Periodic Reporting for period 3 - ANTI-ATOM (Many-body theory of antimatter interactions with atoms, molecules and condensed matter)
Période du rapport: 2022-02-01 au 2023-07-31
Positrons, the antiparticles of the electron, are the simplest form of antimatter. They are produced in abundance in our Galaxy, and are readily obtained on Earth using accelerators, nuclear reactors and radioactive isotopes. Their striking ability to annihilate with electrons, producing a burst of light characteristic of the electron's environment at the instant of annihilation, makes positrons a unique probe of matter. As such, they have important use in medical imaging in PET (Positron Emission Tomography) scans, diagnostics of industrially important materials, and understanding the distribution of antimatter in the Universe. More complicated antimatter: positronium (Ps, an electron-positron pair) and antihydrogen (a proton-antiproton pair), are under intensive study at international laboratories. Ps can be delivered in beams to study quantum-mechanical collisions, is used to determine pore sizes in microporous materials, and probe (anti)gravity. At CERN, antihydrogen has been trapped and is now being interrogated for precision tests of fundamental physical laws, and to explain why we experience a matter-dominated Universe.
When a positron interacts with normal matter (an atom or molecule), it pulls strongly on the atomic/molecular electron cloud, polarising it. The atomic/molecular electron may even temporarily "tunnel" to the positron, forming short-lived "virtual" Ps. These so-called 'correlations' significantly effect positron and Ps interactions with atoms and molecules, e.g. enhancing annihilation rates by many orders of magnitude, modifying the characteristic annihilation signal, and making the accurate description of these systems a challenging many-body problem.
Proper interpretation, modelling and development of the antimatter-based fundamental experiments, materials science techniques and antimatter technologies (positron traps and accumulators, PET etc) require calculations that fully account for the correlations. Current theoretical capability for describing antimatter interactions with atoms, molecules and real materials, however, lags well behind experiment. Sophisticated approaches can successfully describe antimatter interactions with light atoms like hydrogen and helium, but cannot be feasibly scaled to larger many-electron atoms.
A powerful framework that can account for the correlations in a natural, transparent and systematic way is many-body theory. In many-body theory, processes of interest (e.g. positron annihilation with an atomic electron) are represented via relatively simple and intuitive (Feynman) diagrams, enabling identification of the key interactions, efficient computation, and providing keen insight. This project aims to develop the many-body theory and its state-of-the art computational implementation, to enable the most accurate description of positron and Ps interactions (binding, scattering and annihilation) with atoms, molecules, and materials, providing fundamental insight required to enable the accurate interpretation of and develop the difficult and costly antimatter experiments, material science techniques and technologies.
When a positron interacts with normal matter (an atom or molecule), it pulls strongly on the atomic/molecular electron cloud, polarising it. The atomic/molecular electron may even temporarily "tunnel" to the positron, forming short-lived "virtual" Ps. These so-called 'correlations' significantly effect positron and Ps interactions with atoms and molecules, e.g. enhancing annihilation rates by many orders of magnitude, modifying the characteristic annihilation signal, and making the accurate description of these systems a challenging many-body problem.
Proper interpretation, modelling and development of the antimatter-based fundamental experiments, materials science techniques and antimatter technologies (positron traps and accumulators, PET etc) require calculations that fully account for the correlations. Current theoretical capability for describing antimatter interactions with atoms, molecules and real materials, however, lags well behind experiment. Sophisticated approaches can successfully describe antimatter interactions with light atoms like hydrogen and helium, but cannot be feasibly scaled to larger many-electron atoms.
A powerful framework that can account for the correlations in a natural, transparent and systematic way is many-body theory. In many-body theory, processes of interest (e.g. positron annihilation with an atomic electron) are represented via relatively simple and intuitive (Feynman) diagrams, enabling identification of the key interactions, efficient computation, and providing keen insight. This project aims to develop the many-body theory and its state-of-the art computational implementation, to enable the most accurate description of positron and Ps interactions (binding, scattering and annihilation) with atoms, molecules, and materials, providing fundamental insight required to enable the accurate interpretation of and develop the difficult and costly antimatter experiments, material science techniques and technologies.
We have developed the many-body theory of positron interactions with molecules and its state-of-the-art computational implementation in the massively parallelised Gaussian-orbital based many-body theory EXCITON+ software package (developed by our group during the ERC project in collaboration with Prof Charles Patterson of Trinity College Dublin). Our approach involves calculating the self-energy of the positron in the field of the molecule at the GW Bethe-Salpeter-Equation level, and including the positron-electron/hole ladder series that describe the non-perturbative process of virtual-positronium formation.
Using this approach, we have performed the first accurate ab initio description of positron binding in polyatomic molecules, finding excellent agreement with measurements by the UCSD Surko group over the past two decades (accepted to Nature). In addition to supporting the experiments, our work has provided fundamental insight of the mechanisms of positron binding to molecules, notably delineating the effects of distinct correlations, the importance of the anisotropic nature of the interactions, and contributions of individual molecular orbitals and predicted binding in formamide and nucleobases.
We extended our approach to enable calculations of positron scattering and annihilation in small molecules, including H2, N2, CH4 and CF4, delineating the role of positron-molecule correlations: we find excellent agreement with experimental annihilation rates. We also developed a numerical approach to enable the calculation of positron annihilation gamma spectra on molecules. The approach, implemented in our EXCITON+ code, employs a Gaussian basis and is massively parallelised. Parallel efficiency tests have been conducted on ARCHER2, the UK National Supercomputer. Calculations of gamma spectra with a correlated positron wavefunction using a zeroth-order annihilation vertex are currently underway for small molecules that bind the positron. We have also used the approach to calculate positron binding energies for atoms including Be, Mg, Zn and Ca.
We have also considered the problem of positron cooling in molecular gases, namely N2 and CF4, which are commonly used as buffer gases in "Surko" traps used ubiquitously in low-energy positron experiments. Via a Monte Carlo approach we elucidated the cooling mechanisms, e.g. highlighting that the nature of positron cooling and thermalisation can be influenced by cooling proceeding via multiple successive molecular de-excitations followed by a single excitation, and positron-positron interactions (which can Maxwellianize the positron momentum distribution).
Scattering cross sections and pickoff annihilation rates for Ps on Ar, Kr and Xe noble-gas atoms were calculated, finding our annihilation rates to be in excellent agreement with experiment; Ps confined in a cavity was studied using physically motivated potentials (to model Ps in a pore of a microporous material): it was found that the annihilation rate is larger than its vacuum value, in contradiction to other recent calculations that assumed less-realistic confinement potentials, and experimental data. A new B-spline-based code to solve the Hartree-Fock equations for arbitrary central potentials was developed and used to consider the problem of electrons confined in a harmonic potential.
Using this approach, we have performed the first accurate ab initio description of positron binding in polyatomic molecules, finding excellent agreement with measurements by the UCSD Surko group over the past two decades (accepted to Nature). In addition to supporting the experiments, our work has provided fundamental insight of the mechanisms of positron binding to molecules, notably delineating the effects of distinct correlations, the importance of the anisotropic nature of the interactions, and contributions of individual molecular orbitals and predicted binding in formamide and nucleobases.
We extended our approach to enable calculations of positron scattering and annihilation in small molecules, including H2, N2, CH4 and CF4, delineating the role of positron-molecule correlations: we find excellent agreement with experimental annihilation rates. We also developed a numerical approach to enable the calculation of positron annihilation gamma spectra on molecules. The approach, implemented in our EXCITON+ code, employs a Gaussian basis and is massively parallelised. Parallel efficiency tests have been conducted on ARCHER2, the UK National Supercomputer. Calculations of gamma spectra with a correlated positron wavefunction using a zeroth-order annihilation vertex are currently underway for small molecules that bind the positron. We have also used the approach to calculate positron binding energies for atoms including Be, Mg, Zn and Ca.
We have also considered the problem of positron cooling in molecular gases, namely N2 and CF4, which are commonly used as buffer gases in "Surko" traps used ubiquitously in low-energy positron experiments. Via a Monte Carlo approach we elucidated the cooling mechanisms, e.g. highlighting that the nature of positron cooling and thermalisation can be influenced by cooling proceeding via multiple successive molecular de-excitations followed by a single excitation, and positron-positron interactions (which can Maxwellianize the positron momentum distribution).
Scattering cross sections and pickoff annihilation rates for Ps on Ar, Kr and Xe noble-gas atoms were calculated, finding our annihilation rates to be in excellent agreement with experiment; Ps confined in a cavity was studied using physically motivated potentials (to model Ps in a pore of a microporous material): it was found that the annihilation rate is larger than its vacuum value, in contradiction to other recent calculations that assumed less-realistic confinement potentials, and experimental data. A new B-spline-based code to solve the Hartree-Fock equations for arbitrary central potentials was developed and used to consider the problem of electrons confined in a harmonic potential.
Our many-body approach has provided a new state-of-the-art for positron-molecule interactions. The the massively parallelised GW@BSE+ladders Gaussian-orbital based many-body theory EXCITON+ software package (developed by our group during the ERC project in collaboration with Prof Charles Patterson of Trinity College Dublin), which includes the process of virtual-positronium formation, is unrivalled for positron-molecule interactions.
We are incorporating positrons in a version of EXCITON+ that can handle condensed matter (3D periodic crystal structures): to shed light on the correlated interactions of positrons with atoms, molecules and condensed matter, keeping in mind more general applications, and are now considering alternative computational methodologies (including stochastic summation of diagrams) that may allow more efficient calculations for larger molecules/condensed matter systems, and also problems beyond the positron-molecule one.
We are incorporating positrons in a version of EXCITON+ that can handle condensed matter (3D periodic crystal structures): to shed light on the correlated interactions of positrons with atoms, molecules and condensed matter, keeping in mind more general applications, and are now considering alternative computational methodologies (including stochastic summation of diagrams) that may allow more efficient calculations for larger molecules/condensed matter systems, and also problems beyond the positron-molecule one.