# Development of high-accuracy atomic theory 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 (known as "correlations") need to be taken into account using perturbation theory.

One major difficulty, however, is the typical perturbation series doesn't seem to converge. For example, third-order calculations are actually significantly worse than those performed at second-order!

Therefore, in order to be accurate, clever techniques must be used to include correlations to all-orders.

There are several techniques for this.

One popular method is the coupled-cluster approach, which is highly accurate though extremely computationally demanding.

Another approach, used by our group, is based on a Feynman diagram technique, which is also extremely accurate, and very computationally efficient.

Both methods have advantages and disadvantages.

Importantly, there are certain correlation effects which are included in each method that are not included in the other.

The goal of this project is to extend and improve the Feynman diagram technique.

In particular, we can identify certain classes of correlation effects which are included in the coupled-cluster approach and systematically account for them in the Feynman diagram method.

This will maximise the accuracy of the calculations, while still being a highly computationally efficient method.

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.).