Benjamin Roberts

Atomic physics as a probe of the Standard Model

The Standard Model is extremely effective at describing the fundamental particles and interactions, but is widely believed to be incomplete. For example, the Standard Model cannot explain the asymmetry between matter and antimatter, and there is so far no leading candidate for a theory of dark matter or dark energy. Recent advances in both theory and experiment for atomic physics have opened a number of new and exciting avenues for discovery, and have placed this field at the forefront of probing fundamental physics and searching for dark matter. Further, the different energy scales involved in atomic processes make such experiments sensitive to a different range of new physics signatures than conventional searches, such as those at largescale high-energy physics experiments, like colliders at CERN, or large underground neutrino detectors. Input is needed from atomic theory both to interpret the results of experiments in terms of new physics theories, and to direct future experiments.

In particular, high-precision atomic physics experiments play an important role in testing the Standard Model of particle physics at low energy. Highly accurate atomic structure calculations are required in order to interpret the experiments in terms of fundamental physics parameters. Atomic physics calculations involve treating the many-electron atomic Hamiltonian approximately. In order to achieve high accuracy, a number of many-body effects need to be taken into account using perturbation theory. This project is to continue to develop and test techniques for extending many-body methods for high-precision calculations of atomic systems with the aim of extending and improving atomic probes of fundamental physics.

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Dark matter induced atomic ionisation

Develop and test atomic methods for calculating dark matter interactions with atoms. This includes atomic excitation and ionisation caused by the scattering of dark matter particles by atoms, as well as the absoroption of dark matter particles by atoms (so-called dark photo-electric effect).

The project will involve aspects of quantum mechanics (elementary atomic theory, scattering theory) and particle astrophysics (application to dark matter direct detection experiments, and interpretation of results in terms of dark matter and particle physics models). It will also involve some basic programming (in c++ and/or python), though no prior knowledge of programming is required.

For some details, see: * "Electron-interacting dark matter: Implications from DAMA/LIBRA-phase2 and prospects for liquid xenon detectors and NaI detectors." Physical Review D, 100, 063017 (2019) [http://arxiv.org/abs/1904.07127]

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Atomic physics as a probe of the Standard Model

The Standard Model is extremely effective at describing the fundamental particles and interactions, but is widely believed to be incomplete. For example, the Standard Model cannot explain the asymmetry between matter and antimatter, and there is so far no leading candidate for a theory of dark matter or dark energy. Recent advances in both theory and experiment for atomic physics have opened a number of new and exciting avenues for discovery, and have placed this field at the forefront of probing fundamental physics and searching for dark matter. Further, the different energy scales involved in atomic processes make such experiments sensitive to a different range of new physics signatures than conventional searches, such as those at largescale high-energy physics experiments, like colliders at CERN, or large underground neutrino detectors. Input is needed from atomic theory both to interpret the results of experiments in terms of new physics theories, and to direct future experiments.

In particular, high-precision atomic physics experiments play an important role in testing the Standard Model of particle physics at low energy. Highly accurate atomic structure calculations are required in order to interpret the experiments in terms of fundamental physics parameters. Atomic physics calculations involve treating the many-electron atomic Hamiltonian approximately. In order to achieve high accuracy, a number of many-body effects need to be taken into account using perturbation theory. This project is to continue to develop and test techniques for extending many-body methods for high-precision calculations of atomic systems with the aim of extending and improving atomic probes of fundamental physics.

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Dark matter induced atomic ionisation

Develop and test atomic methods for calculating dark matter interactions with atoms. This includes atomic excitation and ionisation caused by the scattering of dark matter particles by atoms, as well as the absoroption of dark matter particles by atoms (so-called dark photo-electric effect).

The project will involve aspects of quantum mechanics (elementary atomic theory, scattering theory) and particle astrophysics (application to dark matter direct detection experiments, and interpretation of results in terms of dark matter and particle physics models). It will also involve some basic programming (in c++ and/or python), though no prior knowledge of programming is required.

For some details, see: * "Electron-interacting dark matter: Implications from DAMA/LIBRA-phase2 and prospects for liquid xenon detectors and NaI detectors." Physical Review D, 100, 063017 (2019) [http://arxiv.org/abs/1904.07127]

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Theoretical characterisation of systems for the development of atomic clocks

Atomic clocks are the most precise instruments ever constructed. They work by locking the frequency of radiation source (e.g., a laser) to the resonance of an atomic transition.

As well as the canonical application of clocks (positioning, navigation, and timing), their unparalleled stability makes them exceptional tools for fundamental physics studies as well. Atomic clocks may be used to: - test quantum mechanics with extraordinary precision - probe for evidence of exotic physics, such as violations of the equivalence principle - search for or constrain possible variations of the fundamental constants - search for dark matter and dark energy

It is currently an exciting time for atomic clocks, with the best optical atomic clocks approaching a staggering precision of parts in 10^20! There are many proposals to develop new optical atomic clocks in alkali atoms (Rb, Cs) and alkali-like ions (Sr+, Ba+, Ra+). In order to develop the most accurate atomic clocks, a thorough theoretical understanding of the atomic properties is required. This may be achieved by calculating the atomic wavefunctions using highly-precise atomic structure methods, which will be used and developed in this project. Quantities that must be calculated include atomic spectra, lifetimes of excited states, atomic polarisabilities, transition rates, light shifts (the perturbation of atomic levels by the lasers required for the clock operation), black-body radiation shifts, and many others.

Sensitivity coefficients, which determine how sensitive a particular clock transition is to variations in the fine-structure constants, will also be calculated.

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Development of high-accuracy atomic physics methods

High-precision atomic physics experiments play an important role in testing the Standard Model of particle physics at low energy. Highly accurate atomic structure calculations are required in order to interpret the experiments in terms of fundamental physics parameters. Atomic physics calculations involve treating the many-electron atomic Hamiltonian approximately. In order to achieve high accuracy, a number of many-body effects need to be taken into account using perturbation theory. This project is to continue to develop and test techniques for extending many-body methods for high-precision calculations of atomic systems.

Atomic physics calculations involve treating the many-electron atomic Hamiltonian approximately. In order to achieve high accuracy, a number of many-body effects need to be taken into account using perturbation theory. In particular, one such class of effects, known as "ladder diagrams", are missing from some calculations. Though small, these corrections seem to be important in some cases. The ladder-diagram method has been applied previously to energies with high success (see: Physical Review A, 78, 042502.) The plan here is to extend this method to include "ladder diagram" corrections directly into atomic wavefunctions. These wavefunctions can then be used to compute relevant atomic properties (for example, hyperfine splittings, transition rates, lifetimes etc.). The project will involve aspects of quantum mechanics (elementary atomic theory) and numerical methods (application of existing code libraries to new problems in atomic physics). It will also involve some basic programming (in c++ and/or fortran), though no prior knowledge of programming is required.

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Enlightening the search for dark matter (and other exotic physics)

Despite overwhelming astronomical and cosmological evidence for its existence, the microscopic composition of dark matter remains a complete mystery. The vast majority of the effort to detect dark matter has focused on weakly interacting massive particles (WIMPs), with masses ~10 – 1000 GeV. WIMPs in that mass range may scatter off atomic nuclei leaving detectable recoil energy in experiments. However, this represents only a tiny sliver of the possible mass range for dark matter particles, which may have masses down to < ~ 10^(-20) eV. Current experiments are blind to the majority of this parameter space. Taking advantage of atomic (rather than nuclear) phenomena, however, may drastically increase the range of masses we can search for.

As the dark matter (DM) mass drops much below the nucleus mass (<GeV), no appreciable nuclear recoils are observable. However, DM particles may instead scatter of atomic electrons, leading to observable ionisations. As the DM mass drops below that of the electron (<~MeV), there are no detectable electron recoils, however, a detectable signal may instead come from DM absorption ("dark" photoelectric effect). Finally, as the DM mass drops below the ~eV scale, it behaves as a classical radiation field. Then, the observable effect comes in the form of atomic interactions with the classical DM field, such as energy shifts caused by dark-matter-induced effective variation of fundamental constants.

Combining ideas from particle astrophysics with theoretical atomic physics, this project is to identify and quantify new observable effects that can be used to search for evidence of new particles and fields, which may be due to dark matter, dark energy, or something even more exotic. In particular, it will involve investigating and calculating rates of scattering, absorption, energy-level shifts in atomic systems.

Relativistic effects in atomic structure theory

In heavy atomic systems, the electron wavefunction must be treated relativistically (Dirac equation) to accurately calculate atomic properties. The inter-electron Coulomb interaction, however, is still typically treated using a non-relativistic formalism. The lowest-order relativistic correction to the electron-electron repulsion is given by the Breit Hamiltonian (see, e.g., Ref. [1]), which accounts for magnetic and finite-speed-of-light effects.

This typically leads to only very small correction. However, for certain transitions in ionised atoms, the relativistic effects are expected to be greatly enhanced. This project would involve calculating Breit corrections to highly-charged ions, to determine if the lowest-order Breit correction is sufficient, or if new methods must be developed.

A strong theoretical understanding of the structure of ions is important for a number of applications, including high-precision tests of the Standard Model and electroweak theory at low energy, and searches for dark matter and exotic physics. Highly-charged ions are also great candidates for next-generating atomic clocks, and highly-accurate theoretical calculations are required to aid in their development.

[1] Bethe and Salpeter, Quantum Mechanics of One-and Two-Electron Atoms (1977).

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