A new approach to treat the attenuation of β-rays in thin absorbers in planar geometry including covering foils

Expanding the exponential relations found for collimated beams yields new relations applicable in planar geometry including covering foils. These relations predict that in planar geometry the transmission curve falls off much faster than the one observed experimentally for a collimated beam. When the top angle of the detector decreases, the transmission curves converge to the exponential decay for collimated transmission although the apparent attenuation coefficient can differ considerably from the true one.Our predictions agree with experiments and Monte Carlo prediction in 2π geometry up to ∼10 mg/m2 and good agreement with experimental results is found up to 300 mg/m2 aluminium when the top angle is 38°. Therefore, it is concluded that the derived relations give a good approximation of the attenuation in thin, low Z, absorbers.