A comment on Hönl-London factors

The literature on the Hönl-London factors of diatomic molecules, the factors in intensity formulas dependent on the rotational quantum numbers, is somewhat confused for the case of perpendicular transitions. We derive a formula, Eq. (23), for allowed singlet-singlet transitions between levels of definite parity, and show that it is consistent with standard sum rules. As an illustration, the formula is applied to the calculation of lifetimes in the B¹Π_u state of Na₂, showing that the corrected formula gives results in good agreement with experimental measurements.     

Measurement of NO22B2 state g values by optical radio frequency double resonance

The g values for some selected levels of the NO₂ 6126 and 5933 Å bands were measured using optical radio frequency double resonance. The g values are found to be well described by the Hund's case (b) coupling scheme.     

Mössbauer studies and magnetic studies of Ni doped orthoferrites PrFe1−xNixO3 (x≤0.3)

The magnetic properties of polycrystalline PrFe_1−xNi_xO₃ (x≤0.3) system were studied using Mössbauer spectroscopy and magnetization measurements. The Mossbauer spectra exhibit six line spectra which loses its sharpness as the Ni substitution increases within the system. As the Ni concentration in the system increases, the hyperfine field and isomer shift shows decrease, which is vivid from the sluggish nature of the sextets. The small value of quadrupole splitting confirms the octahedral environment of the Fe⁺³ ions. The magnetization curves show the reversible behavior and represent the fall in negative molecular field leading to AFM frustration. From these results, we conclude that sagging in the spectra reveals the change from antiferromagnetic state to ferromagnetic state, which can be attributed to mixed state of Fe⁺³ ions i.e. high spin (HS) and low spin (LS) which is a consequence of progressive collapse of Hund’s rule due to HS→LS transition. These results confirm the weak ferromagnetic component due to canted-AFM spin arrangement of Fe³⁺ magnetic moments.     

Frequency measurement of pure rotational transitions in the v2 = 1 state of H2O

Frequencies of pure rotational transitions in the v₂ = 1 vibrationally excited state of H₂¹⁶O were measured with a tunable far-infrared spectrometer in the frequency range of 0.5-5 THz. Molecular parameters of Watson’s A-reduced Hamiltonian have been obtained to reproduce the observed frequencies.     

Effect of satellite Q-branches on temperatures computed from oxygen vibrational raman intensities

Splitting of the ³Σ^-_g ground state of molecular oxygen has a small but noticeable effect on the intensity distribution in the fundamental and hotband Raman Q-branches. An analysis of oxygen Q-branch spectra [computed for Hund's coupling case (b) and pure anisotropic scattering], with expressions corresponding to ¹Σ theory, results in temperature errors of -2.0% to -0.5% in the range 500–2000 K.     

On the cΠ (v = 0) state of carbon monoxide

A full analysis of the near infrared c³Π-b³Σ⁺ (0-0) band is given and term values for both states determined. The c³Π (v = 0) state was jointly analysed with the perturbing k³Π (v = 2) state and data from the c³Π-X¹Σ⁺ (0-0) transition and 3A band system were included. It is shown that the available data are consistent with the c³Π (v = 0) state having near Hund’s case b coupling with a spin-orbit constant of A = 0.45 ± 0.02 cm⁻¹, a homogeneous perturbation with the k³Π (v = 2) state, and Λ-type doubling arising predominantly from its interaction with the j³Σ⁺ state. A discrepancy with a more recent report of the 3A band system is identified and discussed. The perturbed b³Σ⁺ state term values are consistent with a previously reported five state interaction model.     

Constructions and properties of k out of n scalable secret image sharing

Recently, Wang et al. introduced a novel (2, n) scalable secret image sharing (SSIS) scheme, which can gradually reconstruct a secret image in a scalable manner in which the amount of secret information is proportional to the number of participants. However, Wang et al.’s scheme is only a simple 2-out-of-n case. In this paper, we consider (k, n)-SSIS schemes where a qualified set of participants consists of any k participants. We provide two approaches for a general construction for any k, 2 ? k ? n. For the special case k = 2, Approach 1 has the lesser shadow size than Wang et al.’s (2, n)-SSIS scheme, and Approach 2 is reduced to Wang et al.’s (2, n)-SSIS scheme. Although the authors claim that Wang et al.’s (2, n)-SSIS scheme can be easily extended to a general (k, n)-SISS scheme, actually the extension is not that easy as they claimed. For the completeness of describing the constructions and properties of a general (k, n)-SSIS scheme, both approaches are introduced in this paper.     

On Λ-type doubling in multiplet states of diatomic molecules

Explicit expressions valid in the neighborhood of Hund's case (a) and (b) are obtained for the width of Λ-type doubling of multiplet Π terms up to septet multiplicity. Moreover, a relation between the constants occurring in the expressions of Hund's cases (a) and (b) is given.     

Model calculation of the electronic structure and spectroscopy of Hg2

Energy curves and transition moments of the excited valence states of Hg₂ were obtained in a model calculation based on calculated Mg₂ energy levels and the assumption that the asymptotic spin-orbit matrix elements for the Hg atom are applicable to the molecular states. The spin-orbit and orbital-rotational interaction of the excited states of Hg₂ is analyzed in both a Hund's case (c) and (a) representation. The intermediate (a) → (c) transition moments are obtained as a function of the internuclear distance. The effect of the orbital-rotational interaction which introduces Hund's case (b) and (e) couplings is found to be small for transitions among excited states under the conditions normally encountered for populating excimer states.Using the energy level positions and transition moments, the observed spectra and predicted spectra are compared for both radiative transitions including the ground state and among the excited states. The lifetime of the $\text{1}{}_{\mathrm{u}}\text{(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ excimer state is calculated to be 1.4 μsec with the 335 nm band assigned to the $\text{1}{}_{\mathrm{u}}\text{→ X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition. The 485 nm bands cannot be assigned to any Hg₂ transitions. Strong bound-continuum absorptions are predicted for the 485 nm bands. On the other hand, the 335 nm emission is predicted to be absorbed by bound-bound transitions only.     

A reduced form of the spin-spin centrifugal distortion Hamiltonian for orthorhombic asymmetric top molecules

The spin-spin centrifugal distortion Hamiltonian for an asymmetric top molecule in a given vibrational level of an open-shell electronic state with S ? 1 may contain more parameters than can be determined from the observed energy levels. This paper describes the reduction of the Hamiltonian by means of a unitary transformation to a form suitable for fitting to observed energies. It is established that there are six determinable spin-spin centrifugal distortion parameters for a molecule of orthorhombic symmetry; the corresponding matrix elements are derived for both Hund’s case (a) and case (b) coupling schemes.     

On the determination of molecular parameters for NO

All available high precision measurements on the ground state of NO have been used simultaneously in a weighted least squares procedure to determine the molecular parameters. In the present work the theoretical values were computed according to a model referred to as Hund's case (c_α), since this model seems to combine simplicity and high accuracy. The agreement between theoretical and observed frequencies is excellent and better than in previous investigations, even with a lower number of molecular parameters. Term values for NO are also computed, and they should be useful for predicting unobserved transitions.     

Submillimeter-wave spectroscopy of VN (XΔr) and VO (XΣ): A study of the hyperfine interactions

The pure rotational spectra of VN (X³Δ_r) and VO (X⁴Σ⁻) have been recorded in the frequency range 290-520 GHz using direct absorption spectroscopy. These radicals were synthesized in the gas-phase from the reaction of VCl₄ with either N₂ or H₂O in an AC discharge. Seven rotational transitions were recorded for each molecule; in both sets of spectra, fine and hyperfine structures were resolved. The data sets for VN and VO were fit with Hund’s case (a) and case (b) Hamiltonians, respectively, and rotational, fine structure, and hyperfine constants determined. For VN, however, an additional hyperfine parameter, Δa, was necessary for the analysis of the Ω = 2 sublevel to account for perturbations from a nearby ¹Δ state, in addition to the usual Frosch and Foley constants. Determination of Δa suggests that the ¹Δ state lies ∼3000 cm⁻¹ above the ground state. In VO, the hyperfine structure in the F₂ and F₃ components was found to become heavily mixed due to an avoided crossing, predicted by previous optical studies to be near the N = 15 level. The hyperfine constants established for these two molecules are consistent with the proposed σ¹δ¹ and σ¹δ² electron configurations.     

The rotational analysis of the gamma system (A 3Φ - X′ 3Δ) of the spectrum of zirconium oxide

Rotational analyses of the (0,0), (1,1) and (2,2) bands, and a partial analysis of the (3,3) band, of the γ-system (A³Φ - X′³Δ) of the molecules ⁹⁰Zr¹⁶O, ⁹⁴Zr¹⁶O, ⁹⁶Zr¹⁶O have been performed. The measured wave numbers and their assignments are presented up to high quantum numbers. The rotational constants are calculated and an estimate is made of the spin-coupling coefficients. Both states belong closely to Hund's coupling case a.     

Rotational line strengths in the Lyman and Werner bands of H2

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)].     

The pure rotational spectrum of TiS (XΔr) at submillimeter wavelengths

The pure rotational spectrum of TiS in its X³Δ_r ground state has been measured using millimeter-wave direct-absorption techniques in the frequency range of 313-425 GHz. This free radical was created by the reaction of titanium vapor, produced in a high-temperature Broida-type oven, with H₂S. Eight to ten rotational transitions were recorded for the main titanium isotopologue, ⁴⁸TiS, in the v = 0 and v = 1 levels, as well as for the v = 0 state of ⁴⁶TiS, observed in natural abundance (⁴⁸Ti:⁴⁶Ti = 74:8). All three Ω components were observed in almost every recorded transition, with no evidence for lambda-doubling. The data were fit with a Hund’s case(a) Hamiltonian, and rotational, spin-orbit, and spin-spin constants were determined, as well as equilibrium parameters for ⁴⁸TiS. Relatively few fine structure parameters were needed for the analysis of TiS (A, A_D, and λ), unlike other 3d metal species. The rotational pattern of the three fine structure components suggests the presence of a nearby excited ¹Δ state, lying ∼3000 cm⁻¹ higher in energy. From the equilibrium parameters, the dissociation energy for TiS was estimated to be ∼5.1 eV, in reasonable agreement with past thermochemical data.     

Sn Mössbauer spectroscopy and specific heat studies of the stannides RETSn (RE=Gd-Er and T=Cu,Ag)

The stannides RETSn (RE=Gd-Er and T=Cu,Ag), NdPtSb type structure, space group P6₃mc, have been investigated by ¹¹⁹Sn Mössbauer spectroscopy and specific heat studies. Small transferred magnetic hyperfine fields are detected at the tin nuclei at 4.2 K in the ¹¹⁹Sn Mössbauer spectra of RECuSn (RE=Tb,Dy and Ho) which reveal that these compounds undergo magnetic transitions at low temperatures. Heat capacity (C) measurements show that the title compounds undergo antiferromagnetic ordering. In order to explore the magnetic behaviour below the Néel temperature (T_N), the magnetic part of heat capacity was obtained by subtracting the lattice part of heat capacity obtained from the isostructural non-magnetic stannides Y TSn (T=Cu,Ag). of GdCuSn exhibits an equal moment (EM) magnetic structure and also exhibits multiple transitions below T_N, revealing higher order exchange interactions. Among the REAgSn stannides, the magnetic part of heat capacity for RE=Dy and Er exhibits non-T³ behaviour at low temperatures.     

Calculation of T=2 → T=1 → T =0 M1 decays in A =20 and A =32 nuclei

Absolute strenghts and branching ratios are calculated for M1 transitions between states of different isospin in two A = 4n nuclei of the sd-shell.     

Infrared and near infrared emission spectra of TeH and TeD

The vibration-rotation emission spectra for the X²Π ground state and the near infrared emission spectra of the X²Π_1/2-X²Π_3/2 system of the TeH and TeD free radicals have been measured at high resolution using a Fourier transform spectrometer. TeH and TeD were generated in a tube furnace with a DC discharge of a flowing mixture of argon, hydrogen (or deuterium), and tellurium vapor. In the infrared region, for the X²Π_3/2 spin component we observed the 1-0, 2-1, and 3-2 vibrational bands for most of the eight isotopologues of TeH and the 1-0 and 2-1 bands for three isotopologues of TeD. For the X²Π_1/2-X²Π_3/2 transition, we observed the 0-0 and 1-1 bands for TeH and the 0-0, 1-1, and 2-2 bands for TeD. Except for a few lines, the tellurium isotopic shift was not resolved for the X²Π_1/2-X²Π_3/2 transitions of TeH and TeD. Local perturbations with Δv = 2 between the two spin components of the X²Π state of TeH were found: X²Π_1/2, v = 0 with X²Π_3/2, v = 2; X²Π_1/2, v = 1 with X²Π_3/2, v = 3. The new data were combined with the previous data from the literature and two kinds of fits (Hund’s case (a) and Hund’s case (c)) were carried out for each of the 10 observed isotopologues: ¹³⁰TeD, ¹²⁸TeD, ¹²⁶TeD, ¹³⁰TeH, ¹²⁸TeH, ¹²⁶TeH, ¹²⁵TeH, ¹²⁴TeH, ¹²³TeH, and ¹²²TeH.     

Λ-type doubling and term formulae for a 5Π state in the intermediate case between Hund's cases (a) and (b)

Explicit expressions valid for all values of Y intermediate between Hund's cases (a) and (b) are obtained for the multiplet term formula and for the width of the Λ-type doubling of a ⁵Π state.