Based on two properties of the generalized oscillator strength densities: (1) continuity in an excitation channel and (2) quasiscaling relation along an isoelectronic sequence, the corresponding parameters in the Bethe's formula (namely the Bethe's physical parameter set) have similar behaviors. According to the Bethe's formula, excitation cross sections for spin allowed processes can be easily calculated in terms of the Bethe 's physical parameter set which characterizes the excitations of target atoms. In the present article, we introduce corrected functions defined as the ratios between the exact cross sections and the Bethe's cross sections. The corrected functions reveal a nice universal scaling feature within 50%. Thus, various cross sections as well as rates, which correspond to electron impact excitations from an initial state to infinite final states-forming a so called "excitation channel", can be obtained conveniently.