Energy loss of electrons in random motion

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Abstract
A subexcitation electron (energy range 1–6 eV or so) in a molecular medium losses energy in the excitation of molecular vibrations or phonons. One of the loss mechanisms involves the transient electric field generated by the motion of the electron and this paper presents an investigation of such energy loss. Ensembles of random tracks generated by a Monte Carlo procedure are considered. The Fourier transform of the electron displacement of each track is obtained by a fast Fourier transform (FFT) algorithm and the ensemble‐averaged square of this transform provides a frequency spectrum which determines the average energy loss of the electron. Two mechanisms are considered as examples: the loss to dipolar relaxation in water, and the loss to infrared‐active vibrations in benzene and polyethylene. The rate of energy loss to dipolar relaxation in water is in the range of 1013 eV/sec and the rate of loss to infrared‐active vibrations in hydrocarbons is less by perhaps a factor of 3 or more. The relationship of this classical model to a more rigorous quantum mechanical treatment and the numerical methods are discussed in the Appendices.

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