Localization of a quantum-mechanical particle in classical simple fluids

Abstract

We present a self-consistent scheme to study the localization of a light particle obeying quantum mechanics immersed in classical simple fluids. The interparticle correlations between the particles of the host fluid are analyzed with the Percus-Yevick approximation using the Lennard-Jones potential. The interaction between the light particle and the fluid particles is represented by a contact potential. The Percus-Yevick approximation is also used to describe the density distribution of the fluid particles around the light particle. The effective potential acting on the light particle and the wave function of the light particle are self-consistently determined by the coupled Percus-Yevick and Schrodinger equations. The formalism was used to investigate ortho-positronium localization and annihilation in liquids He and Ne. The theory is found to be in fairly good agreement with existing experiments.PACS number(s): 51.90.+r, 71.50.+t, 78.70.Bj

Path integral studies of positrons and positronium in fluids

“…Recent ab-initio studies of the e + -~e system demonstrates that there is a virtual resonance in the interaction potential near zero energy, which may contribute to the strong peak in gfp .I271 This should be kept in mind when considering DFT type models which typically replace the actud interaction potential with a mathematically more tractable contact potential. [28] PIMC strongly suggests that the details of the potential strongly affect the lifetime predictions because they directly influence the short range behavior of gfp which, along with the electron density, determines the mean decay rate. The same could be said for the Ps-Xenon studies, where the choice of the hard sphere interaction 1121 failed to produce the degree of localization suggested by the laboratory measurements of the pick-off decay rate.…”

Self-Trapping at the Liquid-Vapor Critical Point

“…11 An interesting improvement was obtained by employing the Percus-Yevick equation to include the effect of qp-atom and atom-atom correlations in the mean field formalism. 12 An advantage of MFT is that computations are reduced to numerically integrating a pair of coupled ordinary differential equations. However, in practice, they have only proved useful for fluids at low temperatures.…”

“…However, in practice, they have only proved useful for fluids at low temperatures. 7,10,12,13 This problem may arise because mean field theories only include a single bound state for the qp. More microscopically complete models have evolved during the last few decades based on the Feynman-Kac path integral 14 which overcome the major shortcomings of the earlier work.…”

“…Later versions of mean field theory (MFT) permitted a continuous density profile [7,10] and took into account the atomic nature of the host at an intermediate level [11]. An interesting improvement was obtained by employing the Percus-Yevick equation to include the effect of qp-atom and atom-atom correlations in the mean field formalism [12]. An advantage of MFT is that computations are reduced to numerically integrating a pair of coupled ordinary differential equations.…”

“…An advantage of MFT is that computations are reduced to numerically integrating a pair of coupled ordinary differential equations. However, in practice, they have only proved useful for fluids at low temperatures [7,10,12,13]. This problem may arise because mean field theories only include a single bound state for the qp.…”