Theoretical study on 2s2p6np Rydberg states of Cu19+ ion

We report on the calculations of transition wavelengths and weighted oscillator strengths for 2s²2p⁶-2s2p⁶ⁿp (4 ≤ n ≤ 20) electric dipole (E1) transitions of Cu¹⁹⁺ ion. The flexible atomic code (FAC) has been adopted for the calculations. Comparisons are made with the experimental data available, showing that the present results for 4 ≤ n ≤ 6 are more accurate than the previous calculated values. Furthermore, combining the quantum defect theory (QDT) with the transition energies of 2s²2p⁶-2s2p⁶np, the quantum defects for 2s2p⁶np Rydberg series of Cu¹⁹⁺ ion are determined. In addition, the energies of any highly excited states (n > 20) for this series can be reliably predicted using the QDT and the given quantum defects. The ionization energies for Cu¹⁹⁺ and Cu²⁰⁺ ions are also calculated and they excellently accord with previous experimental and calculated values.     

Oscillator strengths for 22S--n2P transitions of the lithium isoelectronic sequence from Z = 11 to 20

The dipole-length, dipole-velocity and dipole-acceleration absorption oscillator strengths for the 1s22s-1s2np (3≤n≤9) transitions of lithium-like systems from Z=11 to 20 are calculated by using the energies and the multiconfiguration interaction wave functions obtained from a full core plus correlation method, in which relativistic and mass-polarization effects on the energy, as the first-order perturbation corrections, are included. The results of three forms are in good agreement with each other, and closely agree with the experimental data available in the literature. Based on the quantum defects obtained with quantum defect theory (QDT), the discrete oscillator strengths for the transitions from the ground state to highly excited states 1s2np (n≥10) and oscillator strength densities corresponding to the bound-free transitions are obtained for these ions.     

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.     

Transition energy and dipole oscillator strength for 1s22p-1s2nd of Cr2l+ ion

The transition energies, wavelengths and dipole oscillator strengths of 1s^22p-1s^2nd （3 ≤ n ≤ 9） for Cr^21＋ ion are calculated. The fine structure splittings of 1s^2nd （n ≤ 9） states for this ion are also calculated. In calculating energy, we have estimated the higher-order relativistic contribution under a hydrogenic approximation. The quantum defect of Rydberg series 1s^2nd is determined according to the quantum defect theory. The results obtained in this paper excellently agree with the experimental data available in the literature. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for the transitions from initial state 1s^22p to highly excited 1s^2nd states （n ≥ 10） and the oscillator strength density corresponding to the bound-free transitions are obtained.     

Transition Energy and Oscillator Strength of 1s22p-12nd for Fe23 ion

Transition energies, wavelengths and dipole oscillator strengths of 1s^2 2p - 1s^2 nd （3 ≤ n ≤ 9） for Fe^23＋ ion nre calculated. The fine structure splittings of 1s^2nd （n ≤ 9） states for this ion are also evaluated. The higher-order relativistic contribution to the energy is estimated under a hydrogenic approximation. The quantum defect of Rydberg series 1s^2nd is determined according to the quantum defect theory. The energies of any highly excited states with （n ≥ 10） for this series can be reliably predicted using these quantum defects as input. The results in this paper excellently agree with the experimental data available in the literature. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for the transitions from same given initial state 1s^2 2p to highly excited 1s^2nd states （n ≥ 10） and the oscillator strength density corresponding to the bound-free transitions is obtained.     

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.     

Ionization Potentials and Quantum Defects of ls^2np^2p Rydberg States of Lithium Atom

Abstract In this work, ionization potentials and quantum effects of ls^2 np^2 P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for ls^2np^2P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the ls^2np （n ≥ 7） channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the ls^2 7p^2P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of ls^2np ^2P （n ≥ 7） Rydberg states. Present calculations are in agreement with recent experimental data in whole.     

Differential and Integral Cross Sections for Electron Impact Excitation of Lithium

The differential and integral cross sections for electron impact excitation of lithium from the ground state 1s22s to excited states 1s22p, 1s23l （l=s, p, d） and 1s24l （l=s, p, d, f）at incident energies ranging from 5 eV to 25 eV are calculated by using a full relativistic distorted wave method. The target state wavefunctions are calculated by using the Grasp92 code. The continuum orbitals are computed in the distorted-wave approximation, in which the direct and exchange potentials among all the electrons are included. A part of the cross sections are compared with the available experimental data and with the previous theoretical values. It is found that, for the integral cross sections, the present calculations are in good agreement with the time-independent distorted wave method calculation, for differential cross sections, our results agree with the experimental data very well.     

M1 transition energy and rate in the ground configuration of Ag-like ions with 62 ≤ Z ≤ 94

Systematic calculations and assessments are performed for the magnetic dipole(M1)transition energies and rates between the ²F^o_5/2,7/2 levels in the ground configuration 4d104f along the Ag-like isoelectronic sequence with 62≤Z≤94 based on the second-order many-body perturbation theory implemented in the Flexible Atomic Code.The electron correlations,Breit interaction and quantum electrodynamics effects are taken into account in the present calculations.The accuracy and reliability of our results are evaluated through comprehensive comparisons with available measurements and other theoretical results.For transition energies,our results are in good agreement with the recent experimental data obtained from the electron beam ion traps within 0.18%.The maximum discrepancy between our results and those obtained with the large-scale multiconfiguration Dirac–Hartee–Fock calculations by Grumer et al.[Phys.Rev.A 89062501(2014)]is less than 0.13%along the isoelectronic sequence.Furthermore,the corresponding M1 transition rates are also reported.The present results can be used as the benchmark and useful for spectra simulation and diagnostics of astrophysical and fusion plasmas.     

Relativistic Configuration Interaction Treatment of Generalized Oscillator Strength for Krypton

A fully relativistic configuration interaction method is developed to investigate the transition energies and general oscillator strengths of the lower lying states of krypton, for both optically allowed and optically forbidden transitions. The calculated results are in agreement with the recent experimental measurements. The calculated transition energies for the 5s and 5s＇ transitions are 9.970 and 10. 717eV, which agree with the experimental data of 10.033 and 10.643 eV. The calculated oscillator strengths are 0.211 and 0. 170, comparable with the experimental results 0.214（±0.012） and 0.194 （±0.012）, respectively. The momentum transfer positions （K^2 in a.u.） of the minimum and maximum GOSs in the 4s^24p^6 → 4s^24p^5 （5s ＋ 5s＇） transitions are 1.105 and 2.225, comparable with the measurements results 1.24 and 2.97 [Phys. Rev. A 67 （2003） 062708].     

Absolute Cross Sections for Near-Threshold Electron-Impact Excitation of the 2s^2S→2p^2P Transition of Li-Like C^3＋, N^4＋, and O^5＋ Ions

Excitation cross sections of 1s^22s ^2S1/2 → 1s^22p^2p1/2,3/2 transition among the fine-structure levels in Li-like C^3＋, N^4＋, and O^5＋ ions are calculated for energies of the near-threshold by using the relativistic distorted-wave program REIE06. The target state wavefunctions are calculated by using the Grasp92 code. The continuum orbitals are studied in the distorted-wave approximation, in which the direct and exchange potentials among all the electrons are included. The results of the Li-like C^3＋ ion settle the discrepancy between several previous experiments by using the crossed-beams fluorescence method, in good agreement with the measurements of Savin et al. Moreover, the results in Li-like N^4＋, and O^5＋ ions are compared with the previous experiments, and a good agreement 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.     

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.     

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.     

Behaviours of the excited states 1s^2np along lithium isoelectronic sequence from Z=11 to 20

Based on the obtained energy values of 1s^2np （n≤ 9） states for lithium-like systems from Z=11 to 20 （by the authors of this paper： Hu M H and Wang Z W 2004 Chin. Phys. 13 662）, this paper determines the quantum defects, as slowly varying function of energy, of this Rydberg series. Using them as input, it can predict the energies of any highly excited states below the ionization threshold for this series a~cording to the quantum defect theory. The regularities of variation for quantum defects of the series along this isoelectronic sequence are physically analysed and discussed. The screening parameters, which are equal to the effective screening charge of the core-electrons, are also obtained.     

Effects of electron correlation and the Breit interaction on one- and two-electron one-photon transitions in double K hole states of He-like ions(10 ≤ Z ≤ 47)

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 selected He-like ions(10 ≤ Z ≤ 47) are calculated using the fully relativistic multi-configuration Dirac–Fock method(MCDF). 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 the 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 the 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.     

Relativistic calculations of 3s2 1S0-3s3p 1P1 and 3s2 1S0-3s3p 3P1,2 transition probabilities in the Mg isoelectronic sequence

Using the multi-configuration Dirac-Fock self-consistent field method and the relativistic configuration-interaction method,calculations of transition energies,oscillator strengths and rates are performed for the 3s 2 1 S 0-3s3p 1 P 1 spinallowed transition,3s 2 1 S 0-3s3p 3 P 1,2 intercombination and magnetic quadrupole transition in the Mg isoelectronic sequence(Mg I,Al II,Si III,P IV and S V).Electron correlations are treated adequately,including intravalence electron correlations.The influence of the Breit interaction on oscillator strengths and transition energies are investigated.Quantum electrodynamics corrections are added as corrections.The calculation results are found to be in good agreement with the experimental data and other theoretical calculations.     

Relativistic Distorted-Wave Collision Strengths of Ni-, Cu- and Zn-like Au Ions

Excitation energies and electron impact excitation strengths from the ground states of Ni-, Cu- and Zn-like Au ions are calculated. The collision strengths are computed by a 213-levels expansion for the Ni-like Au ion, 405- levels expansion for the Cu-like Au ion and 229-levels expansion for the Zn-like Au ion. Configuration interactions are taken into account for all levels included. The target state wavefunctions are calculated by using the Grasp92 code. The continuum orbits are computed in the distorted-wave approximation, in which the direct and exchange potentials among all the electrons are included. Excellent agreement is found when the results are compared with previous calculations and recent measurements.     

Theoretical analysis of ionic autoionization spectra of lanthanum via an intermediate state [Xe]5d6d 1P1

In the framework of multi-channel quantum defect theory, eigenquantum defects μα and the transformation matrices Uiα of La+ are calculated from first principles by relativistic multi-channel theory, while the dipole matrix elements Dα are obtained by fitting with experimental data. Then the ionic autoionization spectra of lanthanum via the inter-mediate state [Xe]5d6d 1P1 in the energy region of 90213-91905 cm-1 are obtained. Experimental peaks are classified and assigned by comparing with the corresponding calculated spectra. More specifically, four ionic autoionization Rydberg series converging to La2+ 5d5/2 2D5/2 and several states converging to higher lying states of La2+ are found and assigned.     

Ionization energies and term energies of the ground states ls22s of lithium-like systems

We extend the Hamiltonian method of the full-core plus correlation （FCPC） by minimizing the expectation value to calculate the non-relativistic energies and the wave functions of ls22s states for the lithium-like systems from Z = 41 to 50. The mass-polarization and the relativistic corrections including the kinetic-energy correction, the Darwin term, the electron-electron contact term, and the orbit-orbit interaction are calculated perturbatively as first-order correction. The contribution from quantum electrodynamic （QED） is also explored by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1 s22s are derived and compared with other theoretical calculation results. It is shown that the FCPC methods are also effective for theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.