Electric Dipole Oscillator Strengths Research Articles

Energy levels, wavelengths, and transition probabilities for transitions in Pd XLII

Energy levels and lifetimes for the lowest 204 fine-structure levels belonging to the 2s22p, 2s2p2, 2p3, 2s23l, 2s2p3l, 2p23l, 2s24l, 2s2p4l, and 2p24l (l = s, p, d, f) configurations of B-like Pd XLII are calculated using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, as well as wavelengths, transition probabilities, weighted oscillator strengths, and line strengths for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among these levels. In the calculations, the contributions from Breit interaction and quantum electrodynamics (QED) corrections are taken into account. Comparisons are made with available theoretical energies and electric dipole oscillator strengths.

Investigation of Li2O–Gd2O3–MO–B2O3–Nd2O3 (MO=Ba/Bi) glasses for laser applications by Judd–Oflet (J–O) theory

In this work, we synthesize Li2O–Gd2O3-MO-B2O3–Nd2O3 glasses (where MO = Ba/Bi) by melt-quenching technique for laser applications; characterize their physical properties, absorption and luminescence spectra; and determine their decay time and Judd-Oflet (J-O) parameters. We confirm the glass phase of the samples by XRD pattern and obtain the J-O parameters for Nd3+ in the glasses from the absorption and photoluminescence emission spectra, while measuring the intensity of the electric dipole transitions and oscillator strengths from absorption spectra and the radiative parameters from photoluminescence emission spectra. We also determine some key parameters of the laser materials, such as radiative decay time, quantum efficiency and stimulated emission cross section. The lifetime decreases with increasing Nd3+ concentration that is indicative of energy transfer between Nd3+ ions. We also demonstrate that the physical properties and absorption spectra are independent of the gadolinium ions (Gd2O3), while the luminescence properties are functions of the Gd2O3 due to the efficient energy transfer from the Gd3+ ions to the incorporated activator (Nd3+). These results suggest that the 50Li2O-15Gd2O3–5Bi2O3-28.5B2O3-1.5Nd2O3 glass is useful for laser applications at 577-nm excitation and at 1.07-μm emission.

Relativistic calculations on the x-ray satellites of platinum with multiply ionized L shell

The energies, electric dipole rates and oscillator strengths of Kα x-ray satellites from 1s–2p transitions in platinum with a single vacancy in the K shell and variously ionized L shell are calculated using multi-configuration Dirac Fock wavefunctions with the inclusion of Breit interaction and quantum electrodynamics effects. The computations have been performed for low ionized (Pt1+–Pt6+) and also for highly ionized (Pt69+–Pt77+) Pt. As Kα x-ray satellites with spectator vacancies only in the L shell, to the best of our knowledge, have been studied for the first time, to check the accuracy of the present work, calculations have also been performed for H-, He-, Li-, Be-, B- and F-like Pt for which theoretical data for comparison exist. The purpose of choosing a high Z element is that the detailed decay properties of heavy ions due to systematic 1s–2p transitions with spectator vacancies in the L shell using fully relativistic treatment are unexplored and the increasing need for reliable data from such ions in various applications that are under investigations in recent years. Also, for heavy ions like Pt, the contribution from the competing non-radiative transitions is less and hence the atomic properties are largely due to radiative transitions. The K X ray satellite energies, rates and resonance photo- ionization cross sections from H-, He-, Li-, Be-, B- and F-like Pt are compared with available data.

Transition probabilities of Er3+ ions in alumino-silicate glasses

The spectroscopic properties of Er-doped Ca3Al2Si3O12 and Mg3Al2Si3O12 glasses produced by the Laser Floating Zone technique are presented in this work. By measuring the absorption spectra and refractive index dispersion of the materials, JO parameters of the Er3+ ions have been obtained in both doped materials, where very good accordance between the experimental and theoretical electric dipole oscillator strengths is found. Using calculated electric and magnetic dipole strengths, the branching ratios of the different optical transition of Er3+ in Ca and Mg glasses have been obtained, where the radiative lifetime of each level has been also calculated. The experimental lifetimes of the 4S3/2, 4I11/2 and 4I13/2 manifolds have been measured under pulse excitation. These values have been related with the radiative lifetime calculated by the JO analysis, allowing to determine the non-radiative probabilities of the levels. In addition, a gap law has been established for both Ca and Mg alumino-silicate glasses. Finally, the covalency of the Er-O bond was studied in terms of the spectroscopic features of these glasses.

Oscillator strengths for spin-changing P–D transitions in He I including the effect of a finite nuclear mass and intermediate coupling

We have calculated the electric dipole (E1) oscillator strengths and spontaneous decay rates for 12 spin-changing P–D transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron. The specific transitions for 4He are [Formula: see text] and [Formula: see text] with n = 2, 3, 4 and n′ = 3, 4. To include the effects of intermediate coupling between pure LS and jj, we used the Breit formulation for the spin–orbit and spin–other-orbit operators and combined the results of the exact diagonalization of the 2 × 2 energy matrix with pseudostate expansions to perform the perturbation sums over intermediate states. We calculated both the length and velocity gauges as a check on numerical accuracy and the validity of the transition operators.

Oscillator strengths for 1s2 1S0–1s2p 3P1,2 transitions in helium-like carbon, nitrogen and oxygen including the effects of a finite nuclear mass

We have calculated the electric dipole (E1) and magnetic quadrupole (M2) oscillator strengths and spontaneous decay rates for the spin-changing transitions of helium-like C v, N vi and O vii. We added the effects of the finite nuclear mass and the anomalous magnetic moment of the electron including an extra term derived by Pachucki. For the E1 calculations we used the Breit approximation and pseudostate expansions to perform the perturbation sums over intermediate states in both the length and velocity gauge as a check on numerical accuracy and the validity of the transition operators. There is some cancellation in the corrections for the nuclear mass and the electron anomaly so that if one is included the other should not be ignored

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular Sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron–electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb–Sturmian functions of half integer angular momentum. We show that, in the case of H−, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.

Applications to metal K pre-edges of transition metal dimers illustrate the approximate origin independence for the intensities in the length representation

ABSTRACTX-ray absorption spectroscopy (XAS) in the metal K pre-edge is a standard probe of electronic and geometric structure of transition metal complexes. Simulating the K pre-edge spectra requires contributions beyond the electric dipole, but if that term is non-zero, the second-order terms, e.g. electric quadrupoles, are no longer origin-independent. In the velocity representation, complete origin independence can be achieved by including all terms to the same order in the oscillator strength. Here, we implement that approach in the length representation and use it for restricted active space (RAS) simulations of metal K pre-edges of iron monomers and dimers. Complete origin independence is not achieved and the size of the remaining errors depends on the electric dipole oscillator strength and its ratio in length and velocity representations. The error in the origin independence is in the ANO basis sets two orders of magnitude smaller than the value of the individual contributions. For systems with strong electric dipole contributions, the errors are not significant within 3 Å from a metal centre, far enough to handle many multi-metal systems. Furthermore, we discuss the convergence of the multipole expansion, the possibility to assign spectral contributions, and the origin of negative absorption intensities.

Electric dipole transition probabilities, oscillator strengths, and lifetimes for Co16+

The electric dipole transition probabilities, oscillator strengths, and lifetimes for Co16+ have been calculated within the weakest bound electron potential model (WBEPM) theory using experimental energy levels and theoretical expectation values of orbital radii corresponding to those energy levels under the assumption of the LS coupling scheme. In the calculations both multiplet and fine structure transitions are studied. The present results are consistent with earlier results given in the literature. Moreover, some transition probability and oscillator strength values not existing in the literature are reported for the first time.

Oscillator strengths and lifetimes for Cu I

Electric dipole oscillator strengths and lifetimes for Cu I have been calculated within the weakest bound electron potential model theory and the quantum defect orbital theory under the assumption of the LS coupling scheme. In the calculations, many transition arrays including both multiplet and fine-structure transitions are considered. The present results are consistent with earlier theoretical calculations and experimental measurements. Some of these results are reported for the first time.

Controlling of spectral and optical parameters of the F8T2 liquid–crystalline polymer (LCP) by molarity for optoelectronic devices

In here, spectral and optical properties of the F8T2 polymer for different molarities were investigated by solution technique for optoelectronic applications. The interesting and useful results were obtained for optoelectronic applications. The absorption band of F8T2 polymer exhibits a vibronic structure with two peaks at 288 and 453nm due to π–π* electronic transition. The electronic spectra of the F8T2 can be characterized visible (Q) band and Soret (B) band. The significant spectral parameters such as absorption coefficient, molar extinction coefficient, mass extinction coefficients, electric dipole line strength and oscillator strength of the F8T2 polymer were calculated. The direct allowed band gap (Egd) and indirect allowed band gap (Egid) values (2.230 and 2.251eV, respectively) of the F8T2 polymer for 1.200μM are the highest values, while the Egd and Egid values (1.723 and 2.033eV, respectively) of the F8T2 for 9.460μM are the lowest values. The Egd values of the F8T2 polymer are lower than the Egid values. The real part of dielectric constant of the F8T2 polymer is composed normal and anomalous dispersion regions. F8T2 polymer can be used in the fabrication of many optoelectronic devices due to good soluble, spectral and optical properties.

Empirically constructed dynamic electric dipole polarizability function of magnesium and its applications

The dynamic electric dipole polarizability function for the magnesium atom is formed by assembling the atomic electric dipole oscillator strength distribution from combinations of theoretical and experimental data for resonance oscillator strengths and for photoionization cross sections of valence and inner shell electrons. Consistency with the oscillator strength (Thomas-Reiche-Kuhn) sum rule requires the adopted principal resonance line oscillator strength to be several percent lower than the values given in two critical tabulations, though the value adopted is consistent with a number of theoretical determinations. The static polarizability is evaluated. Comparing the resulting dynamic polarizability as a function of the photon energy with more elaborate calculations reveals the contributions of inner shell electron excitations. The present results are applied to calculate the long-range interactions between two and three magnesium atoms and the interaction between a magnesium atom and a perfectly conducting metallic plate. Extensive comparisons of prior results for the principal resonance line oscillator strength, for the static polarizability, and for the van der Waals coefficient are given in the Appendix.

Spectroscopic analysis of a novel Nd3+-activated barium borate glass for broadband laser amplification

Spectroscopic parameters of a novel Nd3+-activated barium borate (BBONd) glass have been analyzed for broadband laser amplification. The Judd–Ofelt (JO) intensity parameters were determined through a systematic analysis of the absorption spectrum of Nd3+ ions in the BBONd glass. High values of the JO intensity parameters reveal a great centro-symmetrical loss of the Nd3+ sites and high covalency degree of the ligand field. The very high Ω6 intensity parameter value makes evident both a great structural distortion of the Nd3+ sites and a strong electron–phonon coupling between Nd3+ and free OH− ions, which is consistent with the phonon energy maximum (3442.1cm−1) recorded by Raman spectroscopy. This strong electron–phonon coupling favors high effective bandwidth and gain bandwidth values of the laser emission (4F3/2→4I11/2) of Nd3+ ions. The electric-dipole oscillator strengths of all the Nd3+ absorption transitions, and in particular that of the hypersensitive transition (4I9/2→4G5/2), are enhanced by this great structural distortion of the host. Broadband laser amplification of the 4F3/2→4I11/2 emission (1062nm) of Nd3+ ions in the BBONd glass pumped at 805nm (4I9/2→4F5/2+2H9/2) is evaluated through the main fluorescent parameters in competition with non-radiative processes. In general, the BBONd glass exhibits spectroscopic parameters comparable with those reported in the literature for broadband laser amplification into the IR region.

Oscillator strengths and radiative decay rates for spin-changing S–P transitions in helium: finite nuclear mass effects

We have calculated the electric dipole (E1) and magnetic quadrupole (M2) oscillator strengths and spontaneous decay rates for 24 spin-changing transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron augmented by the recently derived Pachucki term. The specific transitions for 4He are and with and for For the E1 calculations we used the Breit approximation and pseudostate expansions to perform the perturbation sums over intermediate states in both the length and velocity gauge as a check on both numerical accuracy and validity of the transition operators. The corrections for the nuclear mass and the electron anomaly tend to cancel, indicating that if one is included, then so should be the other. The tables give mass- and anomaly-dependent coefficients permitting the easy generation of results for the other isotopes of helium.

Relativistic distorted-wave collision strengths and oscillator strengths for the [formula omitted] transitions with [formula omitted] in the 67 C-like ions with [formula omitted

Relativistic distorted-wave collision strengths have been calculated for the 185 Δn=0 transitions with n=2 in the 67 C-like ions with nuclear charge number Z in the range 26≤Z≤92. The calculations were made for the six final, or scattered, electron energies E′=0.03,0.08,0.20,0.42,0.80, and 1.40, where E′ is in units of Zeff2 Ry with Zeff=Z−4.17. In addition, electric dipole oscillator strengths are provided. In the present collision-strength calculations, an improved “top-up” method, which employs relativistic plane waves, was used to obtain the high partial-wave contribution for each transition, in contrast to the partial-relativistic Coulomb–Bethe approximation used in previous work by Zhang and Sampson [H.L. Zhang, D.H. Sampson, At. Data Nucl. Data Tables 63 (1996) 275]. In that earlier work, collision strengths were also provided for the same 185 Δn=0 transitions in C-like ions, but for the more limited list of 46 ions with Z in the range 9≤Z≤54. The collision strengths covered in the present work, particularly those for optically allowed transitions, should be more accurate than the corresponding data given by Zhang and Sampson [H.L. Zhang, D.H. Sampson, At. Data Nucl. Data Tables 63 (1996) 275] and are presented here to replace those earlier results.

Oscillator strengths and transition probabilities for singly ionized terbium

Electric dipole transition probabilities and oscillator strengths for singly ionized terbium (Tb II) have been calculated with the weakest bound electron potential model (WBEPM) theory using experimental energy levels and theoretical expectation values of orbital radii corresponding to those energy levels under the assumption of the Jj coupling scheme. The transition probabilities and the oscillator strengths calculated have been compared with available data in the literature. A good agreement has been obtained. In this work, the WBEPM theory has been applied to heavy atoms, such as Tb II, for the first time.

Relativistic many-body calculation of energies, transition rates, lifetimes, and multipole polarizabilities in Cs-like La iii

Excitation energies of the [Xe]$nd$ ($n=5\ensuremath{-}9$), [Xe]$ns$ ($n=6\ensuremath{-}10$), [Xe]$np$ ($n=6\ensuremath{-}9$), [Xe]$nf$ ($n=4\ensuremath{-}8$), and [Xe]$ng$ ($n=5\ensuremath{-}8$) states in La iii, where [Xe] = $1{s}^{2}2{s}^{2}2{p}^{6}3{s}^{2}3{p}^{6}3{d}^{10}4{s}^{2}4{p}^{6}4{d}^{10}5{s}^{2}5{p}^{6}$, are evaluated. Electric dipole matrix elements for the allowed transitions between the low-lying [Xe]$nd$, [Xe]$ns$, [Xe]$np$, [Xe]$nf$, and [Xe]$ng$ states in the La iii ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar and tensor polarizabilities of the states listed above are evaluated. The uncertainties of the recommended values are estimated. Electric quadrupole and magnetic dipole matrix elements are calculated to determine lifetimes of the $5{d}_{5/2}$ and $6s$ metastable levels. The ground-state $E1$, $E2$, and $E3$ static polarizabilities are calculated. This work provides recommended values critically evaluated for their accuracy for a number of La iii atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.

Relativistic configuration interaction calculations for the K α X-ray transitions of Co XV to Co XXVI ions

Relativistic configuration interaction calculations with the inclusion of the Breit interaction, quantum electrodynamics (QED) and finite nuclear mass corrections have been carried out in the extended optimal level scheme using multiconfiguration Dirac-Fock wave functions on the wavelengths, electric dipole rates, oscillator strengths and line strengths of cobalt ions with a single vacancy in the K shell. The calculated values are compared with the other available data on He-like to Be-like cobalt and are found to be in very good agreement with them. This confirms the present calculations. We predict new data for several levels where no other theoretical and/or experimental results are available. These data provide reference values for level lifetimes, charge state distribution and the average charge of cobalt plasmas.

Ab initio theoretical study of the [formula omitted] and 4f75d manifolds of Tb3+-doped BaF2 cubic sites

An ab initio model potential embedded cluster study on the 4f8 and 4f7 5d manifolds of the long range compensated, cubic, substitutional Tb3+ defects of Tb-doped BaF2 is presented here. 4f–4f and 4f–5d transition energies and 4f–5d absorption electric dipole oscillator strengths for the dipole allowed transitions are reported and comparisons with emission and excitation experimental spectra are presented. We find good agreement with the energies of the experimental 4f–4f green and blue emissions. The characteristic features of the 4f–5d excitation spectrum (spin allowed vs. spin forbidden transitions) are well reproduced by the calculations. The transition energies from the ground state to the different spin nonet and spin septet levels of the 4f7 5d configuration of this ion in the center of the lanthanide series show an error of around 10%, which is in line with previous calculations on other lanthanide ions with lower spin multiplicities and simpler manifolds at the beginning and at the end of the series. The calculation supports a recent assignment of experimental excitation bands between 54,000 and 66,000cm−1 as 4f→5d(t2g) transitions. On the other hand, a new assignment is made of the highest band in the excitation spectrum at around 76,000cm−1: it corresponds to transitions to levels of the 4f7 5d configuration with the 4f7 subshell in the excited 6P term, rather than to a Tb-bound exciton. Preliminary studies on excitonic states of Tb-doped BaF2 indicate that energy levels that can be characterized as Tb-trapped excitons are found in the same spectral region as the spin forbidden 4f→5d(t2g) transitions at ground state Tb–F distances, and their energy lowers very much at shorter Tb–F distances.

Effect of screening on spectroscopic properties of Li-like ions in a plasma environment

This work presents accurate {\it ab initio} investigations of various spectroscopic properties of a few Li-like ions in presence of a plasma environment within the Debye screening potential. The coupled-cluster theory in the relativistic framework has been employed to compute ionization potentials, excitation energies, electric dipole oscillator strengths, and electric quadrupole transition probabilities of Li-like C$^{3+}$, N$^{4+}$, and O$^{5+}$ ions. The unretarded Breit interaction has been implemented to increase the accuracy of the calculations. The effects of ion density and temperature on the ionization potentials, excitation energies, electric dipole oscillator strengths, and electric quadrupole transition probabilities have been investigated in the plasma environment. It is found that the plasma screening leads to a sharp decrease in the ionization potential as the screening strength increases. With increasing strength, the oscillator strengths associated with 2$s ^{2}S_{1/2}$$\rightarrow2 p ^{2}P_{1/2, 3/2}$ transitions increase, whereas the transition probabilities associated with 3$d ^2D_{3/2, 5/2}$$\rightarrow2 s ^2S_{1/2}$ transitions decrease.