A study of errors in trajectory simulation with relevance for 0.2-50 eV electrons in liquid water

A highly simplified model of the elastic scattering of electrons in a nm-size volume of liquid water, where the water molecules are regarded as point scatterers and inelastic scattering is neglected, is studied for electron energies 0.2-50 eV. This model allows an exact quantum mechanical solution of the multiple elastic scattering problem. The exact solutions are compared with the corresponding trajectory simulations. Two different data sets for the elastic scattering mean free path are discussed and used, one based on cross sections for water molecules in the gas phase and the other on cross sections derived from scattering in amorphous ice. In each case, the comparison provides a detailed insight into the character and magnitude of the error in the trajectory simulation, and gives a preliminary indication of an upper bound to the limits of validity of trajectory simulation in the real case of electron scattering in liquid water. Main results: with a fully random distribution of scatterers, the trajectory simulation is found to be a surprisingly good approximation down to quite low electron energies (∼10eV). Below a few eV, the error increases rapidly with decreasing electron energy. A substantial increase of the error in trajectory simulation results when short-range order (minimum distance between scatterers) is introduced; the observed effect may partly be understood from the theory of kinematic diffraction in liquids. At very low electron energies (a few eV) one may note a quantum effect in the form of a standing wave pattern in the average distribution of scattering events