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arXiv:1601.04086 · Physical Review A

Transition rates for a Rydberg atom surrounded by a plasma

Chengliang Lin, Christian Gocke, GERD RÖPKE, H. Reinholz

Published Apr 27, 2016• 8 citations
arXivHTMLPDF

Abstract

We derive a quantum master equation for an atom coupled to a heat bath represented by a charged particle many-body environment. In the Born-Markov approximation, the influence of the plasma environment on the reduced system is described by the dynamical structure factor. Expressions for the profiles of spectral lines are obtained. Wave packets are introduced as robust states allowing for a quasiclassical description of Rydberg electrons. Transition rates for highly excited Rydberg levels are investigated. A circular-orbit wave-packet approach has been applied in order to describe the localization of electrons within Rydberg states. The calculated transition rates are in a good agreement with experimental data.

DOI
10.1103/physreva.93.042711

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We derive a quantum master equation for an atom coupled to a heat bath represented by a charged particle many-body environment. In the Born-Markov approximation, the influence of the plasma environment on the reduced system is described by the dynamical structure factor. Expressions for the profiles of spectral lines are obtained. Wave packets are introduced as robust states allowing for a quasiclassical description of Rydberg electrons. Transition rates for highly excited Rydberg levels are investigated. A circular-orbit wave-packet approach has been applied in order to describe the localization of electrons within Rydberg states. The calculated transition rates are in a good agreement with experimental data.
We present extensive Monte Carlo calculations of electron-impact-induced transitions between highly excited Rydberg states and provide accurate rate coefficients. For moderate energy changes, our calculations confirm the widely applied expressions in P. Mansbach and J. Keck [Phys. Rev. 181, 275 (1969)] but reveal strong deviations at small energy transfer. Simulations of ultracold plasmas demonstrate that these corrections significantly impact the short-time dynamics of three-body Rydberg atom formation. The improved rate coefficients yield quantitative agreement with recent ultracold plasma experiments.
Rydberg atom formation is a source of heating in plasmas. The rate of three-body recombination in an ultracold neutral plasma was measured and electron temperature was derived from it using standard equilibrium recombination rates. With large-scale Monte Carlo and particle-in-cell simulations, we have calculated ab initio the rate of excitation, de-excitation, ionization (and recombination) in electron-Rydberg atom collision and investigated the short-time dynamics of three-body recombination in an ultracold neutral plasma. Comparison with observed rates is quite good. Particular attention is paid to the low-frequency microfield effect on Rydberg state cut-off in the plasma.
Recent experiments have demonstrated the spontaneous evolution of a gas of ultracold Rydberg atoms into an expanding ultracold plasma, as well as the reverse process of plasma recombination into highly excited atomic states. Treating the evolution of the plasma on the basis of kinetic equations, while ionization/excitation and recombination are incorporated using rate equations, we have investigated theoretically the Rydberg-to-plasma transition. Including the influence of spatial correlations on the plasma dynamics in an approximate way, we find that ionic correlations change the results quantitatively but not qualitatively.
Coupled rate equation calculations demonstrate that the variational rate theory models for the three-body electron–electron–ion scattering dynamics associated with ultracold plasma evolution scale with density in accordance with the classical mechanics of a Coulomb system. Completeness of scaling requires a broad domain of Rydberg levels over which a quasi-equilibrium can be established. For given initial conditions, the predicted evolution of electron temperature with time changes with the choice of n max , i.e. the highest Rydberg orbital populated by three-body recombination. But, if the criterion that defines n max scales with density, then the results scale. Molecular dynamics calculations distinguish bound Rydberg states by an electron–ion distance criterion, R max , which is represented in scaled coordinates by R max = r max a ws , where a ws represents the Wigner–Seitz radius and r max is chosen arbitrarily. The rate equation calculations best conform with the output of molecular dynamics simulations for values of n max defined by a thermal criterion, . In a hydrogenic limit, the thermal criterion equates with a scaled distance criterion when r max = Γ e /2, where Γ e = e 2 /4π 0 a ws k B T e describes the degree of electron correlation. Molecular dynamics simulations conventionally attenuate the Coulomb potential by means of a term, C , . Reference to rate equation calculations suggests a connection between the soft-core term, C , and n min , the lowest Rydberg level considered in the relaxation of the plasma to a quasi-steady state.
We present a kinetic model based on coupled rate-equation simulations that accounts for state-detailed rate processes in the evolution of a molecular Rydberg gas to plasma. Calculations support a steady-state picture of Rydberg predissociation and its contribution to plasma dissipation. Inelastic collisions of electrons with Rydberg states efficiently transfer energy from and to the thermal bath of free electrons, giving rise to quasi equilibria of relatively high temperature. Dissipative effects that remove low- n population change the time course of this heating. Including statistically sampled channels of Rydberg predissociation with n - and ℓ-dependent lifetimes slows the relaxation to quasi equilibrium and retards the initial electron temperature increase. At later times, the dissociative loss of low- n population displaces this quasi equilibrium leading to continuous electron heating. Dissociation products appear at a rate that is controlled initially by the rate of Rydberg relaxation to quasi equilibrium. Thereafter, the overall rate at which the total dissociation consumes neutral molecules determines the decay rate for all levels. Simulations predict a total predissociation rate that is smaller than the initial rate of direct electron–ion dissociative recombination. At later times, residual predissociation displays an apparent first-order decay with a rate constant that fits well with experimental observations.