Magnetic field on a fast charged particle traversing a ferromagnet: Random-phase approximation

Linear response theory is applied to a calculation of the dynamic magnetic field experienced by a particle of charge $\mathrm{Ze}$ when it passes through a ferromagnet with a velocity $v\gg Z{v}_0$ ($v_0$ is the Bohr velocity). The wave-vector-dependent dielectric function and polarizability of an electron gas as calculated in the random-phase approximation are used in describing the response of the electrons in the ferromagnet to the Coulomb field of the traversing charge. The calculation results in a magnetic field acting on the moment of the charge of (0.86 ± 0.01) $4\pi M_{0}Z\left(\frac{v_0}{v}\right)$, where $M_0$ is the magnetization of the ferromagnet.