Photoionization of CO2 - Experimental Procedure

This experiment was carried out on the 5 m normal incidence monochromator fitted to a beamline at the Daresbury SRS, providing a photon flux of ≈ 10¹⁰ photons/s within a bandpass of 0.1 Å in the spectral region from 650 Å to 840 Å [24]. The light was brought into the experimental chamber by a 2 mm internal diameter glass capillary light guide whose capillary aperture was placed close to the exit slit of the monochromator. In addition to offering a low-loss transport for the vacuum ultraviolet radiation, the capillary also served to maintain a pressure differential between the experimental chamber and the ultra high vacuum of the optical monochromator. A schematic diagram of the experimental apparatus is shown in Fig. 1. The light guide extends from the exit slit, EX in Fig. 1, to the interaction region above the gas entrance tube, GS in Fig. 1, and can be as long as 30 cm dependent upon exact placement of the experimental chamber with respect to the monochromator.

The electron spectrometer system comprises two 100 mm mean radius hemispherical analyzers, one rotatable about the incoming light beam as an axis and the other fixed, contained in a chamber shielded from magnetic fields by three layers of µ-metal. The radiation from the monochromator is polarized, its polarization depending upon the optics of the monochromator and the subtended angles of acceptance of the synchrotron radiation. In our configuration, the light is polarized with between 75 % and 80 % of the light intensity having its electric field vector E→ perpendicular to the plane of the paper in Fig. 1. In this configuration, the fixed analyzer accepts electrons ejected parallel to the E→ of the incident radiation. The fixed analyzer is ES-2 in Fig. 1. The other electron spectrometer is rotatable about an axis defined by the direction of the light and hence collects electron in the plane of the E→. This movement allows the angular distribution of the photoelectrons to be explored completely and is sufficient to determine the angular asymmetry parameter for the scattering process. The entrance lenses for the spectrometers are three element zoom lenses based upon the design of Harting and Read [25]. The entrance cone to the lens system has a small aperture, usually about 1 mm in our experiments, which acts as the limiting aperture for determining both the energy and angular resolution of the system. The zoom lens focuses the electrons from a small interaction volume determined by the size of the light beam exiting the capillary and the size of the gas jet exiting the gas entrance tube onto the entrance plane of the hemispheres. The pass energy of the electron analyzer and focus voltages are set by external controls. The pass energy remains fixed for a particular set of experiments, and the other voltages are appropriately varied to scan the electron energy spectrum as required by using an automated data control system. The electrons are dispersed upon passing through the analyzer hemispheres and focused on the hemisphere exit plane. Since the apparatus was first described in the literature, the electron spectrometers have been fitted with position sensitive detectors which are placed near the exit focal plane of the hemispheres [26]. This allows for the simultaneous detection of a range of energies in the photoelectron spectra and thereby improves the data quality for a given period of data accumulation, compared to using a conventional electron multiplier behind an exit slit.

The polarization of the incoming light was measured using a three mirror polarizer with tungsten mesh and plate photodiodes which could be rotated with the rotatable analyzer through 90° in order to determine the light polarization. The polarization detection device was constructed based upon considerations given by Horton et al. [27]. The polarization was checked frequently since small movements in the storage ring beam position, and the mirrors focusing the light onto the entrance slit of the monochromator, can have a marked effect on the polarization. It was found that, provided the pre-mirror adjustments were kept optimized for maximum photon flux at the exit slit of the monochromator, the polarization would remain stable during the accumulation of a particular data set. The tungsten wire mesh at the entrance of the polarizer served as a photocathode for monitoring the intensity of the incoming light beam. A tungsten plate serving as a second photocathode collected the beam remaining after three reflections of the beam. The ratios of these photocurrents as a function of the angular position of the movable electron spectrometer provided the data necessary to determine the polarization of the light.

Calibration of the energy response of the analyzers was performed using the known values of the cross section and asymmetry parameters for argon or helium gas and following standard procedures outlined in the literature [28-30]. For all the spectra reported here the electron spectrometer resolution was determined from the rare gas calibration to be 41 meV for the fixed analyzer and 46 meV for the rotatable analyzer. The 5 m monochromator resolution was 0.1 Å (≈ 2 meV) for the measurements taken at wavelengths shorter than 750 Å. At wavelengths longer than this, where the structure in the absorption spectrum is less dense the resolution requirements could be relaxed and a wavelength resolution of 0.2 Å was used. The data were accumulated by simultaneously taking photoelectron spectra at two angles with respect to the polarization direction by utilizing both electron spectrometer systems. Since the two analyzers could be positioned at different angles, a particular data point did not require rotation of the movable electron spectrometer system. The wavelength on the monochromator was then incremented by 0.1 Å and another set of photoelectron spectra taken. The light polarization was checked periodically by a 90° rotation of the movable electron spectrometer. During data accumulation, the time spent at a particular electron kinetic energy was determined by integration of the light flux signal to some predetermined amount so that all the points in a particular data set would be correctly normalized to the same total light flux.

The differential cross section for photoabsorption in the dipole approximation for a randomly oriented gas may be expressed as

$${{\textstyle{\rm d}\sigma_v}\over{\textstyle{\rm d}\Omega}} = {{\textstyle\sigma_v}\over{\textstyle 4\pi}} ~   \left[ 1 + {\textstyle\beta_v\over \textstyle 4}~(3P \cos 2\theta +1)\right]$$

where θ is the angle between the major polarization axis and the ejected electron, P is the degree of polarization of the incoming light, Ω is the solid angle of collection of the photoelectrons, and σ_v is the partial cross section for the vibrational-electronic channel corresponding to the photoelectron being detected. The total cross section for a particular electronic channel is the sum of the partial cross sections of the individually resolved vibrational channels. The vibrational branching ratio is defined as the partial cross section for that channel divided by the total cross section for the electronic state. The number of photoelectrons per steradian per unit light flux, dN/dΩ is proportional to the differential cross section and hence we can recast the above equation into one that refers to the measurable parameters of the experiment:

$${{\textstyle{\rm d}N_v}\over{\textstyle{\rm d}\Omega}} = {{\textstyle N_v}\over{\textstyle 4\pi}} ~   \left[ 1+{\textstyle\beta_v\over \textstyle 4}~(3P\cos 2\theta +1)\right] ~.$$

N_v is the total number of electrons detected in a particular vibrational channel summed over the all solid angles. Measurements were made simultaneously at θ=0° and θ=90° and hence β_v and N_v could be directly deduced from the two spectra [31]. The branching ratio for a particular transition is the ratio of N_v with respect to the sum of all the N_v for a particular electronic excitation. The data reported here were taken only for transitions that left the CO₂⁺ molecule in the X ²Π_g ground electronic state. Altogether about 1500 data sets were taken in the wavelength region 650 Å to 890 Å.

Figure 2 shows the photoionization efficiency (relative photoionization cross section) for CO₂⁺ in the wavelength region of interest in the present study. The data were taken using a rotationally cooled sample of CO₂ and a laboratory light source coupled to a quadrupole mass filter [16, 32]. A one meter near-normal incidence monochromator provided dispersed radiation with a wavelength resolution of 0.12 Å. This rotationally-cooled spectrum shows more detailed and sharper structure, particularly near ionization onset, than does the spectrum obtained by Berkowitz [33] with a slightly better wavelength resolution of 0.07 Å. The spectrum shows members of the TO series that have as limits the A state of CO₂⁺ vibrational levels. The notation A n_v(TO) n = 4,5, ... etc., means the level is a member of the TO series having the n_v vibrational level of the A state of CO₂⁺ as its limit. The symbol B n₀(s,d) n = 3,4,...etc. is a Rydberg level of quantum number n having as its series limit the B state of CO₂⁺ in the vibrational ground state. The s or d refers to the Hennings sharp or diffuse series. The notation A 3_v(L) v = 0,... refers to a level of the Lindholm series with principal quantum number 3 that has the A state as its limit and has a vibrational excitation of v in the symmetric stretch mode.