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General

In measuring the electron-impact excitation cross sections for multicharged ions, we have employed the JILA/ORNL Merged Electron-Ion Beams Energy Loss (MEIBEL) technique. Compared with the crossed beams fluorescence technique by which most absolute measurements of electron-impact excitation of positive ions have been obtained [For example, see R. A. Phaneuf, AIP Conf. Proc. 295, 18th Intl. Conf. on the Physics of Electronic and Atomic Collisions, eds. T. Andersen et al., New York, AIP, pp. 405-414], MEIBEL has a number of advantages. The detection sensitivity is a factor of 103 (or more) greater, the electron energy distribution is narrower, and one can observe not only dipole transitions but also non-dipole transitions.

A very detailed description of the MEIBEL technique and apparatus has been published [E. W. Bell et al., Phys. Rev. A 49, 4585 (1994)] so we will provide only an overview here, along with describing improvements and changes since the listed reference was published. A schematic diagram of the experimental setup is shown below.

Schematic of the MEIBEL apparatus

The portion of the apparatus shown in the figure is immersed in a uniform magnetic field (~3 mT). Electrons from the electron gun enter a region of crossed E and B fields, which is a trochoidal analyzer called the merger. Here the electrons perform two cyclotron orbits whilc undergoing an E x B drift, so that upon exiting the merger the electrons have the same vectorial velocity as when they entered, but their trajectory has been moved perpendicular to the entering axis. Along the exiting axis, the electrons merge with a multicharged ion beam from an electron-cyclotron resonance (ECR) ion source. The two beams are essentially colinear in the interaction region, an electric field free region 63.5 mm long. They then pass through the demerger apertures, after which they enter another trochoidal analyzer (the demerger) that directs the primary electron beam into a Faraday cup collector. Here, also, those electrons which have undergone inelastic collisions are dispersed onto a position-sensitive detector (PSD) consisting of a pair of microchannel plates and a resistive anode. This separation of electrons is based upon the forward velocity as compared to the perpendicular drift velocity vd = E x B/B2 in the crossed E and B fields.

This last point necessitates special consideration of particles scattered at an angle, as elastic collisions between electrons and ions also occur with a large cross section. The demerger apertures (see figure) block those electrons elastically scattered at angles large enough for detection by the PSD if allowed to pass, i.e. those electrons with residual forward velocity comparable to those which have been inelastically scattered.

Ions are bent through 90 degrees and collected in a Faraday cup. Signal collected at the PSD is accompanied by high backgrounds from both the electron and ion beams due primarily to beam-gas scattering, but with some component due to beam-surface scattering. Both beams are thus chopped in a phased four-way pattern; signals with position and timing information are collected in four separate histogram memories, the data from which are corrected for dead time, analyzed, and used to calculate the cross section. The densities of the two beams, G(x,y,z) and H(x,y,z), are measured at a number (usually seven) of positions along their merge path using a phosphorescent video probe [J. L. Forand, et al., Rev. Sci. Instrum. 61, 3372 (1990)], and the data are used to compute the beams' mutual overlap and form factor F.

Cross Section Determination

The excitation cross section at interaction energy Ecm in the center-of-mass system is calculated from the data using the equation

Cross section equation

where R is signal count rate from detection of inelastically scattered electrons by the PSD, D the measured PSD detection efficiency, and ve, vi, Ie, and Ii are the laboratory velocities and currents of the electrons and ions of electric charge -e and qe, respectively. The form factor F is given by

Form factor equation

The count rates registered in separate histogram memories are:

  1. Electron background Be + dark background Bd
  2. Ion background Bi + dark background Bd
  3. Signal S + Be + Bi + Bd
  4. Dark background Bd

The background rates are very high compared to S so corrections for dead time of the channel plates and detector system become very critical. The system as originally configured was limited by a 3.58 µs dead time primarily coming from the position computer. To improve the ability to take accurate data with less concern for dead time, the system has been upgraded with a low-impedance anode in the PSD, a faster position computer, and a fast first-in first-out (FIFO) buffer between the position computer and the histogram memories, giving a net dead time in the strobe channel of 307.0 ± 0.4 ns and in the rate channel of 60.7 ± 0.1 ns.

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Procedures and Conditions

Typical Operation

Typical operating values of the experimental parameters are:

  1. Electron current: 200 nA
  2. Ion current: 50 - 250 nA
  3. Ion energy: 20 - 105 keV
  4. Form factor: 2 - 3 x 10-3 cm
  5. Background pressure: 1.5 x 10-10 Torr
  6. Signal rate: 100 - 200 s-1
  7. Electron background: 40 - 80 s-1/nA
  8. Ion background: 60 - 150 s-1/nA
  9. Dark background: 40 - 400 s-1

The typical data protocol involves tuning the ion and electron beams to achieve minimum backgrounds and to ensure that the beams overlapped reasonably well in front of the demerger apertures and that they did not overlap behind the apertures (so no scattering occurred beyond the demerger apertures). Form factors are then measured. Collection of data in the four channels proceed at a particular electron energy until adequate statistical uncertainties are reached (usually about 30 minutes). The interaction energy is then changed by changing the electron energy. The magnetic field and voltages associated with the electron gun, the merger, and the demerger are carefully scaled by a few percent, and this produces electron beams of near-identical shapes. Thus, form factors can be kept effectively constant and are not measured on subsequent data points until the series of energies is finished, at which time another form factor is measured. If a significant change has occurred, the data series is held suspect and discarded. A number of data runs covering the same energy range are made, and averages of several measurements at each energy constitute the data presented here.

Interaction Energy

In order to precisely fix the absolute energy scale for the interaction, the measured absolute total excitation cross sections for dipole transitions are fitted to the convolution of a Gaussian energy distribution of variable width with a step function at the spectroscopiclly determined threshold. For example, the fit for the 3s2 1S -- 3s3p 1P transition in Ar6+ (threshold at 21.17 eV) yielded a full-width at half maximum (FWHM) interaction-energy spread of 0.24 ± 0.04 eV. A necessary shift in energy in this case was attributed to a "contact potential" of about 1.94 V, and this was used for correcting all laboratory electron energies. The FWHM interaction-energy spread was used to determine the width of a Gaussian used to convolute theoretical results in order to compare with experiment. A similar procedure was used on the other dipole transitions reported on these pages.

Ion Target Purity

Ions from the ECR source are accelerated through a fixed potential, then momentum analyzed so that only particles of a fixed M/q are in the analyzed ion beam. As there are no other likely impurity species for any of the M/q values used in the experiments reported here, the ion beams were deemed pure of other nuclear species. However, some of the ion beams (Si2+, Ar6+, and Kr6+) contained ions in metastable configurations. The metastable fraction of these mixed targets were measured for Si2+ and Ar6+ by routing the ion beam into the ORNL crossed beams apparatus and measuring the apparent ionization cross section of the target ions. The ionization signal observed below the energy threshold for ionizing the ground state could be attributed to the metastable ions. Analyzing the resulting data using the algorithm we have used previously [N. Djuric et al., Phys. Rev. A 47, 4786 (1993)], yielded the fraction of metastables to be 0.301 ± 0.014 for Si2+ and 0.285 ± 0.022 for Ar6+. Due to extremely high backgrounds, the ionization experiment was not feasible for the Kr6+ ion beam; instead, the metastable fraction was estimated to be 0.46 using the measured metastable fractions of Kr4+ and Kr5+.

Electron Backscattering

It was found in the Ar7+ measurements that near-threshold electrons were inelastically scattered primarily in the backward direction in the center-of-mass system. This was also found theoretically [D. C. Griffin et al., Phys. Rev. A 47, 2871 (1993)] and observed for the other transitions studied. Even on a semi-classical basis, is can be shown that one expects backscattering near threshold for dipole transitions. At the threshold for excitation, the scattered electron has zero velocity in the c.m. frame and Vcm in the laboratory frame, where Vcm is the velocity of the center- of-mass in the laboratory frame. At energies above threshold, the electron velocity ve in the laboratory frame is the vector sum of the velocity ve' of the scattered electron in the c.m. frame and Vcm, i.e. ve = ve' cos (theta) + Vcm, where theta is the scattering angle in the c.m. system. So scattered electrons move forward into the detector until ve' cos (theta) becomes negative and larger in magnitude than Vcm. Then ve is negative (the electron moves backward in the lab frame) and will not enter the detector. This limits the above-threshold energy for which one can make measurements without corrections to the data. Also, at higher scattering energies, scattered electrons with sufficient laboratory velocity perpendicular to the beam axis have large enough cyclotron radii that they may be intercepted by the demerger apertures.

In order to calculate the corrections for this backscattering, the demerger/detector portion of the apparatus was modeled using a fully three-dimensional trajectory modeling program [SIMION 3D version 6.0; David A. Dahl, Idaho National Engineering Laboratory]. The beam density information measured with the beam probe was used to determine vertical and horizontal line integrals, thus yielding a two-dimensional density map giving coordinates of where the signal electrons would be starting. At the approximate midpoint along the merge path, five to nine positions were chosen in this plane for launching test trajectories, and the trajectories were weighted with the line integral information. Trajectories were launched from each position and at intervals of 10 degrees from 0 to 180 degrees, with trajectories at a given scattering angle weighted by the appropriate theoretical differential cross section. For each experimental point needing correction, from several hundred to over one thousand trajectories were launched, and the fraction of detector "hits" to total launches defined the fraction detected and thus determined the correction factor.

Uncertainties

The relative uncertainties, which have no correlation between data points, are determined by the quadrature sum of uncertainties resulting from counting statistics and uncertainties in the corrections for the incomplete collection of signal as determined by the SIMION modeling described above. Total relative uncertainties are presented at a 90% confidence level. The expanded combined absolute uncertainty U at a similar level of confidence includes systematic uncertainties, which do not affect the relative shape of the data. Thus, added in quadrature to the relative uncertainties are uncertainties resulting from the metastable content of the ion beam, spatially delimiting the signal on the PSD, spurious signals, signal detection efficiency, form factor, and currents of the electron and ion beams. Uncertainties in PSD dead time and in the particle velocities are usually negligible on the scale of the other uncertainties. For specific values for each of these uncertainties, refer to the original publications as these values vary somewhat from one experiment to another.