Bowers’ theory

The theory of orientation measurements by linearly polarized Raman spectroscopy has been developed in detail by Bower in 1972 [44]. The Raman intensity, I, is given by... 

Most ESR studies of organic radicals were carried out in the 1950s and 1960s. They provided important tests of early developments in valence theory. The results of these early studies are nicely summarized in a review by Bowers.11 Applications of hyperfine splittings to structure determination are discussed in many of the texts and monographs referenced in Chapter 1. 

Bleaney, B., Bowers, K.D., and Pryce, M.H.L. 1955. Paramagnetic resonance in dilute copper salts III. Theory, and evaluation of the nuclear electric quadrupole moments of 63Cu and 65Cu. Proceedings of the Royal Society of London A 228 166-174. 

Substantial evidence supports the theory that psychotic depression represents a distinct type of major depression (Schatzberg and Rothschild 1992). Statistically significant differences between psychotic and nonpsychotic major depression have been noted along many axes, including presenting features (Coryell et al. 1984 Frances et al. 1981 Classman and Roose 1981 Lykouras et al. 1986 J. C. Nelson and Bowers 1978), biology (Carroll et al. 1976a Coryell et al. 1982 Rihmer et al. 1984 Rudorfer et al. 1982), familial transmission (Leckman et al. 1984 W. H. Nelson et al. 1984), course of illness (D. G. Robinson and Spiker 1985), and response to treatment (Chan et al. 1987 Classman and Roose 1981 Kantor and Classman 1977 J. C. Nelson and Bowers 1978 Rothschild 1985). 

Theoretical rate constants are found to agree within 20% of the experimental value. Further refinements of this theory (Su et al., 1978). including conservation of angular momentum, bring the calculated rate constants within experimental error (Su and Bowers, 1979). 

Bovens, M. (1998) The Quest for Responsibility Accountability and Citizenship in Complex Organisations, Cambridge University Press, Cambridge Bowers, J. (1997) Sustainability and Environmental Economics, Addison Wesley Longman, Harlow Canovan, M. (1983) A case of distorted communication A note on Habermas and Arendt , Political Theory, vol 11, ppl05—116... 

C) C.O.Bower, "Practical Shell Forging, Longmans,Green,London(1919) D)US Ordnance Dept Document No 2035, "Theory and Design of Recoil Systems and Gun Carriages, Engineer Reproduction Plant,Washington,DC (1921) E)M.J.Pedersen,ArOrdn 15,347-51(1935)... 

One of the most important theoretical contributions of the 1970s was the work of Rudnick and Stern [26] which considered the microscopic sources of second harmonic production at metal surfaces and predicted sensitivity to surface effects. This work was a significant departure from previous theories which only considered quadrupole-type contributions from the rapid variation of the normal component of the electric field at the surface. Rudnick and Stern found that currents produced from the breaking of the inversion symmetry at the cubic metal surface were of equal magnitude and must be considered. Using a free electron model, they calculated the surface and bulk currents for second harmonic generation and introduced two phenomenological parameters, a and b , to describe the effects of the surface details on the perpendicular and parallel surface nonlinear currents. In related theoretical work, Bower [27] extended the early quantum mechanical calculation of Jha [23] to include interband transitions near their resonances as well as the effects of surface states. 

If redissociation into reactants is faster than stabilization, equations (3.15) and (3.16) simplify into a product of k,/k, and either kr or kcoll. Under these conditions, to obtain a theory for a total association rate coefficient, one must calculate both k,/k i and kr or kco . Three levels of theory have been proposed to calculate k, /k, . In the simplest theory, one assumes (Herbst 1980 a) that k, /k 3 is given by its thermal equilibrium value. In the next most complicated theory, the thermal equilibrium value is modified to incorporate some of the details of the collision. This approach, which has been called the modified thermal or quasi-thermal treatment, is primarily associated with Bates (1979, 1983 see also Herbst 1980 b). Finally, a theory which takes conservation of angular momentum rigorously into account and is capable of treating reactants in specific quantum states has been proposed. This approach, called the phase space theory, is associated mainly with Bowers and co-workers... 

The modified thermal and phase space theories reproduce most three body association data equally well, including the inverse temperature dependence of the rate coefficient (Herbst 1981 Adams and Smith 1981), and are capable of reproducing experimental rate coefficients to within an order of magnitude (Bates 1983 Bass, Chesnavich, and Bowers 1979 Herbst 1985b). They should therefore be this accurate for radiative association rate coefficients if kr is treated correctly. 

A further advance occurred when Chesnavich et al. (1980) applied variational transition state theory (Chesnavich and Bowers 1982 Garrett and Truhlar 1979a,b,c,d Horiuti 1938 Keck 1967 Wigner 1937) to calculate the thermal rate coefficient for capture in a noncentral field. Under the assumptions that a classical mechanical treatment is valid and that the reactants are in equilibrium, this treatment provides an upper bound to the true rate coefficient. The upper bound was then compared to calculations by the classical trajectory method (Bunker 1971 Porter and Raff 1976 Raff and Thompson 1985 Truhlar and Muckerman 1979) of the true thermal rate coefficient for capture on the ion-dipole potential energy surface and to experimental data (Bohme 1979) on thermal ion-polar molecule rate coefficients. The results showed that the variational bound, the trajectory results, and the experimental upper bound were all in excellent agreement. Some time later, Su and Chesnavich (Su 1985 Su and Chesnavich 1982) parameterized the collision rate coefficient by using trajectory calculations. 

Indications of the feasibility of this approach are to be found in the work of Bowers et al. (2, 3) on the photolysis of iodine vapor in the cavity of an EPR spectrometer, and in the theoretical investigations of Beltran-Lopez et al. on the microwave Zeeman spectra of atomic fluorine and chlorine 1, 8). However, these studies were mainly concerned with the precise determination of atomic g factors to verify the Zeeman theory and involved specialized spectral equipment. The present investigation demonstrates that the spectra of atomic fluorine, chlorine, and bromine are readily observable in commercially available EPR equipment and that reasonable estimates may be made of their concentrations. 

Lhlgard ER, Bower GH (1986) Theories of learning. Prentice Hall of India... 

The theory of the coupling of enzyme-catalyzed reactions with transport processes has been investigated for the following limiting cases (Carr and Bowers, 1980) ... 

ALTADENA (Adiabatic Longitudinal Transport after Dissociation Engenders Net Alignment) [56]. All variants are nowadays known under the more generally acronym of PHIP (Parahydrogen Induced Polarization) [52]. The basic theory ofthe PHIP effect in an AX-spin system was given in the review paper of Bowers and Weitekamp [56]. 

McCarthy, R. L., Bower, F. A. and Jesson, J. P., 1977 The fluorocarbon-ozone theory-I. Production and release. World production and release of CCIjF and CC12F2 (fluorocarbons 11 and 12) through 1975. Atmospheric Environment 11, 491-497. 

We will not discuss the general literature on the theory and techniques of gas-phase acidity and basicity here (see, e.g.. Bowers, 1979 Gal and Maria, 1990). They are defined as the Gibbs free energies (AG°add and AG°base) of the ionization for the gas-phase acidity of an acid into the corresponding base and a proton, and analogously for the basicity (see Gal and Maria, 1990, p. 169 ff). The ther-... 

Chesnavich and Bowers (1977a,b 1979) modified the phase space theory model by assuming (a) an orbiting transition state located at the centrifugal barrier, and (b) that orbital rotational energy at this transition state is converted into relative translational energy of the products. The Hamiltonian used for this orbiting transition state/phase... 

Su, T Bowers, M.T., Ion-polar molecule collisions the effect of ion size on ion-polar molecule rate constants the parameterization of the average-dipole-orientation theory, Int. J. Mass Spectrom Ion Phys. 1973, 12, 347-356. 

Su, T., Bowers, M.T., Theory of ion-polar molecule coUisions comparison with experimental charge transfer reactions of rare gas ions to geometric isomers of difluorobenzene and dichloroethylene. J. Chem. Phys. 1973, 58, 3027. 

The first treatment of the theory of the intensities and polarisation effects to be expected in the Raman scattering from an oriented polymer sample appears to be that given by Cornell and Koenig." This treatment must be regarded at best as a very rough approximation, since the tensor nature of the effect is not taken into account properly. Snyder has given a correct account of the theory for rather special distributions of orientations of the Raman scatterers but his work concentrates on the information that can be obtained about the Raman tensors if the orientation distribution is known. The only treatment that has considered how much information can in principle be obtained about the distribution of orientations and what measurements are necessary to obtain it is that of Bower and Bower and Purvis. " In this treatment the similarities and differences between the theories of the fluorescence and Raman methods are apparent and an account of it follows. 

Theoretical work has focused on two aspects of the problem perturbation theory and other calculations of the transition probabilities in the material, and the effect on the transition probability of the statistical nature of the radiation field. Makinson and Buckingham [7,29] were the first to predict the second-order effect and calculate its magnitude based on a surface model of photoemission this work was expanded by Smith [7.30], Bowers [7.31], and Adawi [7.32], The analogous volume calculation was performed by Bloch [7.33] and later corrected by Teich and Wolga [7.24, 25],... 

The validity of the statistical approximation in QET-RRKM-phase-space theories has been tested extensively both experimentally and theoretically. Some of the most incisive tests of statistical theory have been performed with energy-selected ions, prepared as described previously, using methods such as photoelectron-photoion coincidence (PEPICO). Particularly incisive tests of these statistical models have been performed on isomeric C4Hg systems by Baer and Bowers and their co-workers and on C4H by Bowers and collaborators. The latter study provided validation of an important variant of statistical theory called the transition state switching model. 

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