Full Core Plus Correlation Research Articles

Dipole Transition Characteristics of 1s24f — 1s2ng (5 ≤ n ≤ 8) States for Li-Like Isoelectronic Sequence: Vanadium Through Zinc

The transition energies and wavelengths of 1s24f-1s2ng (5 ≤ n ≤ 8) states of lithium-like ions starting from vanadium and ending with zinc are determined by using the full-core-plus-correlation (FCPC) method. Our calculated values are compared with other available data and found to be in good agreement with them. The oscillator strengths of the 1s24f-1s2ng (5 ≤ n ≤ 8) dipole transition under three criteria are explored by using the FCPC method. The consistency of the three criteria proves the accuracy of the constructed wave function over all space. In this paper, the oscillator strength and the oscillator strength density of all discrete and continuous states from any given initial to final state are calculated, and the theoretical prediction of the spectral characteristics of the omnipotence threshold is realized.

Theoretical calculation of ionization potentials and relativistic energies of high angular momentum 1s2ng states of Li-like ions

Abstract The nonrelativistic energy of Li-like isoelectronic sequence from ScXIX to ZnXXVIII in the high angular momentum 1s2ng (5 ≤ n ≤ 8) state is computed by adopting a full-core-plus-correlation (FCPC) method with multiconfiguration interaction wave functions. The relativistic and mass-polarization effects of energies are assessed as the first-order perturbation theory. The contributions of quantum electrodynamic (QED) and higher-order relativistic are also investigated through the use of effective nuclear charge formula to reduce the theoretical uncertainties. In order to assess the accuracy of our present predicted results, our excitation energies of 1s25g states are compared with other theoretical results.

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.

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z = 21 to 30

By using the full-core plus correlation (FCPC) type wave functions, the accurate charge densities ρ(0) at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z = 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to ρ(0) with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 (1991)], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.

Hyperfine-structure studies of the 1s22snp (n=2, 3) 3P states for the beryllium isoelectronic sequence

The hyperfine structure parameters of the 1s22snp (n=2, 3) 3P states for the beryllium isoelectronic sequence from Z= 4 to 10 are calculated with the full-core plus correlation (FCPC) wave functions. For the 1s22s2p 3P state of the beryllium atom, the calculated fine structure parameters are in good agreement with the latest theoretical and experimental data in the literature. It is shown that hyperfine constants of the low-lying excited states for the beryllium atom can be calculated accurately using this theoretical method. For 1s22snp (n=2, 3) 3P states of the beryllium isoelectronic sequence, our predictions may provide valuable reference data for other theoretical calculations and experimental measurements in future.

Full-core-plus-correlation method in cylindrical coordinates: Lithium atom in strong magnetic fields

The energy levels involving the ${0}^{+}$, $(\ensuremath{-}1{)}^{+}$, $(\ensuremath{-}2{)}^{+}$ states of the lithium atom in strong magnetic fields up to $2.35\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ are investigated. Our computational approach is a full-core-plus-correlation (FCPC) method based on a set of anisotropic Gaussian orbitals nonlinearly optimized for different field strength. A detailed comparison between our method, the FCPC method in spherical coordinates, and the full configuration-interaction method is made. The dipole oscillator strengths of ${1}^{2}{0}^{+}\text{\ensuremath{-}}{1}^{2}(\ensuremath{-}1{)}^{+}$ and ${1}^{2}(\ensuremath{-}1{)}^{+}\text{\ensuremath{-}}{1}^{2}(\ensuremath{-}2{)}^{+}$ transitions, as well as the transition wavelengths for the transitions ${\ensuremath{\nu}}^{2}{0}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{2}(\ensuremath{-}1{)}^{+}$ and ${\ensuremath{\nu}}^{2}(\ensuremath{-}1{)}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{2}(\ensuremath{-}2{)}^{+}$ are also presented.

Energy and Oscillator Strength of V20+ Ion

The ionization potentials and fine structure splittings of 1s2nl (l = s, p, and d; n ⩽ 9) states for lithium-like V20+ ion are calculated by using the full-core plus correlation (FCPC) method. The quantum defects of these three Rydberg series are determined according to the single-channel quantum defect theory (QDT). The energies of any highly excited states with n ⩾ 10 for these series can be reliably predicted using the quantum defects that are function of energy. The dipole oscillator strengths for the 1s22s–1s2np and 1s22p–1s2nd (n ⩽ 9) transitions of V20+ ion are calculated with the energies and FCPC wave functions obtained above. Combining the QDT with the discrete oscillator strengths, the discrete oscillator strengths for the transitions from the given initial state to highly excited states (n ⩾ 10) and the oscillator strength density corresponding to the bound-free transitions are obtained.

Energies of 1s2ng and 1s2nh (n = 5,6,7, and8) States for Lithium Isoelectronic Sequence

The nonrelativistic energies for lithium isoelectronic sequence 1s2ng and 1s2nh (n = 5,6,7, and 8) states from Z = 3 to 8 are calculated by using a full core plus correlation (FCPC)method with multiconfiguration interaction wave functions.Relativistic and mass-polarization effects on the energyare evaluated as the first-order perturbation theory.Our predicted excitation energies are compared with previousexperimental results in the literature.

Excitation Energies of 1s2ns (6 ⩽ n ⩽ 9) States for Lithium-Like Systems from Z =11 to 20

The non-relativistic energies of 1s2ns (6 ⩽ n ⩽ 9)states for the lithium-like systems from Z = 11 to 20 arecalculated by using a full-core-plus-correlation (FCPC) method. Therelativistic and mass-polarization effects on the energy are calculatedby the first-order perturbation corrections. The correction from thequantum-electrodynamics effect is also included using effective nuclearcharge. Based on these results and the quantum defect theory, thequantum defects of 1s2ns series for these ions, as afunction of energy, are determined. The comparisons between theionization potentials for 1s2ns states (6 ⩽ n ⩽ 9)obtained by the FCPC method and the semi-empirical method are carriedout. The results show that their agreement is very well and theenergies of all discrete states (n ⩾ 10) below the ionizationthreshold of this series for the ions can be predicted by using theirquantum defects.

Oscillator Strengths for 2s2–2p2P Transitionsof the Lithium Isoelectronic Sequence from NaIX to CaXVIII

The nonrelativistic dipole-length, -velocity and -acceleration absorptionoscillator strengths for the 1s22s–1s22ptransitions of the lithium isoelectronic sequence fromZ = 11 to 20 are calculated by using the energiesand the multiconfiguration interaction wave functionsobtained from a full core plus correlation (FCPC) method.In most cases, the agreement between the oscillator strengthsvalues from the length and velocity formula is up to four or five digit.Our results are also in good agreement with previous theoreticaldata available in the literature.

Theoretical calculation of ionization potential and term energy of the ground states 1s22s of lithium-like systems from Z=21 to 30

In the paper, the full-core plus correlation (FCPC) and the minimizing the expectation value of the Hamiltonian method is extended to calculate the non-relativistic energies and the wave functions of 1s22s states for the lithium-like systems from Z=21 to 30. The mass-polarization and the relativistic correction included 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 included by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1s22s are given and compared with other's theoretical calculation and experimental results. It is shown that the FCPC methods are also effective to theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.

Inequalities of the electron density at the nucleus and radial expectation values of the ground state for the lithium isoelectronic sequence

The electron density at the nucleus, ρ(0) and the radial expectation values, <rn>(-2⩽n⩽10), of the ground state for the lithium isoelectronic sequence are calculated with a full core plus correlation (FCPC) wavefunctions. By using these obtained expectation values, the accurate inequalities of the electron density at the nucleus and the radial expectation values derived by Gálvez and Porras for these systems are examined and verified. The final results show that FCPC wavefunctions used in this work can give satisfactory results in full configuration space.

The excitation energies and term energies of the excited states 1s 2 n s ( n =3,4,5) and 1s 2 n f ( 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 1s2ns (n=3,4,5) and 1s2nf (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 1s2 core and the valence electron.

Theoretical calculation of the fine-structure and term energy of the excited states 1s~2 nd(n=3,4,5 of lithium-like systems

The fullcore plus correlation (FCPC) and the minimiziation of the expectation value of the Hamiltonian method is extended to calculate the nonreltivistic energies and the wave functions of 1s~2 nd(n=3,4,5) states for the lithium like systems from Z=11 to 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 calculated perturbatively as the first-order correction. The contribution from quantum electrodynamics (QED) is also included by using the effective nuclear charge formula. The excited energies, finestructure, and the termenergy are given and compared with other theoretical calculation and experimental results. It is shown that the correlative wave in the FCPC method embodies very well the strong correlation effect between the 1s~2 core and the valence electron.

Strong magnetic-field effects on the states of the helium negative ion below the He(N=2)threshold

Energy levels of the ${1s2l2l}^{\ensuremath{'}}{}^{2}{S}^{e}$ and ${}^{2,4}{P}^{e,o}$ states of the helium negative ion in magnetic-field strengths up to $4.7011\ifmmode\times\else\texttimes\fi{}{10}^{4}$ T are calculated by using the multiconfiguration interaction approach. The extended full core plus correlation (FCPC) method and the saddle-point technique are used to construct the nonrelativistic wave functions. We have observed that the field effects on the states considered are quite unusual. In the presence of a magnetic field, three previously unobserved stable states associated with the helium $1s2p{}^{1}P$ and $1s2s{}^{3}S$ thresholds are predicted. The possibility of attracting an extra electron by the parent ${1s}^{2}$ state is also analyzed in the low and medium regime $(\ensuremath{\beta}&lt;~0.1$ a.u.). The opening of new decay channels of the ${1s2s}^{2}{}^{2}S$ resonance state connected with the higher threshold due to field effects is analyzed. Two significantly different resonance mechanisms for the ${1s2s}^{2}$ state are proposed and discussed briefly.

Oscillator strengths for 3 [formula omitted]D– [formula omitted]F transitions of the lithium isoelectronic sequence

The nonrelativistic dipole-length, -velocity and -acceleration absorption oscillator strengths for the 1s 23d–1s 2 nf (4≤ n≤9) transitions of the lithium isoelectronic sequence up to Z=10 are calculated by using the energies and the multiconfiguration interaction wave functions obtained from a full core plus correlation (FCPC) method. In most cases, the agreement between the f-values from the length and velocity formulae is up to forth or fifth digits. Combining these discrete oscillator strengths with the single channel quantum defect theory (QDT), the discrete oscillator strengths for the transitions from 1s 23d state to highly excited levels ( n≥10) and the oscillator strength densities corresponding to the bound-free transitions are obtained.

Oscillator strengths for 2 transitions of the lithium isoelectronic sequence

The nonrelativistic dipole-length, -velocity and -acceleration absorption oscillator strengths for the 1s22s-1s2np\(\) transitions of the lithium isoelectronic sequence up to Z=10 are calculated by using the energies and the multiconfiguration interaction wave functions obtained from a full core plus correlation (FCPC) method. In most cases, the agreement between the f-values from the length and velocity formulae is up to forth or fifth digit. Combining these discrete oscillator strengths with the single channel quantum defect theory (QDT), the discrete oscillator strengths for the transitions from the 1s22s state to highly excited levels (\(\)) and the oscillator strength densities corresponding to the bound-free transitions are obtained.

Oscillator strengths for 2

The nonrelativistic dipole-length, -velocity and -acceleration absorption oscillator strengths for the transitions of the lithium isoelectronic sequence up to Z=10 are calculated by using the energies and the multiconfiguration interaction wave functions obtained from a full core plus correlation (FCPC) method. In most cases, the agreement between the f -values from the length and velocity formulae is up to forth or fifth digit. Combining these discrete oscillator strengths with the single channel quantum defect theory (QDT), the discrete oscillator strengths for the transitions from the state to highly excited levels () and the oscillator strength densities corresponding to the bound-free transitions are obtained.

The hyperfine structure of the and states and 5) for the lithium isoelectronic sequence

The non-relativistic hyperfine structure parameters, the Fermi contact, the spin-dipolar, the orbital and the electronic quadrupole terms, of the lithium-like ground state and low-lying states, \(\) and \(\) (n=2, 3, 4, and 5), are calculated with the full core plus correlation (FCPC) wave functions. With the 794- and 1185-term Slater-type expansions, the Fermi contact interactions of the \(\) and \(\) states in \(\) are determined to be 2.90313 a.u. and -0.21359 a.u., respectively. By using the global identities, the Fermi contact term is also given for the ground state in LiI. The typical patterns of convergence of the expectation values of the Fermi contact interaction for the lithium \(\) and \(\) states are analyzed. The contribution from the core polarization is examined. The calculated results of the lithium-like systems from LiI to NeVIII are compared with the previous theoretical results obtained with other methods, and with the experimental data available in the literature.

The hyperfine structure of the

The non-relativistic hyperfine structure parameters, the Fermi contact, the spin-dipolar, the orbital and the electronic quadrupole terms, of the lithium-like ground state and low-lying states, 1s 2 ns 2 S and 1s 2 np 2 P (n = 2, 3, 4, and 5), are calculated with the full core plus correlation (FCPC) wave functions. With the 794- and 1185-term Slater-type expansions, the Fermi contact interactions of the 2 2 S and 2 2 P states in 7LiI are determined to be 2.90313 a.u. and -0.21359 a.u., respectively. By using the global identities, the Fermi contact term is also given for the ground state in LiI. The typical patterns of convergence of the expectation values of the Fermi contact interaction for the lithium 1s 2 2s and 1s 2 2p states are analyzed. The contribution from the core polarization is examined. The calculated results of the lithium-like systems from LiI to NeVIII are compared with the previous theoretical results obtained with other methods, and with the experimental data available in the literature.