Penetration of Low-Energy Electrons in Water

The penetration of low-energy electrons in water has been calculated by combining a suitable stopping power theory with a theory of scattering. For the first part, a low-energy modification of Bethe's formula is adopted which uses the dipole oscillator distribution of Zeiss, Meath, MacDonald, and Dawson. The momentum transfer cross section is constructed from a Rutherford formula with a Moliere screening parameter modified to match various experimental data over a wide span of energy. Both elastic scattering and energy loss are included in a modified Lewis theory to determine the angular distribution of velocities and certain moments of the spatial distribution of an electron as it loses a definite amount of energy. The position distribution of the penetrating electron is calculated approximately using a random walk theory. The mean radial range and the mean penetration of the electron in the original direction of motion are compared to the mean electron path length and the root mean square penetration. Comparison with earlier calculations and application of the results to track structure in irradiated systems are indicated.