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.     

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.     

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.     

Theoretical study on 2s2p^6np Rydberg states of Cu^19＋ ion

We report on the calculations of transition wavelengths and weighted oscillator strengths for 2s 2 2p 6-2s2p 6 np （4≤n≤20） electric dipole （E1） transitions of Cu 19+ 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 2s22p～6-2s2p～6np,the quantum defects for 2s2p 6 np Rydberg series of Cu～（19+）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.     

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.     

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.     

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.     

Ionization energies and term energies of the ground states 1s22s 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 1s22s 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 1s22s 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.     

The excitation energies and term energies of the excited states 1s2ns (n=3,4,5) and 1s2nf (n=4,5) of lithium-like systems of Z=11－20

In this paper, the full-core plus correlation (FCPC) and the Ritz method is extended to calculate the non-relativistic energies of 1s^2ns (n=3,4,5) and 1s^2nf (n=4,5) states and the wavefunctions of the lithium-like systems from Z=11－20. The mass-polarization and the relativistic correction including the kinetic-energy correction, the Darwin term, the electron－electron contact term, and the orbit－orbit interaction are evaluated perturbatively as the first-order correction. The contribution from quantum electrodynamic is also included by using the effective nuclear charge formula. The excited energies, the term-energy and fine structure, are given and compared with the other theoretical calculation and experimental results. It is shown that the correlative wave in the FCPC method embodies well the strong correlation between the 1s^2 core and the valence electron.     

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.     

Oscillator strengths for 2 ^2P-n ^2D transitions of lithium-like systems with Z=11 to 20

The dipole-length, velocity and acceleration absorption oscillator strengths for the 1s^22p－1s^2nd(3≤n≤9) transitions of the lithium-like systems with Z=11 to 20 are calculated using the energies and the multiconfiguration interaction wavefunctions obtained from a full core plus correlation method. The agreement between the f-values calculated from the length, velocity and acceleration formulae is excellent. Our results agree closely with the experimental data available in the literature. Combining these discrete oscillator strengths with the single-channel quantum defect theory, the discrete oscillator strengths for the transitions from 1s^22p state to highly excited states (n≥10) and the oscillator strength densities corresponding to the bound-free transitions are obtained.     

Measurement of quantum defect of nS and nD states using field ionization spectroscopy in ultracold cesium atoms

<正>This paper reports that ultracold atoms are populated into different nS and nD Rydberg states(n=25~52) by two-photon excitation.The ionization spectrum of an ultracold Rydberg atom is acquired in a cesium magneto-optical trap by using the method of pulse field ionization.This denotes nS and nD states in the ionization spectrum and fits the data of energy levels of different Rydberg states to obtain quantum defects of nS and nD states.     

Multi-reference configuration-interaction calculations on multiply charged ions of carbon monosulfide

The potential energy curves for neutrals and multiply charged ions of carbon monosulfide are computed with highly correlated multi-reference configuration interaction wavefunctions.The correlations of inner-shell electrons with the scalar relativistic effects are included in the present computations.The spectroscopic constants,dissociation energies,ionization energies for ground and low-lying excited states together with corresponding electronic configurations of ions are obtained,and a good agreement between the present work and existing experiments is found.No theoretical evidence is found for the adiabatically stable CSq+(q>2) ions according to the present ab initio calculations.The calculated values for 1st-6th ionization energies are 11.25,32.66,64.82,106.25,159.75,and 224.64 eV,respectively.The kinetic energy release data of fragments are provided by the present work for further experimental comparisons.     

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.     

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.     

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.     

Structure and analytical potential energy function for the ground state of the BCx (x=0, －1)

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.     

Effect of hydrostatic pressure and polaronic mass of the binding energy in a spherical quantum dot

Simultaneous effect of hydrostatic pressure and polaronic mass on the binding energies of the ground and excited states of an on-center hydrogenic impurity confined in a Ga As/Ga Al As spherical quantum dot are theoretically investigated by the variational method within the effective mass approximation. The binding energy is calculated as a function of dot radius and pressure. Our findings proved that the hydrostatic pressure led to the decrease of confined energy and the increase of donor binding energy. Conduction band non-parabolicity and the polaron masses are effective in the donor binding energy which is significant for narrow dots not in the confined energy. The maximum donor binding energy achieved by the polaronic mass in the ground and excited states are 2%–19% for the narrow dots. The confined and donor binding energies approach zero as the dot size approaches infinity.     

The Electron－Hole Pair in a Single Quantum Dot and That in a Vertically Coupled Quantum Dot

The energy spectra of low-lying states of an exciton in a single and a vertically coupled quantum dots are studied under the influence of a perpendicularly applied magnetic field. Calculations are made by using the method of numerical diagonalization of the Hamiltonian within the effective-mass approximation. We also calculated the binding energy of the ground and the excited states of an exciton in a single quantum dot and that in a vertically coupled quantum dot as a function of the dot radius for different vaJues of the distance and the magnetic field strength.