Sherman function

[1] It was first evaluated theoretically by the physicist Noah Sherman and it allows the measurement of polarization of an electron beam by Mott scattering experiments.

[2] A correct evaluation of the Sherman function associated to a particular experimental setup is of vital importance in experiments of spin polarized photoemission spectroscopy, which is an experimental technique which allows to obtain information about the magnetic behaviour of a sample.

[4] defined as It is known that, when an electron collides against a nucleus, the scattering event is governed by Coulomb interaction.

Spin orbit interaction can be evaluated, in the rest reference frame of the electron, as the result of the interaction of the spin magnetic moment of the electron with the magnetic field that the electron sees, due to its orbital motion around the nucleus, whose expression in the non-relativistic limit is: In these expressions

Due to spin orbit coupling, a new term will appear in the Hamiltonian, whose expression is[5][page needed] Due to this effect, electrons will be scattered with different probabilities at different angles.

Since the spin-orbit coupling is enhanced when the involved nuclei possess a high atomic number Z, the target is usually made of heavy metals, such as mercury,[1] gold[6] and thorium.

[7] If we place two detectors at the same angle from the target, one on the right and one on the left, they will generally measure a different number of electrons

is a measure of the probability of a spin-up electron to be scattered, at a specific angle

[8][9] It can assume values ranging from -1 (spin-up electron is scattered with 100% probability to the left of the target) to +1 (spin-up electron is scattered with 100% probability to the right of the target).

The value of the Sherman function depends on the energy of the incoming electron, evaluated via the parameter

, spin-up electrons will be scattered with the same probability to the right and to the left of the target.

[8] To measure the polarization of an electron beam, a Mott detector is required.

[12] In order to maximize the spin-orbit coupling, it is necessary that the electrons arrive near to the nuclei of the target.

To achieve this condition, a system of electron optics is usually present, in order to accelerate the beam up to keV[13] or to MeV[14] energies.

Since standard electron detectors count electrons being insensitive to their spin,[15] after the scattering with the target any information about the original polarization of the beam is lost.

Nevertheless, by measuring the difference in the counts of the two detectors, the asymmetry can be evaluated and, if the Sherman function is known from previous calibration, the polarization can be calculated by inverting the last formula.

[7] In the panel it is shown an example of the working principle of a Mott detector, supposing a value for

If an electron beam with a 3:1 ratio of spin-up over spin-down electrons collide with the target, it will be splitted with a ratio 5:3, according to previous equation, with an asymmetry of 25%.