Computation of Resonance Magnetic Fields of CW‑EPR Spectra by Reversion of Power Series

Electron paramagnetic resonance (EPR) spectra are generally recorded as a function of the magnetic field, while keeping the energy of transitions fixed.  Calculations of the EPR spectra, however, are almost always performed at a fixed magnetic field of a given spin-Hamiltonian to determine the energies of various transitions. These two methods, in general, do not produce equivalent spectra. In this pedagogical talk, I will first briefly highlight how various approaches have been used to handle this dichotomy by various workers. I will then describe our recent method to calculate the resonance magnetic fields at a fixed frequency.  With some help from the perturbation theory and the mathematics of reversion of polynominals, our method gives the resonance magnetic fields at a fixed frequency in a relatively simple and straightforward manner.
 
Ref. Vinayak Rane and Ranjan Das, Applied Magnetic Resonance,  https://doi.org/10.1007/s00723-019-01128-6