The HKS model for electron production in liquid water by light ions

The HKS model developed to determine ionization cross sections (ICS) for the interaction of non-relativistic ions with matter, is used for 0.5 MeV protons impinging on liquid water and some inconsistencies between the single (SDCS) and double (DDCS) differential cross section values predicted by the formalism are found. To overcome this problem, new SDCS and DDCS formulas are determined analytically by use of the transition probabilities published by Hansen and Kocbach [J.P. Hansen, L. Kocbach, J. Phys. B 22 (1989) L71]. The new cross section expressions applied to the 0.5 MeV proton on liquid water case, give perfectly consistent SDCS and DDCS values. Furthermore, SDCS and DDCS values predicted from the new formulas for ionization of liquid water by protons (0.5–4.2 MeV/u) and alpha particles (0.3–0.5 MeV/u) are compared with corresponding experimental cross section values reported in the literature for water vapor ionization. Despite of the simplicity of the HKS model, accurate secondary electron energy distributions can be obtained, even for electron energies as low as 10 eV. Although the same accuracy cannot be achieved for electron angular distributions, the HKS formalism can still be used when these distributions are not critical.