Hyperfine definition

Time. The unit of time in the International System of units is the second "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental state of the atom of cesium-133" (25). This definition is experimentally indistinguishable from the ephemetis-second which is based on the earth s motion. 

Two of the three SI base units have in the meantime acquired redefinitions in atomic terms (e.g., the second is now defined as 9 192 631 770 hyperfine oscillations of a cesium atom). However, the definitions (C.2a)-(C.2c) conceal another unfortunate aspect of SI units that cannot be overcome merely by atomic redefinitions. In the theory of classical or quantal electrical interactions, the most fundamental equation is Coulomb s law, which expresses the potential energy V of two charged particles of charge q and 2 at separation R as... 

The g tensors and hyperfine constants of the paramagnetic centers observed in irradiated NH4Y zeolites after various activation treatments are given in Table VIII. Despite the abundance of experimental results, many of the structures proposed for these centers should be regarded as suggestive rather than definitive, as previously noted by Kasai and Bishop (264). Neither the axially symmetric g tensor of the V center associated with two aluminum atoms nor the isotropic g tensor of the V center associated with one aluminum atom reported by Vedrine et al. (266) is consistent with the symmetry of the respective models proposed above. 

Once a description of the electronic structure has been obtained in these terms, it is possible to proceed with the evaluation of spectroscopic properties. Specifically, the hyperfine coupling constants for oligonuclear systems can be calculated through spin projection of site-specific expectation values. A full derivation of the method has been reported recently (105) and a general outline will only be presented here. For the calculation of the hyperfine coupling constants, the total system of IV transition metal centers is viewed as composed of IV subsystems, each of which is assumed to have definite properties. Here the isotropic hyperfine is considered, but similar considerations apply for the anisotropic hyperfine coupling constants. For the nucleus in subsystem A, it can be... 

While warming the sample, the intensity of the odd number hyperfine structures increased relative to the octet, but no definite assignments of these odd line spectra to specific radical structures were attempted. 

The black body shifts are not confined to Rydberg atoms, but also alter the frequency of atomic clock transitions. Itano et al. have shown that the Cs 9 GHz ground state hyperfine interval, the definition of the second, is increased by one part in 1014 when the temperature is raised from 0 K to 300 K.29. 

The CIDNP method is an indirect method, since the hyperfine pattern of a paramagnetic intermediate is derived from the unusual NMR intensities of a diamagnetic product derived from it. Accordingly, it appears necessary to discuss limitations and potential sources of misassignments. First, the CIDNP method does not provide any evidence for the nature of the paramagnetic intermediate, particularly there is no definitive evidence for the presence of the charge. This feature is derived typically on the basis of mechanistic considerations and from supporting secondary experiments. 

While the Overhauser shift is due to delocalised electrons, the ENDOR experiments require more localised electrons. Both groups were able to observe ENDOR on the effective mass donor resonance but not on the deep donor signal. An illustrative ENDOR spectrum is shown in FIGURE 4, in which the 69 71Ga ENDOR lines are observed. The 69Ga line is clearly split by quadrupole interactions just as in the Oveihauser shift measurements, while the quadrupolar interaction is much less resolved in the 71 Ga line, due to its smaller quadrupole moment. In the three samples investigated by the two groups, the linewidths were all too broad to resolve any hyperfine interaction and so no definitive identification of the residual donor was possible. 

PMMA has been known, since the 1950s, to show the ESR spectrum with five intense and four weak hyperfine lines (see the insert of Fig. 9), when it is irradiated with y-rays at room temperature. After a long history of the study on this anomalous ESR spectrum [32-34], the interpretation is now almost settled that it is due to the propagating-type radical -CH2-C(CH3)COOCH3 (the radical expected to form during the radical polymerization of methyl methacrylate) [35, 36], Although the formation of this radical is a definite proof of the radiation-induced scission of the PMMA main-chain, the previous ESR studies have failed to elucidate the mechanism for the formation of this radical. 

These definitions are consistent with those of Gallagher and Johnson [116]. This completes our calculation of the nuclear hyperfine terms in the primitive basis set. 

In order to assign the Zeeman patterns for the three lowest rotational levels quantitatively, one must determine the spacings between the rotational levels, and the values of g/and gr-In the simplest model which neglects centrifugal distortion, the rotation spacings are simply B0. /(./ + 1) this approximation was used by Brown and Uehara [10], who used the rotational constant B0 = 21295 MHz obtained by Saito [12] from pure microwave rotational spectroscopy (see later in the next chapter). The values of the g-factors were found to be g L = 0.999 82, gr = —(1.35) x 10-4. Note that because of the off-diagonal matrix elements (9.6), the Zeeman matrices (one for each value of Mj) are actually infinite in size and must be truncated at some point to achieve the desired level of accuracy. In subsequent work Miller [14] observed the spectrum of A33 SO in natural abundance 33 S has a nuclear spin of 3/2 and from the hyperfine structure Miller was able to determine the magnetic hyperfine constant a (see below for the definition of this constant). 

Taking the different arguments together, it is the author s opinion that the dangling bond model remains the more plausible explanation of the 2.0055 defect. Perhaps within a short time, further studies of the hyperfine interaction or calculations of the defect energy levels, etc. will be able to provide definitive proof one way or the other. In the remainder of this book, for the sake of definiteness, we refer to the 2.0055 ESR spin and the associated deep trap as the dangling bond, recognizing that the interpretation of electrical data involves only the gap state levels and the electron occupancy, not the atomic structure. 

A nuclear quadrupole interaction is by definition anisotropic (parameters P, rj) as is an electronic quadrupole interaction (i.e., zfs parameters D, E), since these are described by a nonzero field gradient. Both of these effects have been briefly mentioned above, but the most important manifestation of anisotropy in ENDOR is with respect to g valnes and to hyperfine coupling interactions. 

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