ELECTRON-SPIN-ECHO ENVELOPE MODULATION ARISING FROM HYPERFINE COUPLING TO A NUCLEUS OF ARBITRARY SPIN

The electron-spin-echo envelope modulation (ESEEM) arising from hyperf ine coupling to a nucleus of arbitrary spin I is investigated. The gen eric ESEEM pulse sequence, consisting of a succession of nonselective microwave pulses and free-evolution periods, is first considered. It i s shown that, when the high-field approximation is valid, the ESEEM fo r a nucleus of arbitrary spin is a function of the ESEEM for a I = 1/2 nucleus subject to the same Hamiltonian and that the functional relat ionship is provided by the Chebyshev polynomials of the second kind. S uch relationship also provides a very efficient method for the numeric al simulation of the ESEEM due to I > 1/2 nuclei. Next, the experiment based on the primary and on the stimulated electron-spin-echo pulse s equences are considered and explicit analytical formulas for arbitrary nuclear spin are given. The central result of the theory developed is that the modulation amplitudes are polynomials of degree 2I in the mo dulation depth parameter k. This nonlinearity introduces two differenc es with respect to the I = 1/2 case. First, the amplitudes of the fund amental pure and combination modulations, already present for spin-1/2 nuclei, are largely nonlinear functions of k; second, harmonics of th e fundamental modulations (up to the 2 Ith) occur in the ESEEM with am plitudes which can be comparable with those of the fundamentals, As a general rule, nonlinear effects are more important when I is large, pr ovided that all the other factors are the same. Since terms of differe nt order in k alternate in sign, the modulation amplitudes show an osc illating behavior and reach their maximum well before k = 1. While the amplitude of the pure modulations is always positive, that of the com bination modulations (which occur only in primary and 2-D stimulated E SEEM) can be either positive or negative, depending on the value of k; thence a new type of suppression effect ensues which is independent o f interpulse delays. Besides, the well-known suppression effect in the 1-D stimulated ESEEM of I = 1/2 nuclei occurs also when I > 1/2 in a similar way. Spectral simulations are presented to illustrate the char acteristics of the ESEEM arising from I > 1/2 nuclei. The theory devel oped is compared with an earlier analysis which neglected nonlinear te rms, and its advantages are demonstrated. (C) 1997 Academic Press.