Quantum number, nuclear spin solids

Quadrupolar nuclei, i.e., those with a nuclear spin quantum number 7 greater than or equal to one, outnumber their spin-1/2 counterparts by a factor of roughly 3 1 and are critically important in the study of many solid materials. For example, nB (spin 7 = 3/2, 80% natural abundance), 14N (7=1, 99.6%), 23Na (7 = 3/2, 100%), 170 (7 = 5/2, 0.04%) and 27A1 (7 = 5/2,100%) comprise some of the most important atomic nuclei in chemistry, materials science, and biology. As is well... 

Mossbauer spectroscopy is based on transition between energy levels of nuclei with different values of the nuclear spin quantum number /. When a nucleus emits a y-ray, the energy of the emitted radiation is lowered by the recoil of the nucleus. Conversely, the energy needed for absorption is higher than that needed for transition, because the absorbing nucleus absorbs energy in the recoil process. For nuclei tightly bound in solids, however, the effective mass of the emitter and... 

Static quadrupole effects in NMR are observed in solids (9) and also in anisotropic liquid crystals (10, 11, 12). For nuclei with spin quantum numbers, I, greater than V2, the distribution of positive charge over the nucleus can be nonspherical and the situation can be described in terms of a nuclear electric quadrupole moment. The interaction between the quadrupole moment, eQ and electric field gradients, eq, shifts the energy levels of the nuclear spin states. 

In spite of impressive experimental demonstrations of basic quantum information effects in a number of different mesoscopic solid state systems, such as quantum dots in semiconductor microcavities, cold ions in traps, nuclear spin systems, Josephson junctions, etc., their concrete implementation is still at the proof-of-principle stage [1]. The development of materials that may host quantum coherent states with long coherence lifetimes is a critical research problem for the nearest future. There is a need for the fabrication of quantum bits (qubits) with coherence lifetimes at least three-four orders of magnitude longer than it takes to perform a bit flip. This would involve entangling operations, followed by the nearest neighbor interaction over short distances and quantum information transfer over longer distances. 

Tables 9.1 and 9.2 list the NMR-active nuclei (i. e., those with 1 > 0) of most relevance for organic and inorganic solids, respectively, together with their nuclear spin quantum numbers, their magnetogyric ratios (y), and natural abundances. (For a comprehensive Hsting of all NMR-active nuclei, the reader is referred to [6]) For spin J = 1/2 nuclei, the two most important anisotropic interactions are...

In addition, molecules may vibrate, and the vibrational energy levels are defined by the vibrational quantum number, v. In the gaseous state, molecules may also rotate freely, and the rotational energy levels are defined by the rotational quantum number, J. In the condensed states of solid and liquid, rotation is restricted. With nuclear spin, the nuclear spin quantum number, I, is important. 

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