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Physical Review A

Density-matrix theory of recombination

Seenipandian Ravi, G. S. Agarwal

Published Jul 1, 1991• 5 citations
Publisher

Abstract

A general formulation for calculating the recombination probability from a system consisting of many autoionizing states interacting with many continuum states is given. The formulation is applied to obtain the recombination probability from two continuum states coupled to an autoionizing state. Explicit expressions for various fundamental processes contributing to recombination probability are also given.

DOI
10.1103/physreva.44.489

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A general formulation for calculating the recombination probability from a system consisting of many autoionizing states interacting with many continuum states is given. The formulation is applied to obtain the recombination probability from two continuum states coupled to an autoionizing state. Explicit expressions for various fundamental processes contributing to recombination probability are also given.
Although dielectronic and radiative recombination are usually treated as distinct noninterfering processes, Alber, Cooper, and Rau [Phys. Rev. A 30, 2845 (1984)] have recently presented a scattering- or S-matrix analysis which provides a unified description of these processes. This description employs a diagonalization of the atom plus radiation field Hamiltonian using a limited basis set consisting of one discrete autoionizing state, a single-electron continuum, and a single-photon continuum. In the present work we extend Mo?ller scattering operator and resolvent operator techniques, which have previously been used to discuss the decay of prepared systems, in order to provide an S-matrix analysis of the electron-ion photorecombination process near an isolated autoionizing resonance. We explicitly allow for degenerate magnetic sublevels of the atomic system and for multiple angular momentum contributions in the partial-wave expansion of the electron-continuum eigenstate. After the introduction of the pole approximation, in which only the \ensuremath{\delta}-function term is retained in the evaluation of the various self-energies that occur in the diagonalization of the Hamiltonian for the combined many-electron radiation-field system, we obtain the total electron-ion photorecombination cross section as the sum of the radiative and dielectronic recombination contributions together with the conventionally ignored interference term.The radiative and dielectronic recombination cross sections reduce to the familiar forms when the continuum-continuum coupling effects are neglected. Alternatively, the combined cross section for the entire electron-ion photorecombination process may be represented by a modified Fano line profile, which is shifted and broadened as a result of the coupling between the autoionization and radiation continua. Recombination processes that involve more than a single state of the initial ion, of the autoionizing resonance, or of the final system can be treated by appropriately augmenting the unperturbed basis set. It is anticipated that the effects of the interference between radiative and dielectronic recombination and of the continuum-continuum coupling will be most important for individual transitions involving low-lying autoionizing levels and will probably be negligible for the total dielectronic recombination rates due to the highly excited levels.
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random matrix Hamiltonian, which can be written as a sum of two non-commutating operators, one can obtain an expression for the density of states of the Hamiltonian from the known density of states of the two component operators by assuming that these operators are mutually free and by using the free additive convolution. In many examples of interacting quantum systems and random matrix models, this procedure is known to provide a reasonably accurate approximation to the exact numerical density of states. We review some of the examples that are known in the literature where this procedure works very well, and also discuss some of the limitations of this method in situations where the free probability approximation fails to provide a sufficiently accurate description of the exact density of states. Subsequently, we describe a perturbation scheme that can be developed from the subordination formulas for the Cauchy transform of the density of states and use it to obtain approximate analytical expressions for the density of states in various models, such as the Rosenzweig-Porter random matrix ensemble and the Anderson model with on-site disorder.
The dc-field-induced interference effects in recombination in a model system consisting of two close-lying autoionizing states are studied. The two states are strongly coupled by a dc field and can decay via both autoionization and spontaneous emission. All possible channels of radiative decay are included for the model system. In special cases the isomorphism of the recombination and photoionization studies is established. The total integrated recombination probability is calculated and its behavior as a function of dc field is presented. Our density-matrix calculations lead to the known results in the limiting case of no dc field.
Presented herein is a second-quantized formulation for a system of interacting nuclei and electrons expressed in terms of the creation and annihilation operators of various species of atoms and ions which can be formed by combining various numbers of the "elementary" particles. Processes such as ionization and recombination appear naturally. Explicit expressions for interatomic forces including exchange effects are generated from a "cluster expansion" reminiscent of the Ursell expansion.