Transition probabilities in electron—nuclear double- and multiple-resonance spectroscopy with non-coherent and coherent radio-frequency fields

Abstract

Within the framework of a generalized operator transform technique the problem of the calculation of (time-proportional) transition probabilities of ESR, ENDOR and electron—nuclear multiple-resonance (EN m MR) transitions to first-order Rayleigh—Schrödinger perturbation theory is treated. Fermi's golden rule is extended to spin systems subject (besides the microwave field) to several (weak) coherent or non-coherent radio-frequency fields (monochromatic or narrowband modulated). It is shown that for recently introduced experimental techniques using either circularly polarized or polarization-modulated radio-frequency fields (CP ENDOR and PM ENDOR, respectively), both modulus and phase of the transition matrix elements for each radio-frequency field are required. Based on the first-order basis functions, analytical expressions for ESR and ENDOR transition probabilities for a general spin hamiltonian and various modulation schemes are given, which explicitly contain both zeroth- and first-order (“hyperfine enhancement”) contributions. The accuracy of the analytical first-order expressions is tested for two spin systems and found to be in excellent agreement with exact numerical calculations.