Analysis of nuclear quadrupole interaction in three pulse electron spin echo modulation spectra

Abstract

The introduction of nuclear quadrupole interaction in electron spin echo modulation by perturbation methods as proposed by Shubin and Dikanov [J. Magn. Reson. 52, 1 (1983)] is extended to the analysis of three pulse electron spin echo envelope modulation spectra. It is shown that an additional frequency difference occurs apart from the amplitude differences discussed by Shubin and Dikanov, because of an oversimplification of the expressions for the ENDOR levels. The effects of such inclusion of quadrupole interaction on the individual components contributing to the final modulation but with different time dependences are critically examined along with the effect of possible nonalignment of the quadrupole and dipolar tensors. The validity of the expressions obtained by the perturbation approach seems to be limited to relatively long electron-nuclear distances (r>0.35 nm for nuclei with I=1 and greater for nuclei with I>1). An independent determination of the magnitude of the quadrupole interaction may be needed to obtain unambiguous fits to experimental echo modulation spectra since the nonalignment of the hyperfine and quadrupole tensors reduces the influence of the quadrupole interaction on the echo modulation amplitudes.