Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly charged ions (HCIs) made HCIs accessible for high-resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in ${\mathrm{Cf}}^{15+}$ and ${\mathrm{Cf}}^{17+}$ ions. Using a high-accuracy relativistic method of calculation, we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric quadrupole, micromotion, and quadratic Zeeman shifts of the clock transitions) that affect the accuracy and stability of the optical clocks. We also calculated magnetic dipole hyperfine-structure constants of the clock states and the blackbody radiation shifts of the clock transitions.

In slow collisions of two bare nuclei with the total charge number larger than the critical value, $Z_{\mathrm{cr}}\approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. Detection of the spontaneous emission of positrons would be the direct evidence of this fundamental phenomenon. However, the spontaneous emission is generally masked by the dynamical positron emission, which is induced by a strong time-dependent electric field created by the colliding nuclei. In our recent paper [I. A. Maltsev et al., Phys. Rev. Lett. 123, 113401 (2019)] it has been shown that the spontaneous pair production can be observed via measurements of the pair-production probabilities for a given set of nuclear trajectories. In the present paper, we have significantly advanced this study by exploring additional aspects of the process we are interested in. We calculate the positron energy spectra and find that these spectra can give a clear signature of the transition from the subcritical to the supercritical regime. It is found that focusing on a part of the positron spectrum, which accounts for the energy region where the spontaneously created positrons can contribute, allows us to get a much stronger evidence of the transition to the supercritical mode, making it very well pronounced in collisions, for example, of two uranium nuclei. The possibility of extending this study to collisions of bare nuclei with neutral atoms is also considered. The probability of a vacancy in the lowest-energy state of a quasimolecule which is formed in collisions of a bare U nucleus with neutral U and Cm atoms has been calculated. The relatively large values of this probability make such collisions suitable for observing the vacuum decay.

We develop a broadly applicable approach that drastically increases the ability to predict the properties of complex atoms accurately. We apply it to the case of ${\mathrm{Ir}}^{17+}$, which is of particular interest for the development of novel atomic clocks with a high sensitivity to the variation of the fine-structure constant and to dark matter searches. In general, clock transitions are weak and very difficult to identify without accurate theoretical predictions. In the case of ${\mathrm{Ir}}^{17+}$, even stronger electric-dipole ($E1$) transitions have eluded observation despite years of effort, raising the possibility that the theoretical predictions are grossly wrong. In this work, we provide accurate predictions of the transition wavelengths and $E1$ transition rates for ${\mathrm{Ir}}^{17+}$. Our results explain the lack of observations of the $E1$ transitions and provide a pathway toward the detection of clock transitions. The computational advances we demonstrate in this work are widely applicable to most elements in the periodic table and will allow us to solve numerous problems in atomic physics, astrophysics, and plasma physics.

A method for calculations of electron-positron pair-creation probabilities in low-energy heavy-ion collisions is developed. The approach is based on the propagation of all one-electron states via the numerical solving of the time-dependent Dirac equation in the monopole approximation. The electron wave functions are represented as finite sums of basis functions constructed from B-splines using the dual-kinetic-balance technique. The calculations of the created particle numbers and the positron energy spectra are performed for the collisions of bare nuclei at the energies near the Coulomb barrier with the Rutherford trajectory and for different values of the nuclear charge and the impact parameter. To examine the role of the spontaneous pair creation, the collisions with a modified velocity and with a time delay are also considered. The obtained results are compared with the previous calculations and the possibility of observation of the spontaneous pair creation is discussed.

The previously developed technique for evaluation of charge transfer and electron-excitation processes in low-energy heavy-ion collisions [Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)] is extended to collisions of ions with neutral atoms. The method employs the active-electron approximation, in which only the active-electron participates in the charge transfer and excitation processes while the passive electrons provide the screening density-functional theory (DFT) potential. The time-dependent Dirac wave function of the active electron is represented as a linear combination of atomic-like Dirac-Fock-Sturm orbitals, localized at the ions (atoms). The screening DFT potential is calculated using the overlapping densities of each ion (atom), derived from the atomic orbitals of the passive electrons. The atomic orbitals are generated by solving numerically the one-center Dirac-Fock and Dirac-Fock-Sturm equations by means of a finite-difference approach with the potential taken as the sum of the exact reference ion (atom) Dirac-Fock potential and of the Coulomb potential from the other ion within the monopole approximation. The method developed is used to calculate the $K$-$K$ charge transfer and $K$-vacancy production probabilties for the Ne$\left(1s^{2}2s^{2}2p^6\right)$-F${}^{8+}\left(1s\right)$ collisions at the F${}^{8+}\left(1s\right)$ projectile energies 130 and 230 keV/u. The obtained results are compared with experimental data and other theoretical calculations. The $K$-$K$ charge transfer and $K$-vacancy production probabilities are also calculated for the Xe-Xe${}^{53+}\left(1s\right)$ collision.