Configuration Interaction Parameters Research Articles

Hyperfine structure of the 4f85d6s2 configuration of the Tb atom

In this work, A and B hyperfine structure constants of electronic levels belonging to the configuration 4f85d6s2 of the terbium atom are presented, obtained via investigation of the hyperfine structure of 42 spectral lines, performed with the method of laser-induced fluorescence (LIF) in a hollow cathode discharge. Results for 14 of the investigated levels belonging to the configuration 4f85d6s2 were obtained for the first time. Also results concerning the hyperfine structure of 29 levels, involved in the transitions as upper levels, are presented. For these levels, almost all the results were obtained for the first time. On the basis of the results obtained within this work and those known from the literature, parametrization of the hyperfine structure was performed. The determined values of one-electron parameters for configuration 4f85d6s2 were compared to the values known from literature, determined so far on the basis of a much lower number of electronic levels. Values of relativistic radial integrals of the hyperfine structure for electrons 4f and 5d of the configuration 4f85d6s2 were calculated with the use of the MCDF code. The comparison of radial integrals calculated semi-empirically with those determined with MCDF method yielded an estimate of the values of configuration interaction parameters in the case of both magnetic dipole and electric quadrupole interactions of the terbium atom.

Quantitative study of valence and configuration interaction parameters of the Kondo semiconductors CeM2Al10 (M = Ru, Os and Fe) by means of bulk-sensitive hard X-ray photoelectron spectroscopy

The occupancy of the 4fn contributions in the Kondo semiconductors CeM2Al10 (M=Ru, Os and Fe) has been quantitatively determined by means of bulk-sensitive hard X-ray photoelectron spectroscopy (HAXPES) on the Ce 3d core levels. Combining a configuration interaction scheme with full multiplet calculations allowed to accurately describe the HAXPES data despite the presence of strong plasmon excitations in the spectra. The configuration interaction parameters obtained from this analysis – in particular the hybridization strength Veff and the effective f binding energy Δf – indicate a slightly stronger exchange interaction in CeOs2Al10 compared to CeRu2Al10, and a significant increase in CeFe2Al10. This shows the existence of a substantial amount of Kondo screening in these magnetically ordered systems and places the entire CeM2Al10 family in the region of strong exchange interactions.

Some aspects of configuration interaction of the 4f(N) configurations of tripositive lanthanide ions.

Some features of the interaction of the 4f(N) configuration of tripositive lanthanide ions (Ln(3+)) with excited configurations have been investigated. The calculated barycenter energies of the same parity 4f(N-1)6p, 4f(N+1)5p(5), and 4f(N-1)5f configurations for Ln(3+), relative to those of 4f(N), are fitted well by exponential functions. The 4f(N) barycenter energies of Ln(3+) in Y3Al5O12/Ln(3+) lie in the band gap, with the exceptions of Tb(3+) and Yb(3+), where they are situated in the conduction and valence bands, respectively. The configuration interaction parameters α, β, and γ, which are fitted in the usual phenomenological Hamiltonian to calculate the crystal field energies of Ln(3+), exhibit quite variable magnitudes in the literature due to incomplete energy level data sets, energy level misassignments and fitting errors. For LaCl3/Ln(3+), 83% of the variation of α and 50% of that for β can be explained by the change in the difference in barycenter energy with the predominant interacting configuration. The parameter γ is strongly correlated with the Slater parameter F(2) and is not well-determined in most calculations. The values of the electrostatically correlated spin-other orbit parameter P(2) vary smoothly across the Ln(3+) series with the barycenter difference between the 4f(N) and 4f(N-1)5f configurations. Calculations of the P(k) (k = 2, 4, and 6) values for Pr(3+) show that 4f → nf excitations only account for ∼65% of the value of P(2) for LaCl3/Pr(3+) and 35% of that in Y3Al5O12/Pr(3+). The role of the ligand is therefore important in determining the value, and a discussion is included of the present state of configuration-interaction-assisted crystal field calculations. Further progress cannot be made in the above areas until more reliable and complete energy level data sets are available for the Ln(3+) series of ions in crystals.

Parametrization of free ion levels of four isoelectronic 4f2 systems: Insights into configuration interaction parameters

The experimental free ion 4f2 energy level data sets comprising 12 or 13 J-multiplets of La+, Ce2+, Pr3+ and Nd4+ have been fitted by a semiempirical atomic Hamiltonian comprising 8, 10, or 12 freely-varying parameters. The root mean square errors were 16.1, 1.3, 0.3 and 0.3cm−1, respectively for fits with 10 parameters. The fitted inter-electronic repulsion and magnetic parameters vary linearly with ionic charge, i, but better linear fits are obtained with (4−i)2, although the reason is unclear at present. The two-body configuration interaction parameters α and β exhibit a linear relation with [ΔE(bc)]−1, where ΔE(bc) is the energy difference between the 4f2 barycentre and that of the interacting configuration, namely 4f6p for La+, Ce2+, and Pr3+, and 5p54f3 for Nd4+. The linear fit provides the rationale for the negative value of α for the case of La+, where the interacting configuration is located below 4f2.

Photoluminescence features of Ho3+ ion doped PbO–Bi2O3 borophosphate glass systems

Spectroscopic and physical properties of Ho3+ doped multi-component glass systems in varying molar compositions of xBi2O3–(50−x) PbO–25MgHPO4–24B2O3–1Ho2O3 (where x=10, 20, 30, and 40) have been investigated. Optical absorption spectra have been used to determine Racah coefficients (E1, E2 and E3), Slater Condon parameters (F2, F4 and F6), spin–orbit coupling parameters (ξ4f), and configuration interaction parameters (α and β). The ratios of E1/E3 and E2/E3 do not deviate much from the hydrogenic ratios. Optical basicity of the glasses is estimated. The Judd–Ofelt parameters (Ω2,Ω4 and Ω6) were computed from the intensities of the energy levels. The radiative lifetimes (τR), branching ratios (β) and absorption cross sections (σa) were evaluated for the lasing levels 5I8→5G6, 5F2, 5F3, 5F4, 5F5, 5I6, and 5I7. The emission cross sections (σe) for the significant lasing transitions 5F4→5I8, 5F5→5I8 and 5S2→5I7 evaluated from the photoluminescence spectra are reported. The lasing potencies estimated for all the glasses under study indicate lasing action in the cw as well as in pulsed regime.

Synthesis and spectroscopic characterization of CaF2:Er3+ single crystal for highly efficient 1.53 μm amplification

A CaF2:Er3+ single crystal was grown by the Tammann–Stober method. The potential of this material as a laser crystal for 1530 nm emission was established by quantitative analysis of the optical absorption and emission spectra. Assuming the tetragonal symmetry of the Er3+ sites, the Bkq crystal field parameters, Racah parameters, spin–orbit interaction parameters, and configuration interaction parameters were derived by fitting the experimental absorption band positions with the model energy Hamiltonian. Judd–Ofelt parametrization was done to compute the radiative decay time and fluorescence branching ratio of various meta stable transitions. Using the measured fluorescence decay time and computed radiative decay time, 100% quantum efficiency is obtained for the 1530 nm band, which is reasonable due to the low multiphonon relaxation, and absence of nonradiative energy transfer processes at the 0.01 at.% Er3+ concentration. The narrow bandwidth (13 nm) and high stimulated emission cross section (3.2×10−20 cm2) support the suitability of CaF2:Er3+ for use in high gain optical amplifiers.

Structure and optical properties of Eu 3+-doped fluoroaluminate and fluorophosphate glasses

Emission spectra of Eu 3+ in fluoroaluminate and fluorophosphate glasses at 80 K were measured as a function of excitation energy by the fluorescence line narrowing (FLN) technique. The magnitudes of the splitting of the 7F 1 manifolds at lower excitation energies increased with increasing phosphate content. The relative intensity of 5D 0 → 7F 2 to 5D 0 → 7F 1 transitions increased by adding the phosphate compound. This increase decreased gradually with increasing excitation energy. The atomic structure around Eu 3+ in these glasses was simulated using molecular dynamics techniques. The Stark splitting and the transition probabilities between 5D 0 and 7F J energy states at each simulated Eu 3+ ion were calculated on the basis of the point-charge approximation. The predicted energy differences between 5D 0 and ( 7F 2, 7F 1 and 7F 0) energy levels agree within 100 cm −1 with the observed ones. The transition probabilities are discussed in terms of the crystal field potential and the configuration interaction parameters, Ξ( k, λ).

Comparative analysis of free-ion energy levels of Er 3+ (4f 11) in various crystal hosts

The best energy level data available in the literature for the trivalent erbium-doped systems of about 30 crystal hosts are analysed in terms of a uniform model free-ion Hamiltonian H fi. H fi consists of 20 free-ion parameters which include the central field E avg, electrostatic repulsion F k ( k = 2, 4, 6), spin-orbit interaction parameter ξ, two-body configuration interaction parameters α, β and γ, three-body configuration interaction parameters T i ( i = 2, 3, 4, 6, 7, 8), spin—other-orbit interaction parameters M j ( j = 0, 2, 4) and electrostatically correlated spin-orbit interaction parameters P k ( k = 2, 4, 6). Our systematic theoretical analysis of crystal free-ion levels results in good correlation between calculated and observed energies. The reanalysis of some systems reported here yields improved fits of calculated to experimental energy levels compared with fits reported previously in the literature. The effects of the crystalline hosts on the empirical parameters are examined.

Optical absorption spectra of Pr3+ in maleato complexes

It is shown that the absorption spectra of Pr3+(4f2) can be conveniently analysed in terms of Racah parameters (E1, E2, E3), spin-orbit coupling constant(ζ) and configuration-interaction parameters (α, β, γ) by incorporating relationships based on the matrix elements corresponding to the 3P1, 3P0, 3F3 and 3H5 terms and experimental transition energies. The proposed method leads to more reliable results than those from the usual Taylor series method. The absorption spectra of Pr(Hmale)3·7H2O (H2male = maleic acid) and Pr3+-doped maleato complexes of Zn2+, Mg2+ and Cd2+ have been analysed for the energy parameters. The parameters E1, E3 and ζ were invariably found to be significantly less than the free-ion values, while E2 remains practically unchanged. These variations are accounted for in terms of weak covalency and the nephelauxetic effect. The spectral intensities have been analysed in terms of the Judd–Ofelt parameters and predicted lifetimes have been calculated for the transitions 3P2â†�3H4, 3P1â†�3H4, 3P0â†�3H4 and 1D2â†�3H4.

Spectroscopic investigations of the Pr(III) ion in certain ternary sulphate glasses

Ternary M-K-Zn (M ≡; Mg, Ca, Ba) sulphate glasses doped with 1 mol.% praseodymium sulphate were prepared by quenching. Absorption spectra were recorded for these glasses in the UV-visible and near-IR regions. The Racah, spin-orbit and configuration interaction parameters were evaluated by least-squares fit from the observed energies of the bands. Using Judd-Ofelt theory, theoretical intensity parameters, radiative lifetimes, branching ratios and absorption cross-sections were calculated for the excited 3P 1, 3P 0 and 1D 2 levels.

Energy levels and intensities of the absorption spectrum of the U 3+ ion in anhydrous formic acid

The absorption spectrum of the U 3+ ion in anhydrous formic acid was recorded in the range 4100–23,000 cm −1. The electrostatic, spin-orbit and configuration interaction parameters obtained from a least-squares fit to eight observed levels are: E 1 = 2882.7 cm −1, E 2 = 13.8 cm −1, E 3 = 285.4 cm −1, ξ 5 f = 1654 cm −1, α = 19.8 cm −1, β = −380.3 cm −1 and γ = 1000.0 cm −1. Intensity calculations gave good agreement with the oscillator strengths of observed bands only if some of the experimental band areas were combined.

Configuration Interaction in the Spectrum of Sr III

Least-squares fits to the 4s24p5(n + 1)s + 4s24p5nd + 4s4p65p and the 4s24p5(n + 2)p + 4s24p5nf + 4s4p64d configurations of Sr III are presented. The latter configurations are found to interact strongly whereas the interactions between the former are relatively small. In particular, the 4s24p5nf ↔ 4s4p64d interaction causes large distorsions of the level distribution in 4s24p5nf. The fitted parameter values are compared to Hartree-Fock results. The fitted 4s24p5nd ↔ 4s4p65p and 4s24p5nf ↔ 4s4p64d configuration interaction parameters are more than a factor of two smaller than the Hartree-Fock values.

Absorption spectrum of BkCl3

The absorption spectrum of thin films of BkCl3 was measured in the region ∞ 3800–48 000 cm−1 at 298°, 77°, and 4°K. The absence of transitions from the ground state to excited J=0 and J=1 states, together with the number of crystal field components observed in several isolated groups, suggested that the ground level BkCl3 is characterized by the crystal quantum number μ=0, as is the case in LaCl3:Tb3+. Assignments were made based in part on a predicted energy level scheme which assumed a systematic variation in energy level parameters over the actinide series. The free-ion electrostatic, spin orbit, and configuration interaction parameters for Bk3+ were calculated by a least squares fitting process involving 23 level assignments.

Energy levels and spectroscopic parameters of some Nd3+ complexes deduced from their solid state diffuse reflectance

AbstractThe values of Slater‐Condon (F2, F4, F6) and Racah (El, E2, E3) interelectronic repulsion and Landé (ζ4f) parameters and electronic energy levels have been computed from the diffuse reflectance spectra of eight Nd3+ complexes. Configuration interaction parameters (α β, Y(22, 1) and Y(22, 3)) have also been computed for the Nd3+ aquo‐ion. The decrease in the F2 values of the complexes as compared to the free ion is greatest among all the parameters. The bonding parameter b1/2 has been computed from the observed nephelauxetic ratio. The relative variation of covalent bonding in the complexes has been discussed, the effects of the crystalline hosts on the Fk and ζ4f parameters have also been examined.

Low-Temperature Absorption Spectrum of Uranium(3+) Formate Energy Level Scheme of Uranium(3+)

The absorption spectrum of thin films of U(HCOO)3 was measured at 298, 77, and 4°K in the range 4000–24 000 cm−1. Electrostatic, spin—orbit, and configuration-interaction parameters were obtained by least-squares fitting to 12 observed levels for U(HCOO)3. The obtained parameter values (in cm−1) are: E1=2779, E2=14.1, E3=271.6, ζ5f=1656.4, α=17.5, β = −479, γ=1000. A good agreement with experiment is observed for all calculated levels and a number of new assignments of excited levels of U(3+) are proposed. Intensity calculations were carried out and considered in the problem of level assignment.

Absorption Spectrum of PuCl3

The absorption spectrum of thin films of PuCl3 was measured at 298, 77, and 4°K in the range 6000–34 000 cm−1. Results were compared to earlier work in LaCl3 :Pu3+, and a number of new assignments were made. Electrostatic, spin–orbit, and configuration-interaction parameters were obtained by direct diagonalization of the energy matrix and a least-squares fitting process to 30 observed levels. The variations in certain energy-level parameters within the actinide series is discussed. Intensity calculations gave only moderate agreement with oscillator strengths of observed bands.

S 1 Level of Pr3+ in Crystal Matrices and Energy-Level Parameters for the 4f2 Configuration of Pr3+ in LaF3

The absorption spectrum of Pr3+ in LaF3, LaCl3, CaF2, Pr(Y)Cl3·6H2O, and Pr2(SO4)3·8H2O was investigated. Evidence for the S01 level in Pr3+:LaF3 at 46 986 cm−1 is presented; this level was not observed directly in absorption in any of the other matrices studied. An analysis of the 13 observed levels in Pr3+:LaF3, based in part upon a re-examination of the experimentally observed crystal-field components of certain levels, gave the following electrostatic, spin–orbit, and configuration-interaction parameters: E1 = 4559.0, E2 = 21.954, E3 = 467.75, ζ4f = 744.44, α = 15.294, β = − 669.02, γ = 1411.8, with an rms deviation= 33 cm−1.

Low-Temperature Optical Absorption of Americium Halides

Absorption spectra at low temperatures are reported for AmCl3, AmBr3, and AmI3. Bathochromic shifts have been generally observed in the series from the chloride to the iodide. These shifts are comparable to those observed in lanthanide halides. Hypersensitive transitions have been observed in AmI3. A number of new assignments of excited levels of Am(III) are proposed on the basis of intensity calculations. Electrostatic, spin–orbit, and configuration-interaction parameters were obtained by direct diagonalization and least-squares fitting to 29 observed levels for AmCl3. The parameter values in cm−1 are: E1 = 3582.8, E2 = 17.276, E3 = 334.30, ξ5f = 2593.3, α = 21.634, β = − 158.48, γ = 1240.4.

Electronic Energy Levels in the Trivalent Lanthanide Aquo Ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+

The free-ion energy-level schemes of the Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+ aquo ions have been determined from their absorption spectra in dilute acid solution at 25°. Energy-level assignments were made by comparison with crystal spectra, and on the basis of correlations between calculated and observed band intensities. For most of the ions, it was possible to identify several transitions giving rise to bands at energies as high as 45 000–50 000 cm−1. Sufficient numbers of assignments were made to justify inclusion of the effects of configuration interaction in the calculation of the energy-level parameters. Variation of the electrostatic, spin–orbit coupling, and configuration-interaction parameters across the lanthanide series is examined.

Optical Spectra of Tripositive Curium−244 in Lanthanum Trichloride

Absorption and emission optical spectra are reported for Cm3+ in LaCl3 between 3000 and 8000 Å. These data are explained in terms of the Racah, spin—orbit, and configuration-interaction parameters: E0=4939.29 E1=4621.47, E2=17.70, E3=399.42, ζ=2841.66, α=57.08, β=−4761.60 cm−1, respectively. Crystal-field splitting of the ground state S728 is observed.