Commenced in January 2007
Paper Count: 31100
Quantum Statistical Mechanical Formulations of Three-Body Problems via Non-Local Potentials
Abstract:In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1+(2,3)→1+(2,3) as well as recombination 1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the threedimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338458Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1463
 L. D. Faddeev” Scattering theory for a three-particle system”, Sov. Phys.-JETP, vol. 12, 1961, pp. 1014-1019.
 A. Maghari and N. Tahmasbi “Scattering properties for a solvable model with a three-dimensional separable potential of rank 2”, J. Phys. A: Math. Gen., vol. 38, 2005, pp. 4469-4481.
 A. Maghari and M. Dargahi “The solvable three-dimensional rank-two separable potential model: partial-wave scattering”, J. Phys. A: Math. Theoret. vol. 41, 2008, pp. 275306-17.
 A. Maghari and V. M. Maleki “Analytical Solution of Partial-Wave Faddeev Equations with Application to Scattering and Statistical Mechanical Properties”, Commun. Theor. Phys. vol. 64, 2015, pp. 22- 28.
 R. G. Newton, “Scattering theory of waves and particles”, Springer- Verlag, Berlin, 1982.
 R. F. Snider “Simple example illustrating the different parametrizations of the Moller operator” J. Chem. Phys. vol. 88, 1988, pp. 6438-6447.
 J. G. Muga and R. F. Snider “Solvable three-boson model with attractive delta -function interactions” Phys.Rev., vol. 57A, 1998, pp. 3317-3329.
 J. G. Muga and J. P. Palao “Solvable model for quantum wavepacket scattering in one dimension” J. Phys. A: Math. Gen. vol. 31, 1998, pp. 9519-34.
 N. Tahmasbi and A. Maghari “Scattering problem with nonlocal separable potential of rank-two: Application to statistical mechanics” Physica A, vol. 382, 2007, pp. 537-548.
 A. Maghari and M. Dargahi “Scattering via a separable potential with higher angular momenta: application to statistical mechanics”, J. Stat. Mech. 2008, P10007.
 Hirschfelder J. O., Curtiss C. F. and Bird R. B., 1954 Molecular Theory of Gases and Liquids (Wiley, New York).
 Chapman S. and Cowling T. G., 1970 The Mathematical Theory of Non- Uniform Gases 3rd ed (London: Cambridge University Press).