Measurement of total and integral cross sections

When a beam of electrons of current I enters a collision chamber containing a target gas of uniform density n, the fractional loss of intensity is given in terms of the total cross section cr by 

Care must be taken in designing the collision apparatus and electron detector (normally a Faraday cup or retarding field analyser) to ensure that equation (2.9) is applicable and small-angle scattering is eliminated (Wagenaar and de Heer, 1985 Bederson and Kieffer, 1971). To allow for 

It is obvious that n and have to be determined accurately, n is usually determined by measuring the pressure, for example with a capacitance manometer such as a baratron, taking care to allow for temperature differences between the gas cell and the measuring region (Blaauw et al, 1980). Usually one has an effusive molecular flow through the entrance and exit apertures, which leads to large density gradients in the gas, and the product mf in the exponent of (2.10) has to be replaced by 

If the energy distribution of the primary beam is not narrow, one has to allow for it in the manner discussed in section 2.1.4. Using this method it is possible to measure aj as a function of q with an accuracy of better than 5%. 

Instead of measuring the transmission of electrons one can measure the transmission of the target particles in a crossed-beam experiment, where a beam of electrons intersects a beam of target particles (Bederson, 1968). The recoil imparted to the target atom or molecule deflects it out of the original beam and the decreased beam intensity is a measure of the total cross section. Usually one uses a d.c. molecular beam and a modulated electron beam and associated phase-sensitive detection of the transmitted molecular beam. If the two beams are rectangular with a common dimension h, then (Bederson, 1968) 

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