By National Conference on Synchrotron Radiation Instrumentation
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Extra info for Synchrotron radiation instrumentation
64) into a symmetric and an antisymmetric part the latter provides nothing new because of the commutation relations. 65) Of these there are exactly six. Five are needed, which allows to introduce a physical condition into the final definition of the Si j : The polarization of the unpolarized ensemble ought to be zero: (Tr(S j ) = Tr(Si j ) = 0). 66) leading to: Sx x + S yy + Szz = 0, Tr (Si j ) = Tr (Si ) = 0. All “polarizations” of the unpolarized ensemble are then zero. Of the three diagonal elements Sii only two are independent.
9) The first factor is a phase factor, the second a matrix element of the reduced rotation I (β). (t + n − m)! 10) The sum goes over all t leading to non-negative factorials. g. a description of the density matrix in a rotated system or— equivalently—of a rotated density matrix in the old coordinate system. 15) The polarization direction is completely determined by the two parameters β, φ. β is the polar angle (relative to the z axis), φ the azimuthal angle = angle of the ( S, z) plane relative to an arbitrarily defined x axis (where x, y, z form a righthanded system).
Or the lab. direction. Then the coordinate system for the analyzer reaction may be defined as before as a right-handed system with: x along y × z , y along z × k out , and z = k out . More detailed discussions on polarization transfer can be found in Ohlsen , Ohlsen and Keaton , Sperisen et al. , Sydow et al. [11, 12]. 3 Coordinate Systems for Spin Correlations In this case two—in principle independent—polarizations have to be considered, because they can be prepared independently with arbitrary spin directions.
Synchrotron radiation instrumentation by National Conference on Synchrotron Radiation Instrumentation