Combined effects of several polarisation mechanisms

1 Generalised formalism for the scattering of polarised electrons by unpolarised targets 

We will again work in the collision system where the z-axis of quantisation is parallel to ko and the scattering plane is the zx-plane (see fig. 8.1). We can write the density matrix (Blum, 1981) for the final state as 

For spin 1/2 particles there are 16 possible combinations of (v-VoVjVo) and therefore 32 real (or 16 complex) parameters. From (9.14) it can be seen that hermiticity requires that 

Reflection invariance with respect to the scattering plane (i.e. parity conservation) yields the further restriction that 

15) and (9.17), which correspond to (8.14) and (8.15), restrict the number of parameters so that only eight independent parameters are required to characterise in general the reduced density matrix of the scattered electrons. In special situations the number of independent parameters can be reduced even further as discussed earlier. 

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