The experimental technique and ion source have been described in considerable detail in the literature [D. C. Gregory et al., Phys. Rev. A 34, 3657 (1986); M. E. Bannister, Phys. Rev. A 54, 1435 (1996)] that will not be repeated here. In general, the experiment consists of well-characterized ion and electron beams that intersect at 90°. Ions which are further ionized by the electron beam are selected by charge state and counted. Accurate measurement of critical quantities allows the cross sections to be put on an absolute scale.

Ion Source

Figure 1 shows a schematic of the ORNL-ECR (Oak Ridge National Laboratory Electron Cyclotron Resonance) ion source [F. W. Meyer, Nucl. Instrum. Methods Phys. Res. B 9, 532 (1985)] which was used in this experiment through 1992. The source includes unique features in its design, although it is similar to several other ECR sources currently in use. For most of its eight-year tenure as the primary source for this research group, it was the only ECR source in the world dedicated solely to atomic physics research. The source is currently inactive, having just been replaced by a more powerful 10 GHz CAPRICE ECR source.

In general use, a gas is introduced into the first stage, where a small ECR surface produces low charge-state ions. These ions drift into the low-pressure second stage, where they are further ionized by electrons accelerated by a larger ECR surface. The entire source floats at the acceleration potential (generally 10 kV), and ions are extracted by acceleration to the ground potential at the exit of the source. A mixture of gases is sometimes used to influence the distribution of charges in the extracted beam, enhancing the production of either higher or lower charges. Most metals are not readily available in acceptable gases, and another method had to be found to introduce metal vapor into the source. Usually, a thin foil is attached to an insulated arm in the second stage of the ECR source; the foil can then be raised using an external manipulator until it approaches the ECR region. The foil then melts or, if thin enough, slowly vaporizes. There is some evidence that a major source of metal vapor is recycled material deposited on the chamber walls.

Another method of metal ion production was developed in 1994 for the CAPRICE ECR ion source. This technique uses a mini-oven that is incorporated into the end of the central electrode of the coaxial microwave injection waveguide, located immediately adjacent to the main plasma stage of the source. Vapor sublimated from volatile metal oxides and halides in the oven supplies metallic ions to the ECR plasma. The first ionization cross sections measured at ORNL using metallic ion beams produced by this method were for Mo⁴⁺ and Mo⁵⁺ [M. E. Bannister et al., Phys. Rev. A 52, 413 (1995)].

The metastable content of ion beams extracted from ECR ion sources is still under study. In general, ECR sources are "hot," producing extracted ion beams with a wide range of charge states. As a rule of thumb, if a source has the energy to produce a significant number of ions in charge states higher than the one of interest, it has plenty of energy to produce metastable ions in the species of interest. If such metastables live long enough to reach the experimental region, the threshold for electron-impact ionization will be observed at an energy lower than that expected for ground-state ions. For most of the measurements summarized here, the metastable fraction of the target beam was determined, or estimated as accurately as possible.

Ion Optics

Two different techniques were used to separate signal ions from the main ion beam for this data. Prior to 1985, a parallel-plate analyzer was utilized to separate the signal ("ionized ions") from the main ion beam [R. A. Falk et al., Phys. Rev. A 27, 762 (1983)]. Using that apparatus, physical space limitations in the collision chamber limited the range of charge states that could be studied. The parallel plate separator could not be made large enough to effectively separate beams with initial/final charge ratios greater than 6/7. In addition, apertures had to be used to separate the beam paths in order to block scattered particles and even photons from the ionized ion detector. Tens of counts/sec of false signal (out of 10¹² ions/sec in the main beam) would dominate the real signal. A final drawback to the parallel-plate analyzer was that the chamber had to be opened and modifications made for almost every change in initial-to-final-ion charge ratio. In order to overcome these limitations, a new ion analysis apparatus was developed.

Figure 2 shows the apparatus used for the great majority of the measurements presented here. The main chamber houses the initial ion optics, a parallel-plate analyzer to reject ions which change charge along the flight path from the ion source, the electron gun and interaction volume, and some post-collision steering optics. The ion beams then enter a double-focusing 90° analyzing magnet. The signal ions are directed into a channel electron multiplier, while the main beam is captured in a deep Faraday cup. The ions effectively see no apertures after the collision volume so that the possibility of "slit-scattering" is virtually eliminated. The double-focusing magnet focuses the collision volume onto the signal ion detector so that a "spot" signal is obtained. The ion analyzer is known as "PACMAG" because of the physical resemblance of the analyzing magnet to the video game creature. The original design was intended to be used for initial-to-final charge ratios between 4/5 and 15/16. An additional main beam cup extended that range down to approximately 1/2, and measurements have been made up to 16/17. Further details and an explanation of the available diagnostics are published elsewhere [D. C. Gregory et al., Phys. Rev. A 34, 3657 (1986)].

Electron Gun

The electron gun used in most of these experiments is essentially the same as that described by Taylor et al.[Rev. Sci. Instrum. 45, 538 (1974)]. Electrons emitted from an indirectly heated cathode are confined and compressed by an axial magnetic field. It was designed to produce an intense, homogeneous, low-divergence electron beam at energies from a few eV to at least 3000 eV. In practice, power supplies, feed-thrus, and power dissipation in the beam collector limit the electron gun operation to 1500 eV or less. The energy resolution of the gun at low energies was measured during early excitation experiments, while the resolution at higher energies must be estimated based on excitation-autoionization features observed during ionization measurements. The latter resolution may be a conservative estimate since sharp ionization features tend to be "softened" or "smeared" by recombination resonances associated with the feature being observed. Typical operating electron beam currents range from 300 µA at 100 eV to 5 mA at 1000 eV. The energy resolution of the gun is known to be less than 2 eV at 100 eV beam energy.

In 1993, a different electron gun was installed in the electron-ion crossed beams apparatus. This present gun uses electrostatic confinement of the beam instead of the previously used magnetic confinement scheme. The new electron gun is expected to have a higher energy resolution than the previous one, which will facilitate measurements involving higher charge states, and will make possible future studies of ejected electrons. Details on this electron gun are published in M. E. Bannister et al. [Phys. Rev. A 49, 4676 (1994].

Cross Section Determination

The one-dimensional spatial distributions of the ion and electron beams, and the overlap of these two beams in the collision region is determined using a movable slit assembly. The current transmitted through a narrow horizontal slit is measured as the probe is moved through the beam vertically. The probe can be rotated so that both the ion and electron beam profiles are measured through the same slit. The probe position and current measurements are computer-controlled so that the overlap of the beams at any absolute vertical position can be determined. The beam profiles and overlap determine the "form factor," given by the relation

where I_i(z) and I_e(z) are the beam intensity profiles in the direction (z) perpendicular to both beams.

The quantities which must be measured in order to determine an absolute cross section are the ion and electron currents (I_i and I_e , in amperes), ion and electron velocities (v_i and v_e, in cm/sec), the form factor (F, in cm), the signal event rate (R, in events/sec), and the signal detection efficiency (D, unitless). The charge state of the incident ions (q) must also be known. Given these quantities, the absolute cross section (in cm²) as a function of the interaction energy (E) is given by

where e is the electronic charge (1.6 x 10^-19 C). The interaction energy (E) is largely determined by the electron beam accelerating voltage, but must be corrected for contact potentials in the electron gun, space charge potentials, and the finite velocity of the target ions. In practice, there is always a background count rate in the signal detector, so the true signal event rate is taken to be the difference between signal-plus-background and background-only count rates.

Uncertainties

Each cross section measurement at each energy is independently absolute, but some quantities in the above formula are assumed constant for a given target ion. For example, the signal event detection efficiency will affect the measured signal rate at each energy by the same multiplicative factor, and the contact potential (a constant) offsets each interaction energy by almost the same amount. In contrast, the statistical uncertainty is independent for each measurement. Thus, to accurately convey the measurement uncertainty, we must specify both "absolute" and "relative" uncertainties for each set of cross section data.

In the data presented here, relative uncertainties are listed and plotted at the equivalent of one standard deviation for a purely statistical uncertainty, unless specified otherwise. The relative uncertainty includes (and is usually dominated by) statistical uncertainties, but also includes (combined in quadrature) relative form factor uncertainties and any other factors which are found to vary during a set of measurements. For a given data set, the shape of the cross section curve and any features observed in the curve may be judged in light of the relative uncertainties. For most of the cross section curves, one-standard-deviation relative uncertainty error bars are plotted when they are larger than the plotted points.

The absolute uncertainty is a combination of the relative uncertainty discussed above with any other factors which would affect all data points the same. The detection efficiency, ion velocity and current, and some aspects of the beams overlap measurement are examples of additional sources of uncertainty in the absolute measurement. The shape and features of the cross section curve will not be affected by the absolute uncertainty, but the vertical scale of the entire curve could vary within the limits of the absolute uncertainty. The absolute uncertainty is generally specified in this report as a percentage of the cross section measurement for a typical point near the peak of the curve. It is given here at the equivalent of two standard deviations for purely statistical uncertainty, corresponding to approximately a 90% certainty for a limited number of measurement sets. For most of these measurements, the absolute uncertainty amounts to approximately 7% before combining it (in quadrature) with the relative uncertainty, which must also be taken at the two-standard-deviation level. For further details concerning absolute uncertainties, refer to D. C. Gregory et al. [Phys. Rev. A 34, 3657 (1986)].