Recent theoretical investigations of pair-production probabilities for given sets of nuclear trajectories predict the observability of spontaneous positron emission in elastic collisions of heavy ions. These calculations are extended to the investigation of ratios $P_{y}(η)/P_{y}(1)$ for partial probabilities of positron emission at small positron energies. The results suggest a possible observability of spontaneous positron emission in elastic collisions of bare heavy ions by analyzing the slope of $P_{y}(η)/P_{y}(1)$ for values of $R_{min}$ $~_{\sim}\!\!\!\!^<$ 0.75 $R_{cr}$. In addition calculations of cross sections for positron emission in U+Cm and Cm+Cm collisions of fully ionized heavy ions are compared with former results with partly ionized projectiles and show an increase by factors of 57 to 72.
A many-body theory approach developed by the authors [Phys. Rev. A 70, 032720 (2004)] is applied to positron bound states and annihilation rates in atomic systems. Within the formalism, full account of virtual positronium (Ps) formation is made by summing the electron-positron ladder diagram series, thus enabling the theory to include all important many-body correlation effects in the positron problem. Numerical calculations have been performed for positron bound states with the hydrogen and halogen negative ions, also known as Ps hydride and Ps halides. The Ps binding energies of 1.118, 2.718…
Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates $Z_{\rm eff}$ and annihilation gamma spectra for positron collisions with the hydrogen-like ions He$^+$, Li$^{2+}$, B$^{4+}$ and F$^{8+}$. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using B-spline basis sets. To elucidate the rôle of the positron-ion repulsio…
We report the dispersion coefficients for the interacting inert gas atoms with the alkali ions, alkaline earth ions and alkali atoms with their singly charged ions. We use our relativistic coupled-cluster method to determine dynamic dipole and quadrupole polarizabilities of the alkali atoms and singly ionized alkaline earth atoms, whereas a relativistic random phase approximation approach has been adopted to evaluate these quantities for the closed-shell configured inert gas atoms and the singly and doubly ionized alkali and alkaline earth atoms, respectively. Accuracies of these results are a…
Using perturbed relativistic coupled-cluster (PRCC) theory we compute the ground state electric dipole polarizability, $α$, of doubly ionized alkaline earth metal ions $\rm{Mg}^{2+}$, $\rm{Ca}^{2+}$, $\rm{Sr}^{2+}$, $\rm{Ba}^{2+}$ and $\rm{Ra}^{2+}$. In the present work we use the Dirac-Coulomb-Breit atomic Hamiltonian and we also include the Uehling potential, which is the leading order term in the vacuum polarization corrections. We examine the correction to the orbital energies arising from the Uehling potential in the self-consistent field calculations as well as perturbatively. Our result…
We present a theoretical study of bound-free electron-positron pair production in the interaction of $γ$-rays with bare ions. Special attention is paid to the longitudinal polarization of both the emitted positrons and the produced hydrogen-like ions. To evaluate this polarization we employed exact solutions of the relativistic Dirac equation and treat the electron-photon coupling within the framework of first-order perturbation theory. Detailed calculations have been performed for both, low- and high-Z ions and for a wide range of photon energies. The results of these calculations suggest tha…
The two-photon annihilation of a positron with an electron bound in the 1s state of a H-like ion is calculated within the fully relativistic QED framework. The interaction with the nucleus is treated nonperturbatively, thus allowing the calculations to be carried out for the annihilation with strongly-bound inner shells of heavy ions. Infrared divergences, appearing when one of the emitted photons approaches the low-frequency limit, are accurately eliminated from final expressions. The total cross section of the two-photon and one-photon annihilation processes are compared for a wide range of …
Energy levels of germanium, tin and lead together with their single, double and triple ionized positive ions have been calculated using the $V^{N-M}$ approximation suggested in the previous work (Dzuba, physics/0501032) (M=4 - number of valence electrons). Initial Hartree-Fock calculations are done for the quadruply ionized ions with all valence electrons removed. The core-valence correlations are included beyond the second-order of the many-body perturbation theory. Interaction between valence electrons is treated by means of the configuration interaction technique. It is demonstrated that ac…
The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.
The current status of tests of quantum electrodynamics with heavy ions is reviewed. The theoretical predictions for the Lamb shift and the hyperfine splitting in heavy ions are compared with available experimental data. Recent achievements and future prospects in studies of the $g$ factor with highly charged ions are also reported. These studies can provide precise determination of the fundamental constants and tests of QED within and beyond the Furry picture at the strong-coupling regime. Theoretical calculations of the electron-positron pair creation probabilities in low-energy heavy-ion col…
We theoretically study orbital alignment in x-ray-ionized atoms and ions, based on improved electronic-structure calculations starting from the Hartree-Fock-Slater model. We employ first-order many-body perturbation theory to improve the Hartree-Fock-Slater calculations and show that the use of first-order-corrected energies yields significantly better transition energies than originally obtained. The improved electronic-structure calculations enable us also to compute individual state-to-state cross sections and transition rates and, thus, to investigate orbital alignment induced by linearly …
Comparative study of nonperturbative electron-positron pair production by intense laser fields colliding with either bremsstrahlung $γ$-rays or relativistic ions
X-ray photoabsorption cross sections have been computed for all magnesium ions using the $R$-matrix method. A comparison with the other available data for Mg II-Mg X shows good qualitative agreement in the resultant resonance shapes. However, for the lower ionization stages, and for singly-ionized Mg II in particular, the previous $R$-matrix results (Witthoeft et al.2009; Witthoeft et al. 2011) overestimate the K-edge position due to the neglect of important orbital relaxation effects, and a global shift downward in photon energy of those cross sections is therefore warranted. We have found th…
We present total and final-state resolved charge transfer (CT) rate coefficients for low-charge Ge, Se, Br, Kr, Rb, and Xe ions reacting with neutral hydrogen over the temperature range 10^2--10^6 K. Each of these elements has been detected in ionized astrophysical nebulae, particularly planetary nebulae. CT rate coefficients are a key ingredient for the ionization equilibrium solutions needed to determine total elemental abundances from those of the observed ions. A multi-channel Landau Zener approach was used to compute rate coefficients for projectile ions with charges q=2-5, and for singly…
Gas phase C$_{70}$ molecules have been ionized with single photons of energies between 16 eV and 70 eV and the electron spectra measured with velocity map imaging in coincidence with the ions. The doubly ionized and unfragmented species was present at photon energies of 22 eV and up, and triply charged ions from 55 eV. The low kinetic energy parts of the spectra are explained with thermal emission of transient hot electrons. Deviations at high photon energies are used to determine a value for the initial electron equilibration time. We propose a generally applicable mechanism, named Resonance …
Large-scale calculations of atomic structures and radiative properties have been carried out for singly, doubly- and trebly ionized cerium. For this purpose, the purely relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method was used, taking into account the effects of valence-valence and core-valence electronic correlations in detail. The results obtained were then used to calculate the expansion opacities characterizing the kilonovae observed as a result of neutron star mergers. Comparisons with previously published experimental and theoretical studies have shown that the results p…
L shell line and total x-ray production cross sections in 78Pt, 79Au, 82Pb, 83Bi, 90Th, and 92U targets ionized by 4-6 MeV/u fluorine ions were measured. These cross sections are compared with available theories for L shell ionization using single- and multiple-hole fluorescence and the Coster-Kronig yields. The ECPSSR and the ECUSAR theories exhibit good agreement with the measured data, whereas, the FBA theory overestimates them by a factor of two. Although for the F ion charge states q = 6-8 the multiple-hole atomic parameters do not significantly differ from the single-hole values, after a…
The time-dependent Dirac equation can be solved exactly for ionization induced by ultrarelativistic heavy ion collisions. Ionization calculations are carried out in such a framework for a number of representative ion-ion pairs. For each ion-ion pair, the computed cross section consists of two terms, a constant energy independent term and a term whose coefficient is ln(gamma). Scaled values of both terms are found to decrease with increasing Z of the nucleus that is ionized.
In recent years, a large number of papers have appeared that dealt with $\EPEM$ pair production in heavy ion collisions at high energies. To a large extent these studies were motivated by the existence of relativistic heavy ion accelerators all over the world. There pair production can be studied in so called ``ultra-peripheral collisions'', where the ions do not come close enough to interact strongly with each other. Various different methods have been used and it is the purpose of this review to present a unified picture of the present status of the field.
X-ray and extreme-ultraviolet spectra from collisions of Ar$^{18+}$ and O$^{8+}$ ions with neutrals
Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Johns Hopkins University（约翰斯·霍普金斯大学）；Helmholtz-Institut Jena（亥姆霍兹耶拿研究所）；GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心）；University of California（加利福尼亚大学）；SRON, Space Research Organisation Netherlands（荷兰空间研究组织）
The two-center Dirac equation for an electron in the external electromagnetic field of two colliding heavy ions in the limit in which the ions are moving at the speed of light is exactly solved and nonperturbative amplitudes for free electron-positron pair production are obtained. We find the condition for the applicability of this solution for large but finite collision energy, and use it to explain recent experimental results. The observed scaling of positron yields as the square of the projectile and target charges is a result of an exact cancellation of a nonperturbative charge dependence …
Lifetimes of the first two metastable states in Sc^{2+} and Y^{2+} are determined using the relativistic coupled-cluster theory. There is a considerable interest in studying the electron correlation effects in these ions as though their electronic configurations are similar to the neutral alkali atoms, their structures are very different from the latter. We have made a comparative study of the correlation trends between the above doubly ionized systems with their corresponding neutral and singly ionized iso-electronic systems. The lifetimes of the excited states of these ions are very importan…
We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using light-front variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic ch…
An exact solution of the time-dependent Dirac equation for ionization and pair production induced by ultrarelativistic heavy ion collisions is presented. Exact transition probabilities, equivalent to those that would be obtained in an untruncated basis coupled channels calculation, are presented. Exact bound-electron positron pair production probabilities are calculated to be mostly smaller than those calculated with the same potential in perturbation theory at impact parameters small enough for differences to occur.
Recent experimental and theoretical (both improved semiclassical and fully quantum-mechanical) results for B III and Ne VII delta n = 0 transitions with n = 2 or 3, respectively, are discussed. The probable reasons for disagreements by about a factor of 2 between the fully quantum-mechanically calculated and both measured and semiclassically calculated widths can be explained in terms of violation of validity criteria and non-thermal Doppler effects. More independent determinations of line widths for multiply-ionized non-hydrogenic ions are called for, but meanwhile caution should be exercised…
Appraising the projected $10^{-18}$ fractional uncertainty in the optical frequency standards using singly ionized ions, we estimate the black-body radiation (BBR) shifts due to the magnetic dipole (M1) and electric quadrupole (E2) multipoles of the magnetic and electric fields, respectively. Multipolar scalar polarizabilities are determined for the singly ionized calcium (Ca$^+$) and strontium (Sr$^+$) ions using the relativistic coupled-cluster method; though the theory can be exercised for any single ion clock proposal. The expected energy shifts for the respective clock transitions are est…
We recall how nearly half a century ago the proposal was made to explore the structure of the quantum vacuum using slow heavy-ion collisions. Pursuing this topic we review the foundational concept of spontaneous vacuum decay accompanied by observable positron emission in heavy-ion collisions and describe the related theoretical developments in strong fields QED.
