Testing for isospin symmetry breaking with extensive calculations of isotope shift factors in potassium

TL;DR

This study uses advanced relativistic coupled-cluster calculations to evaluate isotope shift factors in potassium, providing insights into isospin symmetry breaking and offering benchmarks for nuclear models affecting fundamental physics parameters.

Contribution

The paper presents the first comprehensive relativistic coupled-cluster calculations of isotope shift factors in potassium, highlighting the importance of many-body and relativistic effects and linking atomic data to nuclear symmetry breaking.

Findings

IS factors computed with finite-field method agree with experimental data

The isospin symmetry breaking in potassium is consistent with zero

Updated nuclear radii provide stringent benchmarks for nuclear models

Abstract

Precise evaluation of the isotope shift (IS) factors for seven low-lying potassium (K) states is achieved using relativistic coupled-cluster (RCC) theory. The energies of these states are assessed and compared with experimental data to confirm the accuracy of the wave functions calculated at varying RCC theory approximations and highlight the significance of many-body and relativistic effects in determining the energies and IS factors of K. Various methods are used to compute the IS factors, with the finite-field (FF) approach yielding results that align with observed and semi-empirical data. This consistency is attributed to orbital relaxation effects that are naturally present in the FF method but emerge only through complex interactions in other techniques. Using the IS factors derived from FF, we review the mean square radius difference between $^{38m}$K and $^{39}$K. From this difference and muonic atom x-ray spectroscopy, we deduce the absolute radius of $^{38m}$K using an updated calculation of the nuclear polarizability effect. Finally, we evaluate the isospin symmetry breaking (ISB) in this isotriplet by integrating the radius of $^{38m}$K with an updated radius of $^{38}$Ca, concluding that the ISB is compatible with zero. This finding offers a stringent benchmark for nuclear model calculations of ISB corrections in nuclear beta decay, which play a key role in determining the $V_{ud}$ matrix element.