Recent advancements in atomic many-body methods for high-precision studies of isotope shifts

TL;DR

This paper reviews recent advances in atomic many-body computational methods, focusing on their application to isotope shift studies in highly charged and neutral ions, which are crucial for nuclear and fundamental physics research.

Contribution

It introduces new relativistic many-body methods, including RMBPT and RCC frameworks, for accurate isotope shift calculations in various atomic systems.

Findings

Demonstrated the importance of QED effects in isotope shift calculations.

Developed RCC methods for one-valence and two-valence atomic systems.

Provided theoretical insights to support upcoming experiments in nuclear physics.

Abstract

The development of atomic many-body methods, capable of incorporating electron correlation effects accurately, is required for isotope shift (IS) studies. In combination with precise measurements, such calculations help to extract nuclear charge radii differences, and to probe for signatures of physics beyond the Standard Model of particle physics. We review here a few recently-developed methods in the relativistic many-body perturbation theory (RMBPT) and relativistic coupled-cluster (RCC) theory frameworks for calculations of IS factors in the highly charged ions (HCIs), and neutral or singly-charged ions, respectively. The results are presented for a wide range of atomic systems in order to demonstrate the interplay between quantum electrodynamics (QED) and electron correlation effects. In view of this, we start our discussions with the RMBPT calculations for a few HCIs by rigorously treating QED effects; then we outline methods to calculate IS factors in the one-valence atomic systems using two formulations of the RCC approach. Then we present calculations for two valence atomic systems, by employing the Fock-space RCC methods. For completeness, we briefly discuss theoretical input required for the upcoming experiments, their possibilities to probe nuclear properties and implications to fundamental physics studies.