A New Spin on Photoemission Spectroscopy Page: 33 of 259
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state electronic structures and can give rise to spin-polarization effects in photoemission
experiments from non-magnetic systems. It is also the interaction at the heart of the most
popular type of instrument for electron spin analysis.
The spin-orbit interaction falls naturally out of the Dirac equation without any extra
assumptions. A more intuitive understanding can be gained by describing it as due to the
interaction of the electron spin with an external electric field, E. At first glance, it is not
obvious that the spin should interact with an electric field. However, if the electron is
moving through E in the lab reference frame with velocity v, relativity requires that the
electron experiences a magnetic field in its rest frame given by
Bef = -v x E. (1.17)
The electron's spin magnetic moment directly interacts with this magnetic field with the
HLS = - - Bef. (1.18)
Using equation 1.16 for and substituting in equation 1.17 gives
HLS = 2BS [ x E]
= 2- S [p x E]. (1.19)
This expression is in fact not quite right, and results in atomic fine structure splittings a
factor 2 too large. This was explained by Thomas in 19269 as due to neglecting the fact that
the electron's rest frame is not an inertial frame; when treated correctly, an extra factor
1/2 is discovered, correcting the above expression to
HLS= S [p x E]. (1.20)
If the electric field is that of a central potential, V(r), as in the case of a hydrogen-like
atom, the electric field can be expressed as
E 1 dVx
E(= )vVc(r)z( . ' (1.21)
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Jozwiak, Chris. A New Spin on Photoemission Spectroscopy, thesis or dissertation, December 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc1014237/m1/33/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.