Spin Magnetic Effect on the Polarization of the Electron-Atom Impact Radiation

Abstract

A new mechanism is proposed to explain the discrepancies between the measured and the expected polarization of the electron-atom impact radiation at threshold energy. The idea is the following: At threshold scattering, the spin of the scattered electron interacts magnetically with the orbital motion of the atomic electrons. The component of this magnetic interaction along the quantization axis, which is perpendicular to the incident electron direction, will split the magnetic sublevels of the atomic excited states. This splitting will cause the coherent interference of the radiation, which originates from two degenerate upper levels and ends on a single lower level, to become ineffective. The polarization of the radiation is thereby affected and in fact decreases. The expected polarization $P$ is modified by a depolarization factor $f={(1+{〈{\ensuremath{\omega}}^{2}〉}_{\mathrm{av}}{\ensuremath{\tau}}^{2})}^{\ensuremath{-}1}$, where $\ensuremath{\omega}$ is the frequency splitting of the excited state, and $\ensuremath{\tau}$ is the lifetime of the transition from the excited upper state to a lower state. By using a simple product wave function for the state, the $\ensuremath{\omega}$ and hence the $P$ for various singlet-singlet transitions and triplet-triplet transitions have been calculated for the helium atom. In general, when the principal quantum number $n$ of the excited state, where the radiation originates, increases, $f$ also increases and approaches unity. Consequently, $P$ increases and approaches the expected value. For example, $P$ for the $3^{1}P\ensuremath{\rightarrow}2^{1}S$ (5016 \AA{}) line turns out to be 1.2%, whereas for the $4^{1}D\ensuremath{\rightarrow}2^{1}P$ (4922 \AA{}) line it turns out to be 50%. The expected values are 100% and 60%, respectively. In the case of triplet-triplet transitions, the spin-spin interaction between the scattered electron and the atomic electrons is also included.