Bethe found his formula using quantum mechanical perturbation theory. Hence, his result is proportional to the square of the charge z of the particle. The description can be improved by considering corrections which correspond to higher powers of z. These are: the Barkas-Andersen-effect (proportional to z, after Walter H. Barkas and Hans Henrik Andersen), and the Felix Bloch -correction (proportional to z). In addition, one has to take into account that the atomic electrons of the material traversed are not stationary (" shell correction ").