Theory of the Schwarz-Hora Effect

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Abstract
A theory of the Schwarz‐Hora effect is proposed. Using a simple model of the mechanism of light emission at the target, we first calculate the spectrum of radiation which is emitted when an electron whose wave function is modulated passes the surface of the target. We find that the spectrum has no peak at the frequency of modulation. This is because the electron is recoiled, so that it can take a continuous range of the kinetic energy after the interaction. We then propose that the Schwarz‐Hora effect is a phenomenon where many electrons whose velocities are uniform participate coherently. Then, the recoilless process has the amplitude of the order of N, and we find a peak at the modulation frequency. Furthermore, we show that modulation is even unnecessary to obtain the peak. The essential thing is not that we do not know exactly whether the electron has absorbed a photon or not, but that we do not know exactly which one of the electrons has absorbed the photon. We use a simple model of the mechanism of light emission at the target, in which the target is replaced by a transparent dielectric medium. With this model, we find that the above‐mentioned features are realized. We calculate the intensity, the direction, and the polarization of the Schwarz‐Hora radiation. A question of the relative and absolute intensity of the radiation is discussed.

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