Theoretical study on K, L, and M X-ray transition energies and rates of neptunium and its ions

The transition energies and electric dipole （El） transition rates of the K, L, and M lines in neutral Np have been theoretically determined from the MultiConfiguration Dirac-Fock （MCDF） method. In the calculations, the contributions from Breit interaction and quantum electrodynamics （QED） effects （vacuum polarization and self-energy）, as well as nu- clear finite mass and volume effects, are taken into account. The calculated transition energies and rates are found to be in good agreement with other experimental and theoretical results. The accuracy of the results is estimated and discussed. Furthermore, we calculated the transition energies of the same lines radiating from the decaying transitions of the K-, L-, and M-shell hole states of Np ions with the charge states Np1＋ to Np6＋ for the first time. We found that for a specific line, the corresponding transition energies relating to all the Np ions are almost the same; it means the outermost electrons have a very small influence on the inner-shell transition processes.     

Energy levels of 1s~2n d(n≤9)states for lithium-like ions

The full-core plus correlation method with multi-configuration interaction wave functions is extended to the calculation of the non-relativistic energies of 1s²nd (n ≤ 9) states for the lithium isoelectronic sequence from Z = 11 to 20. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation correction. The quantum-electrodynamics correction is also included. The fine structure splittings are determined from the expectation values of spin—orbit and spin—other-orbit interaction operators in the Pauli—Breit approximation. Combining the term energies of lowly excited states obtained with the quantum defects calculated by the single channel quantum defect theory, each of which is a smooth function of energy and approximated by a weakly varying function of energy, the ion potentials of highly excited states (n ≤ 6) are obtained with the semi-empirical iteration method. The results are compared with experimental data in the literature and found to be closely consistent with the regularity.     

QUANTUM EFFICIENCY AND MULTIPHONON NONRADIATIVE TRANSITION OF Er3+ IONS IN FLUORIDE GLASS

Optical absorption, emission and excitation spectra, lifetimes of ⁴S_3/2 state and ⁴F_9/2 state from 10K to 500K, and Raman spectra were measured for Er³⁺ ions in fluoride glass. The radiative transition probabilities were calculated on the basis of Judd-Ofelt theory. The nonradiative transition probabilities and the quantum efficiencies were determined by calculating the difference between the measured lifetimes and the calculated radiative transition probabilities. The temperature dependence of nonradiative transition provavility was investigated using the Huang-Rhys theory of multiphonon relaxation , in which two kinds of phonons as well as the parameter s were taken into consideration. A fairly good agreement of the theoretical calculation with the experimental results has been obtained. The value of s is estimated and the effect of s is discussed.     

Theoretical investigation on forbidden transition properties of fine-structure splitting in ~2D state for K-like ions with 26≤Z≤36

Excitation energies, magnetic dipole, and electric quadrupole transition probabilities of the 3d~2 D_(3/2)–3d~2D_(5/2) transition in the potassium-like(K-like) sequence with 26≤Z≤36 are investigated by using the multi-configuration Dirac–Hartree–Fock(MCDHF) method. The contributions of the electron correlations, Breit interaction, and the leading-order quantum electrodynamic(QED) effects on the transition properties are analyzed. The present results are interested in the laboratory tokamak and the astronomical observations. Furthermore, the feasibility of these ions for the highly charged ion(HCI) clocks is discussed. Considering the wavelength of lasers and manipulation process of the atomic clocks, Cu~(10+)and Zn~(11+)are recommended as promising candidates with achievable quality factors at the 10~(15) level.     

Excitation and decay dynamics of 1s2s inner-shell double-vacancy states of neon atoms

The photo-excitation and Auger decay processes of inner-shell double vacancy states 1s2s2p^6（1,3^S）3s3p of neutral neon atoms have been studied theoretically. Multi-configuration Dirac-Fock （MCDF） calculations have been carried out, with electron correlation effects taken into consideration. The relaxation of core and excited orbitals and configuration interaction are found to be crucial to creating the double vacancy states by single photo-absorption. The predominant decay paths for the double vacancy states turn out to be of the LLM Auger decay to 1s 2s^22p^53s（3p）, KLL Auger decay to 1s^22s2p^43s3p, and KLM Auger decay to 1s^22p^63s（3p）. They lead to further Auger decay, creating the neon ions of multiple charge states. For both double and single vacancy states the spectator type of Auger process is dominated in all the Auger decay processes. Theoretical Anger electron spectra are presented for further investigations, experimental and theoretical.     

Relativistic Configuration Interaction Calculations on Kα X-Ray Satellites of Manganese

With contributions from Breit interaction, quantum electrodynarnics （QED） corrections and nuclear mass corrections to the initial and final levels are taken into account. The transition energies, transition probabilities, and absorption oscillator strengths of Kα x-ray from Mn XVII to Mn XXIV have been calculated by using relativistic configuration interaction （RCI） and multi-configuration Dirac Fock （MCDF） method in the active interaction approach. Compared with the only available experimental transition data on He-like and Li-like manganese, the present results are in good agreement with them, and the rest of transition data of the present results are new ones. These wide range data can provide useful parameters for the study of the manganese plasma.     

Energy and fine structure of 1s2np(n≤9) states for lithium-like systems from Z=11 to 20

A new variation method is extended to study the atomic systems with higher nuclear charges and in more highly excited states. The non-relativistic energies of 1s^2np (n≤9) states for the lithium-like systems from Z=11 to 20 are calculated using a full-core-plus-correlation method with multi-configuration interaction wavefunctions. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation corrections. The fine structures are determined from the expectation values of spin-orbit and spin-other-orbit interaction operators in the Pauli－Breit approximation. The quantum-electrodynamics correction is also included. Our results are compared with experimental data in the literature.     

KLL dielectronic recombination process of He-like to O-like xenon ions

In this work,the KLL dielectronic recombination (DR) processes of highly charged He-like to O-like xenon ions are studied systematically by using a DR program,which is based on the multi-configuration Dirac-Fock (MCDF) method.The KLL DR resonant energies and the corresponding resonant strengths are calculated,emphasizing especially the effect of the Breit interaction on the DR strengths.The theoretical KLL DR spectra are obtained and compared with the latest experimental results obtained in the Shanghai Electron Beam Ion Trap.     

Geometry and electronic properties of Cu2(n≤9)

The equilibrium geometries and the atomization energies of Cu_n(n≤9) clusters have been calculated using the B3LYP/LANL2DZ method. It is shown that the clusters do not copy the bulk structures and undergo significant geometrical changes with size and the atomization energy per atom increases monotonically with size. By analysing the energy level distribution, the Fermi level, HOMO－LUMO gaps, the electron affinities and the ionization potentials are calculated and the results are in reasonable agreement with experiment. These electronic properties are found to be strongly structure dependent, which can be used to determine which of the low-lying structures is observed experimentally.     

Electron Impact Excitations and Linear Polarization for 1s2 1S0-1s2p3,1P1 Lines of Fe24＋ Ions under Screened Coulomb Interactions

Electron impact excitation cross sections from the ground state to the individual magnetic sublevels of 1s2p 3＇1P1 states in high-temperature dense plasmas are calculated for highly charged He-like Fe24＋ ions by using a fully relativistic distorted-wave method. The Debye-Huckel screening model is used to screen the projectile electron from the nucleus and target electrons. The linear polarization degrees for these lines are obtained. It is found that the cross sections at all incident energies decrease with the increase of the screening for these excitations. The influence of screening on linear polarization degrees of the 1P1 line is very small. The linear polarization degrees of aP1 line decrease sharply at low incident energy with the increase of the screening.     

Static electric dipole polarizability of lithium atoms in Debye plasmas

<正>The static electric dipole polarizabilities of the ground state and n≤3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium.The plasma screening of the Coulomb interaction is described by the Debye-H（u|¨）ckel potential and the interaction between the valence electron and the atomic core is described by a model potential.The electron energies and wave functions for both the bound and continuum states are calculated by solving the Schrodinger equation numerically using the symplectic integrator.The oscillator strengths,partial-wave,and total static dipole polarizabilities of the ground state and n≤3 excited states of the lithium atom are calculated.Comparison of present results with those of other authors, when available,is made.The results for the 2s ground state demonstrated that the oscillator strengths and the static dipole polarizabilities from np orbitals do not always increase or decrease with the plasma screening effect increasing, unlike that for hydrogen-like ions,especially for 2s→3p transition there is a zero value for both the oscillator strength and the static dipole polarizability for screening length D = 10.3106a₀,which is associated with the Cooper minima.     

Energy levels of ls2n d （n ≤ 9） states for lithium-like ions

The full-core plus correlation method with multi-configuration interaction wave functions is extended to the calcu- lation of the non-relativistic energies of ls2nd （n ≤9） states for the lithium isoelectronic sequence from Z = 11 to 20. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation correction. The quantum-electrodynamics correction is also included. The fine structure splittings are determined from the expectation values of spin-orbit and spin-other-orbit interaction operators in the Pauli-Breit approximation. Combining the term energies of lowly excited states obtained with the quantum defects calculated by the single channel quantum defect theory, each of which is a smooth function of energy and approximated by a weakly varying function of energy, the ion potentials of highly excited states （n ≥ 6） are obtained with the semi-empirical iteration method. The results are compared with experimental data in the literature and found to be closely consistent with the regularity.     

Polarization of Radiation Emitted after Electron Impact Excitation

A programme is developed to calculate the polarizations of the radiation emitted after electron impact excitation. The fully relativistic distorted-wave method is used in cross-section calculations. The programme is applied to He- and Li-like ions. The calculated values of line polarization are compared with other theoretical results and experimental values. For He-like U, at lower incident energy, the present polarization agrees with the other theoretical ones within 1%, while at higher energy, the differences increase up to about 10%. For He-like Fe and Ti, the present results of polarization degree for most of the lines agree with the experimental data within the experimental error bars. For the Li-like Ti line q （ls2s2p^2p3/2 to ls^22s）, the present value of the polarization agree excellently with another theoretical one, and both the values are consistent with the measured data within the experimental error bar.     

Theoretical Investigation of Decay Process in a Doubly Excited 2s^2 ^1S0 State of He-Like Ions

In the framework of multi-configuration Dirac-Fock theory, a detailed calculation is performed for the decay rates and the energies of the doubly excited 2s^2 ^1So state of He-like ions, of which atomic number Z ranges from 6 to 92. The 2s^2 ^1So - ls ^2S1/2 Auger decay is predominant at low Z regime, whereas the 2s^2 ^1So - 1s2p ^1,3P1 two-electron one-photon transitions become quite important in moderate and high Z regimes. For heavy ions with Z ≥ 72, the contribution of 2s^2 ^1So - 1s2s ^3S1 M1 transition is significant. The Breit interaction considerably enhances the 2s^2 ^1So - 1s ^2S1/2 Auger rate at high Z regime.     

OPTICAL PROPERTIES OF δ-DOPED GaAs AND GaAs/Al0.1Ga0.9As SUPERLATTICES

Radiative transition in δ-doped GaAs superlattices with and without Al_0.1Ga_0.9As barriers is investigated by using photoluminescence at low temperatures. The experimental results show that the transition mechanism of δ-doped superlattices is very different from that of ordinary superlattices. Emission intensity of the transition from the electron first excited state to hole states is obviously stronger than that from the electron ground state to hole states due to larger overlap integral between wavefunctions of electrons in the first excited state and hole states. Based on the effective mass theory we have calculated the self-consistent potentials, optical transition matrix elements and photoluminescence spectra for two different samples. By using this model we can explain the main optical characteristics measured. Moreover, after taking into account the bandgap renormalization energy, good agreement between experiment and theory is obtained.     

Theoretical Calculations of Opacity for Non-Local-Thermodynamic-Equilibrium Plasmas

A method is presented to calculate the spectral-resolved opacity for non-local-thermodynamic-equilibrium plasmas. With the present method, the configuration population is obtained by solving the rate equations within the framework of configuration-averaged approximation in which the cross sections are calculated based on the first-order perturbation theory. The transition properties are calculated by using the unresolved transition array model. As the illustration, the frequency-dependent opacities of AI and Au plasmas are calculated and compared with the simulation results of the super configuration collisional radiative code. General agreements are obtained and there are some discrepancies for opacity of high-Z elements.     

OPTICAL PROPERTIES OF δ-DOPED GaAs AND GaAs/Al0.1Ga0.9As SUPERLATTICES

Radiative transition in δ-doped GaAs superlattices with and without Al_0.1Ga_0.9As barriers is investigated by using photoluminescence at low temperatures. The experimental results show that the transition mechanism of δ-doped superlattices is very different from that of ordinary superlattices. Emission intensity of the transition from the electron first excited state to hole states is obviously stronger than that from the electron ground state to hole states due to larger overlap integral between wavefunctions of electrons in the first excited state and hole states. Based on the effective mass theory we have calculated the self-consistent potentials, optical transition matrix elements and photoluminescence spectra for two different samples. By using this model we can explain the main optical characteristics measured. Moreover, after taking into account the bandgap renormalization energy, good agreement between experiment and theory is obtained.     

Excitation Energies of 1s^2 ns （6 ≤ n ≤ 9） States for Lithium-Like Systems from Z = 11 to 20

The non-relativistic energies of 1s^2 ns (6 ≤ n ≤ 9) states for the lithium-like systems from Z = 11 to 20 are calculated by using a full-core-plus-correlation (FCPC) method. The relativistic and mass-polarization effects on the energy are calculated by the first-order perturbation corrections. The correction from the quantumelectrodynamics effect is also included using effective nuclear charge. Based on these results and the quantum defect theory, the quantum defects of 1s^2ns series for these ions, as a function of energy, are determined. The comparisons between the ionization potentials for 1s^2ns states (6 ≤ n ≤ 9) obtained by the FCPC method and the semi-empirical method are carried out. The results show that their agreement is very well and the energies of all discrete states (n ≥ 10) below the ionization threshold of this series for the ions can be predicted by using their quantum defects.     

Forbidden transition properties of fine-structure 2p~3 ~4S_(3/2)–2p~3 ~2D_(3/2,5/2) for nitrogen-like ions

Based on relativistic wave functions from multiconfiguration Dirac–Hartree–Fock and configuration interaction calculations, E2 and M1 transition probabilities of 2p~3 ~4S_(3/2)–2 p~3 ~2D_(3/2,5/2) are investigated in the nitrogen-like sequence with7 ≤ Z ≤ 16. The contributions of the electron correlations, Breit interaction, and the quantum electrodynamic(QED) effects on the transition properties are analyzed. The present results can be used for diagnosing plasma. In addition, several N-like ions can also be recommended as a promising candidate for a highly charged ion(HCI) clock with a quality factor(Q) of transition as high as 10~(20).     

L—shell absorption measurement and simulation of x—ray—heated constrained material

Using the newly-designed multi-layered target, we obtain a homogeneous Al sample plasma at high density, low electron temperature, and in near local thermodynamic equilibrium. L-shell resonance absorption lines of Li-like and Be-like ions, as well as satellites are clearly observed. Transition arrays such as 2s－3p, 2s²－2s3p and 2s2p－2p3p are identified. We present the calculation method based on the unresolved transition array model, and we compare the measured transmission spectrum with the calculated results. The electron temperature of the constrained sample plasma is determined to be 34eV with a variation of ±2eV.