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The visible spectrum of Mo$^{15+}$ ions was measured using a high-temperature superconducting electron-beam ion trap at the Shanghai EBIT Laboratory, with an electron beam energy $E_{e}$=400 eV, significantly lower than the ionization potential (IP=544.0 eV) of Mo$^{14+}$ ions in the ground state. To expound on the experiment, the energy level structure, radiative transition properties, electron-impact excitation, and electron-impact ionization cross section for both the ground state and low-lying excited state of the Mo$^{14+}$ ions were calculated using Dirac-Fock-Slater method with a local central potential and distorted wave approximation. The results demonstrated reasonable agreement with both available experimental and theoretical data. Through an analysis of the related atomic processes of Mo$^{14+}$ ion, a scenario involving the stepwise ionization of the metastable state 3p$^{6}$3d$^{9}$4s was proposed to explain the presence of the Mo$^{15+}$ ions with a lower energy of the incident electron. Finally, the significance of the metastable levels in ionizing Mo$^{14+}$ ions is highlighted.

We have calculated the transition energies and probabilities of one-electron one photon and one-electron two photon transitions of middle-Z and high-Z He-like ions using the fully relativistic multiconfiguration Dirac-Hartree-Fock method with active space method. The relativistic, electron correlation, Breit and QED effects are systemically taken into account in the present work. Results showcase consistent agreement with the experimental and theoretical data, uncovering intriguing inversion phenomena in One-Electron One-Photon transitions energy, particularly in double-hole states. Theoretical spectra intensities provide valuable insights into high-energy X-ray radiation processes from double \textit{K}-hole states.

We introduce the RHDLPP, a flux-limited multigroup radiation hydrodynamics numerical code designed for simulating laser-produced plasmas in diverse environments. The code bifurcates into two packages: RHDLPP-LTP for low-temperature plasmas generated by moderate-intensity nanosecond lasers, and RHDLPP-HTP for high-temperature, high-density plasmas formed by high-intensity laser pulses. The core radiation hydrodynamic equations are resolved in the Eulerian frame, employing an operator-split method. This method decomposes the solution into two substeps: first, the explicit resolution of the hyperbolic subsystems integrating radiation and fluid dynamics, and second, the implicit treatment of the parabolic part comprising stiff radiation diffusion, heat conduction, and energy exchange. Laser propagation and energy deposition are modeled through a hybrid approach, combining geometrical optics ray-tracing in sub-critical plasma regions with a one-dimensional solution of the Helmholtz wave equation in super-critical areas. The thermodynamic states are ascertained using an equation of state, based on either the real gas approximation or the quotidian equation of state (QEOS). Additionally, RHDLPP includes RHDLPP-SpeIma3D, a three-dimensional spectral simulation post-processing module, for generating both temporally-spatially resolved and time-integrated spectra and imaging, facilitating direct comparisons with experimental data. The paper showcases a series of verification tests to establish the code's accuracy and efficiency, followed by application cases, including simulations of laser-produced aluminum (Al) plasmas, pre-pulse-induced target deformation of tin (Sn) microdroplets relevant to extreme ultraviolet lithography light sources, and varied imaging and spectroscopic simulations.

The energy levels and electric dipole ($E1$) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic $E1$, magnetic dipole ($M1$) and electric quadrupole ($E2$) polarizabilities as well as the hyperpolarizabilities of the $2s^2~^1S_0$ and $2s2p~^3P_0$ states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of $2s^2~^1S_0 \rightarrow 2s2p~^3P_0$ clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity $I$ is in the range of 14.3 $\sim$ 15.9 kW/cm$^{2}$ and the detuning $\delta$ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7 $\sim$ 40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 $\times$ 10$^{-18}$. While, when $I$ is in the range of 15.01 $\sim$ 15.46 kW/cm$^{2}$ and $\delta$ is in the range of 40.73 $\sim$ 40.76 MHz, the fractional Stark shifts are lower than 1.0 $\times$ 10$^{-19}$., Comment: 18 pages, 3 figures

The double electron E1 transition energies, probabilities, and oscillator strengths between the $2s2p^{n}$ and $1s^{2}2p^{n-1}$($1\!\leq\!n\leq\!6$) configurations of Xe$^{q+}$($47\!\leq\!q\leq\!52$) ions with different spectator electrons have been calculated based on the multi-configuration Dirac-Hartree-Fock method. A reasonable electron correlation model is constructed with the aid of the active space method. The finite mass of nuclear, Breit interaction and QED effects have also been included. The calculated results are in good agreement with the available data. The theoretical spectra of different spectator electrons of the double K hole state have been predicted. The spectator electron effects on the transition spectra have been analyzed in detail. The present results will be helpful for analyzing the high energy X-ray spectrum observed from the interaction between high energy highly charged ions and the surface.

The wavelength and rate of the $5p-5s$ transition of W XIV - W XVI ions have been calculated by the relativistic configuration interaction (RCI) method with the implementation of Flexible Atomic code (FAC). A reasonable collisional-radiative model (CRM) has been constructed to simulate the $5p - 5s$ transition spectrum of W XIV - W XVI ions which had been observed in electron beam ion trap (EBIT) device. The results are in reasonable agreement with the available experimental and theoretical data, and might be applied to identify the controversial spectra. The confusion on the assignment of the ionization stage are solved in the present work.

The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state $2s2p$ to the $1s2s$ and $1s^{2}$ configurations of 11 He-like ions ($10\!\leq\!Z\!\leq\!47$) are evaluated using the fully relativistic multi-configuration Dirac-Fock method. An appropriate electron correlation model is constructed with the aid of the active space method, which allows the electron correlation effects to be studied efficiently. The contributions of electron correlation and the Breit interaction to the transition properties are analyzed in detail. It is found that the two-electron one-photon (TEOP) transition is correlation sensitive. The Breit interaction and electron correlation both contribute significantly to the radiative transition properties of the double K hole state of He-like ions. Good agreement between the present calculation and previous work is achieved. The calculated data will be helpful to future investigations on double K hole decay processes of He-like ions., Comment: 9 pages, 2 figures and 4 tables

A detailed-level collisional-radiative model for the M1 transition spectrum of the Ca-like W$^{54+}$ ion as observed in an electron beam ion trap (EBIT) was constructed based on atomic data calculated by the relativistic configuration interaction method and distorted wave theory. The present calculated transition energy, rate and intensity of W$^{54+}$ M1 transitions are compared with previous theoretical and experimental values. The results are in reasonable agreement with the available experimental and theoretical data. The synthetic spectrum explained the EBIT spectrum in the 12-20 nm region, while a new possibly strong transition has been predicted to be observable with an appropriate electron beam energy. The present work provides accurate atomic data that may be used in plasma diagnostics applications.

A detailed level collisional-radiative model of the E1 transition spectrum of Ca-like W$^{54+}$ ion has been constructed. All the necessary atomic data has been calculated by relativistic configuration interaction (RCI) method with the implementation of Flexible Atomic Code (FAC). The results are in reasonable agreement with the available experimental and previous theoretical data. The synthetic spectrum has explained the EBIT spectrum in 29.5-32.5 \AA ,, while several new strong transitions has been proposed to be observed in 18.5-19.6 \AA , for the future EBIT experiment with electron density $n_e$ = $10^{12}$ cm$^{-3}$ and electron beam energy $E_e$ = 18.2 keV.

X-ray spectra of K-shell hollow krypton atoms produced in single collisions with 52 - 197 MeV/u Xe54+ ions are measured in a heavy-ion storage ring equipped with an internal gas-jet target. Energy shifts of the K{\alpha}_1,2^s, K{\alpha}_1,2^(h,s), and K\b{eta}_1,3^s transitions are obtained. Thus, the average number of the spectator L-vacancies presented during the x-ray emission is deduced. From the relative intensities of the K{\alpha}_1,2^s and K{\alpha}_1,2^(h,s) transitions, the ratio of K-shell hollow krypton to singly K-shell ionized atoms is determined to be 14 - 24%. In the considered collisions, the K-vacancies are mainly created by the direct ionization which cannot be calculated within the perturbation descriptions. The experimental results are compared with a relativistic coupled channel calculation performed within the independent particle approximation., Comment: 5 figures, 9 pages. Accepted by Physical Review A

The electron correlation effects and Breit interaction as well as Quantum Electro-Dynamics (QED) effects were expected to have important contribution to the energy level and transition properties of heavy highly charged ions. The ground states [Ne]$3s^{2}3p^{6}3d^{2}$ and first excited states [Ne]3s$^{2}3p^{5}3d^{3}$ of W$^{54+}$ ion have been studied by using Multi-Configuration Dirac-Fock method with the implementation of Grasp2K package. A restricted active space was employed to investigate the correlation contribution from different models. The Breit interaction and QED effects were taken into account in the relativistic configuration interaction calculation with the converged wavefunction. It is found that the correlation contribution from 3s and 3p orbital have important contribution to the energy level, transition wavelength and probability of the ground and the first excited state of W$^{54+}$ ion.

Plasma diagnostics in magnetic confinement fusion plasmas by using visible spectrum strongly depends on the knowledge of fundamental atomic properties. A detailed collisional-radiative model of W$^{26+}$ ions has been constructed by considering radiative and electron excitation processes, in which the necessary atomic data had been calculated by relativistic configuration interaction method with the implementation of Flexible Atomic Code. The visible spectrum observed at an electron beam ion trap (EBIT) in Shanghai in the range of 332 nm to 392 nm was reproduced by present calculations. Some transition pairs of which the intensity ratio are sensitive to the electron density were selected as potential candidate of plasma diagnostics. Their electron density dependence are theoretically evaluated for the cases of EBIT plasmas and magnetic confinement fusion plasmas.

Hyperfine induced $2s2p~^3P_0 \rightarrow 2s^2~^1S_0$ transition rates in an external magnetic field for Be-like $^{47}$Ti were calculated based on the multiconfiguration Dirac-Fock method. It was found that the transition probability is dependent on the magnetic quantum number $M_F$ of the excited state, even in the weak field. The present investigation clarified that the difference of the hyperfine induced transition rate of Be-like Ti ions between experiment [Schippers {\sl et al.}, Phys Rev Lett {\bf 98}, (2007) 033001(4)] and theory does not result from the influence of external magnetic field.

The hyperfine induced $2s2p ^3P_0, ^3P_2 \to 2s^2 ^1S_0$ E1 transition probabilities of Be-like ions were calculated using grasp2K based on multi-configuration Dirac-Fock method and HFST packages. It was found that the hyperfine quenching rates are strongly affected by the interference for low-Z Be-like ions, especially for $2s2p ^3P_0 \to 2s^2 ^1S_0$ transition. In particular, the trends of interference effects with atomic number $Z$ in such two transitions are not monotone. The strongest interference effect occurs near Z=7 for $2s2p ^3P_0 \to 2s^2 ^1S_0$ E1 transition, and near Z=9 for $2s2p ^3P_2 \to 2s^2 ^1S_0$ E1 transition., Comment: 19 pages, 3 figures

Hyperfine induced $1s2s ^1S_0 \to 1s^2 ^1S_0$ M1 transition probabilities of He-like ions have been calculated from relativistic configuration interaction wavefunctions including the frequency independent Breit interaction and QED effects. Present results for {$^{151}$}Eu and {$^{155}$}Gd are in good agreement with previous calculations [Phys. Rev. A {\bf 63}, 054105 (2001)]. Electronic data are given in terms of a general scaling law in $Z$ that, given isotopic nuclear spin and magnetic moment, allows hyperfine induced decay rates to be estimated for any isotope. The results should be helpful for future experimental investigations on QED and parity non-conservation effects., Comment: 9 pages, 2 figures