Energy Level Data Research Articles

Spectroscopic Data for Neutral Francium (FrI)

Energy levels and hyperfine structure constants have been compiled for the sixteen longest lived isotopes of francium (Z=87). For most isotopes with atomic weights in the range 199 ≤A≤232 the only measurements made are for the 7sS1∕22 and 7pP1∕2,3∕2°2 levels. Additional energy-level data are available for Fr210, Fr212, and Fr221. Wavelengths with classifications and transition probabilities are tabulated for Fr212. In addition, the ionization energy is included for isotopes for which a sufficient number of levels have been measured, Fr212 and Fr221.

Spectroscopic and 1.06 μm laser properties of Nd 3+-doped K–Sr–Al phosphate and fluorophosphate glasses

Optical absorption, fluorescence and decay curves for the 4F 3/2 level of Nd 3+ ions in phosphate (P 2O 5–K 2O–SrO–Al 2O 3) and fluorophosphate (P 2O 5–K 2O–SrO–Al 2O 3–AlF 3 and P 2O 5–K 2O–SrO–Al 2O 3–BaF 2) glasses doped with three concentrations (0.1, 1.0 and 2.0 mol%) of Nd 3+ ions have been investigated. The Judd–Ofelt (JO) theory has been applied to the absorption spectra of 1.0 mol% Nd 3+-doped glasses to derive JO intensity parameters which are in turn used to calculate the radiative properties of the Nd 3+ ion fluorescent levels. The assigned energy level data of Nd 3+ (4f 3) ions are analysed in terms of a parametrized free-ion Hamiltonian model that consists of 20 interaction parameters of atomic nature. The stimulated emission cross section and branching ratios have been calculated using the emission spectra. The relatively higher branching ratio for 4F 3/2 → 4I 11/2 transition shows the suitability of these glasses for laser application. It is interesting to note that the measured decay curves of the 4F 3/2 level remain nearly single exponential even for higher Nd 3+ ion concentration but with shortening of lifetime.

Spectroscopic analysis of LiKGdF 5:Er 3+, Sm 3+ single crystal

Low temperature photoluminescence spectra were measured under the selective excitation to the energy levels of Gd 3+, Er 3+ and Sm 3+, respectively. Corresponding transitions were assigned with the help of fluorescence decay measurements. By assuming that the rare earth ion is in C 2v symmetry instead of the actual C 2, crystal field calculations were carried out based on the deduced experimental energy level data of Er 3+ and Sm 3+. The theoretical result is in good agreement with the experimental data.

Quantum mechanics in curved space-time

In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom spectrum is calculated. A comparison of the calculated spectrum with the numerical data of the deuterium energy levels shows a significant improvement of the accord, and the deviations are almost five times smaller then the ones obtained with the Dirac theory. The implications of the theory considering the strong interactions are also discussed.

Can the low symmetry crystal (ligand) field parameters be considered compatible and reliable?

This paper stems from our recent efforts to clarify the inconsistencies between the crystal-field parameter (CFP) data sets reported in the literature for various low symmetry transition ion–host systems. Prompted by the results of these studies, in this paper we consider the intricate properties of CF Hamiltonians, hitherto not fully understood. The term ‘low symmetry’ here includes the continuous rotational symmetry cases, i.e. hexagonal II, tetragonal II, trigonal II, monoclinic, and triclinic ones, as well as orthorhombic ones. The following fundamental intricate aspects are considered: (1) selection of the axis systems, (2) types of CFPs and their properties, (3) introduction of a new notion of a nominal axis system for the fitted CFP data sets, (4) implications of the Noether's theorem and the algebraic symmetry of CF Hamiltonians, (5) correlation properties among CFP data sets, (6) the rotational degrees of freedom and the reduction of the number of independent CFPs, which are of special importance for triclinic symmetry cases, and (7) extension of the multiple correlated fitting technique, including a quantitative method for CFP data sets comparison. Clarification of these intricate aspects enables us to provide a general framework aimed at achieving an increased compatibility and reliability of CFP data sets for transition ions at low symmetry sites in crystals. This framework may be especially useful for trivalent lanthanides in technologically important low symmetry hosts for which only limited energy-level data are available.

Spectroscopic investigations of Nd 3+-doped alkali chloroborophosphate glasses

Optical absorption spectra were studied in wavelength region 400–900 nm for the Nd 3+-doped alkali (R=Li, Na and K) chloroborophosphate glasses at room temperature. The energy level scheme of the 4f 3 electron configuration was deduced from the observed energy level data using a parametrized Hamiltonian ( H F1) model which includes 20 free-ion interaction parameters. Reasonable correlation was obtained between the experimental and calculated energy levels. The Judd–Ofelt model for the intensity analysis of induced electric dipole transitions has been applied to the measured oscillator strengths of the absorption bands to determine the three phenomenological intensity parameters Ω 2, Ω 4 and Ω 6 for each glass. Using these parameters, the total radiative transition rates ( A T), non-radiative relaxation rates ( W NR), branching ratios ( β R), integrated cross-sections for the stimulated emission ( Σ), excited state emission intensities ( f ESE) and excited state absorption intensities ( f ESA) have been theoretically calculated for certain excited Nd 3+ fluorescent levels. From the results obtained, the conclusion is made about the possibility of using these glasses as laser media.

Formula omitted] Rydberg states of O 2

Experimental observations of the gerade ( g) states of O 2 that exist between the dissociation limit of the B 3 Σ u − state and the X 2 Π g ground state of O 2 + are reexamined. Emphasis is placed on the assignment of electronic structures of the [X 2 Π g]ndλ 1,3 Λ g Rydberg states for which experimental data can be obtained from the literature: mainly, ndπ g - and ndδ g -based 1,3 Λ g states with n=3–5 and the ndπ g 1 Σ g + and 3 Σ g − series with n=6–11. In many cases, characterizations of these electronic structures are limited by the quality of existing experimental data and, in cases where rotational band structures were analyzed, by the unavailability of most of the rotational energy level data upon which reported parameterizations were based. Thus, while a general picture of some segments of the ndπ g - and ndδ g -based structures can be presented, quantitative descriptions of these structures and unique identification of the causes of many apparent structural irregularities will not be possible until a new well-calibrated, rotationally resolved database is developed.

Vibrational and Electronic Energy Levels of Polyatomic Transient Molecules. Supplement B

A summary is presented of recently published, critically evaluated experimental vibrational and electronic energy level data for approximately 1700 neutral and ionic transient molecules and high temperature species possessing from three to sixteen atoms. Although the emphasis is on species with lifetimes too short for study using conventional sampling techniques, there has been selective extension of the compilation to include data for isolated molecules of inorganic species such as the heavy-metal oxides, which are important in a wide variety of industrial chemical systems. Radiative lifetimes and the principal rotational constants are included. Observations in the gas phase, in molecular beams, and in rare-gas and diatomic molecule matrices are evaluated, and several thousand references are cited. The types of measurement surveyed include conventional and laser-based absorption and emission techniques, laser absorption with mass analysis, and photoelectron spectroscopy.

Challenges and solutions for realistic room simulation

Virtual room acoustic simulation (auralization) techniques have traditionally focused on answering questions related to speech intelligibility or musical quality, typically in large volumetric spaces. More recently, auralization techniques have been found to be important for the externalization of headphone-reproduced virtual acoustic images. Although externalization can be accomplished using a minimal simulation, data indicate that realistic auralizations need to be responsive to head motion cues for accurate localization. Computational demands increase when providing for the simulation of coupled spaces, small rooms lacking meaningful reverberant decays, or reflective surfaces in outdoor environments. Auditory threshold data for both early reflections and late reverberant energy levels indicate that much of the information captured in acoustical measurements is inaudible, minimizing the intensive computational requirements of real-time auralization systems. Results are presented for early reflection thresholds as a function of azimuth angle, arrival time, and sound-source type, and reverberation thresholds as a function of reverberation time and level within 250-Hz–2-kHz octave bands. Good agreement is found between data obtained in virtual room simulations and those obtained in real rooms, allowing a strategy for minimizing computational requirements of real-time auralization systems.

Calculated gadolinium atomic electron energy levels and Auger electron emission probability as a function of atomic number Z

Auger electron interaction with matter is gaining importance in particular in medical application of radiation. The production probability and energy spectrum is therefore of great importance. A good source of Auger electrons is the 157 Gd (n,γ) 158 Gd reaction. The present article describes calculations of electron levels in Gd atoms and provides missing data of outer electron energy levels. The energy of these electron levels missing in published tables, was found to be in the 23–24 and 6–7 eV energy ranges respectively. The probability of Auger emission was calculated as an interaction of wave function of the initial and final electron states. The wave functions were calculated using the Hartree–Fock–Slater approximation with relativistic correction. The equations were solved using a spherical symmetry potential. The error for inner shell level is less than 10%, it is increased to the order of 10–15% for the outer shells. The width of the Auger process changes from 0.1 to 1.2 eV for atomic number Z from 5 to 70. The fluorescence yield width changes five orders of magnitude in this range. Auger electron emission width from the K shell changes from 10 −2 to ∼1 eV with Z changing from 10 to 64, depending on the final state. For the L shell it changes from 0 to 0.25 when it Z changes from 20 to 64.

High-Lying Rotational Levels of Water: An Analysis of the Energy Levels of the Five First Vibrational States

As a continuation of the work carried out on the ground and (010) vibrational states of water (R. Lanquetin, L. H. Coudert, and C. Camy-Peyret, 1999, J. Mol. Spectrosc.195, 54–57), rotational energy levels for these two states are revisited here and new accurate rotational energy levels are considered for the three next vibrational states, that is, the (020), (100), and (001) states. Experimental rotational energies, along with their uncertainties, are retrieved through analyses of already published data sets and of discharge and flame emission spectra. The maximum value of J for the obtained levels is 25 for the ground state, 21 for the (010) state, and 20 for the three next states. Based on the bending-rotation Hamiltonian approach (L. H. Coudert, 1997, J. Mol. Spectrosc.181, 246–273), a new theoretical approach is proposed to calculate rotational energies in the five interacting vibrational states under consideration and is used to carry out an analysis of the experimental energies. Comparisons with other existing energy level data sets are also presented.

Branching Fractions for the 5s25p2 – 5s25p6s Supermultiplet in the Sn Isoelectronic Sequence

Recent studies of the Si and Ge isoelectronic sequences have shown that branching fractions within the ns2np2–ns2np(n + 1)s supermultiplets are accurately described by a semiempirical model that uses spectroscopic energy level data to characterize intermediate coupling. It was also recently shown that a similar model applied to alkaline-earthlike ns2–nsnp transitions can be advantageously generalized to include the effects of spin-other-orbit interaction and differences between the singlet and triplet radial wave functions. These two formalisms are combined, extended, and applied here to obtain a predictive systematization of branching fractions for the 5s25p2–5s25p6s supermultiplet of the ions Sn I–Cs VI in the Sn sequence.

Predictive data-based exposition of5s5p1,3P1lifetimes in the Cd isoelectronic sequence

Experimental and theoretical values for the lifetimes of the $5s5p{}^{1}{P}_{1}$ and ${}^{3}{P}_{1}$ levels in the Cd isoelectronic sequence are examined in the context of a data-based isoelectronic systematization. Lifetime and energy-level data are combined to account for the effects of intermediate coupling, thereby reducing the data to a regular and slowly varying parametric mapping. This empirically characterizes small contributions due to spin-other-orbit interaction, spin dependences of the radial wave functions, and configuration interaction, and yields accurate interpolative and extrapolative predictions. Multiconfiguration Dirac-Hartree-Fock calculations are used to verify the regularity of these trends, and to examine the extent to which they can be extrapolated to high nuclear charge.

Branching Fractions and Transition Probabilities for Ga II, In II and Tl II from Measured Lifetime and Energy Level Data

Branching fractions and relative transition probabilities are predicted for the ns2-nsnp and nsnp-nsnd supermultiplets in Ga II, In II and Tl II through a data-based systematization of measured lifetime and spectroscopic energy level data. A formalism is used that parametrizes the effects of Coulomb exchange, spin-orbit and spin-other-orbit interactions, and differences between the radial wave functions of the singlet and triplet states to deduce effective intermediate coupling amplitudes. Connections between singlet and triplet lifetimes and among triplet lifetimes are examined and predictions are made where data do not currently exist.

On the Stark broadening of the Ar VIII 115.47 and 116.19 nm lines

The analysis of energy level data and plasma conditions show that the Ar VIII VUV lines 115.47 and 116.19 nm, measured in another experiment, are not isolated and that Debye shielding may be partially responsible for non-linear Stark width versus electron density dependence. For the line shape calculations in this case the Debye shielding and non-isolated line assumption should be taken into account.

Energy level data recommendation by screening constant

Energy level data recommendation by the screening constant is more useful and more accurate than that by quantum defect for high- Z ions. While the quantum defect converges to a small value as Z increases, the screening constant monotonically decreases. Z dependence of the screening constant is approximately Z 3 for Z=10– 40, Z 3.5 for Z=40–70, and Z 4 for Z>70. By the simple Z dependence, we have made a fitting formula for He-like ions. The same Z dependence of the screening constant has been found in different ions, Li-like, Be-like, and etc. This simple Z 3 dependence of the screening constant could be explained as the spin–orbit interaction of the hydrogenic wave function in the Coulomb potential.

Judd–Ofelt parametrization and radiative transitions analysis of Tm 3+ doped alkali chloroborophosphate glasses

Absorption spectra for Tm 3+ doped alkali chloroborophosphate glasses are recorded in the UV–VIS and NIR regions. The assigned energy level data of Tm 3+ (4f 12) in these glasses are analysed in terms of a parametrized Hamiltonian model that includes 14 free-ion parameters. From the measured oscillator strengths of the absorption bands, the intensity parameters, Ω λ , are calculated by using the Judd–Ofelt theory. Using these data, radiative transition probabilities, radiative lifetimes, branching ratios and integrated absorption cross-sections for 3P 0, 1D 2 and 1G 4 fluorescent levels are calculated. Certain laser transitions are predicted.

High-Lying Rotational Levels of Water: Comparison of Calculated and Experimental Energy Levels for (000) and (010) up toJ= 25 and 21

Emission spectra of methane–oxygen low-pressure flames have been recorded at a resolution of 0.02 cm−1with an infrared Fourier transform spectrometer in the spectral ranges 780–1370 and 1800–5000 cm−1. The flame temperature was about 1850 K and a large number of transitions involvingJvalues as high as 34 for an extended set of vibrational states could be assigned. Combined with already published data sets on H2O, our line position analysis yielded rotational energy levels for many of these states, but only the results relevant to the ground and the (010) states are presented here. The experimental energies for these two states have been fitted with the help of the bending-rotation Hamiltonian approach [L. H. Coudert,J. Mol. Spectrosc.181, 246–273 (1997)], and for each rotational level, the calculated energy along with its uncertainty is reported and compared with the observed value. Comparisons with other available energy level data sets for the ground and (010) states are also presented.

Vibrational and Electronic Energy Levels of Polyatomic Transient Molecules. Supplement A

A summary is presented of recently published, critically evaluated experimental vibrational and electronic energy level data for neutral and ionic transient molecules and high temperature species possessing from three to sixteen atoms. Although the emphasis is on species with lifetimes too short for study using conventional sampling techniques, there has been selective extension of the compilation to include data for isolated molecules of inorganic species such as the heavy-metal oxides, which are important in a wide variety of industrial chemical systems. Radiative lifetimes and the principal rotational constants are included. Observations in the gas phase, in molecular beams, and in rare-gas and diatomic molecule matrices are evaluated. The types of measurement surveyed include conventional and laser-based absorption and emission techniques, laser absorption with mass analysis, and photoelectron spectroscopy. Not counting isotopic species, 904 molecules are surveyed, and 2696 distinct references are given.

Electronic State Structure and Optical Properties of Tb(oda)(3)(3)(-) Complexes in Trigonal Na(3)[Tb(oda)(3)].2NaClO(4).6H(2)O Crystals.

Polarized optical absorption and emission measurements are used to locate and assign 95 crystal-field energy levels split out of the 4f( )(8) electronic configuration of Tb(3+) in single crystals of Na(3)[Tb(oda)(3)].2NaClO(4).6H(2)O (where oda denotes an oxydiacetate ligand). The absorption measurements span the 235-490 nm wavelength range, and the emission measurements span the 485-685 nm wavelength range. The combined absorption and emission spectra measurements provide access to the energy-level structures of 46 different 4f( )(8)[SL]J multiplet manifolds of Tb(3+) (all multiplet manifolds with baricenter energies <42 400 cm(-)(1) above ground). The site symmetry of the Tb(3+) ions in Na(3)[Tb(oda)(3)].2NaClO(4).6H(2)O is D(3), and the point-group symmetry of the tris-terdentate Tb(oda)(3)(3)(-) coordination complexes is also D(3). The Tb(oda)(3)(3)(-) complexes are chiral, and they exist in just one, fully resolved enantiomeric form in single crystals of Na(3)[Tb(oda)(3)].2NaClO(4).6H(2)O. The crystals exhibit strong chiroptical activity in their absorption and emission spectra, and results obtained from both circularly polarized and linearly polarized optical spectra measurements are used in making transition line assignments. The energy-level data acquired from the spectroscopic measurements are analyzed in terms of a model Hamiltonian that includes consideration of both isotropic and nonisotropic 4f electron/crystal-field interactions, and the interaction parameters derived from this analysis are discussed and then compared with those obtained for other Na(3)[Ln(oda)(3)].2NaClO(4).6H(2)O systems and for Tb(3+) in other crystalline hosts.