Energy-angle differential and total probabilities of positron creation in slow supercritical collisions of two identical heavy nuclei are calculated beyond the monopole approximation. The time-dependent Dirac equation (TDDE) for positrons is solved using the generalized pseudospectral method in modified prolate spheroidal coordinates, which are well suited for description of close collisions in two-center quantum systems. In the frame of reference where the quasimolecular axis is fixed, the rotational coupling term is added to the Hamiltonian. Unlike our previous calculations, we do not discard this term and retain it when solving the TDDE. Both three-dimensional angle-resolved and angle-integrated energy distributions of outgoing positrons are obtained. Three-dimensional angle-resolved distributions exhibit a high degree of isotropy. For the collision energies in the interval 6 to 8 MeV/u, the influence of the rotational coupling on the distributions and total positron creation probabilities is quite small. Published by the American Physical Society 2025

We introduce the pCI software package for high-precision atomic structure calculations. The standard method of calculation is based on the configuration interaction (CI) method to describe valence correlations, but can be extended to attain better accuracy by including core correlations via many-body perturbation theory (CI +MBPT) or the all-order (CI + all-order) method. The software package enables calculations of atomic properties, including energy levels, g-factors, hyperfine structure constants, multipole transition matrix elements, polarizabilities, and isotope shifts. It also features modern high-performance computing paradigms, including dynamic memory allocations and large-scale parallelization via the message-passing interface, to optimize and accelerate computations. To improve accuracy of the calculations, we include a supplementary program package to calculate QED corrections via a variant of QEDMOD, as well as a package to include core correlations.

We present the results of calculations for the total energies, ionization energies, and one-electron binding energies for ground-state configurations of neodymium ions Nd I to Nd59+. 59+ . These calculations are based on the Dirac-Fock approximation taking the Breit and quantum electrodynamics corrections into account. The configuration interaction method, taking into account all relativistic configurations corresponding to the non-relativistic one, is used to obtain total energies and wave functions in the intermediate coupling scheme. Comparison is given with other available data.

A non-empirical relativistic calculation of the potential energy curve of the ground X 1Σ+ state of the carbon monoxide (CO) molecule in the internuclear distances range RAB ∈ [0.5, 30.0] a.u. is performed. The calculation is carried out by the multireference configuration-interaction method in the basis of the Dirac–Fock–Sturm orbitals. For the entire specified range of distances, multi-electron quantum-electrodynamic corrections to the CO energy are calculated by the method of the model Lamb shift operator. The contributions of the quantum electrodynamic corrections to the value of the equilibrium internuclear distance R_AB^e , the dissociation energy De and the vibrational constant ωe of the CO molecule are obtained.

The problem of orbital collapse of the 5g and 6 f electrons in atoms of superheavy elements (SHEs) is considered. Previously, the presence of the orbital collapse was established for the 4 f and 5 f elements of the periodic table. Because of the large centrifugal term for the f and g electrons, the effective radial potential has two wells, one narrow and deep and the other wide but shallow. Depending on the external parameters, the electron can be localized in either the outer well with low binding energy and large average radius or the inner well with higher energy and smaller radius. In this paper, we demonstrate the existence of the orbital collapse for the 5g electrons when changing the total angular momentum J of the atom. We also find that for some SHEs two different solutions of the same Dirac-Fock equations may coexist, with the 5g electron localized in either the inner or outer well. In both cases, the radial wave functions are nodeless. The problem of the dual-state coexistence is studied by the configuration-interaction method in the Dirac-Fock-Sturm orbital basis as well.

Resonant photoelectron diffraction (RPED) and its use for studies of lanthanides are presented. To demonstrate the potential of this technique, we show how the ground-state properties of the heavy-fermion compound YbRh2Si2 and its trivalent counterpart YbCo2Si2 can be determined from RPED measurements and modeling. By providing a modeling recipe and exploring RPED capabilities and limitations, we anticipate wide applications of this method for insights into the properties of lanthanide-based systems.

The $^{229}$Th nucleus has a long-lived isomeric state $A^*$ at 8.338(24) eV [Kraemer et al, Nature, \textbf{617}, 706 (2023)]. This state is connected to the ground state by an M1 transition. For a hydrogenlike Th ion in the $1s$ state the hyperfine structure splitting is about 0.7 eV. This means that the hyperfine interaction can mix the nuclear ground state with the isomeric state with a mixing coefficient $\beta$ about 0.03. If the electron is suddenly removed from this system, the nucleus will be left in the mixed state. The probability to find the nucleus in the isomeric state $A^*$ is equal to $\beta^2\sim 10^{-3}$. For the $2s$ state the effect is roughly two orders of magnitude smaller. An atom with a hole in the $1s$ or $2s$ shell is similar to the hydrogenlike atom, only the hole has a short lifetime $\tau$. After the hole is filled, there is a non-zero probability to find the nucleus in the $A^*$ state. Estimates of this probability are presented along with a discussion of possible experiments on Th-doped xenotime-type orthophosphate crystals and other broad band gap materials.

The ground X 1 Sigma+ state potential energy curve (PEC) and dipole moment curve (DMC) of CO molecule have been revisited within the framework of the relativistic coupled-cluster approach, which incorporates nonperturbative single, double, and triple cluster amplitudes (CCSDT) in conjunction with a finite-field methodology. The generalized relativistic pseudopotential model was used for the effective introducing the relativity in all-electron correlation treatment and accounting the quantum-electrodynamics (QED) corrections within the model-QED-operator approach. The diagonal Born-Oppenheimer correction to PEC has been evaluated using the CCSD approach. The sensitivity of resulting PEC and DMC to variations in basis set parameters and regular intramolecular perturbations were considered as well. The present ab initio results are in a reasonable agreement with their most accurate semiempirical counterparts.

Positron creation probabilities as well as energy and angular distributions of outgoing positrons in slow collisions of two identical heavy nuclei are obtained within the two-center approach beyond the monopole approximation. The time-dependent Dirac equation for positron wave functions is solved with the help of the generalized pseudospectral method in modified prolate spheroidal coordinates adapted for variable internuclear separation. Depending on the nuclear charge, the results are obtained for both subcritical and supercritical regimes of the positron creation. The signatures of transition to the supercritical regime in the total positron creation probabilities and energy spectra are discussed. The angular distributions of emitted positrons demonstrate a high degree of isotropy.

We present a theoretical and computational study of positron supercritical resonances in systems consisting of two highly-charged bare nuclei. The resonance positions and widths depending on the internuclear separation are calculated with the help of the complex-scaling generalized pseudospectral method in modified prolate spheroidal coordinates. The results are applied to estimate the probability of spontaneous positron creation in slow U ^92+ –U ^92+ and Cm ^96+ –Cm ^96+ collisions.

A formula for calculating the relativistic electron localization function (RELF) within the framework of the Dirac-Fock method is obtained. An approach similar to that used earlier in [A.D. Becke and K.E. Edgecombe, The Journal of Chemical Physics 92, 5397 (1990)] in deriving an expression for the nonrelativistic electron localization function (ELF) is applied. It is demonstrated that the expression for RELF differs from the expression for ELF with replacement of the nonrelativistic electron density by its relativistic counterpart. Relativistic calculations of ELF and RELF for a number of superheavy elements are performed and the results are compared. By several examples it is shown that the ELF value equal to 0.5 does not necessarily correspond to the distribution density of homogeneous electron gas. Keywords: relativistic electron localization function, Dirac-Fock method, superheavy elements, electron gas.

The presence of the orbital collapse of the g-orbitals in the excited state of the atom with the nuclear charge number Z = 124 and in the ground state of the atom with Z = 125, which belong to the 8th period of the extended periodic table, is demonstrated. In both cases, the orbital collapse occurs within the same configuration when increasing the total angular momentum J, which characterizes the relativistic term of the atom in the jj coupling. All calculations are performed by means of the relativistic Dirac–Fock method.

The ab initio approach is used to evaluate the excitation energies of the 2s2p 2S+1 PJ states from the ground state as well as the 2s2p 3P1 - 2s2p 3P0 and 2s2p 3P2 - 2s2p 3P1 transition energies for selected Be-like highly charged ions over a wide range: from Ar14+ to U88+. The issue of a strong level mixing due to the proximity of states with the same symmetry is addressed by applying the QED perturbation theory for quasidegenerate levels. The employed approach combines a rigorous perturbative QED treatment up to the second order with electron-electron correlation contributions of the third and higher orders calculated in the Breit approximation. The higher-order QED effects are estimated using the model-QED-operator approach. The nuclear-recoil and nuclear-polarization effects are taken into account as well. The performed calculations are accompanied with a thorough analysis of uncertainties due to uncalculated effects. The most accurate theoretical predictions for the excitation and transition energies in Be-like ions are obtained, which, in general, are in perfect agreement with the available experimental data.

For heliumlike uranium, the energies of the singly-excited 1sns, 1snp, and 1snd states with n ≤ 4 and the probabilities of the one-photon 1s3d -> 1s2p, 1s3p -> 1s2s, 1s3p -> 1s2p and 1s4d -> 1s2p transitions are evaluated. The calculations are performed within the Breit approximation using the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals. The QED corrections to the energy levels are calculated employing the model-QED-operator approach. The nuclear recoil, frequency-dependent Breit-interaction, nuclear polarization, and nuclear deformation corrections are taken into account as well.

For superheavy elements with atomic numbers $120\leq Z \leq 170$, the concept of the ground-state configuration is being reexamined. To this end, relativistic calculations of the electronic structure of the low-lying levels are carried out by means of the Dirac-Fock and configuration-interaction methods.The magnetic and retardation parts of the Breit interaction as well as the QED effects are taken into account. The influence of the relativistic, QED, and electron-electron correlation effects on the determination of the ground-state is analyzed.

The presence of the orbital collapse of the g-orbitals in the excited state of the atom with the nuclear charge number Z=124 and in the ground state of the atom with Z=125, which belong to the 8th period of the extended periodic table, is demonstrated. In both cases, the orbital collapse occurs within the same configuration when increasing the total angular momentum J, which characterizes the relativistic term of the atom in the jj coupling. All calculations are performed by means of the relativistic Dirac-Fock method.

For heliumlike uranium, the energies of the singly-excited $1sns$, $1snp$, and $1snd$ states with $n\leq 4$ and the probabilities of the one-photon $1s3d\to 1s2p$, $1s3p\to 1s2s$, $1s3p\to 1s2p$ and $1s4d\to 1s2p$ transitions are evaluated. The calculations are performed within the Breit approximation using the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals. The QED corrections to the energy levels are calculated employing the model-QED-operator approach. The nuclear recoil, frequency-dependent Breit-interaction, nuclear polarization, and nuclear deformation corrections are taken into account as well.

The disorder-to-order (crystallization) process in phase-change materials determines the speed and storage polymorphism of phase-change memory devices. Only by clarifying the fine-structure variation can the devices be insightfully designed, and encode and store information. As essential phase-change parent materials, the crystallized Sb-Te binary system is generally considered to have the cationic/anionic site occupied by Sb/Te atoms. Here, direct atomic identification and simulation demonstrate that the ultrafast crystallization speed of Sb-Te materials is due to the random nature of lattice site occupation by different classes of atoms with the resulting octahedral motifs having high similarity to the amorphous state. It is further proved that after atomic ordering with disordered chemical occupation, chemical ordering takes place, which results in different storage states with different resistance values. These new insights into the complicated route from disorder to order will play an essential role in designing neuromorphic devices with varying polymorphisms.

The binding-energy differences for ^163Ho^q + and ^163Dy^q + ions with ionization degrees q = 38 , 39, and 40 are calculated. The calculations are performed using the large-scale relativistic configuration-interaction and relativistic coupled-clusters methods. The contributions from quantum-electrodynamics, nuclear-recoil, and frequency-dependent Breit-interaction effects are taken into account. The final uncertainty does not exceed 1 eV. Combining the obtained results with the binding-energy difference for neutral atoms calculated in [I.M. Savelyev, M.Y. Kaygorodov, Y.S. Kozhedub, I.I. Tupitsyn, and V.M. Shabaev, Phys. Rev. A 105 , 012806 (2022)], we get the secondary differences of the ion–atom binding energies. These values can be used to evaluate the amount of energy released in the electron capture process in ^163Ho atom (the Q value), provided mass differences of highly charged ions ^163Ho^q + and ^163Dy^q + is known from experiment. The Q value is required by experiments on the determination of the absolute scale of the electron neutrino mass by studying the beta-decay process.

Получена формула для вычисления релятивистской функции локализации электронов (relativistic electron localization function, RELF) в рамках метода Дирака-Фока. Применен подход, аналогичный использованному ранее в работе [A.D. Becke and K.E. Edgecombe, The Journal of Chemical Physics 92, 5397 (1990)] при выводе выражения для нерелятивистской функции локализации электронов (electron localization function, ELF). Продемонстрировано, что выражение для RELF отличается от выражения для ELF с заменой нерелятивистской электронной плотности на ее релятивистский аналог. Выполнены релятивистские расчеты ELF и RELF для ряда сверхтяжелых элементов, проведено сравнение полученных результатов. На нескольких примерах показано, что значение ELF, равное 0.5, не обязательно соответствует плотности распределения однородного электронного газа. Ключевые слова: релятивистская функция локализации электронов, метод Дирака-Фока, сверхтяжелые элементы, электронный газ.