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If the spins of the primary/scattered particles are described by | j1, m1 and | j3, m3 respectively (with j1, j3 =1/2 for EELS, j1, j3 =1 for RIXS), while the total angular momenta of the initial/final states of the target are described by | j2, m2 and | j4, m4 , respectively, then the amplitude of the transition probability via an intermediate state | J,M is given by ω12→34 (j1 j2 m1 m2 | JM |) (j3 j4 m3 m4 | JM |), with the bracket terms describing Clebsch-Gordan coefficients. If a peak is formed by contributions of final states with different j4, then, both techniques may provide different excitation energies (as given by the center of gravity of the contributing j4 states) due to the different weight of each j4 contribution.
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If the spins of the primary/scattered particles are described by | j1, m1 and | j3, m3, respectively (with j1, j3 =1/2 for EELS, j1, j3 =1 for RIXS), while the total angular momenta of the initial/final states of the target are described by | j2, m2 and | j4, m4, respectively, then the amplitude of the transition probability via an intermediate state | J,M is given by ω12→34 (j1 j2 m1 m2 | JM |) (j3 j4 m3 m4 | JM |), with the bracket terms describing Clebsch-Gordan coefficients. If a peak is formed by contributions of final states with different j4, then, both techniques may provide different excitation energies (as given by the center of gravity of the contributing j4 states) due to the different weight of each j4 contribution.
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