Antimatter and Atomic ManyBody Theory
Last updated February 3, 2020 by Gleb Gribakin
Positron interactions with atoms and molecules
The positron is the simplest piece of antimatter. Its characteristic signature is usually in the form of two 511 keV gamma quanta produced when it annihilates with an electron. The annihilation signal is key to almost all positron studies and applications, from detecting antimatter in our galaxy to detecting the presence of tumors or onset of Alzheimer’s desease in PET (Positron Emission Tomography) scans, or as a diagnostic in heavyion radiotherapy. Positron annihilation is used to map the shape and topology of Fermi surfaces in metals and probe intramolecular vibrational relaxation in polyatomic molecules. The simplest neutral matterantimatter system, the atom of Positronium (Ps), which is a bound electronpositron pair, is employed to measure free volume or detect phase transitions in microvoids in various materials. Positrons or Ps is also one of the key ingredients (together with antiprotons) for producing antihydrogen, which is actively pursued at CERN.
The basic fundamental process of electronpositron annihilation is described by Quantum Electrodynamics (QED). Positronium annihilation and spectroscopic studies provide some of the stringent tests for testing of this quantum field theory. When positrons annihilate with electrons in the laboratory or in space, the electrons are usually not free, but bound in atoms or molecules, or occupy certain energy bands in solids. Prior to annihilation, the positrons normally experience many ionising and other inelastic collisions, and slow down to eV or lower, thermal, roomtemperature energies.
The interaction of slow positrons with an electronic system, be this an atom or a molecule, is strongly affected by the collective response of the electronic “cloud” to the presence of the positron (socalled correlations). In molecules, excitation of vibrational, and in some case, rotational, degrees of freedom can also have a dramatic effect on positron annihilation. Understanding these interactions, both qualitatively and quantitatively, has been the main theme of our research.
For atoms, one of the best tools for understanding the interactions of slow positrons with atoms is manybody theory [1]. It enables one to achieve an excellent description of elastic scattering, annihilation rates and gammaray spectra in atoms, both simple and complex (e.g., noblegas atoms) and positions ions [24]. A very interesting feature of the positronatom interactions is the ability of electronpositron correlations to overcome the repulsive electrostatic positronatom potential, and give rise to positron bound states. The initial predictions [5] made against the strong scepticism among the positron community, gave way to widely accepted acknowledgement of the importance of positron binding to neutral atomic and molecular species. Accurate predictions of positronatom binding energies for most, especially openshell species is still an open question, and we have recently used linearised couplecluster manybody theory method to advance in this direction [6]. In spite of a wealth of theoretical predictions, positronatom bound states have not been observed experimentally, because of the associated difficulties. We have proposed some schemes which should enable to do this using existing technologies [7,8]. Manybody theory also proved to be an excellent tool for calculating positron bound states with negative ions [9].
Our understanding in the area of positron annihilation in molecules, which remained a big puzzle for halfacentury, has seen a rapid advance over the past ten years. This came as a result of concerted efforts by the experimental group of Prof Cliff Surko (University of California in San Diego), and Queen’s theorists, as well as other efforts worldwide. The main and largely unexpected and surprising feature of our findings is the fundamental role played by positron capture in vibrational Feshbach resonances (VFR) that occurs for most polyatomic molecules (see our review [10]). This process is underpinned by the strong positronmolecule attraction and binding, one hand, and the ability of positrons to effectively excite nuclear vibrations, in spite of the huge difference in masses. A further ingredient of the VFR annihilation mechanism that produces ordersofmagnitude enhancement in larger polyatomics, is the intramolecular vibrational energy redistributions (IVR). This process is a paradigm in most of the usual, electronmolecule collisions and chemistry. Positron annihilation through VFR serves as a unique timing signal, providing an additional means for studying this important process [11,12,13].
Encouraged by our nearcomplete understanding of the details of positron annihilation in atoms, and the corresponding gammaray spectra, we have analysed the key features which affect positron gammaray spectra in molecules [14]. This is a first step in the development of modern quantum chemistry approaches to the problem of positronmolecule annihilation spectra [15].
 G. F. Gribakin and J. Ludlow, Manybody theory of positronatom interactions. Phys. Rev. A, 70, 032720 (2004).
 D. G. Green and G. F. Gribakin, Positron scattering and annihilation in hydrogenlike ions, Phys. Rev. A 88, 032708 (2013).
 D. G. Green, Ph.D. thesis, Queen’s University Belfast, 2011.
 D. G. Green, J. A. Ludlow, and G. F. Gribakin [Phys Rev. A (to be published)].
 V. A. Dzuba, V. V. Flambaum, G. F. Gribakin, and W. A. King. Bound states of positrons and neutral atoms. Phys. Rev. A 52, 45416 (1995).
 V. A. Dzuba, V. V. Flambaum, G. F. Gribakin, and C. Harabati, Relativistic linearized coupledcluster singledouble calculations of positronatom bound states, Phys. Rev. A 86, 032503 (2012).
 V. A. Dzuba, V. V. Flambaum and G. F. Gribakin, Detecting positronatom bound states through resonant annihilation, Phys. Rev. Lett. 105, 203401 (2010).
 C. M. Surko, J. R. Danielson, G. F. Gribakin and R. E. Continetti, Measuring positronatom binding energies through laserassisted photorecombination, New J. Phys. 14, 065004 (2012).
 J. Ludlow and G. Gribakin, Manybody theory calculations of positron binding to negative ions, Int. Rev. At. Mol. Phys. 1, 73 (2010).
 G. F. Gribakin, J. A. Young and C. M. Surko, Positronmolecule interactions: Resonant attachment, annihilation, and bound states, Rev. Mod. Phys. 82, 25572607 (2010).
 J. A. Young, G. F. Gribakin, C. M. R. Lee and C. M. Surko, Role of combination vibrations in resonant positron annihilation, Phys. Rev. A 77, 060702 (2008).
 G. F. Gribakin and C. M. R. Lee, Positron annihilation in large polyatomic molecules. The role of vibrational Feshbach resonances and binding, Eur. Phys. J. D 51, 51 (2009).
 A. C. L. Jones, J. R. Danielson, M. R. Natisin, C. M. Surko and G. F. Gribakin, Ubiquitous nature of multimode vibrational resonances in positronmolecule annihilation, Phys. Rev. Lett. 108, 093201 (2012).
 D. G. Green, S. Saha, F. Wang, G. F. Gribakin and C. M. Surko, Effect of positronatom interactions on the annihilation gamma spectra of molecules, New J. Phys. 14, 035021 (2012).
 F. Wang, X. G. Ma, L. Selvam, G. F. Gribakin and C. M. Surko, Effects of quantum chemistry models for bound electrons on positron annihilation spectra for atoms and small molecules, New J. Phys. 14, 085022 (2012).
Electronion recombination and manybody quantum chaos
There are two aspects to this direction of research. At the more fundamental level it concerns the physics of finite manyfermion 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 twobody 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 meansquared characteristics, such as matrix elements of various perturbations, but also to introduce typical statistical quantities, e.g., temperature, in a finite, stronglyinteracting system of as few as 4 of 5 active particles [2].
Examples of systems which exhibit the above behaviour which can be termed manybody quantum chaos, are heavy nuclei [3] and openshell 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 manybody 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. Electronion recombination is crucial for the balance of charge and energy in plasmas, from astrophysical to laboratory, including TOKAMAK plasmas. In manyelectron ions recombination is usually enhanced by the socalled dielectronic recombination. In this process the incident electron is captured in a doublyexcited 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 openshell structure of the ions, which, upon capture of the incident electron, promotes the formation of quantumchaotic multiplyexcited 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.
 V. V. Flambaum and G. F. Gribakin, Statistical theory of finite Fermi systems with chaotic excited eigenstates, Philosophical Magazine B 80, 214373 (2000).
 G. F. Gribakin, A. A. Gribakina, and V. V. Flambaum, Quantum chaos in multicharged ions and statistical approach to the calculation of electronion resonant radiative recombination, Aust. J. Phys. 52, 44357 (1999).
 V. V. Flambaum V.V. and G. F. Gribakin. Enhancement of parity and timeinvariance violating effects in compound nuclei. Prog. Part. Nucl. Phys. 35, 423503 (1995).
 V. V. Flambaum, A. A. Gribakina, G. F. Gribakin, and I. V. Ponomarev, Quantum chaos in manybody systems: What can we learn from the Ce atom? Physica D 131, 20520 (1999).
 V. V. Flambaum, A. A. Gribakina, G. F. Gribakin, and C. Harabati, Electron recombination with multicharged ions via chaotic manyelectron states, Phys. Rev. A 66, 012713 (2002).
 V. A. Dzuba, V. V. Flambaum, G. F. Gribakin and C. Harabati, Chaosinduced enhancement of resonant multielectron recombination in highly charged ions: Statistical theory, Phys. Rev. A 86, 022714 (2012).

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