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Acta Physica Sinica

THEORETICAL TREATMENT OF RADIATION TRAPPING OF ATOMIC FLUORESCENCE IN V-E ENERGY TRANSFER

WANG CHU-JI, Jian Wang, MA XING-XIAO, 中国科学技术大学化学物理系，合肥 230026

Published Jan 1, 1998• 0 citations
Publisher

Abstract

A differential-integral equation system of Holstein type is used to describe the kinetic process in V-E energy transfer between molecules and atoms with radiation trapping.A reduced solution of a finite series has been presented,which allows to describe the whole temporal behavior of fluorescence.The further derivative is an analytical expression of the fluorescence decay rate as a function of rate constants and the maximum eigenvalue of the integral operator appearing in the rate equations.This will be especially useful and convenient for experimental determinations.Results are schematically illustrated and mutually compared by means of numerical calculations.

DOI
10.7498/aps.47.198

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A differential-integral equation system of Holstein type is used to describe the kinetic process in V-E energy transfer between molecules and atoms with radiation trapping.A reduced solution of a finite series has been presented,which allows to describe the whole temporal behavior of fluorescence.The further derivative is an analytical expression of the fluorescence decay rate as a function of rate constants and the maximum eigenvalue of the integral operator appearing in the rate equations.This will be especially useful and convenient for experimental determinations.Results are schematically illustrated and mutually compared by means of numerical calculations.
Abstract A differential integral equation system of Holstein type is used to describe the kinetic process in V E energy transfer between molecules and atoms with radiation trapping.A reduced solution of a finite series has been presented,which allows to describe the whole temporal behavior of fluorescence.The further derivative is an analytical expression of the fluorescence decay rate as a function of rate constants and the maximum eigenvalue of the integral operator appearing in the rate equations.This will be especially useful and convenient for experimental determinations.Results are schematically illustrated and mutually compared by means of numerical calculations.
The purpose of this paper is to propose a theoretical treatment of radiation trapping in a multiple lines coupled system in which coupling includes collisional energy transfer and cross absorption between the excited states. First, to describe the coupled system, the Holstein equation of radiation trapping is extended to an integral differential master equation group in which the vector and matrix form is adopted. Then by use of operator manipulations, the asymptotic solution in the form of a series expansion in terms of operators is presented. Finally, the asymptotic solution is reduced, leading to a result which can not only give the system a complete description, but also has far more advantages than the simple cut off solution. A numeral illustration of a two excited states system is also presented.
The key to the treatment of the resonance radiation imprisonment lies in the solution to Holstein's equation. A new method to solve Holstein's equation is proposed in this paper, which integrates the equation directly by means of operator calculation and results in a formula for the excited particles in an infinite series in an integral operator. Our study on the behavior of the high-ordercoefficients of this series leads to the success in overcoming the difficulty to obtain the sum of infinite terms, and a formula of finite terms under any given precision is acquired, which applies to the whole time scale.
The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.
Rate equations for the population dynamics of multilevel systems in laser-induced fluorescence spectroscopy are solved by the aid of perturbation theory. This leads to a general expression for the population of the level pumped by the laser radiation. Arbitrary laser pulse shapes as well as collisional processes are admitted. In the first-order approximation three functions depending on time and the properties of the laser pulse remain. These functions have been tabulated for a bell-shaped laser pulse. The results are used in several characteristic situations and are compared with the numerical solutions of the rate equations.
Theoretical treatment of resonance radiation trapping under steady-state conditions, particularly of quenching experiments, is presented. Applying operator manipulations, Holstein's equation of radiation trapping [Phys. Rev. 72, 1212 (1947)] is solved by a perturbation expansion, which can be physically interpreted in terms of multiple scatterings. The resulting expression shows that in a steady-state quenching experiment radiation trapping invalidates the relation of the Stern-Volmer type except when the amount of the buffer gas is small. In the limit of low buffer-gas pressure, a simple expression is given for the effective lifetime in the Stern-Volmer relation: the average time of the detected resonant photons remaining within the enclosure. While it is true that this suggested approach is perturbative in nature, the asymptotic behavior of the high-order expansion coefficients, however, enables us to reduce the summation over infinitely many alternatives to some leading terms. Such a reduction procedure helps curtail the computation time and improve the precision. Finally, some numerical illustrations of our suggested ideas are presented, which shows this approach is a good tool to treat the steady-state trapping effect.