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A method for calculating the field shift contribution to isotope shifts in many-electron atoms, incorporating quantum electrodynamics (QED) effects, is introduced. We also implement the model QED approach to incorporate QED contribution to the nuclear recoil effect at the high-order correlation effects treatment level. The proposed computational scheme is used to revise the value of the root-mean-square (rms) nuclear charge radius of the isomer of aluminium-26, $^{26m}$Al. This radius is important for the global analysis of the $V_{ud}$ element of the Cabibbo-Kobayashi-Maskawa matrix. The difference in mean-square nuclear charge radii of $^{27}$Al and $^{26m}$Al, obtained by combining the calculated atomic factors with recently measured isotope shift (IS) of the $3s^23p~^2P_{3/2} \to 3s^24s~^2S_{1/2}$ transition in Al, is $0.443(44)(19)~{\rm fm}^2$, where the first and second uncertainties are experimental and theoretical ones, respectively. The latter is reduced by a factor of 4 with respect to the previous study. Using this value and the known value of the rms charge radius of $^{27}$Al, the resultant value $R_c(^{26m}$Al) = 3.132(10)~fm is obtained. With the improved accuracy of the calculated IS factors the error in $R_c(^{26m}$Al) is now dominated by the experimental uncertainty. Similar revision of rms charge radii is made for the $^{28}$Al, $^{29}$Al, $^{30}$Al, $^{31}$Al and $^{32}$Al isotopes using existing IS measurements. Additionally, atomic factors are computed for the $3s^23p~^2P_{3/2} \to 3s^24s~^2S_{1/2}$, $3s^23p~^2P_{1/2} \to 3s^25s~^2S_{1/2}$ and $3s^23p~^2P_{3/2} \to 3s^25s~^2S_{1/2}$ transitions in Al, which can be used in future experimental studies.

The effects induced by the time-reversal ($\mathcal{T}$) and spatial parity ($\mathcal{P}$) violating electron-nucleus and electron-electron interactions mediated by the axion-like particles (ALPs) in the BaF molecule were estimated. Molecular parameters characterizing these interactions were calculated across a wide range of ALP masses. In case of the electron-nuclear interaction, the effect of the extended nucleus was studied and shown to be significant for heavy ALPs. Based on the calculated molecular parameters, we obtained a link between the $\mathcal{T}$,$\mathcal{P}$-violating energy shift which can be measured in the ongoing experiment designed to search for the electron electric dipole moment using the BaF molecule [A. Boeschoten et al., arXiv:2303.06402 (2023)] and the products of coupling constants of the ALP-electron or ALP-electron and ALP-nucleus interactions.

The nuclear charge radius of $^{32}$Si was determined using collinear laser spectroscopy. The experimental result was confronted with ab initio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of $^{32}$Si completes the radii of the mirror pair $^{32}$Ar - $^{32}$Si, whose difference was correlated to the slope $L$ of the symmetry energy in the nuclear equation of state. Our result suggests $L \leq 60$\,MeV, which agrees with complementary observables.

Recently, upper bounds on the static time-reversal ($\mathcal{T}$) and spatial parity ($\mathcal{P}$)-violating electron electric dipole moment ($e$EDM) and dimensionless constant characterizing the strength of the $\mathcal{T}$,$\mathcal{P}$-violating scalar-pseudoscalar nucleus-electron interaction have been updated in the JILA experiment using the HfF$^+$ cations [T.S. Roussy et al, arxiv:2212.11841 (2022)]. We considered other two sources of the $\mathcal{T}$,$\mathcal{P}$,-violation in HfF$^+$ -- axionlike-particle-mediated (ALP) scalar-pseudoscalar electron-electron and nucleus-electron interactions. To estimate the magnitude of effects, induced by such interactions in HfF$^+$ we have developed and applied a method which implies direct use of the ab-initio relativistic coupled cluster theory to calculate molecular parameters that characterize the interactions. Using these parameters, we showed that an order of magnitude updated laboratory constraints on the ALP-mediated electron-electron and nucleus-electron interactions can be derived from the experimental data on $\mathcal{T}$,$\mathcal{P}$-violating effects in HfF$^+$ for a wide range of ALP masses.

Electronic factors for the field and mass isotope shifts in the $6p\ ^{2}P_{3/2} \to 7s\ ^{2}S_{1/2}$ (535 nm), $6p\ ^{2}P_{1/2} \to 6d\ ^{2}D_{3/2}$ (277 nm) and $6p\ ^{2}P_{1/2} \to 7s\ ^{2}S_{1/2}$ (378~nm) transitions in the neutral thallium were calculated within the high-order relativistic coupled cluster approach. These factors were used to reinterpret previous experimental isotope shift measurements in terms of charge radii of a wide range of Tl isotopes. Good agreement between theoretical and experimental King-plot parameters was found for the $6p\ ^{2}P_{3/2} \to 7s\ ^{2}S_{1/2}$ and $6p\ ^{2}P_{1/2} \to 6d\ ^{2}D_{3/2}$ transitions. It was shown that the value of the specific mass shift factor for the $6p\ ^{2}P_{3/2} \to 7s\ ^{2}S_{1/2}$ transition is not negligible compared to the value of normal mass shift in contrary to what had been suggested previously. Theoretical uncertainties in mean square charge radii were estimated. They were substantially reduced compared to the previously ascribed ones and amounted to less than 2.6%. The achieved accuracy paves the way to a more reliable comparison of the charge radii trends in the lead region.

The refined values of the magnetic dipole moments of $^{185}$Re and $^{187}$Re nuclei are obtained. For this, we perform a combined relativistic coupled cluster and density functional theory calculation of the shielding constant for the ReO$_4^-$ anion. In this calculation, we explicitly include the effect of the finite nuclear magnetization distribution in the single-particle nuclear model using the Woods-Saxon potential for the valence nucleon. By combining the obtained value of the shielding constant $\sigma=4069(389)$~ppm with the available experimental nuclear magnetic resonance data we obtain the values: $\mu(^{185}{\rm Re})=3.1567(3)(12) \mu_N, \mu(^{187}{\rm Re})=3.1891(3)(12) \mu_N$, where the first uncertainty is the experimental one and the second is due to theory. The refined values of magnetic moments are in disagreement with the tabulated values, $\mu(^{185}{\rm Re})=3.1871(3) \mu_N, \mu(^{187}{\rm Re})=3.2197(3) \mu_N$, which were obtained using the shielding constant value calculated for the atomic cation Re$^{7+}$ rather than the molecular anion. The updated values of the nuclear magnetic moments resolve the disagreement between theoretical predictions of the hyperfine structure of H-like rhenium ions which were based on the tabulated magnetic moment values and available experimental measurements. Using these experimental data we also extract the value of the parameter of nuclear magnetization distribution introduced in [J. Chem. Phys. \textbf{153}, 114114 (2020)], which is required to predict hyperfine structure constants for rhenium compounds.