Nuclear magnetic moment distribution

The complicated Fe SRPAC spectrum of Ni ferrite was quite unexpected for us at the beginning. However, by including partial alignment of the nuclear magnetic moments, distribution of internal magnetic fields and the elastic scattering contribution into the theoretical model, we reproduced the spectrum very well, and the result is consistent with our Mossbauer data. This indicates that SRPAC can reveal very detailed hyperfine interactions. 

The main difference between the quoted papers lies in the modeling of the magnetic moment distribution in the nucleus a bulk distribution is assumed in the present paper and in paper [11] and a surface distribution is adopted in ref [22]. A systematic 1% difference is observed, which cannot be explained by the uncertainty in the nuclear radius. However, it is known that variations of the nuclear size within reasonable limits can lead to variations in the value of A of several orders of magnitude [11, 14]. This question will be analysed in a separ-ate paper. 

Besides the above interactions between the nuclear and electronic charge distributions, the nucleus also interacts with magnetic fields. In the presence of such a field at the nucleus, different orientations of the nuclear magnetic moment g with respect to the field direction will have different energies M (e.g 29, 30, 32) ... 

Let us mention several papers by Ya.B. on various problems of molecular physics and quantum mechanics which have not been included in this volume. Among the problems considered are the peculiar distribution of molecules according to their oscillatory modes when the overall number of oscillatory quanta does not correspond to the temperature of translation [9], the influence of the nuclear magnetic moment on the diffusion coefficient [10] and on absorption of light by prohibited spectral lines [11],... 

There is one other type of relaxation process that must be mentioned at this point. After irradiation ceases and B, disappears, not only do the populations of the m = + and m = states revert to the Boltzmann distribution, but also the individual nuclear magnetic moments begin to lose their phase coherence and return to a random arrangement around the z axis (Figure 2.1a). This latter process, called spin-spin (or transverse) relaxation, causes decay of MJ>y at a rate controlled by the spin-spin relaxation time T2. Normally, T2 is much shorter than T. A little thought should convince you that if T2 < Th then spin-spin (dephasing) relaxation takes place much faster than spin-lattice (Boltzmann distribution) relaxation. 

NMR has proved to be one of the most valuable techniques to obtain information on electron distribution and dynamics [3], as well as on dimensionality and on the role of electron-electron interactions, in organic conductors. Since they contain atoms such as C, H, N, S, and Se, having isotopes with nuclear spin, they have nuclear magnetic moments of the form... 

Hyperfine interactions, that is the interaction of a nuclear magnetic moment with extranuclear magnetic fields and the interaction of a nuclear quadrupole moment with electric field gradients from extranuclear charge distributions, are measured via time differential perturbed angular correlation (TDPAC) of y-rays emitted from radioisotopes. 

Relaxation behavior is deduced from measurements of various transient phenomena. Current interpretations of these phenomena dictate the definition of two processes by which the orientations of the nuclear magnetic moments reach the equilibrium distribution. These processes are described by characteristic times, designated Ti and T2. The first, Ti, is called the thermal or longitudinal relaxation time. 

The detection of energy at this transition frequency is the basis of NMR spectroscopy. The actual detection of NMR signals, however, is made possible through the bulk magnetization (AT) of the nuclear system that arises from the resultant of the individual nuclear magnetic moments that are distributed between the various energy levels. The rotating components (x and y) of p transverse to the direction (z) of B0 at nonresonant equilibrium have no phase coherence and A7x = My = 0,... 

Figure 9. Excitation and relaxation in a population of spins, (a) Before pulse, (b) Induction of phase coherence along y by Hi, and consequent tipping of macroscopic magnetization, M. (c) Dephasing of nuclear magnetic moments by spin-spin relaxation, i.e., M,. = 0. (d) Re-establishment of the Boltzmann distribution (Afj is at its equilibrium value)(a = d).

While the early optical measurements suffered from limited resolution, the development of atomic beam methods provided a useful tool in the study of atomic and nuclear magnetic moments [ 12,13] (for a review see [ 14]) and it became possible to measure the nuclear magnetic moments (and nuclear spins) in a direct way for both stable and radioactive isotopes, by using a variety of methods ] 15]. The study of optical IS was, however, limited to Doppler-limited optical spectroscopy until the invention of the laser and the development of suitable high-resolution optical methods (a review can be found in [16]). It is also possible to obtain information on the nuclear charge distribution by electron scattering experiments and from muonic X-ray transitions and electron K X-ray IS [17], perhaps even with a higher accuracy than with optical spectroscopy. 

Another important quantity related to the current density distribution is the nuclear magnetic moment density distribution (or magnetization density distribution) m(r) = r x j(r), which integrates to the magnetic moment = f d r m(r) briefly mentioned above. Finally, the magnetic induction field, generated by the nuclear current density distribution, can be obtained from the vector potential or from the current density distribution as... 

A nucleus with nuclear spin I greater than has an electric quadrupole moment in addition to a nuclear magnetic moment. An electric quadrupole moment arises from an asymmetry of the distribution of the electrical charges in the nucleus and does not depend on the net charge. It is often viewed as two electric dipoles displaced from one another and... 

Generally speaking, the density p ri —ta)-, which appears in the nuclear spin-dependent terms, does not coincide with the nucleon density relevant for the nuclear spin-independent term (see for instance also equation 26 in ref. [90]). The situation is reminiscent of the magnetic moment distribution... 

Mossbauer spectroscopy is a powerful technique that may give information on electronic distribution on about 44 different nuclei as a consequence of their structural environment [1-9], The effects of interaction between the nuclear magnetic moment, an external magnetic field, electric charges and moments of the absorbing and surrounding atoms are known as hyperfine interactions [10]. 

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