Some aspects of the averaging effects in the measurement of differential scattering cross sections

The averaging over theoretical cross sections leads to an 11-dimensional integral which cannot be correctly computed because of the great numerical effort involved. The reported investigation shows that this numerical effort can be very significantly reduced by the introduction of an apparatus function. The case of spherically symmetrical elastic interaction effects is considered. An expression is presented for the number of particles which are measured at the detector for a given position of the detector in space. The expression is transformed and an apparatus function is defined. The advantages of the described approach are discussed.