Zeeman interaction resonance condition

Before we develop the resonance conditions for systems with hyperhne and with zero-held interactions, we return to the electronic Zeeman term S B as an example interaction to discuss a hitherto ignored complexity that is key to the usefulness of EPR spectroscopy in (bio)chemistry, namely anisotropy the fact that all interactions... 

Let us rewrite the resonance condition of an S = 1/2 system subject to the Zeeman interaction only as... 

When the hyperfine interaction is much smaller than the Zeeman interaction ( much means approximately two orders of magnitude or more), as is usually the case in X-band, then the resonance condition is... 

We have considered here the influence of dispersion asymmetry and Zee-man splitting on the Josephson current through a superconductor/quantum wire/superconductor junction. We showed that the violation of chiral symmetry in a quantum wire results in qualitatively new effects in a weak superconductivity. In particularly, the interplay of Zeeman and Rashba interactions induces a Josephson current through the hybrid ID structure even in the absence of any phase difference between the superconductors. At low temperatures (T critical Josephson current. For a transparent junction with small or moderate dispersion asymmetry (characterized by the dimensionless parameter Aa = (vif — v2f)/(vif + V2f)) it appears, as a function of the Zeeman splitting Az, abruptly at Az hvp/L. In a low transparency (D Josephson current at special (resonance) conditions is of the order of yfD. In zero magnetic field the anomalous supercurrent disappears (as it should) since the spin-orbit interaction itself respects T-symmetry. However, the influence of the spin-orbit interaction on the critical Josephson current through a quasi-ID structure is still anomalous. Contrary to what holds... 

One key aspect of ENDOR spectroscopy is the nuclear relaxation time, which is generally governed by the dipolar coupling between nucleus and electron. Another key aspect is the ENDOR enhancement factor, as discussed by Geschwind [294]. The radiofrequency frequency field as experienced by the nucleus is enhanced by the ratio of the nuclear hyperfine field to the nuclear Zeeman interaction. Still another point is the selection of orientation concept introduced by Rist and Hyde [276]. In ENDOR of unordered solids, the ESR resonance condition selects molecules in a particular orientation, leading to single crystal type ENDOR. Triple resonance is also possible, irradiating simultaneously two nuclear transitions, as shown by Mobius et al. [295]. 

For nitroxides in dilute liquid solution, the generally anisotropic spin Hamilton operator is simplified tremendously and, if imresolved proton hyperfine couplings are treated as line broadening, only the electron-Zeeman interaction and the hyperfine coupling to the magnetic nucleus (7 = 1) remain [20]. The g- and hyperfine (4-) tensors are averaged to isotropic values due to fast motion of the spin probe and the resonance condition for the irradiated microwave becomes... 

The correlation patterns are more complex if the nuclear quadrupole, the hyperfine, and the nuclear Zeeman interactions are of the same order of magnitude. This situation is often encountered in X-band HYSCORE spectra of weakly coupled nitrogen nuclei in transition metal complexes. A special case, where the spectrum is considerably simplified, is the so-called exact cancellation condition, where Xs 2 coi. Under this condition, the nuclear frequencies within one of the two ms manifolds correspond to the nuclear quadrupole resonance (NQR) frequencies coq = 2Kt], co = K(3 - t]), and cu+ = K 3 + rj) [43], which are orientation independent. Consequently, correlation peaks involving these frequeneies appear as narrow features in the nuclear frequency spectrum. 

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