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Positron binding and annihilation in molecules

School of Mathematics and Physics | PHD

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Reference Number
Application Deadline
21 February 2020
Start Date
1 October 2020


An investigation on positron binding to molecules

The positron is the antiparticle of the electron. It was the first antimatter particle ever discovered, first theoretically by Paul Dirac in 1931, and then experimentally by Carl Anderson in 1932, both physicists awarded the Nobel Prize soon after. Positrons are also the simplest and most abundant form of antimatter. They come from β+ radioactive decays, can be generated in accelerators, and are produced in large quantities (15×109 tonnes per second!) near the centre of our Galaxy. The ability of positrons to annihilate with electrons and emit characteristic annihilation gamma rays, underpins their use in various diagnostics, from positron lifetime spectroscopy of solids to positron emission tomography (PET) in medicine. When partnered with antiprotons, positrons can form antihydrogen, currently under intense investigation at CERN.
The electrons with which positrons annihilate are usually not free but packed in atoms or molecules. As a result, the process of positron annihilation is strongly affected by the positron interaction with the target. For example, positrons are repelled by atomic nuclei, so they usually annihilate only with the outermost, valence electrons. On the other hand, when a positron approaches an atom or molecule, it polarises (i.e., distorts) the electron cloud. This gives rise to an attractive polarisation potential acting on the positron. Another important effect is “hopping” of an atomic electron to the positron, temporarily forming an electron-positron “atom” called positronium (Ps). This increases the positron-atom attraction and strongly enhances the positron annihilation probability (see, e.g., detailed calculations for noble-gas atoms [1]).
For many atoms, the attraction is so strong that it overcomes the positron-nucleus repulsion and allows the creation of positron-atom bound states (predicted in [2] and proved variationally in [3]). To date, positron binding to about ten atoms has been predicted in state-of-the-art calculations. There are also firm expectations that many more atoms are capable of binding [4, 5], but there have not been any experimental conformation of this phenomenon yet [6].
What makes the problem of binding so important is the effect it has on positron annihilation in molecules [7]. When a positron collides with a molecule, it can be captured into the bound state by transferring its excess energy into molecular vibrations. This gives rise to resonances and orders-of-magnitude enhancement of the annihilation rates. Annihilation studies of resonances have enabled measurements of positron binding energies for more than 80 molecules (see [8] and references therein). In contrast, a significant theoretical effort towards computing positron- molecule bound states resulted in only a handful of predictions that can be compared with experiment, with the best agreement being at 25% level [9]. Also, most of the calculations performed to date considered strongly polar molecules (i.e., those with a large permanent dipole moment), because positron binding to these species is easier to describe. Model calculations [10] aside, there is very little theoretical understanding of positron binding to nonpolar molecules.
The aim of the project is to explore positron binding to molecules by developing a new approach to this difficult problem. The positron-molecule attraction and binding are due to electron-positron correlation effects, such as polarisation and virtual Ps formation. These effects are notoriously difficult to describe theoretically. Even modern quantum chemistry approaches cannot provide the accuracy required for the calculation of small positron-molecule binding energies (from few to a few tens of millielectronvolts), making reliable ab initio calculations impossible. On the other hand, the main features of the positron-molecule interaction are clear, e.g., from our extensive studies of positron-atom interactions [1]. Based on this, one can construct physically meaningful positron-molecule correlation potentials that will contain one or two adjustable parameters [11]. These parameters are chosen by comparison with existing high-quality calculations or by using experimental data for a small subset of molecules. The correlation potentials thus determined, positron bound state energies and wavefunctions will then be computed for a wide range of molecules. This should allow us to obtain theoretical understanding of many trends of positron- molecule binding, such as linear scaling with molecular dipole polarisability and dipole moment (surpassing the results of simple modelling of the latter [12]); see our latest work [13].
On the technical side, calculations of positron binding and annihilation rates are done by expanding the capabilities of GAMESS [14], an advanced, free quantum-chemistry package. This work is currently led by Dr Andrew Swann, a post-doctoral research associate, supported by the EPSRC grant “Positron bound states and annihilation in polyatomic molecules”, with Dr Gribakin being the principal investigator. A very interesting extension of the work will be computation of positron-molecule annihilation gamma-ray spectra, an area where large amounts of experimental data await proper theoretical understanding.
[1] D. G. Green, J. A. Ludlow, and G. F. Gribakin, Phys. Rev. A 90, 032712 (2014); D. G. Green and G. F. Gribakin, Phys. Rev. Lett. 114, 093201 (2015).
[2] V. A. Dzuba, V. V. Flambaum, G. F. Gribakin, and W. A. King, Phys. Rev. A 52, 4541 (1995).
[3] G. G. Ryzhikh and J. Mitroy, Phys. Rev. Lett. 79, 4124 (1997).
[4] J. Mitroy, M. W. J. Bromley and G. G. Ryzhikh, J. Phys. B 35, R81 (2002).
[5] V. A. Dzuba, V. V. Flambaum, and G. F. Gribakin, Phys. Rev. Lett. 105, 203401 (2010); V. A. Dzuba, V. V. Flambaum, G. F. Gribakin, and C. Harabati, Phys. Rev. A 86, 032503 (2012); C. Harabati, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. A 89, 022517 (2014).
[6] A. R. Swann, D. B. Cassidy, A. Deller, and G. F. Gribakin, Phys. Rev. A 93, 052712 (2016).
[7] G. F. Gribakin, J. A. Young and C. M. Surko, Rev. Mod. Phys. 82, 2557 (2010).
[8] J. R. Danielson, A. C. L. and Jones, J. J. Gosselin, M. R. Natisin, and C. M. Surko, Phys. Rev. A 85, 022709 (2012).
[9] M. Tachikawa, Y. Kita, and R. J. Buenker, Phys. Chem. Chem. Phys. 13, 2701 (2011); M. Tachikawa, J. Phys. Conf. Ser. 488, 012053 (2014).
[10] G. F. Gribakin and C. M. R. Lee, Nucl. Instrum. and Methods B 247, 31 (2006); Eur. Phys. J. D 51, 51 (2009).
[11] A. R. Swann and G. F. Gribakin, Calculations of positron binding and annihilation in polyatomic molecules, J. Chem. Phys. 149, 244305 (2018).
[12] G. F. Gribakin and A. R. Swann, J. Phys. B 48, 215101 (2015).
[13] A. R. Swann and G. F. Gribakin, Positron binding and annihilation in alkane molecules,
Phys. Rev. Lett 123, 113402 (2019).
[14] M. W. Schmidt et al., J. Comput. Chem. 14, 1347 (1993); M. S. Gordon and M. W. Schmidt, in Theory and Applications of Computational Chemistry: the first forty years, edited by C. E. Dykstra et al. (Elsevier, Amsterdam, 2005) pp. 1167–1189.
[15] G. F. Gribakin, J. F. Stanton, J. R. Danielson, M. R. Natisin, and C. M. Surko, Mode coupling and multiquantum vibrational excitations in Feshbach-resonant positron annihilation in molecules, Phys. Rev. A 96, 062709 (2017).

Funding Information

Project Summary
Professor Mauro Paternostro
Mode of Study

Full-time: 3 years

Funding Body
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Physics overview

The scientific research within the School of Mathematics and Physics was highly rated in the 2014 REF peer-review exercise, with 70% of research being judged as internationally excellent or world-leading. Physics research activity in the School is focused into five specific Research Centres; all members of academic staff belong to one of these Research Centres, listed below.

Astrophysics (PhD/MPhil)
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Atomistic Simulation (PhD/MPhil)
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Nanostructured Media (PhD/MPhil)
Find out more below, or email Professor Marty Gregg (

Plasma Physics (PhD/MPhil)
Find out more below, or email Professor Marco Borghesi (

Theoretical Atomic, Molecular and Optical Physics (PhD/MPhil)
Find out more below, or email Professor Mauro Paternostro (

Registration is on a full-time or part-time basis, under the direction of a supervisory team appointed by the University. You will be expected to submit your thesis at the end of three years of full-time registration for PhD, or two years for MPhil (or part-time equivalent).

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Course content

Research Information

Research Themes
Astrophysics (PhD/MPhil)

You’ll be involved in the search for distant supernovae and where they came from; study the asteroid and comet population in the Solar system; look for planets orbiting other stars in our Galaxy; study flares and other dynamic processes in the atmosphere of the Sun. You’ll have the opportunity to spend extensive periods at world-leading research centres such as the European Southern Observatory and NASA Goddard Space Flight Center.

At Queen’s we lead major European consortia and are supported by a multi-million pounds portfolio of research grants from a range of sources, including the UK Science and Technology Facilities Council, the Royal Society, and European Union.

Research Themes
Atomistic Simulation (PhD/MPhil)

Atomistic Simulation is the development and use of theoretical and computational methods to study structural, dynamical, and optical properties of molecules, liquids, solids and plasmas at the nanoscale. Computational experiments are used to interpret existing experimental data and to predict phenomena yet unobserved.
You’ll study problems at the interfaces between condensed matter physics, materials science, chemistry, biology, and engineering. You’ll interact with laboratory-based colleagues at Queen's and internationally, addressing fundamental and/or practical questions, and you will develop and program novel simulation methodologies to model situations presently out of reach, like electronic excitations, optical properties of materials, and the interaction between electric currents, heat and light.

Themes that are presently studied in the ASC include: magnetism, 2-D materials, non-linear optics, plasmonics, laser and ion-matter interactions, radiation damage in biology and nuclear materials, conduction in nanowires, nucleation, and crystallisation. Tools include DFT and TDDFT, Many-body perturbation theory, classical molecular dynamics and Monte Carlo, and machine learning.

Research Themes
Centre for Nanostructured Media (PhD/MPhil)

Human history is defined by the materials we use to underpin our technology: stone, bronze, iron, silicon. As a PhD student in the Centre for Nanostructured Media, you will be playing a part in the development of materials systems which will, in some way, define our technology for the future. How can this not be exciting ? You will seek to reveal the physics of material behaviour at the boundary of current global knowledge and, at the same time, become proficient in techniques for materials growth, patterning and characterisation that are highly valued in high-tech companies and commercial research institutions, as well as in academic research settings. Our laboratories are extremely well-equipped for international-level research and our links to other research teams throughout the world in both academia and industry are strong and you should expect to travel, should you wish to, as part of your PhD experience.

Research Themes
Plasma Physics (PhD/MPhil)

Your research will involve identifying, and responding to, major contemporary issues within ionised matter physics, with major activities in laser- and electrically-produced plasmas, ultra-fast atomic and molecular physics and the interaction of ionising radiation and plasmas with matter, including biological systems. This research will employ local, national and international facilities, including some of the most powerful laser systems worldwide. You will also benefit from transferring your research findings into the industrial and medical sectors.

Research Themes
Theoretical Atomic, Molecular and Optical Physics (PhD/MPhil)

You’ll contribute to a body of work with recent major developments including strong field laser interactions with atoms and molecules, quantum information processing, quantum optics, and quantum thermodynamics, antimatter interactions with atoms and molecules, electron scattering by very complex targets such as the iron peak elements, and by Rydberg atoms, quantum many-body physics, ultra-cold atomic systems, and simulation of their features, and foundations of quantum mechanics.

Postgraduate research programmes within CNM provide experience and training in state-of-the art academic research: many of our research strands are world-leading, as evidenced by performance in REF2014. In addition, most of our postgraduate researchers are exposed to functional materials and photonics in major multinational companies.

Prof Marty Gregg - School of Mathematics and Physics
Career Prospects

Alumni Success
Our graduates have progressed into jobs such as Data Scientist, Software Engineer, Financial Software Developer, IT Graduate Associate, Technology Consultant, Research Physicist, Telescope Operator and R&D Engineer.

People teaching you

Dr Myrta Gruening
Director of Research - Atomistic Simulation Centre
School of Maths and Physics

Prof Francis Keenan
Director of Research - Astrophysics Research Centre
School of Maths and Physics

Prof Marco Borghesi
Director of Research - Centre for Plasma Physics
School of Maths and Physics

Prof Marty Gregg
Director of Research - Centre for Nanostructured Media
School of Maths and Physics

Prof Mauro Paternostro
Director of Research - Centre for Theoretical and Atomic Molecular Physics
School of Maths and Physics

Learning Outcomes

Course structure


The School has invested over £12 million in new world-class student and staff facilities since 2014. A new teaching centre opened in 2016 which includes experimental physics laboratories, two large computer rooms and plenty of student study and interaction space.

Entrance requirements

The minimum academic requirement for admission to a research programme is normally an Upper Second Class Honours degree from a UK or ROI HE provider, or an equivalent qualification acceptable to the University. Further information can be obtained by contacting the School of Mathematics and Physics.

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English Language Requirements

Evidence of an IELTS* score of 6.0, with not less than 5.5 in any component, or an equivalent qualification acceptable to the University is required. *Taken within the last two years

International students wishing to apply to Queen's University Belfast (and for whom English is not their first language), must be able to demonstrate their proficiency in English in order to benefit fully from their course of study or research. Non-EEA nationals must also satisfy UK Visas and Immigration (UKVI) immigration requirements for English language for visa purposes.

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As a result of the COVID-19 pandemic, we will be offering Academic English and Pre-sessional courses online only from June to September 2020.

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Tuition Fees

Northern Ireland (NI) £4,407
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