PHYSICAL REVIEW A VOLUME 30, NUMBER 6 DECEMBER 1984 Electron spectroscopy of multiple ionization of argon by electron impact R. Hippler, K. Saeed, A. J. Duncan, and H. Kleinpoppen Atomic Physics Laboratory, University of Stirling, Stirling FK94LA, United Kingdom I,Received 20 July 19S4) Doubly differential cross sections (DDCS) for electron ejection in electron-argon collisions have been studied for ejected electron energies 25 to 300 eV, ejection angle 8&=90, and incident electron energies Gf 300 eV to 8 keV. Performing a charge-state analysis of the recoil ion in coincidence with the ejected elec- tron, we were able to distinguish between singly and multiply ionizing collisions. It was observed that the relative importance of multiple ionization events increases with increasing energy of the ejected electron. At an ejected electron energy corresponding to LMMAuger transitions, Ar + and Ar + are predominantly produced by L-shell ionization. Fram an analysis of the corresponding DDCS, information about simul- taneous L- and M-shell ionization is obtained. I. INTRODUCTION Recently, there has been an increasing interest in the study of multiple ionization events. While a large body of data already exists for photoionization, ' studies of ioniza- tion by particle impact seem to be only at their beginning (e.g. , Refs. 3-6, and references therein). Experimental in- vestigations by particle impact have so far made use of the detection of multiply charged ions (e.g. , Ref. 7, and refer- ences therein), or used vacuum ultraviolet, ' Auger elec- tron, ' or x-ray spectroscopy. " Few attempts have been made to measure energy and angular differential cross sec- tions for electron ejection in multiple ionizing collisions. Van der Wiel and Wiebes'2 have obtained energy differen- tial cross sections for multiple ionization in electron-argon collisions measuring the energy loss of the incident electron in coincidence with the ions of a certain charge state. The present investigation is similar to the recent work of Hippler, Bossier, and Lutz, 6 who measured doubly differen- tial cross sections for electron ejection in proton — rare-gas collisions in coincidence with the product ion, thereby ob- taining the different contributions from singly and multiply ionizing collisions. In particular, we have investigated the following process perpendicular to the direction of the electric field for ion detection were detected in a 30'-parallel plate electrostatic analvzer. !n order to increase its detection efficiency, the analyzer was operated with a modest energy resolution of about 12% full width at half maximum (FWHM). No sig- nificant change in the measured energy distribution of the ejected electrons with and without applied electric field was observed, provided the electron kinetic energy was corrected to allow for the potential difference between target and elec- tron analyzer. Electrons ejected in an e-fold ionization process were identified by simultaneous detection of the product ion. The ionic charge state was determined in a time-of-flight (TOF) setup, measuring with the help of standard coin- cidence electronics (time-to-pulse height converter, mul- tichannel analyzer) the time delay of the product ion rela- tive to the ejected electron. . Typically, this time delay was of the order of few p, s; depending on the ionic charge state and mass and the length of the TOF drift tube (about 3 cm). Several peaks corresponding to ionic charge states n =1 up to n =4 were observed in the time spectra. After subtract- ing random coincidences, the number of true coincidences, N, " were related to a doubly differential cross section (DDCS) for n-fold ionization, d'a"/(dE dQ), by. e + Ar [ne ]+Ar" ++ ea d'~ "/(dE d 0 ) = (N, /Nj) ~,/(b, Ed n e, ) . (2) Detection of the product ion in coincidence with the ejected electron (ea ) allows identification of n-fold ionization events. No information is obtained on the systems within the square brackets, which would require a higher-order coincidence experiment. II. EXPERIMENTAL PROCEDURE The experimental arrangement has been described in some detail previously. ' The measurements have been per- formed by injecting an energetic electron beam into a dilute argon gas target. Ions prod. uced by the ionization process were extracted from the collision region by a small electric field (about 25 V/cm) between a lower plate and an upper grid, both of I cm diameter and separated 1 cm from each other. The target gas was introduced into the chamber through a small orifice in the lower plate. Electrons ejected at 90' with respect to the incident electron direction and o. I is the total cross section for ion production, N the number of detected ions, es the efficiency of the electron detection system, and AE and AA energy bandwidth and solid angle of the electron analzyer, respectively. For the total ionization cross section crI we used the cross sections for 3s and 3p ionization given by McGuire, ' extrapolated to higher incident electron energies with the help of Bethe's f'ormula (see, e.g. , Ref. &5) o. ;= (I/E) [3 ln(E/I)+8] (3) Here, E is the incident electron energy, I the ionization en- ergy for a particular subshell, and A and Bare two constants determined from McGuire's calculations. The inner shell (K, L shell) contribution to the total ionization cross section is negligibly small; its largest contribution is at 8 keV where it accounts for less than 4% of o. ;. Alternatively, one could have used experimental cross sections for o. ;, which on an absolute scale deviate about 15% from McGuire's data and 3328 1984 The American Physical Society