Nuclear spin-dependent effects

In addition to the dominant PNC interaction given in Eq. (45), there are other smaller PNC interactions that must be considered. First, there is the interaction between the nuclear axial-vector current and the electron vector current from Z exchange. In the limit of nonrelativistic nucleon motion, this interaction is given by the spin-dependent Hamiltonian 

7 = 7/2 and K2 = —0.05 for the valence proton of Cs. Additionally, parity violation in the nucleus leads to to a parity-violating nuclear moment, the anapole moment mentioned above, that couples elec-tromagnetically to the atomic electrons. The anapole-electron interaction is described by a Hamiltonian similar to (103), 

The parameter Ka — 0.24 — 0.33 is determined from nuclear model calculations [49]. These two interactions can be treated together using (104) with Ka K = Ka — 7C2(k — 1/2)1 K. The resulting spin-dependent correction was evaluated in the Dirac-Fock approximation including weak core-polarization corrections. Combining that calculation with the previous spin-independent result, we obtain 

These values of A F, F) agree to within 10% with results of semiempirical [50] and MBPT [51] calculations. Linear combinations of amplitudes in 

The interference between the hyperfine interaction and the spin-independent PNC interaction leads to a tiny spin-dependent interaction [52,53] that can also be included in the above analysis by adjusting the value of K in (105) slightly. 

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In contrast, high-resolution nuclear magnetic resonance measurements of chiral compounds aim at a detection of parity violating frequency shifts which are caused by parity violating nuclear spin-dependent effects [53, 54,56,67]. These effects are also expected to contribute predominantly to... 

The theory underlying this effect depends critically on two selection principles (1) the nuclear spin dependence of intersystem crossing in a radical pair, and (2)... 

The theory of CIDNP depends on the nuclear spin dependence of intersystem crossing in a radical (ion) pair, and the electron spin dependence of radical pair reaction rates. These principles cause a sorting of nuclear spin states into different products, resulting in characteristic nonequilibrium populations in the nuclear spin levels of geminate (in cage) reaction products, and complementary populations in free radical (escape) products. The effects are optimal for radical parrs with nanosecond lifetimes. 

The first four-component calculations on parity violating effects in chiral molecules were performed in 1988 by Barra, Robert and Wiesenfeld [54] within an extended Hiickel framework. Interestingly, this study was on parity violating chemical shift differences in the nuclear magnetic resonance (NMR) spectra of chiral compounds and hence focused as well on the nuclear spin-dependent term of Hpv. Shortly later, however, also the first four-component results on parity violating potentials obtained with an extended Hiickel method were published by Wiesenfeld [150]. 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

Here, A is the nearly isotropic nuclear coupling constant, I is the nuclear spin (Iun = I), and m is the particular nuclear spin state. It may be observed that the zero field splitting term D has a second-order effect which must be considered at magnetic fields near 3,000 G (X-band). In addition to this complication nuclear transitions for which Am = 1 and 2 must also be considered. The analysis by Barry and Lay (171) of the Mn2+ spectrum in a CsX zeolite is shown in Fig. 35. From such spectra these authors have proposed that manganese is found in five different sites, depending upon the type of zeolite, the primary cation, and the extent of dehydration. 

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