Mott scattering

Mott scattering derives from a 1929 paper by Nevill Mott which proposed a mechanism for experimentally verifying free electron spin quantization. Samuel Goudsmit and George Eugene Uhlenbeck had proposed electron spin and spin-orbit coupling to explain line splitting in atomic spectra in 1925 and by 1928 Paul Dirac had a relativistic quantum theory incorporating these ideas. As Mott details in the first part of his paper, direct observation of free electron spin was thought to be impossible due to issues with the uncertainty principle. Mott proposed double scattering of a high energy beam of electrons from atomic nuclei. The first backscattering event would polarize the beam transverse to the scattering plane; the second scattering event above or below the plane would then have measurable intensity differences to the left or right in an amounts according to the degree of polarization. The predicted effect was finally observed experimentally 1942. used this technique. == Electron polarimeter ==

In Mott's original paper he proposed measuring the free electron spin with two scattering events, one that created polarization and one that measured the degree of polarization. The second half of this concept forms an electron polarimeter. The electron beam is directed at a gold foil. Gold has a high atomic number (Z), is non-reactive (does not form an oxide layer), and can be easily made into a thin film (reducing multiple scattering). Two detectors are placed the same scattering angle to the left and right of the foil to count the number of scattered electrons. The measured asymmetry A, given by: :A = \frac{I^{\rm right}-I^{\rm left}}{I^{\rm right}+I^{\rm left}} is proportional to the degree of spin polarization P according to A = SP, where S is the Sherman function. spin dependence of electrons scattered or emitted from magnetic surfaces, measuring parity violation in high energy inelastic scattering from atoms, and tests of special relativity. == Theory ==

Qualitatively, Mott scattering can be analyzed with classical models. In the frame of the electron, the in-coming nuclear charge represents a Coulomb scattering center and a magnetic field circulating in a plane perpendicular in coming charge. The magnetic field interacts with the electron dipole, pushing spin "up" electrons to the right and spin "down" electrons to the left. At backscattering angles the smaller spin-dependent forces can alter the cross section to a measurable amount. Relation to electron diffraction When an experimentally found diffraction pattern deviates from the mathematically derived Mott scattering, it gives clues as to the size and shape of an atomic nucleus == References ==