Line Strength Factors Research Articles

Weld line strength factors in a reinforced injection molded part: Relationship with predicted fiber orientation

In this work, the residual strength of a fiber-reinforced injection molded part containing a hot weld line—or meld line—was evaluated. Injected plates were generated using a double-gated mold under four different process conditions. Quantification of the weld line detrimental effect was made in base on a fracture mechanics experiment. Specimens with and without the weld line—obtained from the same plates—were tested under a clamped single edge notched tension (SENT) configuration. For each set of process conditions, a relative weld line strength factor was defined in terms of the maximum applied stress intensity factor (KImax) as: KImax of specimens with weld line/KImax of specimens without weld line. In parallel, the fiber distribution pattern was obtained by process simulation software Moldex3D. An orientation factor was determined from simulation in order to quantify the effect of the local fiber orientation around the weld line. Optimal process condition and the most significant variable influencing the weld line strength were calculated via statistical analysis. Results showed a clear correlation between the weld line strenght factors and the orientaion factor. It was demonstrated that the fracture performance of the weld line region is controlled by the fiber orientation arrangement developed on that zone.

Einstein A coefficients and absolute line intensities for the E 2Π–X 2Σ + transition of CaH

Einstein A coefficients and absolute line intensities have been calculated for the E 2Π–X 2Σ + transition of CaH. Using wavefunctions derived from the Rydberg–Klein–Rees (RKR) method and electronic transition dipole moment functions obtained from high-level ab initio calculations, rotationless transition dipole moment matrix elements have been calculated for all 10 bands involving v′=0,1 of the E 2Π state and v″=0,1,2,3,4 of the X 2Σ state. The rotational line strength factors (Hönl–London factors) are derived for the intermediate coupling case between Hund's case (a) and (b) for the E 2Π–X 2Σ + transition. The computed transition dipole moments and the spectroscopic constants from a recent study [Ram et al., Journal of Molecular Spectroscopy 2011;266:86–91] have been combined to generate line lists containing Einstein A coefficients and absolute line intensities for 10 bands of the E 2Π–X 2Σ + transition of CaH for J-values up to 50.5. The absolute line intensities have been used to determine a rotational temperature of 778±3 °C for the CaH sample in the recent study.

Photoelectron spectroscopy of the Cl−…H2∕D2 anions: A model beyond the rotationless and Franck–Condon approximations

A model for simulating photoelectron spectra of the triatomic van der Waals complexes containing stable atomic anion and diatomic molecule is proposed and applied to the Cl(-)...H(2) and Cl(-)...D(2) anions. The model assumes adiabatic separation of the electronic and nuclear motions and localization of the photodetachment act at the atomic chromophore. Under these approximations, the electronic transition dipole moment matrix elements are evaluated using the atoms-in-molecule approach and explicit expressions for the rovibrational line strength factors are derived. The energies and intensities of a number of rovibronic photoelectron transitions are calculated for the Cl(-)...H(2) and Cl(-)...D(2) anions within the adiabatic bender model, i.e., with the full separation of the vibrational motions, whereas the simulations of the broad spectral envelopes are performed using the equilibrium conditions, asymmetric line shape function, and two choices of the relative abundances of the para- and ortho-forms of the complex. The simulations reproduce experimental spectra reasonably well allowing for their unambiguous assignment in terms of vibronic transitions fully consistent with the previous time-dependent calculations. Agreement with the previous theoretical works, manifestations of non-Franck-Condon effects, and implications to the assessment of the neutral potential energy surfaces are discussed.

High-resolution spectroscopy of the 2(2)Piu

The electronic absorption spectrum of the (0,2), (1,3), and (6,9) bands of the B4Sigmau(-)-X4Sigmag- system of C2+ was obtained using the velocity modulation technique in conjunction with heterodyne detection. The rotationally resolved spectrum shows perturbations, which are attributed to the 2(2)Piu state. The mixing between the B4Sigmau- state and the 2(2)Piu state for nearly degenerate levels generated enough intensity borrowing to observe twenty 2(2)Piu<--X4Sigmag- forbidden transitions. The parameters of a model Hamiltonian were fit to the bands and their corresponding forbidden transitions. Line position measurements, line strength factors, and expectation values for the orbital angular momentum Lambda' for the forbidden transitions are reported. Molecular parameters from the global fit of each band, including their corresponding forbidden transitions, are reported.

Line Intensities and Molecular Opacities of the FeHF4Δi–X4ΔiTransition

We calculate new line lists and opacities for the $F^4\Delta_i-X^4\Delta_i$ transition of FeH. The 0-0 band of this transition is responsible for the Wing-Ford band seen in M-type stars, sunspots and brown dwarfs. The new Einstein A values for each line are based on a high level ab initio calculation of the electronic transition dipole moment. The necessary rotational line strength factors (H\"onl-London factors) are derived for both the Hund's case (a) and (b) coupling limits. A new set of spectroscopic constants were derived from the existing FeH term values for v=0, 1 and 2 levels of the $X$ and $F$ states. Using these constants extrapolated term values were generated for v=3 and 4 and for $J$ values up to 50.5. The line lists (including Einstein A values) for the 25 vibrational bands with v$\leq$4 were generated using a merged list of experimental and extrapolated term values. The FeH line lists were use to compute the molecular opacities for a range of temperatures and pressures encountered in L and M dwarf atmospheres. Good agreement was found between the computed and observed spectral energy distribution of the L5 dwarf 2MASS-1507.

Interference in two-photon rotational line strengths of diatomic molecules

A general formalism describing two-photon absorption of an isotropic ensemble of diatomic molecules is presented, and practical simplifications are discussed. Explicit rotational line strength factors are given for transitions between electronic doublet states, which are intermediate between Hund's angular momentum coupling cases (a) and (b) and including these limiting cases. The theory is validated by comparison with an experimental room temperature spectrum of the C2Π (ν = 0) ← X2Π (ν = 0) two-photon band of NO near 382 nm. The absence of certain Λ-doublet resolved rotational branches is shown to arise from interfering virtual absorption paths, which causes interference between components of the two-photon absorption tensor. Previous listings of two-photon rotational line strength factors are not correct for transitions between Π states, since they cannot describe such interference effects.

REMPI spectroscopy of internal state populations in HBr+Ar free jets: Rotational relaxation of HBr

The (2+1) resonance enhanced multiphoton ionization spectra of HBr were obtained through the E 1 Σ + state for HBr seeded in Ar free jets. Analysis of the two-photon absorption line strength factors allowed determination of quantitative populations for the HBr rotational manifold. A study of the terminal HBr rotational state distributions was made for a wide variety of p 0 D values of the jets. These nonequilibrium population distributions were then modeled by numerical solutions of the set of coupled kinetic equations describing the rotationally inelastic collisions with the buffer. Using a power-law relaxation model, the j– j′ rotationally state specific relaxation cross-sections and rate coefficients were determined as a function of temperature over the range present in the post-continuum zone of the free jet flows (180 to 15 K).

Multiplex spectroscopy of jet-cooled NO2

We report the multiplexing (use in tandem) of laser-induced fluorescence (LIF) and degenerate four-wave mixing (DFWM) spectroscopies to probe jet-cooled NO2 near 487 nm. We find that the multiplexing of these methods can be used to determine relative line strength factors and the ratio of populations in different energy levels, and to elucidate the transition dipole moment dependence of the DFWM signal.

Detection of DCl by multiphoton ionization and determination of DCl and HCl internal state distributions

A study of the 2+1 resonantly enhanced multiphoton ionization (REMPI) spectrum of DCl is reported. Transition energies for excitation of the F 1Δ–X 1Σ+ (0,0) and (1,0) bands, as well as the V 1Σ+–X 1Σ+(v′,0) bands, for v′=15–19, are presented. The derived molecular constants for the F–X (0,0) and the V–X bands agree well with those previously obtained from analysis of the one-photon VUV absorption spectrum [A. E. Douglas and F. R. Greening, Can. J. Phys. 57, 1650 (1979)]. The ion signals for excitation through various rotational lines in the E–X (0,0) and F–X (0,0) and (1,0) bands are compared with theoretical two-photon line strengths. Extensive power- and J′-dependent ion fragmentation is observed for the former band. No fragmentation is observed in the F–X bands; however, the ion signal strengths are found to vary strongly with J′. This variation of REMPI signal strengths vs J′ was shown to be due to an indirect predissociation, as in HCl. Tables of experimental line strength factors for the F–X (0,0) and (1,0) bands of HCl and DCl are reported. Finally, the relative REMPI detection sensitivities for HCl and DCl, through their respective F–X (0,0) R(1) lines, are compared.

Measurement of the rotational temperature of oxygen in a high-power inductively coupled plasma

In a high-power (30 kW), inductively coupled argon-oxygen plasma used as a tool to deposit high-temperature superconducting YBa2Cu3O7-x films rotational bands of the Schumann-Runge system B3 Sigma (u-)-X3 Sigma (g-) oxygen were detected in the spectral regions around 340 and 360 nm. After derivation of the line strength factors for the triplet system, rotational temperatures can be determined by fitting calculated relative intensities to those observed experimentally, and the contributions of R and P branches to the lines observed can be identified. The rotational temperature 7 at a distance of 34.5 cm from the exit of the plasma torch where the deposition of superconducting films takes place lies in the range 1850-2050 K depending on the RF power input which was varied in the range 8-27 kW. Near the torch exit, temperatures in the range 2600-3400 K are observed. They depend strongly on gas composition and gas flow rate, in contrast to positions far away from the torch exit. Excitation temperatures near the torch exit which were derived from Ar lines are considerably higher than the rotational temperatures, indicating that the latter are typical of the colder outer parts of the plasma.

Electronic fine structure transitions and rotational energy transfer of NO(X 2Π) in collisions with He: A counterpropagating beam study

The collision dynamics of NO(X 2Π) with He is investigated at a collision energy of 147 meV using the method of counterpropagating pulsed molecular beam scattering. One-dimensional product velocity distributions are determined through ion time-of-flight analysis. State specific detection of NO is achieved through (2+1) resonance enhanced multiphoton ionization detection via the E 2Σ+ intermediate state. Calculated frequencies and line strength factors for the two-photon transition enable the extraction of state resolved degeneracy averaged integral and differential cross sections. The overall behavior of the integral cross sections for fine structure conserving and changing transitions, weighted by the degeneracy of the final state, is well described by two different exponential energy gap laws. Differential cross sections for both types of transitions exhibit very different rotational rainbow structures. For the multiplet changing transition, the scaling law suggests an increased energy transfer efficiency while the rotational rainbow structure indicates a larger effective anisotropy. Therefore, the dynamics at the probed collision energy is clearly dominated by fine structure changing collisions when magnetic sublevel specific cross sections for a specified energy transfer are compared.

Empirical lifetimes for 4s4p P1,31∘ levels in the zinc isoelectronic sequence

Empirical predictions are reported for the lifetimes of the 4s2–4s4p resonance and intercombination transitions in the Zn isoelectronic sequence. The approach uses a direct-mapping reduction of available energy-level and lifetime data and imposes no theoretical assumptions or restrictions. Measured spectroscopic energy-level data are used to characterize intermediate coupling effects in terms of an effective singlet–triplet mixing angle, which is then used to convert lifetime data into mixing-reduced effective line strength factors. Through a linearizing screening parameterization, these reduced line strength factors are found to exhibit regularities permit accurate interpolation, extrapolation, and smoothing and also provide a convenient exposition for that sensitive comparison between experimental results and ab initio calculations.

The B1Σ +- a3Π i and D1Δ- a3Π 1 intercombination systems of the MgO molecule

The MgO B 1Σ +- a 3Π i (0-0) and (0–1) and D 1Δ- a 3Π (0-0) and (1-1) intercombination bands have been observed, rotationally analyzed, and reduced to molecular constants by a nonstandard procedure which made extensive use of an elaborate but highly constrained effective Hamiltonian model. The MgO a 3Π state is important because it is low lying ( T e = 2620.6 cm −1), it correlates to Mg( 1S) + O( 3P) ground state atoms (unlike the X 1Σ + state), it is the lower state of the exceedingly complex near UV triplet-triplet bands, and many Mg + oxidant reactions significantly populate various Ω , e f components of the a 3Π state. The fit model, observed transitions, and computed eigenvalues and eigenvectors for MgO a 3Π v = O and 1 will aid in the analysis of triplet-triplet bands and will be especially valuable in providing transition frequencies and relative Ω , e f , and J-dependent rotational linestrength factors for population monitoring. The present results reaffirm the validity and utility of various semiempirical relationships between fine structure, Λ-doubling, and perturbation parameters. Moreover, by showing that the Λ-doubling in the a 3Π state is dominated by interactions with the X 1Σ + and b 3Σ + states, an ab initio prediction of the location of the as yet unobserved b 3Σ + state is confirmed. The B 1Σ +- a 3Π transition borrows its oscillator strength from the B 1Σ +- X 1Σ + and B 1Σ +- A 1Π transitions. The pattern of a 3Π, A 1Π, and X 1Σ + vibrational levels is such that, for v ≤ 4, the predominant perturber characters admixed into the a 3Π, v a level are v x = v a + 3 and v A = v a . Interference effects between transition amplitudes borrowed from B- X and B- A transitions will cause intensity to be transferred from R Ω (J) to P Ω (J) or vice versa. These e-level interference effects will be strongly dependent on v B , v a , J, and Ω . Although the pattern of interference effects will appear complicated, all such effects are determined, in sign and magnitude, by the following product of eight signed quantities. 〈ν A = ν α|ν α〉 〈ν α|ν X = ν α + 3〉 〈ν X = ν α + 3|ν B〉 〈ν B|ν A = ν α〉 A α−X A α−A μ B−A μ B−X. Note that each vibrational wavefunction and each electronic wavefunction appear twice, once as a bra and once as a ket. The sign of the interference effect can be experimentally determined and cannot depend on arbitrary phase choices.

Isoelectronic smoothing of line strengths in intermediate coupling

A method is presented that accounts for the effects of singlet-triplet mixing in measured lifetimes of resonance and intercombination lines in alkaline-earthlike and inert-gaslike isoelectronic sequences. The method uses measured lifetimes and spectroscopic energy levels as its only inputs, and yields mixing-reduced line strength factors that can be isoelectronically linearized for precision interpolation, extrapolation, and smoothing. The method is applied to predictively systematize lifetimes in the Be, Mg and Ne iso-electronic sequences.

Scaling of state multipoles in rotationally inelastic transfer

Laser excitation of molecules in thermal cells gives rise to an anisotropic distribution of m states and thus fluorescence from these states, and from levels populated by inelastic collisions, is polarized. Neglect of fluorescence polarization can give rise to misleading conclusions concerning population transfer in the excited state. Precise measurements of the transfer of population, orientation, and alignment, through polarization ratios, can provide an excellent means for testing the various fitting laws for rotationally inelastic transfer through modified ‘‘sudden’’ scaling laws. The justification for this is fourfold: rotational line strength factors and laser power fluctuations do not affect the degree of polarization; thirdly, the effect of multiple collisions is less significant on the inelastic polarization transfer than it is on the population transfer as measured in conventional total fluorescence intensity measurements; and fourthly, the leading parameters present in fitting laws cancel out, reducing the number of fitting parameters by one. Scaling laws appropriate to polarization measurements are derived and various fitting relations are tested against Li*2/He and Li*2/Ar rotationally inelastic polarization data.

Vibronic intensities and rotational line strength factors for the three-photon absorption spectrum of ammonia

A perturbation theory approach is used to analyze the rovibronic structure of the three-photon resonant absorption of ammonia. The vibronic selection rules are presented in a convenient pyramid mnemonic in terms of irreducible representations of the rotation group and of the D3h point group. The analysis is presented for each possible situation, namely, all three photons are different, two photons are identical and one different, and all three photons are identical. The experimentally important case of three identical photons implies only two polarizations and two vibronic tensor elements for each symmetry type. With both the B̃ and C̃′ systems of ammonia one expects a ratio of 5 to 2 in the absorbance for circularly versus linearly polarized light for the N, O, S, and T branches. For the P, Q, and R branches one expects a 21 to 4 ratio of the weight-1 versus weight-3 tensor contributions to the C̃′ system in linearly polarized light (21 to 6 for B̃). Weight-1 terms are absent with circularly polarized light. These predictions are confirmed experimentally. The complete set of rotational line strength factors for three-photon absorption are given in algebraic form for the first time. The combination of vibronic factors, rotational line strengths, and statistical weights allows one to predict the three-photon absorption spectrum. Such calculated spectra are presented for ammonia at 45 K and they compare very favorably with the experimental spectra for both the B̃ system (a perpendicular band) and for the C̃′ system (a parallel band) in both linearly and circularly polarized light.

Selection rules and line-strength factors for multiphoton transitions in gas phase molecular spectroscopy

Multiphoton transitions are discussed in terms applicable to experimental spectroscopy. A simple tensor operator for the equations governing multiphoton transitions in molecules is obtained. Selection rules for these processes are derived by symmetry considerations and procedures for calculation of rotational line-strength factors are given. For the general transition, the rovibronic n-photon selection rules can be determined by the symmetry product of a n-photon operator with the rovibronic wavefunctions. The line-strength factors are found by considering the integral over rotations of the nth rank tensor operators. The line-strength evaluations do not depend on exact knowledge of the vibronic overlap, to within a constant factor.

Technique for measuring rotational temperature of microwave excited diatomic sulfur

A technique has been devised to measure the temperature of discharge excited diatomic sulfur. The bandshape of the transition from the upsilon' = 8 level in the B(3)Sigma(-) electronic state of the upsilon" = 0 level in the X(3)Sigma(-) state is due to unresolved rotational structure. The observed bandshape was compared to the results of a computer simulation that used the line strength factors of Tatum and Watson for spin-rotation coupling intermediate between Hund's cases (a) and (b).

Rotational line strengths in the Lyman and Werner bands of H 2

Rotational line strengths in the Lyman and Werner bands of molecular hydrogen are affected by the nonadiabatic interaction between the B and C states. Numerical results are presented for the effect of this interaction on relative rotational line strengths for V x = 0 and V B ≤ 25, V c ≤ 9. The B- C interaction is shown to have a pronounced effect for many levels. This difference in rotational line strength factors from the usual Hönl-London factors should be taken into account when relating line oscillator strengths to band oscillator strengths. Relative rotational line strengths are also computed for transitions between C-state levels and excited vibrational levels in the X state. Comparison is made to the measured Werner band emission line intensities of Schmoranzer and Geiger [ J. Chem. Phys., 59, 6153 (1973)].

Collision Induced Far Infrared Absorption of Solutions of CH4 and CD4 in Liquid Argon

The far infrared spectra of CH4 and CD4 dissolved in liquid argon were recorded to probe the dynamics of this liquid state system. Broad bands devoid of any fine structure were observed. Methane does not possess a permanent dipole moment and the observed absorption results from a dipole induced by the octopolar field of the molecule during a collision. For octopole induced rotational transitions the selection rules are ΔJ=0–3. Assuming free rotor energy levels and line strength factors, and a modified Lorentzian band shape, synthetic spectra were generated which agree quite well with the experimental data. The integrated absorption coefficient is much smaller than that predicted for binary collisions. This is expected since binary interactions in the liquid state cannot be isolated from higher order interactions with neighboring atoms. The dipole moment induced during a collision is partially cancelled by many-body interactions so the absorption coefficient in the liquid state is diminished, compared to the low density gas. Time correlation functions were determined from the far infrared data as well as from near infrared and Raman spectra of methane and compared. The quantum mechanical free rotor time correlation functions were calculated and found to agree with the experimental results for times shorter than liquid state collision times. Since the far infrared correlation function is due to an induced dipole moment, it is damped accordingly. We estimate that the duration of collision is ≈ 2 × 10−13sec. The good agreement of the synthetic spectra and free rotor correlation functions with experiment indicate a barrier to rotation that is comparable to the magnitude of rotational energies observed. Hindered rotation in liquids is also discussed in terms of collisional effects.