Ramsey expressions

A compromise between the opposing interpretations of Pople and Mason is offered by Webb and co-workers (46). These authors conclude that it is improper to equate the diamagnetic terms used by the two authors, since in contrast to Pople s o A, Flygare s contains significant and variable nonlocal contributions and is comparable rather to the gauge-dependent term in the original Ramsey expression (29). 

This expression was deduced by the Rayleigh-Schrodinger perturbation theory. The Ramsey expression contains the electron exited states related to the energy E, and the operators A A and A which describe the involved electron interactions. The coupling of the external field to the orbital motion is expressed by a sum of orbital angular-momentum operators... 

According the Ramsey expression, the chemical shift tensor can be consi-... 

There are several books to which one can refer for more detailed technical information but, in general, chemical shifts for heavy and/or quadrupolar nuclei are rationalized on the basis of the Ramsey expression, equation (l) 5- 8 jqj. overall shielding (cr), made up of diamagnetic (oj) and paramagnetic (paramagnetic parameter, reflects the electron density in the immediate... 

NMR for some dinitrogen compounds are presented in Table 11 while data for nitrosyl species appear in Table 10. These data suggest the following overall shielding order CO>P(Alk)3>P(Ar)3>N2>NJ s NCR > NO > N=NR > N-NRI . Clearly, all the terms in the Ramsey expression are important here. Few new data for nitrosyl and thionitrosyl compounds have been reported since the last review. ... 

In Ramsey expressions, the diamagnetic electronic and spm-orbit operators are given by... 

The explicit incorporation of the nephelauxetic ratio into the Ramsey expression for a [(equation (6)] has been demonstrated for orthoaxial complexes of Co(III) which include ligators from different rows of the periodic table. Angular momentum integrals were calculated for intermediate ligand fields from optical spectral parameters. The cobalt shifts are linearly related to the optical parameter hJP), where hi is the energy of the first spin-allowed d-d band, so that can be factored out. It seems, however, that Rh(III) shifts are better described by an optical parameter containing rather than j8. ... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

A similar model is provided by what is called Ramsey pricing, after the economist Frank Ramsey.1213 This author showed that if the above conditions for market segmentation are fulfilled, social welfare is maximized in a particular market when the profit margin that is added to the marginal cost of production in order to determine the ex-factory price is inversely proportional to the price elasticity of demand. In other words, the price is always fixed above the marginal cost in order to recover the sunk costs, but this margin is inversely proportional to the sensitivity of demand in that market. Formally, this can be expressed as follows ... 

Equations relating and the spin-rotation constants have been given by Ramsey 9, 77, 78) for linear molecules and by Flygare 24) for symmetric top, spherical top, and asymmetric molecules. A simple expression for the general case, and neglecting vibrational effects, is... 

Both of these expressions are catered for in the thermodynamic approach to the concept of ion pairs outlined by Denison and Ramsey (44). Their treatment assumes at the outset that the two oppositely charged ions of an electrolyte (1 1) can only be in physical contact (tight or contact ion pair) or infinitely for apart In other words, the critical approach distance is synonomous with the sum of the ionic radii, and the association energy is numerically far in excess of thermal energy k T. Hence the change in the electrostatic free energy of the system resulting from the dissociation... 

Note that in the above expressions we conform with Ramsey [7] by making the replacements,... 

There is considerable controversy over the value of the radius of the hydrated proton (51-57), and it has been reported from 0.945-4.5 A. However, overwhelming experimental as well as theoretical work seems to suggest that the hydrated proton species is H904+ with a radius of 3.0 A. Hydrated anionic radii (r.) were calculated using this value of the hydrated proton, and these are compiled in Table VIII. What do these radii mean The term (l/r+ + l/r ) in Equation 32 really implies the sum of reciprocals of the minimum distances of approach of the two ions or some function of it. In the Dennison and Ramsey (58) treatment of the Bom model this term is 1/r, where r is the minimum distance of approach of the two ions. Implicit in the expression (l/r+ + 1/r.) is the assumption that both ions are monatomic and spherical therefore, the minimum distance of approach of the two ions may be apportioned as the hydronium ion radius and the anion radius. Although it might be possible to assign a value to the hydronium ion radius, the anionic radius... 

There is a theoretical treatment, by Ramsey (1684), of the diamagnetic shielding expressed in an expansion in inverse powers of p. Considering only the functional dependence upon p, Ramsey s expression has the form... 

Morris JC, Ramsey WJ, Wildner O, et al. A phase I study of intralesional administration of an adenovirus vector expressing the HS V-1 thymidine kinase gene (AdV.RSV-TK) in combination with escalating doses of... 

A general theory of chemical shifts of magnetic nuclei has been given by Ramsey, and the screening constant for a particular nucleus has been conveniently expressed in terms of three main contributions by equation (9)—... 

We wish to express our appreciation to J. W. Boyle, C. W. Nestor, Jr., M. H. Lietzke, and D. C. Ramsey of the Oak Ridge National Laboratory for their invaluable assistance in writing the program SLOPULSE. 

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