Nuclear quadrupole effects on two and three pulse electron spin echo patterns: A first order perturbation approach for nuclear quadrupole interaction only

Abstract

The nuclear modulation of electron spin echo signals is evaluated by an approach which handles only the nuclear quadrupole interaction as a perturbation of the eigenvectors and eigenvalues of the nuclear Hamiltonian including nuclear Zeeman and hyperfine terms. The theory is shown in detail for a first order perturbation treatment for both two and three pulse methods. Final formulas are obtained which are valid for any value of the electron–nuclear distance r, thus removing the limit of previous approaches. The modulation envelopes for I=1(2D) and I=5/2 (27A1) nuclear spin systems are critically analyzed at different electron–nuclear distances including possible misalignment between quadrupole and dipolar hyperfine tensors. Comparison with a first order perturbation approach for both hyperfine and nuclear quadrupole interactions as perturbations of the nuclear Zeeman Hamiltonian is made and shows that the exact treatment of the hyperfine interaction considerably reduces the apparent nuclear quadrupole effects on the overall echo modulation envelopes, particularly at small electron–nuclear distances.