On the derivation of the ionisation threshold law

The different procedures for derivation of the electron-atom ionisation threshold law have been analysed and the reasons for discrepancies in the results are pointed out. It is shown that if the wavefunction has a linear node at equal electron distances (r1=r2), then the threshold law for the total cross section has the form sigma approximately E3m, where sigma approximately Em is the Wannier law. The distribution of energy between escaping electrons is non-uniform and has a parabolic node at equal energies ( epsilon 1= epsilon 2). The linear node at opposite directions of electrons ( theta = pi ) does not change the Wannier law but leads to a parabolic node in angular distribution at theta = pi . The existence of both nodes leads to the threshold law sigma approximately E3m and to parabolic nodes in energy and angular distributions.