[en] Simple analytical approximations are deduced for the variables X-ray cross section sigma and stopping power S. Based on these approximations the characteristic Lsub(α) X-ray intensity is calculated including self-absorption of the emitted X-rays in thick samples. In addition, a mathematically simple approximation is obtained, which permits the calculation of the resulting Lα X-ray intensity of thick samples without any summation method. Thus, is possible to calculate the signal intensity of PIXE studies of thick samples fast and with good accuracy by a semiempirical method. The calculated results are in good agreement with experimental PIXE data of rare-earth elements in different matrices of low atomic number. (orig.)