Studying quantum interference in photorecombination (PR) is crucial not only for understanding the spectral line shapes of resonances but also for developing a complete quantum-mechanical formalism that unifies the treatment of radiative recombination (RR) and dielectronic recombination (DR) as interfering pathways. In this work, we present a theoretical study of total PR cross sections for high-Z He-like ions using a relativistic projection-operator formalism, which provides a unified quantum-mechanical description of RR and DR. Detailed calculations are performed for the KLL resonance structures in He-like Xe52+, W72+, and U90+, revealing pronounced interference-induced asymmetries in the PR cross sections. We find that the interference effects of RR and DR occur predominantly at the KL12L3 resonances in high-Z ions, consistent with previous experimental observations at electron beam ion traps [Tu et al., Phys. Rev. A 93, 032707 (2016)]. These interference effects should also be observable in the total PR cross sections of He-like Xe52+, W72+, and U90+ ions in the electron-ion recombination experiments at storage rings.

Studying quantum interference in photorecombination (PR) is crucial not only for understanding the spectral line shapes of resonances but also for developing a complete quantum-mechanical formalism that unifies the treatment of radiative recombination (RR) and dielectronic recombination (DR) as interfering pathways. In this work, we present a theoretical study of total PR cross sections for high-Z He-like ions using a relativistic projection-operator formalism, which provides a unified quantum-mechanical description of RR and DR. Detailed calculations are performed for the KLL resonance structures in He-like Xe ^52+ , W ^72+ , and U ^90+ , revealing pronounced interference-induced asymmetries in the PR cross sections. We find that the interference effects of RR and DR occur predominantly at the KL_12L_3 resonances in high-Z ions, consistent with previous experimental observations at electron beam ion traps [Tu et al., Phys. Rev. A 93, 032707 (2016)]. These interference effects should also be observable in the total PR cross sections of He-like Xe ^52+ , W ^72+ , and U ^90+ ions in the electron-ion recombination experiments at storage rings.

Hyperfine splitting in highly charged ions provides a powerful probe for testing strong-field quantum electrodynamics and investigating nuclear structure. In this work, we theoretically investigate the hyperfine-resolved dielectronic recombination process near to the threshold for selected Li-like highly charged ions. Numerical computations were carried out using a multiconfiguration Dirac-Fock method to address dielectronic recombination resonances for Li-like ions. Our calculations reproduce the previous experimental results of Li-like 45Sc18+ ions with nuclear spin I = 72 [M. Lestinsky et al., Phys. Rev. Lett. 100, 033001 (2008)]. We further extended the calculation to two highly charged heavy ions, Li-like 119Sn47+ (I = 12) and 187Re72+ (I = 52), revealing distinct hyperfine-split dielectronic recombination resonances in the low-energy region. These calculations identify promising candidate ions and provide theoretical guidance for high-resolution dielectronic recombination experiments using the new storage-ring merged-beam technique.

Electron-ion collision spectroscopy at heavy-ion storage rings aims at precision measurements of reson-ance features that occur in the cross sections of electron collision processes such as electron-impact ionization of ions or electron-ion recombination.As part of the international Facility for Antiproton and Ion Research(FAIR)project,the low-energy ion storage ring CRYRING@ESR has been coupled with the heavy-ion accelerators oper-ated by the GSI Helmholtz Center for Heavy-Ion Research in Darmstadt,Germany.This has created a new oppor-tunity for stringent strong field quantum electrodynamics tests through electron-ion collision spectroscopy of heavy few-electron ions.The present contribution provides details of the electron-ion collision spectroscopy setup at CRYRING@ESR and associated data-analysis procedures along with first results for nonresonant and resonant re-combination of berylliumlike lead ions.A recombination rate enhancement factor of 3.5 was observed for nonreson-ant recombination at zero electron-ion collision energy.For resonant recombination excellent agreement with recent theoretical results was obtained when these were shifted by 340 meV in energy.

Dielectronic recombination (DR) experiments of highly charged ions not only provide essential atomic benchmark data for astrophysical and fusion plasma research but also serve as a stringent test for strong-field quantum electrodynamics (QED) effects, relativistic effects, and electron correlation effects. High-intensity heavy-ion accelerator facility (HIAF), currently under construction at Huizhou, China, will have a high- precision spectrometer ring (SRing) equipped with a 450 kV electron-cooler and an 80 kV ultracold electron- target. This advanced setup facilitates precise measurements of the DR process for highly charged ions in a broad range of center-of-mass energy, from meV to tens of keV. In this work, we carry out the molecular dynamics simulation of the electron beam temperature distribution of the ultracold electron-target at the SRing. The simulation results indicate that after treatment by the designed adiabatic magnetic field and acceleration field, the transverse and longitudinal electron beam temperature generated by the thermionic electron gun can be reduced from 100 meV to below 5 meV and 0.1 meV, respectively. Furthermore, we analyze the influence of this ultracold electron beam temperature on the resonance peak and energy resolution in DR experiment. The resolution gain at the SRing electron-target is particularly pronounced at small electron-ion collision energy, which provides unique experimental conditions for the DR experiments. Taking lithium-like (129)(54)Xe(51+ )and U-238(92)89+ ions for example, we simulate the DR resonance spectra at the SRing and compare them with the simulated results from the experimental cooler storage ring CSRe. The results reveal that the SRing experiments can resolve fine DR resonance structures with ultra-high energy resolution compared with those from the CSRe. This work lays a solid foundation for precise DR spectroscopy of highly charged ions at the SRing to stringent test of strong field QED effect and extraction nuclear structure information. [GRAPHICS] .

With the advancement of synchrotron and free-electron laser,X-ray quantum optics has emerged as a novel frontier for exploring light-matter interactions at high photon energies.A significant challenge in this field is achieving well-defined two-level systems through atomic inner-shell transitions,which are often hindered by broad natural linewidths and local electronic structure effects.This study aims to explore the potential of tungsten disilicide(WSi2)as a two-level system for X-ray quantum optics applications.Utilizing high-resolution resonant inelastic X-ray scattering(RIXS)near the W-L3 edge,in this work,the white line of bulk WSi2 is experimentally distinguished,overcoming the spectral broadening caused by short core-hole lifetime.The measurements are conducted by using a von Hamos spectrometer at the GALAXIES beamline of the SOLEIL synchrotron.The results reveal a single resonant emission feature with a fixed energy transfer,confirming the presence of a discrete 2p-5d transition characteristic of a two-level system.Additional high-resolution XAS spectra,obtained via high energy resolution fluorescence detection method and reconstructed from off-resonant emission(free from self-absorption effect for bulk WSi2 sample)method,further support the identification of a sharp white line.These findings demonstrate the feasibility of using WSi2 as a model system in X-ray cavity quantum optics and establish RIXS as a powerful technique to resolve fine inner-shell structures.

With the advancement of synchrotron and free-electron laser developments, X-ray quantum optics has emerged as a novel frontier for exploring light-matter interactions at high photon energies. A major challenge in this field is the well-defined two-level systems using atomic inner-shell transitions, which are often hindered by broad natural linewidths and their overlap with the ionization continuum. This study aims to explore the potential of tungsten disilicide (WSi2) as a two-level system for X-ray quantum optics applications. Utilizing high-resolution resonant inelastic X-ray scattering (RIXS) near the W-L3 edge, this work experimentally resolves the pre-edge white line from the ionization continuum, overcoming the spectral broadening caused by short core-hole lifetimes. The measurements were conducted using a von Hamos spectrometer at the GALAXIES beamline of the SOLEIL synchrotron. The results reveal a single resonant emission feature with a fixed energy tranfer (shown as below, same as Fig 4), confirming the presence of a discrete 2p–5d transition characteristic of a two-level system. Additional high-resolution XAS spectra, obtained via high energy resolution fluorescence detection (HERFD) method and reconstructed from off-resonant emission (HEROS) method, further support the identification of a sharp white line. These findings demonstrate the feasibility of using WSi2 as a model system in X-ray cavity quantum optics and establish RIXS as a powerful technique to resolve fine inner-shell structures.

Employing the dual laser plasma technique, we measured the extreme ultraviolet (EUV) photoabsorption spectrum of F2+ ions, spanning the energy range from 53 to 93 eV with an energy resolution (E/ΔE) of 866. The measured spectrum is carefully analyzed by comparing with the available reference data and theoretical calculation using the Cowan code. We identify prominent transitions to the Rydberg series 2s22p2ns/nd and 2s2p3np from the ground level and remarkable transitions to the 2s22p2(1D)nd2D states from the 2s22p32D metastable level. Transition energies and line profile parameters are determined by fitting the identified absorption features. The calibration of the spectrometer with well-known transitions allows us to provide line positions for well-resolved resonances with an uncertainty of 20 meV. The reported experimental data of F2+ significantly contribute to the fundamental atomic database, offering valuable benchmarks for theoretical calculations with potential applications in astrophysics and plasma sciences.

The experimental study of precision spectroscopy of dielectronic recombination (DR) of highly charged ions is not only important for astronomical plasma and fusion plasma, but also can be used as a new precision spectroscopy to test the strong-field quantum electrodynamic effect, measure isotope shift, and extract the radius of atomic nuclei. An specially designed electron beam energy detuning system for electron-ion recombination precision spectroscopy experiments has been installed on the heavy ion storage ring CSRe in Lanzhou, China, where the electron-ion collision energy in the center-of-mass system can be detuned to 1 keV, and an independently-developed plastic scintillator detector and multiwire proportional chamber detector have been installed downstream of the electron cooler of the CSRe for detecting recombined ions. The multiwire proportional chamber detector has the ability to non-destructively monitor the profile of the ion beam in real-time while acquiring the recombined ion counts, providing guidance for optimizing the ion beam. On this basis, the first test experiment on dielectronic recombination of Kr25+ ions is carried out at the CSRe, and the dielectronic recombination rate coefficients in a range of 0–70 eV in the frame of center-of-mass are measured. In order to fully understand the experimental results, we calculate the dielectronic recombination rate coefficient of the Kr25+ ion by using the flexible atomic code (FAC) and make a detailed comparison with the experimental result, showing that they are in good agreement with each other, and only the resonance energy values of the two resonance peaks at 1.695 eV and 2.573 eV are significantly different. In addition, the DR resonance energy values and intensities are obtained by fitting the experimental results in a range of 0–35 eV, and we find that the transition 3s→4l (∆n = 1) contributes significantly to the experimental spectral lines. Furthermore, we compare the plasma rate coefficients derived from the DR rate coefficients with those derived from the AUTOSTRUCTURE and FAC theories, which differ by 20 percent in a temperature range less than 106 K. The experimental results show that the DR experimental platform of the CSRe has very good stability and reproducibility, and can provide support for the future DR experiments of highly charged ion, i.e. for testing strong-field quantum electrodynamics effect and measuring the properties of atomic nuclei.

Electron-ion collision spectroscopy of the KLL dielectronic recombination (DR) resonances of hydrogenlike xenon ions was performed at a heavy-ion storage ring with a resolving power that is competitive with x-ray spectroscopy of inner-shell transitions in highly charged ions. The KL_1/2L_1/2 , KL_1/2L_3/2 , and KL_3/2L_3/2 resonance groups and even parts of their fine structure are individually resolved. The resonance strengths were measured on an absolute scale and compared with results from multi-configuration Dirac–Fock (MCDF) calculations. These are in excellent agreement with the experimental findings when QED effects on the resonance energies and the Breit interaction are considered. As already found for DR of hydrogenlike uranium (Bernhardt et al. in Phys Rev A 83:020701(R), 2011), this interaction is particularly strong for the KL_1/2L_1/2 resonance group. For U ^91+ , it increases the KL_1/2L_1/2 DR resonance strength by 40 ^53+ , the increase is found to amount to 25

Absolute generalized oscillator strengths of the valence-shell excitations of krypton have been determined with an incident electron energy of 1500 eV and an energy resolution of about 80 meV. By employing the relative flow technique with a dilute target, the pressure effect is excluded and the accuracy of the measured generalized oscillator strengths is improved. By comparing the present generalized oscillator strengths with the previous experimental and theoretical results, it is found that the first Born approximation is not reached at the squared momentum transfer larger than 1 a.u.. The optical oscillator strengths have been obtained by extrapolating the measured generalized oscillator strengths to zero squared momentum transfer, which cross-checks the previous electron impact and photoabsorption results. With the aid of the BE-scaling method, the integral cross sections of krypton have been determined from the excitation threshold to 5000 eV. The present oscillator strengths and integral cross sections supplement the fundamental database of the electron scattering of krypton and provide a benchmark for the theoretical methods.

Over the past decade,X-ray quantum optics has emerged as a dynamic research field,driven by significant advancements in X-ray sources such as next-generation synchrotron radiation facilities and X-ray free-electron lasers,as well as improvements in X-ray methodologies and sample fabrication techniques.One of the most successful platforms in this field is the X-ray planar thin-film cavity,also known as the X-ray cavity QED setup.To date,most studies in X-ray cavity quantum optics have focused on Mössbauer nuclear resonances.However,this approach is constrained by the limited availability of suitable nuclear isotopes and the lack of universal applicability.Recently,experimental realizations of X-ray cavity quantum control in atomic inner-shell transitions have demonstrated that cavity effects can simultaneously modify transition energies and core-hole lifetimes.These pioneering studies suggest that X-ray cavity quantum optics based on inner-shell transitions will become a promising new platform.Notably,the core-hole state is a fundamental concept in various modern X-ray spectroscopic techniques.Therefore,integrating X-ray quantum optics with X-ray spectroscopy holds the potential to open new frontiers in the field of core-level spectroscopy. In this review,we introduce the experimental systems used in X-ray cavity quantum optics with inner-shell transitions,covering cavity structures,sample fabrications,and experimental methodologies.We explain that X-ray thin-film cavity experiments require high flux,high energy resolution,minimal beam divergence,and precise angular control,necessitating the use of synchrotron radiations.Grazing reflectivity and fluorescence measurements are described in detail,along with a brief introduction to resonant inelastic X-ray scattering techniques.The review also outlines simulation tools,including the classical Parratt algorithm,semi-classical matrix formalism,quantum optical theory based on the Jaynes-Cummings model,and the quantum Green's function method.We discuss the similarities and unique features of electronic inner-shell transitions and highlight recent advancements,focusing on cavity-induced phenomena such as collective Lamb shift,Fano interference,core-hole lifetime control,etc.Observables such as reflectivity and fluorescence spectra play a central role in these studies.Finally,we review and discuss potential future directions for the field.Designing novel cavities is crucial for addressing current debates regarding cavity effects in inner-shell transitions and uncovering new quantum optical phenomena.Integrating modern X-ray spectroscopies with X-ray cavity quantum optics represents a promising research frontier with significant application potential.Furthermore,X-ray free-electron lasers,with much higher pulse intensity and shorter pulse duration,are expected to propel X-ray cavity quantum optics into the nonlinear and multiphoton regimes,opening new avenues for exploration.

Dielectronic recombination (DR) rate coefficients for carbon-like Kr30+ have been measured over the collision energy of 0-60 eV using the heavy-ion storage ring CSRe at the Institute of Modern Physics in Lanzhou, China. The present DR spectrum covers the resonances associated with the 2s(2)2p(2)[(3)P0]-* 2s22p(2)[(3)P1,2], 2s2p(3) and 2p(4 )(?n = 0) core excitations. The corresponding DR resonance energies and strengths have been calculated by using the flexible atomic code (FAC) to understand the measured results. An overall agreement has been obtained between the experiment and theory, except for the data at the collision energies below 7 eV and in 35-38 eV, where the electronic correlation effect is strong. In particular, the resonances from the trielectronic recombination due to 2s(2)2p(2) + e(-)-* 2p(4)[D-1(2)]6l have been identified with the help of the FAC calculation. Temperature-dependent plasma recombination rate coefficients were derived from the measured DR rate coefficients for the temperature range 10(3)-10(7) K and compared with our FAC calculations as well as the previous AUTOSTRUCTURE calculations by Zatsarinny et al (2004 Astron. Astrophys. 417 1173-81). The FAC and AUTOSTRUCTURE calculations are in good agreement with the presently derived plasma rate coefficients. The present work provides the benchmark data for astrophysical and laboratory plasma modeling.

Dielectronic recombination (DR) is one of the dominant electron–ion recombination mechanisms for most highly charged ions (HCIs) in cosmic plasmas, and thus, it determines the charge state distribution and ionization balance therein. To reliably interpret spectra from cosmic sources and model the astrophysical plasmas, precise DR rate coefficients are required to build up an accurate understanding of the ionization balance of the sources. The main cooler storage ring (CSRm) and the experimental cooler storage ring (CSRe) at the Heavy-Ion Research Facility in Lanzhou (HIRFL) are both equipped with electron cooling devices, which provide an excellent experimental platform for electron-ion collision studies for HCIs. Here, the status of the DR experiments at the HIRFL-CSR is outlined, and the DR measurements with Na-like Kr 25+ ions at the CSRm and CSRe are taken as examples. In addition, the plasma recombination rate coefficients for Ar 12+, 14+ , Ca 14+, 16+, 17+ , Ni 19+ , and Kr 25+ ions obtained at the HIRFL-CSR are provided. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00092 .

Generalized oscillator strengths (GOSs) of the valence shell excitations to the A1Σ−+B1Δ, C1Π, D1Σ+ and 21Π states in nitrous oxide have been determined by employing an angle-resolved electron energy loss spectrometer operated at an incident energy of 1500 eV and an energy resolution of about 80 meV. Detailed comparisons with the previous data indicate that the higher-order Born terms play a significant role in the GOSs of C1Π and D1Σ+ states at either low impact energies or large momentum transfers, and the GOSs of A1Σ−+B1Δ and C1Π states measured with the gas cell may suffer from the pressure effect. The measured GOS data are fitted with the Lassettre formula to determine the corresponding optical oscillator strengths (OOSs) and calculate the integral cross sections (ICSs) based on the BE-scaling method. The oscillator strengths and cross sections in this work provide a cross check on the previous data and can serve as a benchmark for testing the developed theoretical models and computational codes.

The generalized oscillator strengths (GOSs) of the valence-shell excitations of CH3Cl have been determined at an incident electron energy of 1500 eV and an energy resolution of about 70 meV. The momentum transfer dependence behaviors of the GOSs of the valence-shell excitations have been carefully analyzed, and the A band shows a strong dipole-forbidden characteristic. By extrapolating the GOSs to the limit of a zero squared momentum transfer, the optical oscillator strengths have been obtained, which provide an independent cross-check for the previous experimental and theoretical results. The BE-scaled integral cross sections (where B is the binding energy and E is the excitation energy) of the valence-shell excitations of CH3Cl have been derived systematically from the threshold to 5000 eV with the aid of a BE-scaling method. The results provide the fundamental spectroscopic data of CH3Cl and have important applications in photochemical modeling for atmospheric physics.

The angular distribution and the degree of linear polarization of the dielectronic hypersatellite lines of highly charged helium-like ions are studied by using the multiconfiguration Dirac-Fock method and density matrix theory with a focus on the multipole mixing effects. Detailed calculations have been carried out for the emission of characteristic X-rays from the (2s2p)P1,23 and P11 resonant states decay to the (1s2s)S13 state following the KLL dielectronic recombination of initial hydrogen-like ions with atomic nuclear charge from Z=22 to Z=100. It is shown that the mixing of electric dipole (E1) and magnetic quadrupole (M2) radiations significantly alters the angular distribution and the degree of linear polarization, in which the shifts are dependent on the resonant capture states and the atomic nuclear charges. The E1+M2 mixing has opposite effects for the (2s2p)P23 and (2s2p)P11 resonant states, except for the (2s2p)P11 resonance of the heavy ions with Z≳90, where the profile of angular distribution is reversed by strong mixing effects due to the contribution of the M2 term and its interference with the E1 radiative channel. The results should be of particular interest to the diagnosis of anisotropic plasmas and the test of fundamental physics in few-electron heavy ions.

Difluoromethane ( CH2F2 ) is a commonly used etching gas in manufacturing very-large-scale integrated circuits as the fluorine source. Electron impact excitation cross sections for CH2F2 are important input data for modeling the reactive etching plasmas. In this work, we present the experimental generalized oscillator strengths for the 3s←2b2 , 11A2←X 1A1 , and 3p←2b2 transitions on the absolute scale. The measurement was realized by employing the crossed-beam based relative flow technique at an angle-resolved electron energy loss spectrometer, operating at an incident energy of 1500 eV and a resolution of 80 meV. The dipole-forbidden transition 11A2←X1A1 at around 9.7 eV is identified for the first time. The measured data are fitted with the well-known Lassettre formula to yield analytical expressions and optical oscillator strengths at K2=0 for dipole-allowed transitions. The analytical expressions enable integrations over momentum transfer to obtain the Born integral cross sections for electron impact excitations from the threshold to 5000 eV. The integral cross sections for dipole-allowed transitions are scaled to a more reliable level by using the BE-scaling method. The experimental data can benchmark theoretical calculations and supplement the molecular database for plasma modelers.