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.

We estimate the relative contribution of nuclear structure and new physics couplings to the parity non-conserving spin-independent effects in atomic systems, for both single isotopes and isotopic ratios. General expressions are presented to assess the sensitivity of isotopic ratios to neutron skins and to couplings beyond standard model at tree level. The specific coefficients for these contributions are calculated assuming Fermi distribution for proton and neutron nuclear densities for isotopes of Cs, Ba, Sm, Dy, Yb, Pb, Fr, and Ra. The present work aims to provide a guide to the choice of the best isotopes and pairs of isotopes for conducting atomic PNC measurements.

Ions of the isomer 229m Th are a topic of high interest for the construction of a "nuclear clock" and in the field of fundamental physics for testing symmetries of nature. They can be efficiently captured in Paul traps which are ideal for performing high precision quantum logic spectroscopy. Trapping and identification of long-lived 232 Th + ions from a laser ablation source was already demonstrated by the TACTICa collaboration on Trapping And Cooling of Thorium Ions with Calcium. The 229m Th is most easily accessible as α-decay daughter of the decay of 233 U. We report on the development of a source for slow Th ions, including 229(m) Th for the TACTICa experiment. The 229(m) Th source is currently under construction and comprises a 233 U monolayer, from which 229(m) Th ions recoil. These are decelerated in an electric field. Conservation of the full initial charge state distribution of the 229(m) Th recoil ions is one of the unique features of this source. We present ion-flight simulations for our adopted layout and give a final design for the source delivering low-energy single Th ions into a linear Paul trap for spectroscopy investigations.