analyzed by the Polaroid and the mica quarter-wave phase plate in front of theentrance slit of the monochromator. The phase plate is placed after the polarizer, is rigidly coupled to it,and used to cancel the polarizing effect of the monochromator. A photomultiplier tube with the cooledcathode is used to analyze and detect the emitted light. The spectroscopic analysis of the emission in thevacuum ultraviolet region is performed with the Seya-Namioka vacuum monochromator, incorporating atoroidal diffraction grating. The radiation was recorded by the secondary electron multiplier used underintegrating or pulse-counting conditions. The outputs of the photomultiplier and the secondary electronmultiplier were recorded by the electrometers. The polarization of the radiation in the vacuum ultravioletwas not taken into account. The absolute excitation cross sections for the resonance lines of sodium thatare determined by comparing the measured output signal with one that due to the excitation of a nitrogenby an electron impact. A particular attention is devoted to the reliable determination and control of therelative and absolute spectral sensitivity of the light–recording system. This was done by measuring thesignal due to the emission of molecular bands and atomic lines excited by electrons in collisions with H ,N , O , and Ar. For this, an electron gun was placed directly in front of the entrance slit of the collisionchamber. The relative spectral sensitivity, and the values of the absolute cross sections, is obtained bycomparing the cross sections for the same lines and molecular bands reported in Refs. [39–43]. Theuncertainties in the excitation cross sections for the Na + − Ar system are estimated to be 20% and theuncertainty of the relative measurements does not exceed 5%.
III. EXPERIMENTAL RESULTS AND ANALYSIS
In what follows, the results for Na + ion collisions with the Ne and Ar atoms and Ne + and Ar + ionscollisions with the alkali metal target atom Na are presented and the findings are compared with datafrom the literature. The results for the cross section measurements are shown in Figs. 2–6. The energydependences of the charge–exchange, ionization and excitation for Na + –Ne and Na + –Ar collisions arepresented in Figs. 2, 3 and 4, respectively. Here for the comparison we also present data of other authors.Results of the first measurement of the energy dependence of ionization cross sections for the processes(8) and (10) are presented in Fig. 5. Fig. 6, where we plot the reduced cross section ̺ = θ sin θσ ( θ ) versusreduced angle τ = Eθ, shows the typical example of angular and energy dependences of differential crosssections in the laboratory system when Na + ions are scattering on the Ar atoms at a fixed energy E = 5 Ion energy (keV) C ha r ge e xc hange c r o ss s e c t i on ( - c m ) (x5) / / // FIG. 2: Dependences of the absolute charge–exchange cross sections on energy of a Na + ion in Na + − Ne andNa + –Ar collisions. Curves: 1 – Na + –Ne, present data; 1 ′ – Na + − Ne, data from Ref. [16]; 1 ′′ – Na + − Ne, datafrom Ref. [4]; 2 – Na + − Ar, present data; 2 ′ – Na + − Ar, data from Ref. [4]; ◦ – Na + − Ar, electron capture inresonance state, data from Ref. [17]; (cid:3) – Na + − Ar, electron capture with the excitation of target ion, data fromRef. [17] are multiplied by factor of 5. keV . The reduced scattering angle is defined as τ = Eθ, where E is the energy of the incident beam inkeV and θ is a scattering angle in degrees. The filled squires in Fig. 6 represent the elastic scattering ofthe Na + ions, while by the solid circles are shown results of the direct excitation of the Ar atoms in 4pand 3d Rydberg states. In addition, we estimated the electron energies released in Na + − Ne and Na + − Arcollisions. The estimates were obtained from the measurements of the dependences of electron currentin the measuring electrodes on the potential applied to these electrodes for the collection of electrons. Itwas found that the energy of the most liberated electrons is below 10 −
15 eV.The results for the charge-exchange cross section for Na + − Ne and Na + − Ar collisions along with thedata from literature are shown in Fig. 2. The comparison of our measurements for the charge–exchangecross section with the results obtained in [16] at two fixed energy E = 1 keV and E = 2 keV showsexcellent agreement. However, a dramatic difference by about 2 orders in the magnitude, as well as inthe behavior of the energy dependences are observed, when one compares our results with the resultsobtained in [4]. The same tendency, but the discrepancy in the magnitude by about 1 order observedwhen one compares our results for the Na + − Ar pair with the data from Ref. [4]. Our results for thecharge–exchange processes (1), (4) can be compared with the cross sections obtained in Ref. [17] byintegrating the differential cross section over the scattering angle for an electron capture and a capturewith the excitation of a target ion at energy of E = 1 . . × − cm and 1 . × − cm , respectively. This comparison shows that the discrepancy is threefold.The results for the ionization cross section for Na + − Ne and Na + − Ar collisions along with the data ofprevious measurements are shown in Fig. 3. The comparison of our ionization cross section for the process(5) with the results obtained in [4] shows a satisfactory agreement at low energies but the discrepancyincreases for the energies of ions
E > + − Ne collision between our results and the results from [3], especially in the energy dependence of thecross sections. A rather significant discrepancy is observed if one compares our results with the resultsreported in Ref. [10]. Within the accuracy of measurements an excellent agreement is observed between / / // (x2)1 /// I on i z a t i on c r o ss s e c t i on ( - c m ) Ion energy (keV)
FIG. 3: Dependences of the absolute ionization cross sections on energy of Na + ion in Na + − Ne and Na + − Arcollisions. Curves: 1 – Na + − Ne, present data; 1 ′ – Na + − Ne, data from Ref. [3]; 1 ′′ – Na + − Ne, data from Ref.[10] are multiplied by a factor of 2; 1 ′′′ – Na + − Ne, data from Ref. [16], at fixed E = 2 keV; 2 – Na + − Ar, presentdata; 2 ′ – Na + –Ar, data from Ref. [4]. our results and the results obtained in Ref. [16] at a fixed ion energy E = 2 keV.The excitation function for Na + − Ar collisions is presented in Fig. 4. Our data of the excitationfunction for the resonance lines of sodium (curve 1) and argon atoms (curves 2 and 3) can be comparedonly with the results obtained in Ref. [17] and only for the collision energy of E = 1 . ′ states (curves 2 and 3, respectively)are in reasonable agreement with the data obtained in [17].To the best of the authors’ knowledge in the energy range considered there are no experimental mea-surements of the ionization cross sections for the process of ionization of alkali metal Na by Ne + andAr + ions. The first measurements of the absolute ionization cross sections for Ne + − Na and Ar + − Nacollisions are presented in Fig. 5. As it seen from Fig. 5 the value of the ionization cross section stronglydepends on the mass ratio of the colliding particles. In case of Ne + − Na collisions when the mass ratioof the colliding particles is close to 1, the cross section is larger by a factor of 2 in comparison to theasymmetric case of Ar + − Na collisions when the mass ratio is greater than 1.Distinct features are observed in the differential cross section (DCS) as a function of the reduce scat-tering angle τ shown in Fig. 6. The DCS with the excitation of Ar atoms is smaller than the DCS forthe elastic scattering. Another feature is the alternative behavior of the DCS at small angles: the elasticscattering increases at the small angles, while the DCS of the Rydberg states of Ar decreases. The moststriking feature is that the ratio of the elastic scattering to the excitation cross sections strongly increasesfor small values of τ, while for τ >
20 only varies relatively weakly.The data obtained in this study can be used to make certain conclusions related to possible mechanismsof the investigated processes. To explain these mechanisms one can use a schematic quasimolecular termsfor the system of colliding particles. The quasimolecular nature of the interaction of the above consideredcollision partners can be visually manifested by a representative Na + − Ar colliding pair. Therefore, belowwe discuss the mechanisms of the realized processes for this colliding pair. The corresponding schematiccorrelation diagram constructed based on Bara – Lichten rules [44] is presented in Fig. 7.0
Ion energy (keV) E m i ss i on c r o ss s e c t i on ( - c m ) FIG. 4: Excitation function for sodium and argon atomic lines in Na + − Ar collisions. Curves: 1 – NaI ( λ = 389 . − . λ = 104 . ′ –3p transition); 3 – ArI ( λ = 106 . ◦ and (cid:3) denote the excitation of sodium and argon atoms, respectively, obtained in Ref. [17]. A. Charge exchange in Na + − Ar collisions
For determining the processes responsible for the charge exchange in Na + − Ar collisions, we comparethe total charge exchange cross sections (curve 2 in Fig 2.) with the total cross section of radiation for theresonant lines λ = 389 . − . + − Ar collisionsincreases with the increase of the ion energy, amounting to ∽ × − cm for the ion energy E = 1 . ∽ × − cm for E = 5 − E = 0 . − . E = 3 − E = 2 keV) takes place as a result of the electron captureinto the ground state of a Na atom with the formation of the argon ion in the ground state as well. Theprocess realizes through the channel Na + (2p )+Ar(3p ) → Na(3s)+Ar + (3p ), with the energy defect of∆ E = 10 . + (2p )+Ar(3p ) → Na(3s)+Ar + (3p ( D)4s] − + (3p )with the ground state of the system Na + (2p )+Ar(3p ). Since the Na + (2p )+Ar(3p ) state has only Σsymmetry it follows that the Σ − Σ transition play a dominant role in the low–energy charge–exchangeprocesses. At the energy range
E > + (2p )+Ar(3p ) → Na(3p)+Ar + (3p ) − . − Π transitions (see Fig. 7) associated with the rotation of internuclear axis play a certain role in1 I on i z a t i on c r o ss s e c t i on ( - c m ) Ion energy (keV) FIG. 5: Dependence of the absolute ionization cross sections on energy of Ne + and Ar + ions in Ne + − Na andAr + − Na collisions. Curves: 1 – Ne + − Na; 2 – Ar + − Na. the electron capture to the excited 3p states.
B. Ionization in Na + –Ar collisions Experiments show that the mechanism of ionization in Na + –Ar collisions is characterized by the releaseof predominantly slow electrons with the energies E <
15 eV. In order to determine the channel andmechanism of ionization, we estimate the contribution of several inelastic processes that result in emissionof slow electrons. To estimate the contribution of direct ionization, we calculated the cross section of thisprocess using the results obtained in [45]. According to [45] in the limit of an united atom, the processof ionization is associated with the emergence of the diabatic energy level to the continuum in the rangeof the nonadiabatic interaction of molecular orbitals with the same orbital angular momentum. Analysisof correlations of molecular orbitals in the Na + –Ar system shows (Fig. 7) that the 3p electrons of Aratom, whose ionization is considered, in the limit of the united atom correspond to the 4d electrons ofthe Cu + ion. Thus, for the estimated cross section we choose the orbital angular momentum l = 2. Thebinding energy E nl of electrons in the nonadiabaticity region was assumed to be equal to the bindingenergy of 4d electrons of the Cu + ion. The effective charge Z eff was determined by the interpolation ofthe results obtained by Hartree in Ref. [46]. For the 4d electrons of the Cu + , we obtained Z eff = 3 . + ion correlate withthe 4f electrons of the Cu + ion. For this reason, to estimate the cross section we chose the value for theorbital angular momentum l = 3 and assumed that Z eff = 3.1. In other words, the same as for the 4delectrons of the Cu + ion. One also should estimate the contribution of the stripping process. As a result2
10 20 30 40 50 60110 () a r b . un i t s ) keV deg)12 (x10) FIG. 6: Differential cross sections for Na + − Ar collisions as a function of reduced scattering angles at a beamenergy E = 5 keV. (cid:4) – the DCS of the elastic scattering. • – excitation of the Rydberg states of Ar [3p ( P)4p;3p ( P)3d]. The later data are multiplied by factor of 10. of calculation we found that the contribution of stripping to the total electron yield cross sections is 0 . .
5% for the ion energy of 6 keV. Consequently, we can concludethat the contribution of these processes to the ionization cross section is insignificant in the entire energyrange.The double ionization of Ar atom and capture accompanied by ionization of Ar ion evidently make asmall contribution to the ionization cross section. There are two reasons for this: the absence of pseudo-crossings of the corresponding quasimolecular terms with the ground state term as it seen from diagramin Fig. 7, and the large energy defect for these processes, 43 . . −
15 eV, we draw the conclusion that the main mechanism of their emergence (along with the contribu-tion of other channels) is associated with the decay of autoionization states in an isolated atom. Accordingto Refs. [15] and [17], these states are those with two excited electrons Na + (2p )+Ar(4s) → Na + (2p )+Ar[3p (1D)4s ; 4p ] − . C. Excitation processes in Na + − Ar collisions
Let us consider the excitation mechanisms in Na + − Ar collisions. The most interesting is explorationof the excitation function in Fig. 4 for the argon atom lines λ = 104 . λ = 106 . ′ –3p that show oscillatory structures (curve 2 and 3, respectively). It can be seen fromthe correlation diagram in Fig. 7, the excitation of the Ar(4s) state can occur as a result of i) Σ − Σtransition between the entrance energy level [Na + (2p ) − Ar (3p )] and the level corresponding to theexcitation of the argon atom [Na + (2p ) − Ar (3p ´ )] or ii) due to the 4p–4s cascade transition in anisolated atom. In the later case the state 4p of the excited argon atom is due to the rotational Σ − Πtransition at small internuclear distances. Indeed, the observed oscillatory structure, a comparativelysmall cross section σ ∼ − cm , and a large oscillation depth of the curves 2 and 3 in Fig. 4 indicate,according to [47], that namely the contribution of the rotational Σ − Π transition, with population of the4p energy level of Ar atom, should be significant in the excitation process. Our results for the differential3
FIG. 7: Schematic correlation diagram for Na + − Ar colliding pair. Solid lines indicate Σ states, dashed linesindicate Π state. cross sections presented in Fig. 6 just are the evidence of this fact. Moreover, we have to mention, thatamong the various channels studied, just the elastic scattering channel and excitation of the Rydbergstates 4p and 3d of the argon atom are populated effectively. As to the oscillatory behavior of the data2 and 3 in Fig. 4, these oscillations are due to the interference of very close quasimolecular states of theNa + (2p ) − Ar (3p − Ar + (3p ) systems that have the energy scale defect only 0 .
19 eV.But, if it so, and that is a rule, in accordance with the interference model [48], the energy dependence ofthe excitation cross section for the Na(2p ′ lines of the Ar atom. However, the energy dependence of the excitation cross section of the Na(2p λ = 389 . − . S / and 3d D / )to the sodium 3p level. This assumption was verified indirectly by us from analysis of the ratio of theexcitation cross section of the sodium singlet 3p P / and triplet 3p P / states.It was revealed that the cross section ratio σ (3p P / ) /σ (3p P / ) differs from the statistical populationin the entire energy range and amounts to ∼ . .
5. The probabilities of the cascade electrontransitions from sodium 4s S / and 3d D / levels to the 3p level of sodium atom are such that thetransition from the 4s S / level to the singlet, as well as to the triplet states, is the same and changes thestatistical population just insignificantly. However, the transition from the 3d D / level to the sodiumsinglet 3p level is five times higher compare to the triplet level and, hence, increases the statisticalpopulation significantly. Accordingly, from our estimation, and by taken into consideration that theexcitation function for the sodium 4s and 3p states are the same (this is a relevant because of the defect ∽ . ′ ), to our mind it iscaused not by the direct excitation of the 4s and 4s ′ states of the argon atom. The excitation of argonatom takes place into the 4p state and than from here, through the 4p −
4s cascade transition it becomeapparent in the excitation of the 4s and 4s ′ states.4 I on i z a t i on c r o ss s e c t i on ( - c m ) Ion velocity (10 cm/s) FIG. 8: Velocity dependences of the ionization cross sections for the (NaNe) + and (NaAr) + systems. The resultof the measurements of the ionization cross section are presented for the following collisions: curve 1 – Ne + − Na;curve 2 – Ar + − Na; curve 3 – Na + − Ne; curve 4 – Na + − Ar.
IV. DETERMINATION OF THE TRANSITION PROBABILITIES BETWEEN POTENTIALCURVES OF QUASIMOLECULAR SYSTEM
Let us compare the ionization processes (2), (5), (8) and (10). The velocity dependence of the ionizationcross sections for Na + − Ne, Na + − Ar, Ne + − Na and Ar + − Na collisions are presented in Fig. 8. As is seenfrom Fig. 8 the magnitude of ionization cross sections strongly depends on the ionization energy of thetarget atom. The ionization energy of Na, Ar and Ne atoms are 4 . . . + − Ne collisions are qualitatively interpreted by the electron promotionmodel in Refs. [16, 49]. In order to discuss quantitatively the excitation mechanisms, one has to evaluatethe crossing parameters by collision experiments or ab initio calculations. Unfortunately, the accuracyof the calculations is still not sufficient for many-electron systems. One of the objectives of this work isto show that in some cases (e.g. for Na + − Ne) the information extracted from a theoretical calculation(e.g. the coupling matrix element) can be obtained experimentally using a simple approach, namely bymeasuring the ionization cross section of Na + − Ne and Ne + − Na colliding pairs in a sufficient energyregion.Usually for determination of transition probabilities for quasimolecular systems in a region of pseudo–crossing of the potential curves one measures the cross section of an inelastic transition between thestates, corresponding to these potential curves. What will be shown below, in some cases this probabilitycan be determined, not through a measurement of the cross section for a transition from one channel tothe other, but using two independent measurements: the transition from one and, independently, fromother channels to a third channel. In this case, for determination of the transition probability it is fullysufficient to determine not the absolute value of cross sections, but only their relation.Let us consider this method of determination of the transition probability between potential curves,corresponding to the ground state (potential curve X in Fig. 9) and the states, in which particles arecharge-transferred (potential curve A in Fig. 9) for the system (NaNe) + . As the third channel, in which5 FIG. 9: Schematic presentation of the potential terms for determination of the transition probability and couplingmatrix element for (NaNe) + system. ”X” is the entrance potential curve. ”A” denotes the potential curve thatcorresponds to the charge exchange process. ”C” represents a band of terms corresponding to autoionizationstates. the transition from these two states occurs in considering collisions, can be chosen a channel of atomicautoionization terms (band autoionization states C in Fig. 9). In accordance of choosing of the thirdchannel, it is necessary to have the cross sections for the ionization in Na + − Ne and Ne + − Na collisionsat the same collision velocity. Such data are obtained in this study. The measurements of the ionizationcross sections for the processes (2) and (8) are brought specially to be realized the considered method.In Ref. [16] it was shown, that the ionization in collision of Na + − Ne is realized as a result of thesequence transitions, at first due to a pseudo–crossing of the potential curves X and A in the area of R and then by the potential curve A with the band of curves C in the area R as is shown in Fig.9. In this case, as it easy to see, the mechanism of ionization in Na + − Ne collision is the same, as inNe + − Na collision. The difference in the cross sections of ionization for these pairs are related to theway the system approaches to the pseudo–crossing region: in one case, by the potential curve X, while inthe other case, along the potential curve A. Take this fact into the consideration, in a framework of animpact parameter approach, the cross section of ionization in collisions of Na + − Ne and Ne + − Na pairs,at the same velocity of relative motion, can be presented, as σ = 2 π (1 − P ) Z P AC ( b ) bdb, (12) σ = 2 πP Z P AC ( b ) bdb, (13)where P AC is the transition probability at the pseudo–crossing of the potential curve A with the bandC in the area of R and P is the transition probability between the potential curves X and A in thearea of R , at the some value of the impact parameter b from the region b ≤ R . The later conditionis clear because if this will be not satisfied, particles never reach the region of R and the ionizationwill not be realized. The transition probability P in the expressions (12) and (13) for the cross sectionsshould be under the integral because it is the function of the impact parameter – P ( b ). However, sincelocation of non-adiabatic area is such that R < R , the dependence of P ( b ) on the impact parameter b for b ≤ R is weak and therefore it is physically reasonable to consider P ( b ) = P and pull out from6the integral. Since the dependence of the probability P on the impact parameter b is linked to theradial velocity in the transition region, it is possible to estimate a value of the radial velocity sufficientlyprecisely, corresponding to these probabilities.From the comparison of the ionization cross sections for Na + –Ne and Ne + –Na collisions is obtainedthat in collision of (NaNe) + at the energy 7 . P = 0 .
62. To this value of P , for thevalues of R and R from the article [16], corresponds the radial velocity V R = 0 . v , where v is thevelocity of relative motion of the colliding particles. Now by knowing the transition probability andbehavior of the potential curves in a non-adiabatic region one can find the coupling matrix element H XA for nonadiabatic states using the Landau-Zener formula [50, 51] for the probability of a nonadiabatictransition for the pseudo–crossing potential curves P = exp (cid:16) π | H XA | /V R | ∆ F | (cid:17) . (14)In Eq. (14) ∆ F is the difference of slopes of the intersecting potential curves. Taking the difference of theslopes ∆ F =3 a.u. from Ref. [16], for the coupling matrix element H XA one gets H XA = 0 .
14 a.u. whichsignificantly clarifies the theoretical estimation of the value of this matrix element H XA = 0 . − . V. SUMMARY AND CONCLUSIONS
In this work, we report the results of the experimental study of inelastic processes realized in collisionsof Na + ion with Ne and Ar atoms and Ne + and Ar + ions with Na atoms in the impact energy range0 . −
14 keV. In case of Na + ion Ne, Ar atoms collisions the absolute value of the ionization, charge-exchange and excitation cross section are measured at the energy range of 0 . −
10 keV, while in thecase of Ne + and Ar + ion collision with Na the ionization cross section is measured at the energy rangeof 2 −
14 keV.Using the experimental set-up based on the crossed-beam spectroscopy method and the unique ex-perimental set-up that includes a refined version of the capacitor method, collision spectroscopy andoptical spectroscopy methods of measurements under the same umbrella, and a well–checked calibrationprocedure of the light recording system, we have measured the absolute values of the charge-exchange,ionization and excitation cross sections for (NaNe) + and (NaAr) + systems. The correlation diagram ofthe (NaAr) + system has been employed to discuss the mechanism realized in Na + − Ar collisions.For the charge–exchange processes two nonadiabatic regions was revealed in Na + − Ar collisions. Oneregion is at low energy,
E < Σ symmetry. While the other one is in theenergy region
E > − Πtransition is realized and it is associated with the rotation of the internuclear axis.A primary ionization mechanism for Na + − Ar colliding pair is related to the liberation of slow electronswith the energy of 10 −
15 eV and is associated with the decay of autoionization states in an isolatedatom.The oscillatory behavior of the energy dependence of the excitation cross section of argon atoms isrevealed in Na + –Ar collisions and found that, this excitation is a result of the Σ − Π transition betweenthe entrance energy level and the level corresponding to the excitation of Ar atoms, and also due to the4p–4s cascade transition in the isolated atom.Experimentally measured ionization cross sections, for Na + − Ne and Ne + − Na colliding pairs in con-junction with the Landau-Zener formula, allow us to determine the coupling matrix element and transitionprobability in a region of pseudo-crossing of the potential curves.7
Acknowledgements
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