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The following procedure was carried out when collecting differential cross sections.

1. The electron beam was timed for the required incident energy. This being set by the bias voltage applied between ground and the earth of the lens power supplies (see Figure 3.7).

2. The angular resolution of the electron beam was measured, and the analyser then returned to the zero angle position (see Section 3.8).

3. The gas beam was let into the tank for the required background pressure (see Sections 2.7 and 5.7).

4. The incident electron beam, Iq, was measured, by deflecting it onto the cone in the interaction

region.

5. The bias voltages were measured.

6. The electrons arriving at both the data and reference detectors were counted simultaneously (see Section 4.4.2), as a function of angle. At each angle the collection time was sufficient for at least 10,000 counts to have been collected from both detectors, so giving a statistical accuracy of better than 1%. For each angle the count rates, Dbc and/?bc, were calculated and

recorded.

7. The incident electron beam current, Iq, was remeasured.

8. The gas beam was switched off, and gas let into the experimental chamber via an opening in a side flange (Section 2.7) to give the same background gas pressure.

9. The incident electron beam current, /o', was measured.

10. The count rates Dc and Rc were measured as a function of scattering angle 6 as described in

6 above.

11. The incident electron beam current, /o', was remeasured.

12. The bias voltages were remeasured.

The whole procedure was repeated four or five times, allowing the term on the left hand side of Equation 5.12 to be found: (5.12) (5.13) ' s .( - 9 0 ° ) ^ ( - 9 o r ) d<^ 6K m i c - ~ d Q -g t(e )K - D J 0 ) - - p D J B ) i 0 7 — — 7 'd ■Int I A R U -9 0 0) - 77*c(—90°) - in Z - 7 ' where K =

and is constant for a given molecular target

The cell contribution was found to contribute not more than 5% to the total scattered current.

As already mentioned in Section 4.4.2, the electrical background was usually extremely low allowing the terms in Z in Equation 5.12 to be neglected. However, the noise count rate was measured regularly over the period in which data was being collected and if it was found to approach 1% of the data or reference count rates its value was substituted into Equation 5.12.

Initially when using the reference detector, the term - j W was found to contribute significantly to the

count rate, being up to 50% of R^. Although this would not effect the measurement of the elastic

differential cross section, it made the initial timing of the reference detector difficult. To overcome this a copper shield was made for this detector, the shield fitting around its optical bench. This prevented the electrons which were scattered off the interaction region cylinder from reaching the reference channeltron.

Tr

When using Equation 5.12, the assumptions that Tr — Tr\ Td — Td' and -=^ are constant have to be

made. For this to be true it is necessary that the spectrometer voltages are constant for the beam plus cell and cell alone measurements. For this reason on completing a set of angular measurements for the beam plus cell configuration at a given energy, the corresponding cell measurements were made straight away. The output of the bias supplies were checked at the b e g in n in g and end of each run. Only the data for which the bias voltages had remained unchanged (within ± 2mV) were recorded.

The volumetric term gb(6) in Equation 5.12 varies with angle and must be evaluated to allow the

differential cross section to be found, the method used to evaluate this term is described in the next section.

5.5 The Volumetric Correction

As gb(0) is dependant on the scattering angle for most geometries, a geometrical correction factor

must be found to enable the differential cross section to be determined. Only in the ideal case when the FWHM of the gas beam is well inside the acceptance angle of the detector will this correction be unnecessary, as in the experiment described by Shyn et al (1972). Previously a sin 6 correction has been applied to this apparatus (Curry 1984), however as shown by Brinkman and Trajmar (1980), this can lead to serious error. To find this term therefore, the experiment was repeated with helium. The elastic differential cross section for helium was measured as described in Section 5.4, for the same

energies and over the same angular range as was used for the three molecules being investigated. These measurements were substituted into the right hand side of Equation 5.12 yielding the term

p "I (S')

Williams (1979) has published the phase shifts of helium, calculated from his absolute measurements, with a stated accuracy of better than 5%. These phase shifts were interpolated for the energies used in the present experiment and the corresponding absolute cross sections calculated using the formula given by Nesbit (1979). On substituting the values measured in the present experiment into the right hand side of Equation 5.12, and the value of the absolute cross section into the LHS, the term gb(6)(He) may be found for helium.

Then provided

gb{efmoieak)« &(

)(/fe)

the relative cross sections for the any molecular target may be determined.

In the present experiment the pre and post-interaction region lenses were timed identically to produce and receive a focussed electron beam which had a diameter of the order of 1mm at the centre of the collision region. Therefore the overlap of the incident electron beam with the acceptance cone of the detector was always within the gas beam for all the target gases (the tip of the hypodermic needle being 2.2mm from the centre of the collision region and AB increasing from 40° for helium to 60° for

ethane). The above proportionality is therefore valid.