Spectroscopic investigations and configuration-interaction-assisted crystal field analysis of Pr in YPO4 single crystal

An optical study of a Y_0.99Pr_0.01PO₄ single crystal is presented. Measurements of optical absorption, excitation, and emission by selective excitation into ¹D₂, ³P₀ and ³P₁, at different temperatures between 20 and 295 K, are described. A detailed account of the line assignments is given for absorption in the 4300-23 000 cm⁻¹ spectral range, and for emission in the 6400-23 000 cm⁻¹ range. The lifetimes of the emitting levels are determined. Vibronic sidebands accompanying absorption, emission and excitation spectra are reported. The decay processes of the ³P₁, ³P₀ and ¹D₂ levels are discussed. The aim of this study is a test of the configuration-interaction-assisted crystal field analysis as well as the accurate experimental determination of the energy level scheme. It was reported previously that the introduction of configuration interaction between the ground 4f² configuration with the excited 4f6p configuration always resulted in a decrease (≈50-60%) in the standard deviations between the observed and calculated energy levels. In the present work the 4f5d configuration is included as well. The crystal field is analysed in the theoretical D_2d site symmetry with and without configuration interaction. The results with 4f², 4f²+4f5d, 4f²+4f6p and 4f²+4f5d+4f6p are given. The calculation on the basis of the 315 (4f²+4f5d+4f6p) levels gives the best overall standard deviation lowering it by 75% with regard to the calculation on the 91 4f² levels only.     

Diborane: High resolution infrared rovibration studies of 11B2H6 and 11B2D6

Ground state rotation and quartic distortion constants were obtained for ¹¹B₂D₆ from the analysis of high resolution (～0.05 cm^?1) Fourier transform infrared spectra. The bands studied comprised the ν₁₇, ν₁₈ type A, and ν₁₄, ν₉ + ν₁₅ type C bands of ¹¹B₂H₆ and the ν₁₆, ν₁₇, ν₁₈ type A, ν₈ type B, and ν₁₄ type C bands of ¹¹B₂D₆. In the case of ¹¹B₂H₆, the authors' ground state data were combined with those of Lafferty et al. obtained from a previous study (J. Mol. Spectrosc.33, 345–367 (1970)) at comparable resolution of the ν₁₆ type A and ν₈ type B fundamentals. Information on the ground state rotational energy manifold of ¹¹B₂H₆ was accumulated up to J = 23, K_a = 18, and of ¹¹B₂D₆ up to J = 32, K_a = 22. This permitted rather precise determination of the distortion constants Δ_J⁰, Δ_JK⁰, Δ_K⁰, although δ_J⁰ and δ_K⁰ proved to be too small (< 10^?7 cm^?1) and were constrained to values calculated from the force field. Sets of upper state parameters were determined for all vibrational levels studied. Although these appear to be essentially unperturbed globally, several localized perturbations were observed and identified.     

Electronic absorption spectra of the 5d3 hexafluororhenate(IV) ion

The Γ₈(⁴A_2g) →Γ₇(²T_2g), Γ₈(²T_2g) electronic transitions for the 5d³ hexafluororhenate(IV) ion have been observed at liquid hydrogen temperature in a single Cs₂GeF₆ crystal and in a mixed crystal where the ReF^?2₆ ion is doped in the cubic Cs₂GeF₆ lattice. The electronic transitions have been assigned with a crystal field model to give information about the parameters B, C, Dq, and spin-orbit coupling. The vibrational structure in the mixed crystal system may be assigned to the ungerade modes of the ReF^?2₆ moiety. Comparison of the mixed and pure crystal vibrational structure shows that the pure crystal vibrational structure can be interpreted on the basis of K ≠ 0 lattice effects and a small distortion in the pure crystal.     

The ν5 and ν3 Raman bands of CH2D2

The ν₅ and ν₃ Raman bands of CH₂D₂ have been recorded with a resolution of 0.35 cm^?1. The ν₃ state is well known from infrared studies. Three hundred twenty-nine transitions of the ν₅ band were analyzed, assuming an unperturbed upper state, giving a standard deviation on the fit of the upper-state energies of 0.037 cm^?1, The constants A, B, C, Δ_J, Δ_JK, and Δ_K differed significantly from the ground-state values, and ν₅ was determined as 1331.41 ± 0.05 cm^?1. This work represents the first complete analysis of the fine structure of a rotation-vibrational Raman band for an asymmetric rotor. The ν₅ state could not be analyzed in infrared so this investigation, once more, demonstrates the usefulness of the Raman method.     

Ground state rotational energies of C3v quasi-spherical top molecules: Applications to 16OPF3 and PH3

Rotational spectra of the quasi-spherical symmetric molecules, ¹⁶OPF₃ and PH₃, are analyzed with all the data currently available. In both cases the current formulation that uses rotational contact transformations to completely diagonalize the ground state energy matrix appears to be inadequate, due to the smallness of the quantity |;A₀ ? B₀|. This quantity represents only 5% of A₀ or B₀ in the case of OPF₃ and 11% in the case of PH₃. Thus, both analyses require the resonance terms in ΔK = ±3 and/or ΔK = ±6 to be taken into account through diagonalization of the energy matrix. The ground state parameters as well as the ground state energies are given for both molecules.     

Millimeter-wave spectrum of the C4v molecule iodine oxygen pentafluoride IOF5: K-doubling of the |k| = 2 transitions in the ground state spectrum

Measurements are reported for the rotational spectrum of the C_4v molecule IOF₅ in the ground vibrational state in the range 30–75 GHz (J7 ← 6 to J17 ← 16). The K-doubling of |k| = 2 transitions due to an off-diagonal centrifugal distortion interaction of the type (Δl, Δk) = (0, ±4) has been observed. The centrifugal distortion constants D_J, D_JK, and R₆ have been determined as 0.139(2) kHz, 0.107(4) kHz, and 21(2) Hz, respectively.     

Magnetic and ESR studies of Er3+ in lanthanum dihydride LaH2

Er³⁺ electron spin resonance ESR and magnetic susceptibility have been studied in metallic lanthanum dihydride host. The ESR spectrum contains a single asymmetrical line with g-factor g = 6.68 ± 0.05 close to that expected for Γ₇ as ground state. The experimental magnetic susceptibility was interpreted on the base of LLW cubic crystal field Hamiltonian. The best fit of the experimental data has been obtained for the following B₄ and B₆ crystal field parameters: B₄ = ?5.2 × 10^?3 K; B₆ = 3.8 × 10^?5 K which support the anionic-like character hydridic model of hydrogen atoms in this hydride.     

EPR parameters and local lattice structure study of V ions in CdCl2 and CsMgCl3 crystals

The local lattice structure and EPR parameters (D, g_‖, g_⊥) have been studied systematically on the basis of the complete energy matrix for a d³ configuration ion in a trigonal ligand field. By simulating the calculated optical and EPR spectra data to the experimental results, the local distortion parameters (ΔR, Δθ) are determined for V²⁺ ions in CdCl₂ and CsMgCl₃ crystals, respectively. The results show that the local lattice structure of CdCl₂:V²⁺ system exhibits a compression distortion (ΔR=−0.0868 Å) while that of CsMgCl₃:V²⁺ system exists an elongation distortion (ΔR=0.0165 Å). The different distortion may be ascribed to the fact that the radius of V²⁺ ion is smaller than that of Cd²⁺ ion or larger than that of Mg²⁺ ion. Moreover, the relationships between EPR parameter D and local structure parameters (R, θ) as well as the orbital reduction factor k and g‐factors (g_‖, g_⊥) are discussed.     

The high-resolution infrared spectrum of the ν11 band of allene-d4

The infrared band ν₁₁ around 300 cm^?1 of allene-d₄ has been studied at a resolution of 0.010 cm^?1. The J structure in the central Q branches of this perpendicular band was resolved and P- and R-lines were assigned to subbands with {K″} ≦ 18. A ground-state analysis resulted in B₀ = 0.232187(30) cm^?1, D₀^J = 6.3(1.0) × 10^?8cm^?1, and D₀^JK = 3.0(4) × 10^?6cm^?1. Upper-state constants including η₁₁^J and η₁₁^K were derived. Special attention was paid to the study of l-type doublings. Doublets due to q^(?)-doubling were resolved and accordingly the value q₁₁^(?) = ?0.000160(3) cm^?1 was derived. The more usual q⁽⁺⁾-doubling was also observed, and the result q₁₁⁽⁺⁾ = 0.000144(4) cm^?1 was obtained.     

Far infrared spectrum and spectroscopic constants of AsH3 in the ground state

The far ir spectrum of arsine, AsH₃, was recorded in the range 25–100 cm^?1 with a resolution of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0 rotational transitions were measured and assigned up to J″ = 12. These transitions, together with the presently available microwave and submillimeter-wave data and ground state combination differences, were analyzed on the basis of a rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The derived ground state molecular parameters reproduced the transition frequencies of both allowed and “perturbation allowed” transitions within the accuracy of the measurements. The equilibrium structure was determined for the AsH₃ molecule.     

Exploring CP violation and penguin effects through B0d→D+D- and B0s→D+sD-s

The decay B⁰ _d→D⁺D^- offers an interesting probe of CP violation, but it requires control of penguin effects, which can be done through B⁰ _s→D⁺ _sD^- _s by means of the U-spin flavour symmetry of strong interactions. Recently, the Belle collaboration reported indications of large CP violation in the B⁰ _d decay, which were, however, not confirmed by BaBar, and first signals of the B⁰ _s channel were observed at the Tevatron. In view of these developments and the quickly approaching start of the LHC, we explore the allowed region in observable space for CP violation in B⁰ _d→D⁺D^-, perform theoretical estimates of the relevant hadronic penguin parameters and observables, and we address questions both about the most promising strategies for the extraction of CP-violating phases and about the interplay with other measurements of CP violation and the search for new physics. As far as the latter aspect is concerned, we point out that the B⁰ _q→D_q ⁺D^- _q system provides a setting for the determination of the B⁰ _q–B̄⁰ _q mixing phases (q∈{d,s}) that is complementary to the conventional B⁰ _d→J/ψK_S and B⁰ _s→J/ψφ modes with respect to possible new-physics effects in the electroweak penguin sector.     

Coherent Stokes and anti-Stokes Raman spectra of the ν1 (A1) and ν2 (E) bands of SF6 and UF6

Coherent Stokes and anti-Stokes Raman scattering are used to study the ν₁ and ν₂ spectral band profiles of UF₆ and SF₆. Most of the observed SF₆ “hot” bands are assigned, leading to evaluations of the anharmonicity constants X_ij: X₁₂ = ?(2.80 ± 0.30) cm^?1, X₁₄ = ?(1.00 ± 0.15) cm^?1, X₁₅ = ?(1.00 ± 0.15) cm^?1. For UF₆, a tentative assignment of the “hot” bands is made: X₁₂ = ?(1.80 ± 0.30) cm^?1, X₁₃ = ?(1.60 ± 0.30) cm^?1, X₁₄ = ?(0.20 ± 0.10) cm^?1, X₁₅ = ?(0.25 ± 0.10) cm^?1, and X₁₆ = ?(0.10 ± 0.05) cm^?1. Parameters such as the vibration-rotation coupling constants are determined. For SF₆: α = (7 ± 2) × 10^?5 cm^?1 for the ν₂ band and α = ?(1.02 ± 0.01) 10^?4 cm^?1 for the ν₁ band. The calculated spectral profiles of the coherent Stokes or anti-Stokes spectra, which are in good agreement with experimental results, give values for the resonant and nonresonant parts of the susceptibility in both molecules. They also show, in some cases, the influence of neighboring combination bands.     

Crystal field in the CeAl3 heavy-fermion compound

An analysis of inelastic neutron scattering in the CeAl₃ heavy fermion compound is presented. Using single-crystal magnetic-susceptibility and inelastic neutron scattering data, an unambiguous solution for the set of parameters of the electric crystal field Hamiltonian is obtained: B ₂ ⁰ = (5.8 ± 0.2) × 10^?2 meV and B ₄ ⁰ = (2.3 ± 0.1) × 10^?2 meV. The energy level scheme for the ground-state multiplet of the Ce³⁺ ion in CeAl₃ consists of the ground level Γ₉?±3/2〉 and two doublets Γ₈?±5/2〉 and Γ₇?±1/2〉 having close energies of ～6.3 meV at a temperature of 20 K. As follows from comparing the crystal-field parameters in the RAl₃ series (R = Ce, Pr, Nd), the fact that the parameters A ₂ ⁰ 〈r ²〉 and A ₄ ⁰ 〈r ⁴〉 in CeAl₃ differ significantly in value from the respective parameters in PrAl₃ and NdAl₃ cannot be explained in terms of the lattice constants of these isostructural compounds being different but rather is due to the enhanced hybridization of the localized 4f electrons of cerium with conduction electrons.     

Dependence on interatomic distance of exchange coupling in rare-earth Al2 compounds

The effect of pressure on the Curie temperature of the heavy rare-earth dialuminides has been measured up to 3.5 kbar. The derivatives dT_c/d_p are 0.00(4), 0.09, 0.21, 0.39, 0.60 and 0.71 K/kbar respectively for TmAl₂ ErAl₂, HoAl₂, DyAl₂, TbAl₂ and GdAl₂ thus indicating a clear positive correlation between dT_c/dp and the de Gennes factor G. The results are discussed in terms of the RKKY model. However, the phenomenological parameter D/d, where D is the nearest-neighbour R-R distance and d the diameter of the 4f orbital, is used to reflect the non-δ-function character of the sf-coupling parameter Г. The experimental values of Г²D² and T_p/G are found to decrease linearly with increasing D/d. This is in keeping with the RKKY proportionality of $\text{T}{}_{\mathrm{c}}\text{?T}{}_{\mathrm{p}}$ to Γ²E^?1_FG. For GdAl₂, TbAl₂ and DyAl₂ the quantity $\text{?}\text{(}\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{p}\text{)}\text{k}{}_{\mathrm{l}}\text{(}\text{D}\text{d}\text{)}\text{G}$ coincides within the error limits with the slope of the T_p/G vs D/d plot.     

Studies of the crystal field energy levels and g factors for Ce in LiYF4 crystal

The five observed crystal field energy levels and EPR g factors g_//and g_⊥ for Ce³⁺-doped LiYF₄ crystal are calculated together from a complete diagonalization (of energy matrix) method. In the method, the contributions to g factors of ground Kramers doublet from all the rest doublets within the ground and excited manifolds ²F_5/2 and ²F_7/2 are included. The calculated results show reasonable agreement with the experimental values. The calculations suggest that the crystal field parameter B₂₀ > 0 in LiYF₄: Ce³⁺ crystal. The opinion of the parameter B₂₀ < 0 in the previous paper is not correct. Since this opinion is based on the calculation of g factors using a very simple method where only the contributions to g factors from the doublets within the ground manifold ²F_5/2 are considered, it is suggested that this simple method is not effective in the calculation of g factors for 4f¹ ions in crystals.     

Ethane spectrum between 1940 and 2152 cm−1: Ground state parameters

The absorption spectrum of ethane was recorded between 1940 and 2152 cm^?1 at a resolution of 0.025 cm^?1. Ground state parameters were determined from the principal band in this region, ν₉ + ν₁₂(E_u): B₀ = 0.6630353 cm^?1, D₀^J = 1.0406 × 10^?6 cm^?1, D₀^JK = 2.575 × 10^?6 cm^?1 (standard errors are 7, 8, and 13, respectively, in the last digits quoted). The quoted values are from the analyses of 269 ground state combination differences, the standard deviation of the least-squares analysis was 0.0032 cm^?1.     

Acetylene spectra with a tunable diode laser: (ν4 + ν5)0+−ν41fQ branches of 12C2H2 and 12C13CH2

The rotational structure of the Q branches of the (ν₄ + ν₅)⁰⁺?ν₄^1f bands of ¹²C₂H₂ and ¹²C¹³CH₂ at 13.7 μm has been observed in a natural sample of acetylene by using a tunable diode laser as a source in a high-resolution infrared grating spectrometer equipped with a precision grating drive. Altogether 23 lines from J = 6 to 28 for ¹²C₂H₂ and 15 lines from J = 6 to 20 for ¹²C¹³CH₂ have been identified. The observed full width at half maximum of the resolved lines of these Q branches is very close to the calculated Doppler width. Molecular constants ν₀ + B″, B′ ? B″ ? 2D″, D′ ? D″, and H′ ? H″ have been derived from the measured line positions of the rotational structure.     

Crystal fields of Pr in LiYF4 under pressure

Fluorescence spectra of LiYF₄:Pr³⁺ have been measured between 12,000 and 22,000 cm⁻¹ under pressures up to 10 GPa. In total, 25 crystal field energy levels were obtained and used for the determination of free-ion and crystal field parameters under pressure. According to the nephelauxetic effect, the free-ion parameters decrease with increasing pressure. The relative decrease is larger for the Slater than for the spin-orbit coupling parameter. This behavior is consistent with former studies on Pr³⁺ in different crystals and can be explained by a special covalency model. According to an effective D_2d symmetry, five crystal field parameters B₀²(f,f), B₀⁴(f,f), B₄⁴(f,f), B₀⁶(f,f), and B₄⁶(f,f) are non-zero. The pressure-induced changes of these parameters have been determined up to the maximum pressure of 10 GPa. In order to improve the calculation of the crystal field levels, the configuration interactions with the 4f¹6p¹ configuration have been taken into account. The effect of these interactions are also analyzed under pressure and distinct improvements of the energy level calculations have been obtained.     

Theoretical study of EPR spectra and local structure for (NiO6) cluster in LiNbO3:Ni and Al2O3:Ni systems

For a d⁸ configuration ion, the 45×45 complete energy matrix, which contains the electron-electron repulsion interaction, the ligand-field interaction, the spin-orbit coupling interaction as well as the Zeeman interaction, has been established. By diagonalizing the complete energy matrix, the local lattice structure, EPR parameters (D, g_//, g_⊥) and optical absorption spectra for Ni²⁺ ions doped in LiNbO₃ and Al₂O₃ have been investigated. The local structure distortion parameters ΔR, Δθ₁ and Δθ₂ are determined for LiNbO₃:Ni²⁺ and Al₂O₃:Ni²⁺ systems, simultaneously. These results show that local structure of (NiO₆)¹⁰⁻ cluster exhibits an elongation distortion in both LiNbO₃:Ni²⁺ and Al₂O₃:Ni²⁺ systems, in spite of the different reasons of the elongation in both systems. In addition, we have found that the orbit reduction effect is very important to understand the anisotropic g-factors for Ni²⁺ ions doped in LiNbO₃ and Al₂O₃ crystals.     

Diborane : High resolution infrared rovibration studies of B2H6 and B2D6

Ground state rotation and quartic distortion constants were obtained for ¹¹B₂D₆ from the analysis of high resolution (0.05 cm⁻¹) Fourier transform infrared spectra. The bands studied comprised the ν₁₇, ν₁₈ type A, and ν₁₄, ν₉ + ν₁₅ type C bands of ¹¹B₂H₆ and the ν₁₆, ν₁₇, ν₁₈ type A, ν₈ type B, and ν₁₄ type C bands of ¹¹B₂D₆. In the case of ¹¹B₂H₆, the authors' ground state data were combined with those of Lafferty et al. obtained from a previous study (J. Mol. Spectrosc. 33, 345–367 (1970)) at comparable resolution of the ν₁₆ type A and ν₈ type B fundamentals. Information on the ground state rotational energy manifold of ¹¹B₂H₆ was accumulated up to J = 23, K_a = 18, and of ¹¹B₂D₆ up to J = 32, K_a = 22. This permitted rather precise determination of the distortion constants Δ_J⁰, Δ_JK⁰, Δ_K⁰, although δ_J⁰ and δ_K⁰ proved to be too small (< 10⁻⁷ cm⁻¹) and were constrained to values calculated from the force field. Sets of upper state parameters were determined for all vibrational levels studied. Although these appear to be essentially unperturbed globally, several localized perturbations were observed and identified.