Electron-ion recombination and many-body quantum chaos
There are two aspects to this direction of research. At the more fundamental
level it concerns the physics of finite many-fermion systems at excitation
energies where several active particles can occupy a number of orbitals.
In such systems there is a large number of ways in which the particles can be
distributed among the orbitals. This results in a large density of
multiparticle states (configurations), many of which are nearly degenerate
in energy. The two-body interaction between the particles gives rise to strong
mixing between the configration states, producing chaotic eigenstates.
A direct numerical calculation of such eigenstates is often prohibitively
expensive. However, with the system being in the regime of strong, chaotic
mixing, a statistical theory can be developed to describe its properties .
In particular, this theory allows one to determine mean-squared
characteristics, such as matrix elements of various perturbations, but also to
introduce typical statistical quantities, e.g., temperature, in a finite,
strongly-interacting system of as few as 4 of 5 active particles .
Examples of systems which exhibit the above behaviour which can be termed
many-body quantum chaos, are heavy nuclei  and open-shell atoms and positive
ions . Other examples include vibrational states in polyatomic molecules,
where multiquantum excitations of several vibrational modes are mixed
together by anharmonic interactions, producing "vibrational chaos" which
manifests in Intramolecular Vibrational energy Redistribution (IVR).
A practical interest in many-body quantum chaos comes from the need to
understand processes involving such systems. Of particular interst for us
here is electron recombination with complex positive ions. Electron-ion
recombination is crucial for the balance of charge and energy in plasmas, from
astrophysical to laboratory, including TOKAMAK plasmas. In many-electron ions
recombination is usually enhanced by the so-called dielectronic recombination.
In this process the incident electron is captured in a doubly-excited state
of the compound ion, which is then stabilised by photoemission. For complex
targets such as Au25+, U28+ and W20+, accurate measurements, in particular
those using ion storage rings, reveal large discrepancies between the measured
recombination rates and those computed by adding the direct and dielectronic
In our work we seek explanations for the strongly enhanced recombination
rates for these and similar ions. The key feature here is the open-shell
structure of the ions, which, upon capture of the incident electron, promotes
the formation of quantum-chaotic multiply-excited eigenstates. The spectrum of
such states is much denser than that of the simple dielectronic excitations.
This leads to increased lifetimes of the resonant states with respect to
autoinisation, hence promoting radiative stabilisation of the system and
enhancing the recombination rates greatly . Development of the statistical
theory allows quantitative predictions of the recombination rates . The key
advantage of this theory is that it enables one to calculate the properties of
the system without diagonalising very large Hamiltonian matrices. From a
physical point of view, our approach matches the expermental situation, with
the spectrum of eigenstates being so dense that individual resonances cannot
in principle be resolved.
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systems with chaotic excited eigenstates, Philosophical Magazine B 80,
G. F. Gribakin, A. A. Gribakina, and V. V. Flambaum, Quantum chaos in
multicharged ions and statistical approach to the calculation of electron-ion
resonant radiative recombination, Aust. J. Phys. 52, 443-57 (1999).
V. V. Flambaum V.V. and G. F. Gribakin. Enhancement of parity and
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35, 423-503 (1995).
V. V. Flambaum, A. A. Gribakina, G. F. Gribakin, and I. V. Ponomarev,
Quantum chaos in many-body systems: What can we learn from the Ce atom?
Physica D 131, 205-20 (1999).
V. V. Flambaum, A. A. Gribakina, G. F. Gribakin, and C. Harabati, Electron
recombination with multicharged ions via chaotic many-electron states,
Phys. Rev. A 66, 012713 (2002).
V. A. Dzuba, V. V. Flambaum, G. F. Gribakin and C. Harabati, Chaos-induced
enhancement of resonant multielectron recombination in highly charged ions:
Statistical theory, Phys. Rev. A 86, 022714 (2012).