Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Stylized facts from a threshold-based heterogeneous agent model

A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their effects upon the market dynamics. The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible alternatives for introducing such long-term volatility correlations are then identified and discussed.     

Observation of satellite signals due to scalar coupling to spin-1/2 isotopes in solid-state nuclear magnetic resonance spectroscopy

A method is introduced to select the signal from a spin-1/2 nucleus I specifically bound to another spin-1/2 nucleus S for solid-state magic angle spinning nuclear magnetic resonance (NMR) spectroscopy via correlation through the heteronuclear J coupling. This experiment is analogous to the bilinear rotation decoupling (BIRD) sequence in liquid-state NMR spectroscopy which selects for signals from 1H directly bound to 13C. The spin dynamics of this modified BIRD experiment is described using the product-operator formalism, where experimental considerations such as rotor synchronization and the effect of large chemical shielding anisotropies on I and S are discussed. Two experiments are proposed that accommodate large chemical shielding anisotropies on S: (1) by stepping the inversion pulse frequency through the entire S spectral range or (2) by adiabatically inverting the S spins. Both these experiments are shown to successfully select the signal of 19F bound to 129Xe in XeF+ salts, removing the contributions from isotopomers containing non-spin-1/2 Xe isotopes. The feasibility in obtaining isotope-selective 19F spectra of inorganic fluoride compounds is discussed, and further modifications are proposed to expand the application to other chemical systems.     

Effect of xenon on fullerene reactions

Solutions containing 3He@C60, 129Xe@C60, and varying amounts of 9,10-dimethylanthracene (DMA) were allowed to reach equilibrium, and the 3He and 129Xe NMR spectra were taken at the same temperature. Each spectrum showed peaks for the unreacted X@C60 and for the monoadduct. The ratios of the peak heights show that the included xenon atom substantially changes the equilibrium constant. This change is temperature dependent, meaning that the xenon atom changes both DeltaH and DeltaS for the reaction. DMA is more reactive with He@C60 at low temperatures and with Xe@C60 at higher temperatures. The difference in chemical shift between the monoadduct and the unreacted X@C60 is more than twice as large for Xe than for He and in the opposite direction. Calculations show that the electron density in Xe@C60 is higher than that in empty C60 on the outside of the cage.     

Zur Analyse der Cellulose

Ohne Zusammenfassung