Low energy (e,2e) studies of the noble gases in the perpendicular plane

Abstract

Abstract\nDetailed (e, 2e) studies of the electron impact ionization of the noble gases helium, neon, argon, krypton and xenon have been carried out from near threshold to intermediate energies, where the outgoing electrons carry equal energy from the interaction. The experiments were conducted in the perpendicular plane, where the outgoing electrons are both detected orthogonal to the incident electron beam. For electrons to emerge in this geometry they must undergo multiple scattering, including scattering from the nucleus of the target, and so this geometry provides a highly sensitive test of the most sophisticated scattering theories. The data show the cross sections undergo complex variations as a function of incident energy, and in particular ionization of the heaviest target is at variance to all others that have been studied here. PACS No. 34.80.Dp 1.0 Introduction. The (e, 2e) process provides the most precise experimental data for the study of the ionization of atomic and molecular targets by electron impact [ 1 ]. In these experiments a single electron of well defined momentum impacts with a target in the interaction region, resulting in target ionization and a scattered and an ejected electron which emerge after the interaction has taken place. By determining the momenta of the scattered and ejected electrons in a time correlated coincidence measurement, the differential ionization cross section (DCS) is derived for comparison with theoretical models. Since the scattered and ejected electrons may emerge over a wide range of different angles, experiments usually define a specific scattering geometry in which to carry out the measurements. In Manchester, the (e, 2e) apparatus can access a wide range of geometries from a coplanar geometry, where the incident, scattered and ejected electrons all occupy the same plane, through to the perpendicular geometry, where the scattered and ejected electrons emerge in a plane orthogonal to the incident electron trajectory, as shown in figure 1. Hence it is possible to accumulate a full range of DCS measurements over all scattering angles using this spectrometer [ 2, 3 ]. In the present work, we have constrained the spectrometer to measure the DCS only in the perpendicular geometry, where ? = 90? as in figure 1. For both electrons to emerge in this geometry it is necessary for multiple scattering to occur, where the incident electron strongly interacts with both the target nucleus and with the bound electrons. We have further constrained the outgoing electron energies to be equal, so that the effects of exchange between the electrons also plays an important role in the interaction. The perpendicular plane hence provides a stringent test of current ionization models. Further, we have taken measurements with the incident electron energy (E 0) ranging from near the ionization threshold of the selected target, through to energies up to 80eV above the ionization potential (IP). In this regime the probability of single ionization is a maximum, and so it is here that most ionizing collisions with electrons occur in nature. Understanding these processes is hence important in areas ranging from the production of plasmas in stellar and planetary atmospheres, through to electron impact ionization in lasers and in nuclear reactors. Low energy electron ionization has also been attributed to the production of DNA damage in biological tissue [ 4 ], and so it is important to understand these collisions at a fundamental level to describe the physics of these processes. Unfortunately in this energy regime the demands on sophisticated quantum models of the ionizing collision are also greatest. In these models it is necessary to consider multiple collisions, target polarization, distortions of the wave-functions defining the target and the electrons, and post-collisional interactions in order to produce theoretical cross sections which agree with experimental measurements. There has been excellent success in recent years in theoretically understanding ionization of the simplest targets (eg atomic H and He) using distorted wave Born approximations (DWBA), convergent close coupling (CCC) techniques, time dependent close coupling (TDCC) techniques and other methods [ 5-10 ]. Agreement between theory and experiment has however been less satisfactory for the more complex targets, including that of molecules, although again progress has been forthcoming over the last few years for the simpler diatomic systems [ 11-15 ]. To progress these studies beyond simple atomic targets, we decided to make a systematic study of ionization for the non-radioactive noble gas targets, as is detailed in this paper. We hence present results for ionization of helium from 3eV to 80eV above the IP (24.6eV), results for ionization of neon from 5eV to 50eV above the IP (21.6eV), results for ionization of argon from 2eV to 50eV above the IP (15.8eV), results for ionization of krypton from 2eV to 50eV above the IP (14.0eV), and finally results for ionization of xenon from 2eV to 70eV above the IP (~12.1eV). For xenon, we were able to resolve the 2 P 1/2 and 2 P 3/2 ion states for incident energies up to 30eV above the IP, and so we also present examples of the measured DCS from these individual studies. In all cases results are presented for the outgoing electrons having equal energies at the analysers. The helium results are reproduced from previous studies carried out in Manchester [ 2, 16-19 ], and are given here for completeness. This paper is presented in four sections. Following this introduction the apparatus at Manchester is briefly described, and the experimental conditions chosen for these studies are detailed. Results for ionization of the different noble gas targets are then presented, followed by a discussion of these data. Finally, a summary of the differences seen from individual targets is given, so as to promote discussion in the future. 2.0 The experimental configuration. The experimental apparatus in Manchester has been detailed in a series of papers since being commissioned in 1990 (see [ 20 ] for example). As noted above, the apparatus can measure the DCS from the coplanar to the perpendicular plane geometry by moving the electron gun, gas jet and Faraday cup together around the interaction region (figure 2). This is accomplished by mounting these components on a yoke which has its rotation axis through the interaction region. A photomultiplier tube is also fixed to this assembly so that photons emitted at 450nm ? 50nm from the electron-target interaction can be counted (all targets studied here produce photons in this regime when excited by electron impact). By observing the flux of emitted photons, the electron beam can then be correctly focussed and steered onto the physical centre of rotation of both analysers and electron gun. The electron analysers consist of a 3-element electrostatic lens that focuses electrons from the interaction region into a hemispherical energy selector. By choosing the analyser residual energy to pass electrons around the selector, a channel electron multiplier detects electrons of the specified energy for subsequent amplification and counting. In the experiments carried out here, both detectors are set to measure electrons of equal energy, given by E 1 = E 2 = E 0 ? IP () 2. The combined coincidence energy resolution of the unselected energy electron gun and the analysers is ~1eV, as measured from coincidence energy spectra obtained during these measurements. This resolution arises from the energy spread of the unselected electron gun and the resolution of the energy analysers. The angular range of the measured DCS is dictated by the physical size of the analysers. In the perpendicular plane, only the mutual angle ? = ? 1 + ? 2 is relevant, where ? 1 and ? 2 are as shown in figure 1. For the helium data presented here, the angular range was from ? = 50? ? 310?, whereas for all other targets this range was from ? = 70? ? 290?. This difference arises due to the redesign and installation of new analyser shields in between the time the helium measurements were taken and those measurements for all other targets presented here. The angular resolution of the spectrometer is estimated to be ?? = ?5? in this plane, as calculated from the entrance apertures of the individual analyser electrostatic lenses. The data were taken over a period of several months, and the electron gun current was varied for each of the data sets so as to ensure linearity of the detection system and a reasonable coincidence count rate compared to the random background signal. At these low electron energies it is very difficult to accurately determine the size and shape of the incident electron beam, and therefore its overlap with the target, which would allow a relative normalisation over the different selected energies. The data are hence normalised to unity at the peak of the DCS at each energy. The shape of the DCS for a given energy and target is then of importance, for comparison with future theoretical work. The energies of the incident and scattered electrons in the spectrometer were independently determined by measuring resonances in elastic and inelastic scattering data. The energy of the incident electron beam was determined by observing the negative ion elastic scattering resonance in helium at ~19eV, so as to determine the offset in the gun due to contact potentials. The energies of the outgoing electrons were determined by observing inelastic scattering from the excited targets, and by considering the location of Fano resonances in the ionization continuum. 3.0 The experimental data. The experimental data for helium are taken from previous work carried out in Manchester [ 2, 16-19 ]. These are re-presented here normalised to unity at the peak of the DCS to allow a comparison between this target and the other noble gases. The ground state of helium is 1 S 0, with an electronic configur