Determination of Reaction Cross Sections from Counter-Telescope Data
Measurements on a given reaction provide the experimenter with data in the form of an individual number, or a set of numbers, which we shall refer to as the out put. The output is the number of counts recorded by counters, or the number of tracks in a chamber or on a photographic plate. The output is determined, on the one hand, by the reaction cross section, i.e., the probability of a particular process due to the interaction between an incident particle and a target nucleus or nucleon and, on the other, by the specific experimental conditions such as the size and efficiency of counters, the size of the target, the intensity of the incident particles, and so on. In order to deduce the cross section from the output one must first eliminate all the particular features of the experiment, i.e., introduce corrections for possible output losses due to secondary interactions of the reaction products with the target and the counters, taking into account the counter efficiency, and finally reduce the output to some standard conditions, for example, express it per unit solid angle, per target nucleus, and so on. In general, this is a relatively complicated problem. Thus, owing to ionization energy losses by the recorded charged particles, the effective volume of the target is not equal to its geometric volume, but is a complicated function of the experimental geometry and the incident-particle energy. A similar situation is encountered in the case of the solid angle within which the particles are recorded. The probability that a secondary particle will pass through different points in the detector is not a constant and, owing to the kinematic relation between the energy of the escaping particle and the angle of escape, it is a function of the incident-particle energy, the coordinates of the point of interaction in the target, and the energy discrimination in the counter telescope. The situation becomes exceedingly complicated when it is necessary to take into account multiple scattering of the incident particles during their passage through the target and counters. It is thus clear that an analytic approach to the solution of this problem is unlikely to be successful.
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