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Dependence of the integrated magnetic resonance absorption on resonance frequency and crystal field perturbations for non‐kramers doublets
Author(s) -
Bowden Charles M.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560050877
Subject(s) - resonance (particle physics) , hamiltonian (control theory) , absorption (acoustics) , magnetic field , atomic physics , field (mathematics) , chemistry , condensed matter physics , nuclear magnetic resonance , computational physics , physics , molecular physics , optics , quantum mechanics , mathematics , mathematical optimization , pure mathematics
A model is derived for the frequency dependency of the magnetic resonance integrated absorption for non‐Kramers doublets. On the basis of the model, a frequency squared dependency is predicted for the acoustical paramagnetic resonance ( APR ) integrated absorption which compares favorably with the results of experimental APR absorption data for CaF 2 :U 4+ . A transformation is derived from the spin‐Hamiltonian which transforms the absorption line shape from that in field variation ( H ) to that in frequency variation ( v ). The transformation shows that the line shapes in the two cases are basically different when the absorption line is broadened by crystal field perturbations. The transformation gives the line shape in frequency variation, given the line shape in field variation. The model predicts that the integrated intensity in frequency variation is greater than that in field variation by a term proportional to the average value of the square of the crystal field perturbations. From the model the integrated APR absorption as a function of the square of the resonance frequency gives an intercept explicitly in terms of the zero field splitting between the states of the doublet. The slope gives the strength of the spin‐phonon coupling.