Spin detection by Mott scattering

The transformation back to the laboratory frame brings in the so-called Thomas factor, and one derives [Tho26, ERe85] 

Replacement of E by the gradient of the atomic potential V(r) gives a numerical factor and the vector r, and substitution of r x v by the orbital angular momentum ( of the moving electron yields finally 

This expression says that the interaction energy is due to the spin-orbit interaction which, therefore, is responsible for the spin-dependent effect in Mott scattering. The energy of the spin-orbit interaction adds to the potential of the Coulomb 

With the formulas given it is now possible to derive the required relation for the determination of the transverse spin component of an incident electron beam. If the beam contains Nup electrons with spin up and Ndown electrons with spin 

In order to measure P by spin-dependent Mott scattering, the incident electron has to be accelerated to 120 keV, scattered on a gold foil, and the backscattered intensities at +120°, called /( left) and /( right), have to be recorded. This gives the signals 

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The first prerequisite for measurement of photoelectron spin-polarization is the ability to separately detect the photoelectrons ejected from the different fine-structure levels (e.g., 2n3/2 and 2n1/2 for HX+ X2n). When the molecule contains a heavy atom (e.g., large spin-orbit splitting), it becomes easier to use the electron kinetic energy to distinguish the photoelectrons ejected from the different fine structure channels. For spin-polarization analysis, the accelerated electron beam (20-120 keV) can be scattered by a thin gold foil in a Mott-detector. The spin-polarization is determined from the left-right (or up-down) asymmetry in the intensities of the scattered electrons (Heinzmann, 1978). Spin polarization experiments, however, are difficult because the differential spin-up/spin-down flux of photoelectrons is typically one thousandth that obtained when recording a total photoionization spectrum. 

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