Nuclear parameters

The nuclear spin of the stable isotopes of the halogens has been exploited in nmr spectroscopy. The use of in particular, with its 100% abundance, convenient spin of j and excellent sensitivity, has resulted in a vast and continually expanding literature since chemical shifts were first observed in 1950. The resonances for Cl and Cl were also first observed in 1950. Appropriate nuclear parameters are in Table 17.6. From this it is clear that the F resonance can be observed with high receptivity... 

Similar dependencies and trends are observed for other Mossbauer isotopes, for which more information is found in Chap. 7. It should be pointed out again that the nuclear parameter l RIR is negative for Fe in contrast to many other nuclei. The sign of the isomer shift correlations is inverted for nuclei with A/ // > 0. 

Apart from the determination of nuclear parameters, the Mossbauer transition in Os, especially the 36.2 and 69.6 keV transitions, are suited for chemical applications. As shown below, the 36.2 keV level, in spite of its large half-width, can be well used for the measurement of isomer shifts, whereas the 69.2 keV state is favorable for the characterization of electric quadrupole or magnetic dipole interactions. Both Mossbauer levels are populated equally well by the parent isotope lr, and simultaneous measurement is possible by appropriate geometrical arrangement. 

Determination of Nuclear Parameters of Osmium Mossbauer Isotopes... 

The application of Mossbauer spectroscopy in chemistry requires a prior knowledge of the nuclear states and transitions involved. In this section, we shall describe the determination of nuclear parameters by means of Mossbauer experiments with Os nuclei. 

The accuracy of the method is estimated at 50%. This estimate not only includes the uncertainties in counting methods but also the uncertainties associated with nuclear parameters. 

Another nuclear parameter that can be determined experimentally that depends on nuclear structure is the magnetic moment. The magnetic moment of a nucleus is a measure of the response of that nucleus to an external magnetic field and is made up from the net effect of the motion of the protons plus the intrinsic spins of the protons and neutrons. The magnetic moment, x, of one particle can be written as ... 

Ri. The value of R, will then be compared to the experimentally determined value of Rt for the 57Fe resonance. The result of this comparison taken together with other information will lead to better estimates of R, which will be called R . Finally, the values of R, (our best estimate of Rf) for a particular isotope will be used to decide if that isotope may be of interest in the studies of catalytic and chemical phenomena. It should be noted here that the analysis of the Mossbauer isotopes in terms of the ratio R, provides a simple physical feeling" for the associated nuclear parameters. The treatment in this section is based on nuclear parameters available from a variety of sources (/- 7, 30,85). However, these parameters are not available in a form readily usable for chemists. 

Chemical bonds involving protons and deuterons are very similar to one another. Therefore, since the contact and pseudocontact shifts are independent of the nuclear parameters, the shifts are essentially the same. Both nuclei have the characteristic that only Is orbitals are involved. Therefore, protons and deuterons are discussed together. Sometimes, the use of 2H NMR can be appropriate because it has a smaller linewidth than H (see Section 3.9). 

Table 3.3 Atomic and nuclear parameters for selected ionsa... 

The first charging process is related to the formation in the pure solvent of a void cavity having the appropriate shape and size to accommodate the solute. The electronic properties of the solute are not used here, only the geometrical nuclear parameters... 

There is a kind of atom where the nuclear effects are very large - exotic atoms, containing hadrons, i.e. particles that can interact strongly pions, antiprotons, kaons etc. In such atoms any advanced high-accurate QED theory is not necessary and a goal to study such atoms is to measure these nuclear parameters. An important feature of any spectroscopic measurement is its high accuracy in respect to non-spectroscopic methods. That is very important for exotic atoms, because some, like e.g. pionium (7r+7r -system or bound 7rp-system), are available in very small quantities (a few hundreds) [35],... 

The amplitude of the signal, A, is also determined. It depends on spins, multipolarities, and eventually on mixing ratios of the transitions involved, that is, entirely on nuclear parameters, and thus is a well-known quantity in practice, it is further reduced by solid angle correction factors. If more than one structure at the site of the PAC probe is present in the sample, the relative amplitudes will, in general, directly reflect the relative population of the different sites. 

Uncertainties of the conventional parameters of H-atoms have been addressed since the early applications of X-ray charge density method. Support from ND measurements appears to be essential, because the neutron scattering power is a nuclear property (it is independent of the electronic structure and the scattering angle). The accuracy of nuclear parameters obtained from ND data thus depends mainly on the extent to which dynamic effects (most markedly thermal diffuse scattering) and extinction are correctable. Problems associated with different experimental conditions and different systematic errors affecting the ND and XRD measurements have to be addressed whenever a joint interpretation of these data is attempted. This has become apparent in studies which aimed either to refine XRD and ND data simultaneously [59] (commonly referred to as the X+N method), or to impose ND-derived parameters directly into the fit of XRD data (X—N method) [16]. In order to avoid these problems, usually only the ND parameters of the H-atoms are used and fixed in the XRD refinement (X-(X+N) method). 

A. O. Madsen, H.O. Sorensen, C. Flesburg, R. F. Stewart and S. Larsen, Modeling of the nuclear parameters of H atoms in X-ray charge density studies, Acta Cryst. A60, 550-561 (2004). 

This expression further simplifies for high symmetry molecules. Figure 3 illustrates the relationships between o, Si, measurement, molecular structure, and other nuclear parameters. 

The corresponding experimental nuclear parameters are taken from Ref. [68] in the case of the nucleus and from Ref. [69] for the U. It should be noted that the difference between the results obtained within the different methods is smaller... 

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