g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment.

The bound-electron g factor is a stringent tool for tests of the standard model and the search for new physics. The comparison between an experiment on the g factor of lithiumlike silicon and the two recent theoretical values revealed the discrepancies of 1.7σ [Glazov et al. Phys. Rev. Lett. 123, 173001 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.173001] and 5.2σ [Yerokhin et al. Phys. Rev. A 102, 022815 (2020)PLRAAN2469-992610.1103/PhysRevA.102.022815]. To identify the reason for this disagreement, we accomplish large-scale high-precision computation of the interelectronic-interaction and many-electron QED corrections. The calculations are performed within the extended Furry picture of QED, and the dependence of the final values on the choice of the binding potential is carefully analyzed. As a result, we significantly improve the agreement between the theory and experiment for the g factor of lithiumlike silicon. We also report the most accurate theoretical prediction to date for lithiumlike calcium, which perfectly agrees with the experimental value.

Particle-in-cell simulation method for macroscopic degenerate plasmas.

Nowadays hydrodynamic equations coupled with external equation of states provided by quantum mechanical calculations is a widely used approach for simulations of macroscopic degenerate plasmas. Although such an approach is proven to be efficient and shows many good features, especially for large scale simulations, it encounters intrinsic challenges when involving kinetic effects. As a complement, here we have invented a fully kinetic numerical approach for macroscopic degenerate plasmas. This approach is based on first principle Boltzmann-Uhling-Uhlenbeck equations coupled with Maxwell's equation, and is eventually achieved via an existing particle-in-cell simulation code named LAPINS. In this approach, degenerate particles obey Fermi-Dirac statistics and nondegenerate particles follow the typical Maxwell-Boltzmann statistics. The equation of motion of both degenerate and nondegenerate particles are governed by long range collective electromagnetic fields and close particle-particle collisions. Especially, Boltzmann-Uhling-Uhlenbeck collisions ensure that evolution of degenerate particles is enforced by the Pauli exclusion principle. The code is applied to several benchmark simulations, including electronic conductivity for aluminium with varying temperatures from 2 eV to 50 eV, thermalization of alpha particles in a cold fuel shell in inertial confinement fusion, and rapid heating of solid sample by short and intense laser pulses.

Uniform warm dense matter formed by direct laser heating in the presence of external magnetic fields.

With the recent realization of kilotesla quasistatic magnetic fields, the interaction of a laser with magnetized solids enters an unexplored new regime. In particular, a circularly polarized (CP) laser pulse may propagate in a highly magnetized plasma of any high density without encountering cutoff reflection in the whistler mode. With this, we propose a scheme for producing uniform warm dense matter (WDM) by direct laser heating with a CP laser irradiating onto the target along the magnetic field. It is shown by particle-in-cell simulations, which include advanced ionization dynamics and collision dynamics, moderately intense right-hand CP laser light at 10^{15}W/cm^{2} can propagate in solid aluminum and heat it efficiently to the 100 eV level within picoseconds. By using two laser pulses irradiating from two sides of a thin solid target, uniform heating to WDM can be achieved. This provides a controllable way to create WDM at different temperatures.

Multiple Photodetachment of Carbon Anions via Single and Double Core-Hole Creation.

We report on new measurements of m-fold photodetachment (m=2-5) of carbon anions via K-shell excitation and ionization. The experiments were carried out employing the photon-ion merged-beams technique at a synchrotron light source. While previous measurements were restricted to double detachment (m=2) and to just the lowest-energy K-shell resonance at about 282 eV, our absolute experimental m-fold detachment cross sections at photon energies of up to 1000 eV exhibit a wealth of new thresholds and resonances. We tentatively identify these features with the aid of detailed atomic-structure calculations. In particular, we find unambiguous evidence for fivefold detachment via double K-hole production.

Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation.

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K-shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.

Ab initio QED Treatment of the Two-Photon Annihilation of Positrons with Bound Electrons.

The process of a positron-bound-electron annihilation with simultaneous emission of two photons is investigated theoretically. A fully relativistic formalism based on an ab initio QED description of the process is worked out. The developed approach is applied to evaluate the annihilation of a positron with K-shell electrons of a silver atom, for which a strong contradiction between theory and experiment was previously stated. The results obtained here resolve this longstanding disagreement and, moreover, demonstrate a sizable difference with approaches so far used for calculations of the positron-bound-electron annihilation process, namely, Lee's and the impulse approximations.

Particle-in-cell simulation of transport and energy deposition of intense proton beams in solid-state materials.

A particle-in-cell (PIC) simulation code is used to investigate the transport and energy deposition of an intense proton beam in solid-state material. This code is able to simulate close particle interactions by using a Monte Carlo binary collision model. Such a model takes into account all related interactions between the incident protons and material particles, e.g., proton-nucleus, proton-bound-electron, and proton-free-electron collisions. This code also includes a Monte Carlo model for the collisional ionization and electron-ion recombination as well as the depression of the ionization potential by shielding of surrounding particles. Moreover, for intense proton beams, in order to include collective electromagnetic effects, significantly speed up the simulation, and simultaneously avoid numerical instabilities, an approach that combines the PIC method with a reduced model of high-density plasma based on Ohm's law is used. Simulation results indicate that the collective electromagnetic effects have a significant influence on the transport and energy deposition of proton beams. The Ohmic electric field would increase the stopping power and leads to a shortened range of proton beams in solid. The magnetic field would localize the energy deposition by collimating proton beams, which would otherwise be deflected by the collisions with nuclei.

High-order implicit particle-in-cell method for plasma simulations at solid densities.

A high-order implicit multidimensional particle-in-cell (PIC) method is developed for simulating plasmas at solid densities. The space-time arrangement is based on Yee and a leapfrog algorithm for electromagnetic fields and particle advancement. The field solver algorithm completely eliminates numerical instabilities found in explicit PIC methods with relaxed time step and grid resolution. Moreover, this algorithm eliminates the numerical cooling found in the standard implicit PIC methods by using a pseudo-electric-field method. The particle pusher algorithm combines the standard Boris particle pusher with the Newton-Krylov iteration method. This algorithm increases the precision accuracy by several orders of magnitude when compared with the standard Boris particle pusher and also significantly decreases the iteration time when compared with the pure Newton-Krylov method. The code is tested with several benchmarks, including Weibel instability, and relativistic laser plasma interactions at both low and solid densities.

Maximum Elliptical Dichroism in Atomic Two-Photon Ionization.

Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |Δ_{ED}|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could be used as a sensitive tool for analyzing the polarization state of photon beams produced by free-electron lasers.

Probing Sizes and Shapes of Nobelium Isotopes by Laser Spectroscopy.

Until recently, ground-state nuclear moments of the heaviest nuclei could only be inferred from nuclear spectroscopy, where model assumptions are required. Laser spectroscopy in combination with modern atomic structure calculations is now able to probe these moments directly, in a comprehensive and nuclear-model-independent way. Here we report on unique access to the differential mean-square charge radii of ^{252,253,254}No, and therefore to changes in nuclear size and shape. State-of-the-art nuclear density functional calculations describe well the changes in nuclear charge radii in the region of the heavy actinides, indicating an appreciable central depression in the deformed proton density distribution in ^{252,254}No isotopes. Finally, the hyperfine splitting of ^{253}No was evaluated, enabling a complementary measure of its (quadrupole) deformation, as well as an insight into the neutron single-particle wave function via the nuclear spin and magnetic moment.

Monte Carlo approach to calculate ionization dynamics of hot solid-density plasmas within particle-in-cell simulations.

A physical model based on a Monte Carlo approach is proposed to calculate the ionization dynamics of hot-solid-density plasmas within particle-in-cell (PIC) simulations, and where the impact (collision) ionization (CI), electron-ion recombination (RE), and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal relaxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different compositions. The proposed model is implemented into a PIC code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium at temperature of 1 to 1000 eV, (i) the averaged ionization degree increases by including IPD; while (ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures and shows good agreements with that generated from Saha-Boltzmann model and/or FLYCHK code.

Monte Carlo approach to calculate proton stopping in warm dense matter within particle-in-cell simulations.

A Monte Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. This approach is based on multiple electron-electron, electron-ion, and ion-ion binary collision and accounts for both the free and the bound electrons in the plasmas. This approach enables one to calculate the stopping of particles in a more natural manner than existing theoretical treatment. In the low-temperature limit, when "all" electrons are bound to the nucleus, the stopping power coincides with the predictions from the Bethe-Bloch formula and is consistent with the data from the National Institute of Standard and Technology database. At higher temperatures, some of the bound electrons are ionized, and this increases the stopping power in the plasmas, as demonstrated by A. B. Zylstra et al. [Phys. Rev. Lett. 114, 215002 (2015)]PRLTAO0031-900710.1103/PhysRevLett.114.215002. At even higher temperatures, the degree of ionization reaches a maximum and thus decreases the stopping power due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.

Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion.

Resonant laser ionization and spectroscopy are widely used techniques at radioactive ion beam facilities to produce pure beams of exotic nuclei and measure the shape, size, spin and electromagnetic multipole moments of these nuclei. However, in such measurements it is difficult to combine a high efficiency with a high spectral resolution. Here we demonstrate the on-line application of atomic laser ionization spectroscopy in a supersonic gas jet, a technique suited for high-precision studies of the ground- and isomeric-state properties of nuclei located at the extremes of stability. The technique is characterized in a measurement on actinium isotopes around the N=126 neutron shell closure. A significant improvement in the spectral resolution by more than one order of magnitude is achieved in these experiments without loss in efficiency.

Nuclear Excitation by Two-Photon Electron Transition.

A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied theoretically. As a generic example, detailed calculations are performed for the E1E1 1s2s^{1}S_{0}→1s^{2}^{1}S_{0} two-photon decay of a He-like ^{225}Ac^{87+} ion with a resonant excitation of the 3/2+ nuclear state with an energy of 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be P_{NETP}=3.5×10^{-9} and, thus, is comparable with other mechanisms, such as nuclear excitation by electron transition and by electron capture. The possibility for the experimental observation of the proposed mechanism is thoroughly discussed.

Charge Radii of Neutron Deficient

Bunched-beam collinear laser spectroscopy is performed on neutron deficient ^{52,53}Fe prepared through in-flight separation followed by a gas stopping. This novel scheme is a major step to reach nuclides far from the stability line in laser spectroscopy. Differential mean-square charge radii δ⟨r^{2}⟩ of ^{52,53}Fe are determined relative to stable ^{56}Fe as δ⟨r^{2}⟩^{56,52}=-0.034(13) fm^{2} and δ⟨r^{2}⟩^{56,53}=-0.218(13) fm^{2}, respectively, from the isotope shift of atomic hyperfine structures. The multiconfiguration Dirac-Fock method is used to calculate atomic factors to deduce δ⟨r^{2}⟩. The values of δ⟨r^{2}⟩ exhibit a minimum at the N=28 neutron shell closure. The nuclear density functional theory with Fayans and Skyrme energy density functionals is used to interpret the data. The trend of δ⟨r^{2}⟩ along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects and provides important data for understanding the intricate trend in the δ⟨r^{2}⟩ of closed-shell Ca isotopes.

High-resolution spectroscopy on the laser-cooling candidate La

The bound-bound transition from the 5d^{2}6s^{2} ^{3}F_{2}^{e} ground state to the 5d6s^{2}6p ^{3}D_{1}^{o} excited state in negative lanthanum has been proposed as a candidate for laser cooling, which has not yet been achieved for negative ions. Anion laser cooling holds the potential to allow the production of ultracold ensembles of any negatively charged species. We have studied the aforementioned transition in a beam of negative La ions by high-resolution laser spectroscopy. The center-of-gravity frequency was measured to be 96.592 80(10) THz. Seven of the nine expected hyperfine structure transitions were resolved. The observed peaks were unambiguously assigned to the predicted hyperfine transitions by a fit, confirmed by multiconfigurational self-consistent field calculations. From the determined hyperfine structure we conclude that La^{-} is a promising laser cooling candidate. Using this transition, only three laser beams would be required to repump all hyperfine levels of the ground state.

Observation of coherence in the time-reversed relativistic photoelectric effect.

The photoelectric effect has been studied in the regime of hard x rays and strong Coulomb fields via its time-reversed process of radiative recombination (RR). In the experiment, the relativistic electrons recombined into the 2p_{3/2} excited state of hydrogenlike uranium ions, and both the RR x rays and the subsequently emitted characteristic x rays were detected in coincidence. This allowed us to observe the coherence between the magnetic substates in a highly charged ion and to identify the contribution of the spin-orbit interaction to the RR process.

Electron- and proton-impact excitation of hydrogenlike uranium in relativistic collisions.

The K shell excitation of H-like uranium (U(91+)) in relativistic collisions with different gaseous targets has been studied at the experimental storage ring at GSI Darmstadt. By performing measurements with different targets as well as with different collision energies, we were able to observe for the first time the effect of electron-impact excitation (EIE) process in the heaviest hydrogenlike ion. The large fine-structure splitting in H-like uranium allowed us to unambiguously resolve excitation into different L shell levels. State-of-the-art calculations performed within the relativistic framework which include excitation mechanisms due to both protons (nucleus) and electrons are in good agreement with the experimental findings. Moreover, our experimental data clearly demonstrate the importance of including the generalized Breit interaction in the treatment of the EIE process.

Measurement of the first ionization potential of astatine by laser ionization spectroscopy.

The radioactive element astatine exists only in trace amounts in nature. Its properties can therefore only be explored by study of the minute quantities of artificially produced isotopes or by performing theoretical calculations. One of the most important properties influencing the chemical behaviour is the energy required to remove one electron from the valence shell, referred to as the ionization potential. Here we use laser spectroscopy to probe the optical spectrum of astatine near the ionization threshold. The observed series of Rydberg states enabled the first determination of the ionization potential of the astatine atom, 9.31751(8) eV. New ab initio calculations are performed to support the experimental result. The measured value serves as a benchmark for quantum chemistry calculations of the properties of astatine as well as for the theoretical prediction of the ionization potential of superheavy element 117, the heaviest homologue of astatine.

Spins, electromagnetic moments, and isomers of (107-129)Cd.

The neutron-rich isotopes of cadmium up to the N=82 shell closure have been investigated by high-resolution laser spectroscopy. Deep-uv excitation at 214.5 nm and radioactive-beam bunching provided the required experimental sensitivity. Long-lived isomers are observed in (127)Cd and (129)Cd for the first time. One essential feature of the spherical shell model is unambiguously confirmed by a linear increase of the 11/2(-) quadrupole moments. Remarkably, this mechanism is found to act well beyond the h(11/2) shell.