Simulation methods for looping transitions.

Looping transitions occur in field-swept electron magnetic resonance spectra near avoided crossings and involve a single pair of energy levels that are in resonance at two magnetic field strengths, before and after the avoided crossing. When the distance between the two resonances approaches a linewidth, the usual simulation of the spectra, which results from a linear approximation of the dependence of the transition frequency on magnetic field, breaks down. A cubic approximation to the transition frequency, which can be obtained from the two resonance fields and the field-derivatives of the transition frequencies, along with linear (or better) interpolation of the transition-probability factor, restores accurate simulation. The difference is crucial for accurate line shapes at fixed angles, as in an oriented single crystal, but the difference turns out to be a smaller change in relative intensity for a powder spectrum. Spin-3/2 Cr3+ in ruby and spin-5/2 Fe3+ in transferrin oxalate are treated as examples.