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 [1]. 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 [2].

Examples of systems which exhibit the above behaviour which can be termed many-body quantum chaos, are heavy nuclei [3] and open-shell atoms and positive ions [4]. 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 contributions.

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 [5]. Development of the statistical theory allows quantitative predictions of the recombination rates [6]. 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.

  1. V. V. Flambaum and G. F. Gribakin, Statistical theory of finite Fermi systems with chaotic excited eigenstates, Philosophical Magazine B 80, 2143-73 (2000).
  2. 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).

  3. V. V. Flambaum V.V. and G. F. Gribakin. Enhancement of parity and time-invariance violating effects in compound nuclei. Prog. Part. Nucl. Phys. 35, 423-503 (1995).
  4. 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).
  5. 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).
  6. 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).