Spin-Half Nuclei

The orthonormal basis generally prevalent in numerical simulations is composed of the product functions (henceforth, a), which are the products of the spin functions of the nuclei in all the possible variations. In this case, the fi index of the nucleus can be abandoned, because the order of the atomic functions already defines it. There are 2" product functions in the case of n spin-half nuclei. On this basis, the matrix of the Hamiltonian is composed of the following elements ... 

The REAPDOR experiment (Gullion 1995, 1995a) can be considered as a variation of the TRAPDOR experiment, in which a train of rotor-synchronised 180° pulses is applied to the spin- /2 nucleus, spaced half a rotor period apart. The experiment uses an... 

A number of "X, ""Y coherence transfer experiments involving polarization transfer from or to quadrupolar nuclei were performed by using both INEPT and the universal polarization transfer (UPT) scheme (Fig. 1(a)) which is a generalization of DEPT. The use of the INEPT method is unproblematic. It can be applied without modification for polarization transfer from any number of equivalent spin-half nuclei to a nucleus of arbitrary spin, and a report on successful measurement of C, D INEPT spectra also demonstrated its utilization for magnetization transfer from a quadrupolar to a spin-half nucleus. Application of the UPT scheme requires appropriate adjustment of the variable pulses <(> and 9 to the spin and number of the... 

Having experienced a continuously increasing importance during the last years, two-dimensional experiments represent now the most widespread and most frequently employed methods for "X, "Y shift correlation. Similar to one-dimensional experiments, both direct schemes which excite ""Y and detect "X magnetization, and inverse schemes which start and end with "X magnetization, are in use. Most examples of "X, "Y correlations reported so far involve cases where the indirectly observed "Y nucleus is a spin-half species, while the detected nucleus may be either spin-half or quadrupolar. In... 

Another example of five-co-ordinate phosphorus bound to a transition metal is provided by the reaction of (112) with (113) to form the spirophosphorane (114) in 91 % yield. The n.m.r. shift at + 67 p.p.m. is very broad (1100 Hz at half height) because of coupling with the manganese nucleus (spin 5/2), but n.m.r. and i.r. data serve to substantiate the structure as five-co-ordinate. 

For nearly half a century, Mendeleev s periodic table remained an empirical compilation of the relationship of the elements. Only after the first atomic model was developed by the physicists of the early twentieth century, which took form in Bohr s model, was it possible to reconcile the involved general concepts with the specificity of the chemical elements. Bohr indeed expanded Rutherford s model of the atom, which tried to connect the chemical specificity of the elements grouped in Mendeleev s table with the behavior of electrons spinning around the nucleus. Bohr hit upon the idea that Mendeleev s periodicity could... 

The Co nucleus decays with a half-life of 5.27 years by /5 emission to the levels in Ni. These levels then deexcite to the ground state of Ni by the emission of one or more y-rays. The spins and parities of these levels are known from a variety of measurements and require that the two strong y-rays of 1173 and 1332 keV both have E2 character, although the 1173 y could contain some admixture of M3. However, from the theoretical lifetime shown ia Table 7, the E2 contribution is expected to have a much shorter half-life and therefore also to dominate ia this decay. Although the emission probabilities of the strong 1173- and 1332-keV y-rays are so nearly equal that the difference cannot be determined by a direct measurement, from measurements of other parameters of the decay it can be determined that the 1332 is the stronger. Specifically, measurements of the continuous electron spectmm from the j3 -decay have shown that there is a branch of 0.12% to the 1332-keV level. When this, the weak y-rays, the internal conversion, and the internal-pair formation are all taken iato account, the relative emission probabilities of the two strong y-rays can be determined very accurately, as shown ia Table 8. 

Fig. 5. Decay scheme of showing the energies, spins, and parities of the levels populated in the daughter nucleus, Xe, and the energies in keV, emission probabihties (in %), and multipolarities of the y-ray transitions. There is a strong dependence of the y-ray lifetime on the y-character. The Ml + E2 y-ray of 177 keV has a half-hfe of 2.1 ps the half-hfe of the 164-keV M4 y-ray is 1.03 X 10 s.

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

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