On Born approximation in black hole scattering

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstr\"{o}m and Reissner-Nordstr\"{o}m-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes

Statistical Thermodynamics Of Liquids Using The Monte Carlo Method. Ii. Liquid Chloroform [termodinâmica Estatística De Líquidos Com O Método De Monte Carlo. Ii. O Líquido Clorofórmio]

Thermodynamic properties and radial distribution functions for liquid chloroform were calculated using the Monte Carlo method implemented with Metropolis algorithm in the NpT ensemble at 298 K and 1 atm. A five site model was developed to represent the chloroform molecules. A force field composed by Lennard-Jones and Coulomb potential functions was used to calculate the intermolecular energy. The partial charges needed to represent the Coulombic interactions were obtained from quantum chemical ab initio calculations. The Lennard-Jones parameters were adjusted to reproduce experimental values for density and enthalpy of vaporization for pure liquid. All thermodynamic results are in excelent agreement with experimental data. The correlation functions calculated are in good accordance with theoretical results available in the literature. The free energy for solvating one chloroform molecule into its own liquid at 298 K and 1 atm was computed as an additional test of the potential model. The result obtained compares well with the experimental value. The medium effects on cis/trans convertion of a hypotetical solute in water TIP4P and chloroform solvents were also accomplished. The results obtained from this investigation are in agreement with estimates of the continuous theory of solvation.224574583Reichardt, C., (1988) Solvents and Solvent Effects in Organic Chemistry, , Verlag Chemie, Weinheim, 2nd EditionEvans, M.W., (1985) Dynamical Processes in Condensed Matter, , Willey, New YorkEvans, M.W., (1983) J. Mol. Liquids, 25, p. 211Dietz, W., Heinzinger, K., (1985) Ber. Bunsenges. Phys. Chem., 89, p. 968Dietz, W., Heinzinger, K., (1984) Ber. Bunsenges. Phys. Chem., 88, p. 543Böhm, H.J., Ahlrichs, R., (1985) Mol. Phys., 54, p. 1261Kovaks, H., Kowalewski, J., Laaksonen, A., (1990) J. Chem. Phys., 94, p. 7378Jorgensen, W.L., Briggs, J.M., Contreras, M.L., (1990) J. Chem. 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Statistical Thermodynamics Of Liquids Using The Monte Carlo Method. I. Methodology [termodinâmica Estatística De Líquidos Com O Método De Monte Carlo. I. Metodologia]

Statistical mechanics Monte Carlo simulation is reviewed as a formalism to study thermodynamic properties of liquids. Considering the importance of free energy changes in chemical processes, the thermodynamic perturbation theory implemented in the Monte Carlo method is discussed. The representation of molecular interaction by the Lennard-Jones and Coulomb potential functions is also discussed. Charges derived from quantum molecular electrostatic potential are also discussed as an useful methodology to generate an adequate set of partial charges to be used in liquid simulation.222254262Barke, J.A., Hendersen, D., (1976) Rev. Mod. Phys., 48, p. 587Croxton, C.A., (1978) Progress in Liquids Physics, , Wiley, New YorkAilawadi, N.K., (1980) Phys. Rep.Rev. Sec. Phys. 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