The (e,2e) method for autoionization studies

Present status and pers ectives of further ex eriments on electron-impact excitation of a ! omic autoionizing s ? ates by the col.ncidence (e,2e) method are discussed on the basis of the current theoretical investigations in the Moscow-Dubna-Ulan-Bator group (Balashov, Cm-Crzhimailo, Lhagva, Iagunov,Strakhova). 1 . INTRODUCTION It was more than twenty years ago when it was shown that the coincidence (e,2e) method can be of great use for autoionization studies 111. This suggestion based on the unified theory of direct and resonance ionization of atoms by fast electrons E21 had another origin in nuclear hysics where ers ectives of similar coincidence experiments ! o investi ate ~imu!?tanemsu two-step (via decay, f states) and direct disin egration nuclear reactions drew much attention just at that time 131. The pioneer (e,2e) experiments of the Flinders and Kaiserslautern oups [4,51 have demonstrated real advantages of the new method in pf$sics of autoionization henomena in atoms. The theoretical analysis of the auto !? onization (13,213) process presented here aims to stimulate further progress in the field. 2. COHBNTS 013 RECENT EXPERIMENTS 2. 1 . Helium atom The helium atom always played an extremely important role in the hysics of autoionization phenomena as an excellent "laboratory" to Xevelo and to test new many-body theoretical methods and models in this fyeld. On the other hand the main tendency in experimental. investigation of helium autoi&izing states using the coincidence /,e,2e) method appears more to be a step by step improvement of the enerY resolution in the ejected electron channel: Pbeigold et al. (197 ) 600 meVE41; Pochat et al. (1952) 350 meV E61; Lower and Weigold (1 990) 150 meV 17 1 ; McDonald and Crowe (1 992) 80 meV 181. An objective is, in particular, to resolve the (zp2)' D and (292 )'P states whose natural widths (72 and 35 meV) are only a little sma ler than the separation ener of these two states (235 meV) . P If resonances do noyoverlap then the triple diff erent la1 (: ,2e) cross Section can be written as incoherent sum of indlvldual Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993606 JOURNAL DE PHYSIQUE IV contributions from each resonance. The Fano and the Shore formulae may be used equivalently for this purpose [21: Generally, in the case of near lying resonances one has to sum amplitudes rather than probabilities corresponding to each of them: In particular wlthin the PWBA approach the total mplltude reads: where qr(Q) is the momentum transfer dependent Fano profile index for separate r-resonance. Note extended tails of each resonance profile represented by the formula above. Due to these tails resonance overlapping effects can be sensitive very much not only to the total energ resolution of experiment but also even to the instrumental prof lle. The problem of overlappix resonances is currently becoming increasingly important becouse of the progress of various autoionization studies and so precision electron impact experiments on the (2p2 ) ID(2~2~)lP doublet in He are capital not only fur the spectrosco py of helium atom itself but from this general oint of view as well. On fig.1 one can see noncoincidence ejecte X electron s ectrum for the (e,2e) process in heliun measured several years ago by 8 da et al. 191 with very high resolution at incident electron ener ies of I key. Cum arison between these data and recent PWBA calculatfons of double difTerentia1 cross sections performed by Lhagva [I01 by inte ating the tri 18 differential cross section /2/ over the scatterer electron P ang es seems remising. Nevertheless it would be too hasty to ropose 7 such PlKBA ca culations for theoretical analysis of new very interesting data for the (e,2e) process on He at lower energies from the recent Fllnders University E71 and Mewcastle [SI coincidence is that in the case of excitation the take into consideration on the same level two inducing the optically forbidden transition (Is2)'s (2 ) D. The first one is the one-ste transition due to two electron &Lical correlations in the a ! omlc ground state; the other is a two-step excitation process via Intermediate atomic states, here mainly via the level ( l s2-p)' P. Preliminary calculations show a @owing relative contributlon of this multi-step process in the int emidiat e-energy region [ I I I . Ow ,@oup is worklng now on an extention of the usual DWBA-a proach to describe F 7 electron-im act multi-step excitation of autoion zing states in a way slmllar to hat which had been used earlier for another problem 1123. Fig.1. S ectra of electrons ejected &rom Heo by 1 kev-electron ref. [91. F beam at wo ejection angles ee = 142 and 33 [I 01; data from 2.2. Cadmium atom (e,2e) experiments on Cd performed in 1980-1982 by Kevin Ross's poup in Southampton with 150 eV electron beam C13,141 layed a very lm ortant role in stimulating further develo ments in heory of the ! X 1 au oionization le,2e) process. They clearly emonstrated that the PWBA approach had to give way to something more adequate to s ecific features of the process at intermediate energies. The DWBA went ! o the (e,2e) stage for the first time [ I 5 1 in the context of autoionization. At present these Southam ton ex erlments find a fruiful cont inuat lon in Lexington [ 16,377. The lafest results obtained there by Micolas Martin and his group ut a lot of questions to the theory, F amoy which the problem of in erference between am litudes of dlfferent mult polariries seems to be the most serious. Star ! ing from the PWBA conce ts the Lexindton group brought into use a number of s eciflc y c e $ures to collect data and to analyse it from the point of vfew of his problem. I mean, in particular, their rocedure to sum ejected P electron spectra measured for two opposite d rections arallel and antiparallel to the momentum transfer vector Q to el ? minate some interference effects. On the contrary, difference of such spectra gives the most evident information precisely about these effects. Our theoretical group find many interesti problems connected with current experiments on Cd in Lexington. In %e very near future we must estimate role of multi-step (two-step) transitions via intermediate states in excitation of positive arity levels such as 5p6p to have an unified picture of excitation o$ positive parity and negative parity states in the 4d-'5p region. We see our task also in performing detailed DWBA calculations for various measured (e,2e) 62 JOURNAL DE PHYSIQUE IV characteristics in Cd to make theoretical analysis of them more realistic from the point of view of taking into account distortion and exchange effects. In what follows sather good general agreement between theory and experiment will be shown concerning the (e,2e) process in Cd. But one serious disagreement must be em phasised which remains unclear to us. Fig.2 shows our DWBA caculations 7 and Martin's data for ejected-electron (e,2e) spectra in Cd summed for opposite ejection directions. The theoretical and experimental results are both lven in arbitrary units but these units are the same for left and ri t sides of the picture. So, in spite of a good agreement between t # eory and experlment as it concerns the shape of the spectrum and its transformation with ejection le, they disa ee by about a factor of 2 in the ratlo of total yi8.s of ejectey electrons in the two geometric varlants of the experiment presented here. It is not obvious where the theory is going SO seriously wrong, nor is it evident what steps should be taken to overcome this divergence. F% .2. Sum of (e,2e) ejected-electron spectra in Cd t171; curves D A calculations from LIB]. 3. THE DWBA FOR AUTOIONIZING STATES Our theoretical investigations of distort-ion effects in the autoionization (e,2e) process are made within the DWBA with exch . Earlier we used this approach rather successfully when analyz "8" ng inelastic and superelastic electron scattering at Intermediate energies [191. Here, rocedural aspects of the DWBA calculations will not be treated and ? he discussion will concern only the most pronounced transformations in the theory of the autoionization (e,2e) process when P I T from the simpliest PWBA ap roach to the DWBA. To my knowle e, g % he est paper demonstrating in etail general formalism of the D A theory for autoionization (e,2e) process t&inf into account in a proper way interference between resonant (via au oinization state) and direct (to continuum) is one given several years ago by Grum-Grzhimailo (unfortunately bei published in Rwsian it remains to the (e,2e) cornunit2 According to the the only m=O sublevei with zero rojection of angular on the Q-axis is populated. violating the Q-axis symmetry distortion effects make it necessary to take into consideration a number of additional independent amplitudes of the (e,2e) process corresponding to different m values of the exited states-This leads to a reformulation of basic formulae of the resonance theory. In particular, the Fano profile index q appears in these forlulae as a complex number. In ractice, one needs a lot of special information to make DWBA P calculat ons consistent from point of view of using pro er parameters in atomic wave functions and various interactions. 9 any additional ex eriments should be done to test optical potentials in the entrance X an exit channels and final state interaction between an ejected electron and residual ion. So,experiments of direct (e,2e) rocess in vicinity of autoionizing states as well as traditional inves ! igation of excitation of discrete atomic levels with the (e,ef ) and (e,elu) methods turn out to be intimely linked with the (e,2e) autoionization program. Theoretical description of autoionization (e,2e) expemiments becomes much simplier in specific cases when only a small background of direct (e,2e) process takes place and so one can neglect interference be tween the resonant and direct amplitudes of the ionization process.Since the ioneer work by Southampton group [I31 the cadmium 1: atomattractedmuc attention just from this olnt of view. Tme, recent experiments by Martin et al. indicate tha P real situation with Cd is not so trivial. Navertheless even now it seems to be a realistic first approach to formulate the (e,2e) theory for autoionizing states in this atom as an analog of that for the (e,ely) process concerning discrete atomic levels. Fig.3 shows our latest calculations [IS1 for differential cross-section of inelastic 150eV-electron scattering wlth excitation the 4d-'5p:J=I (12.81eV) autoionizing state in cadmium erformed withih the DWBA with exchange. Contrary to our earlier P I 5 1 we used here intermediate-coupli atomic wave-Iunctions [Eyerwith Hartree-Fock orbitals together wi 9 h an electron-atom optical potential constructed as static potential of the excited state and an effective local excY a otential corres onding to the electron cloud density in this xcite s ate. These mod1 ? lcations move our previous calculations to better agreement with experiment. As for the angular correlation parameter B (esc ) (fig. 4) the agreement is rather good up to about 20' but serious deviations appear for larger esc. 4. ORIENTATION P A W T E E OF AUTOIONIZINC STATES As the backgroug? of direct (e,2e) process into continuum in Cd in the region of the 4d 5 states is small, it is convenient to use the P same polarization and a ingment parameters to describe the spin-density matrix of the autoionizing states as those used traditionally for discrete atomic states in the (e,efy) process. Fi -5 shows reduced statistical tensors Akg=pk /pOO (m the collisional rame) for the 9 P autoionizing state 4d5p: =I at 12.81 e V calculated within the DMBA wlth exchange. Due to a very small contribution of exchange scattering 64 JOURNAL DE PHYSIQUE IV SCATTERING ANGLE (deg) SCATIERING ANGLE (deg) FY3 . Differential cross Fig. 4. The same as on sect on of excitation of the but for the ar correla ion 4d-'Q : J=l (12.81 eV) autoioparameter (~13181. nlzing state in cd by 150 eV electrons [181; data from ref. [ l 41 . * c n ~ . l . . ~ * * s , e ~ -1.5,, 10 20 30 40 50 SCATTERING ANGLE (deg) Fig. 5. Reduced statlstlcal Fig. 6 7 ar distribution tenzors Akq(BSc) for autoionizing of ejected e ectrons from the stare 4d-15p : J=1 (12.81 eV) in state 4d-'5 : J=l (12.81 eV) In cd calculated w1thb-1 DWBA wlth cd at 150 ef; PWBA and WlBA exchange for incoming electron calculations [ 1 8 1 for noncomenergy of 150 eV [ 18 I. planar ( e ,2e ) experlment. amplitudes in the esc region under consideration the orientation parameters as well as the shape of differential cross-sections are about the same for this state and for another J=1 state at 12.06 eV. Various correlation characteristics of the autolonization (e,2e) process via these states includ' those related to spin polarization of ejected electrons (see art 3) can be formed from the set iven in P f ig.5 using standard forma ism of of angular momenta a1 ebra [f!21. In particular, the shift angle @(esc) giving position of f he maximum in the coincidence ejected electron arilar distribution is calculated as follows: t@n=-2~~~ [q2 P20 E7-T 1 -l / 4 / 5. (IN SOME !W (e, 2e ) EXPERIMENTS I would like to discuss here from theoretical point of view perspectives to extend in some new directions experimental investigations of autoionizing states in the (e,2e) method. 5.1. Multichannel decay of autoionizindg states. Up to this oint one class of atomlc autoionizing states has been P considered, name y, those lying between the first and the second ionization thresholds. The states above the second threshold are of seat interest for many purposes. The (e,2e) experiments could give unique information concerning multichannel decay of such states. Strakhova and coauthors have made a number of predictions for experiments on fast electron inelastic on He with excitation of the series of autoionizing states o the n=3 ionization threshold [23 1 . Their calculations, into account the ! both internal and external confiema ion mixing, ive a possibility to trace the variations in the branching ratio for t f e n=l and n=2 decay channels dependent on the electron transfer momentum Q. The correctness of their redictions has been roved. by similar calculations [241 of P various c ~aracteristics of pho ! oionization of the helium atom above the n=2 ionization threshold and performed using the same method to construct atomic wave functions for continuum and autoionizing states as was used for calculation of the electron im act ionization rocess. Amoz these characteristics one finds par ! ial crogs sect E ons of ionization of helium to ls,2s and 2p states of the He ion and the anisotropy parameter p(n=2) in the angular distribution of ejected electron to the n=2 channel. One can think that the present-days multichannel theory of excitation of autoionizing resonances in He above the n=2 threshold can serve as a good guide for future (e,2e) experiments cancernix the multichannel character of their decay. Note in connection with thls suggestion that traditional (e,2e) experiments on direct ionization rocess on atoms and molecules now lays more and more important role To investigate ionization channe s to excited states of residual ions. P 5.2. On noncomplanar (e,2e) ex eriments Well-known (7,2p) exper 7 ments as well as other coincidence experiments in nuc ear physlcs of this type have demonstrated serious advantages of coincidence measurements when performed not only in the complmar versi.0~1 but also out of the scatter?% plane. Recent (e,2e) experiments by Read et al. for direct ionization process in atoms show that this is also true for atomlc physics. We see the main objective of noncomplanar (e,2e) experiments with autnionizirg states as ~ e t ting more detailed information ahout mechanisms of their excita ion and their decay properties. One knows 66 JOURNAL DE PHYSIQUE IV from general theoretical concepts that when cornire down from the energy region of applicability of the PWBA a proach to Intermediate energies the angular correlation function of t R e two electrons in the (e,2e) Lress losses its axial symmetry relatlve the transfer momentum %kc tion a=$-bsc. Qualitatively, the azimutal asymmetry of the two electron correlation function out the scattering plane and the symmetry axis shift in this plane have the same origin in the distortion of wave functions of incoming and of scattered electrons on excitation of the atom. However, quantitatively, the magnitude of these two distortion eff~cts depends on different combinations of density matrix elements (statlstlcal tensors) of the states under consideration. Fig.6 illustrates our recent calculations of lar distribution of the ejected electron over azimutal angle .p in% (e,2e) process e J in Cd performed within the DWBA ap roach with excha ~e for incoml electron energy of 1 50 eV. ~etaile% (e ,2e) measuremen s on decay 3 autoionizing states out of the scattering plane are of great interest from the pant of view of the "complete experiment" aiming to get all the parameters of the excitation process in a model independent way. 5.3. (e,2e with olarized electrons E Recent exper mental and theoretical investigations of inelastic (su erelastic) electron-atom scattering usi olarized electron beams i (an , in some cases, polarized targets as wzl? open wide erspectives to get detailed information concerning transition amplitu g es between discrete atomic levels. The same is ex ected to be true concerning ! coincidence (e,2e) experiments wi h polarized electrons for autoionization transitions. Let us consider, as an example, electron cornblnat ions of direct corresponding to excitation states. Arnorg them are the singlet states of the total transfered to atom separately for the states with definite total spin of the incoming and atomic electrons. Coincidence (e,2e) measurements on decay of the autoionizi states could give important additional information concerning the a1 p e n t angle r of the charge cloud in the excited atom. =? Perhaps more difficult from a technical oint of view but not less informative could be coincidence (e ,2e) experyments with nonpolarized incoming electrons to measure the spin polarization P of the ejected S electron. Fig.5 contains all necessary data to calculate Ps for electrons e jected from the autoionizing+ states 446' 5 :J=1 in Cd for any geometry of a coincidence (e,2e) experment at I50 e !. 6.CCINCLUSION VVe have discussed here some aspects of the resent status of the coincidence ( e ,Ze) method in autoionization studyes. No doubt, it &s good perspectives to be used and developed in further investigations of mechanisms of excitation and decay of autoionizi states. It has been shown also that many problems concerniw the 3 t eoretical basis for current and future experiments on this llne remains to be solved. Our group is continuing to work on many of them and we are interested Very much in closer collaboration with e erimental groups which are working or are intending to work In the fie1 3 . I wish to take thls opportunity of thanking the Organizing Committee (e,2e) '93 for their very Important support given me to participate in the Symposium.