Nonperturbative treatment of structural radiation in atomic structure

The rise of quantum technologies and low-energy tests of fundamental physics has intensified the demand for precise and reliable calculations of atomic systems. Among the key challenges in this field is the accurate treatment of interactions between bound electrons and external perturbations, such as from the hyperfine interaction and core polarisation. State-of-the-art theoretical approaches can incorporate external field effects using the well-established Random Phase Approximation (RPA) technique and higher-order Coulomb corrections can be included through the correlation potential method, also known as the Brueckner Orbital approach. However, these methods only allow for the inclusion of effects that are separable. There exists a class of corrections known as structural radiation, in which the external field and higher-order Coulomb effects are inseparable. The coupled-cluster approach allows these effects to be included to all orders of the Coulomb interaction, though only up to a finite degree of excitation. In the Feynman method, such effects have been included up to third order. In this work, we present a method for accounting for structural radiation to all orders in the screened Coulomb interaction using the Feynman Green's function method. The proposed method is only marginally more computationally expensive than including third-order structural radiation and is stable across numerical parameters.