Isotope shift, non-linearity of King plots and the search for new particles

TL;DR

This paper develops a relativistic formula for isotope shifts, investigates non-linearity in King plots from various effects, and explores their use in detecting new particles and nuclear properties in astrophysical and laboratory spectra.

Contribution

It introduces a new relativistic model for isotope shifts, analyzes sources of King plot non-linearity within the Standard Model, and estimates the potential of King plot measurements to detect new light bosons.

Findings

Nuclear polarizability significantly affects King plot linearity.

Relativistic effects contribute to isotope shift non-linearity.

Predictions set bounds for detecting hypothetical scalar bosons.

Abstract

We derive a mean-field relativistic formula for the isotope shift of an electronic energy level for arbitrary angular momentum; we then use it to predict the spectra of superheavy metastable neutron-rich isotopes belonging to the hypothetical island of stability. Our results may be applied to the search for superheavy atoms in astrophysical spectra using the known values of the transition frequencies for the neutron deficient isotopes produced in the laboratory. An example of a relevant astrophysical system may be the spectra of the Przybylski's star where superheavy elements up to Z=99 have been possibly identified. In addition, it has been recently suggested to use the measurements of King plot non-linearity in a search for hypothetical new light bosons. On the other hand, one can find the non-linear corrections to the King-plot arising already in the Standard Model framework. We investigate contributions to the non-linearity arising from relativistic effects in the isotope field-shift, the nuclear polarizability and many-body effects. It is found that the nuclear polarizability contribution can lead to the significant deviation of the King plot from linearity. Therefore, the measurements of the non-linearity of King plots may be applied to obtain the nuclear polarizability change between individual isotopes. We then proceed with providing a rough analytical estimate of the non-linearity arising solely from the effect of a hypothetical scalar boson. Our predictions give theoretical limitations on the sensitivity of the search for new interactions and should help to identify the most suitable atoms for corresponding experiments.