First- and second-order Coriolis interactions in symmetric top molecules: Application to the microwave spectrum of cyclopentadienyl thallium

Matrix elements are derived for both first- and second-order Coriolis interactions between A₁ and E₁ vibrational modes in symmetric tops, with particular reference to sign. The results are applied to the observed microwave transitions J → J + 1 for A₁ and E₁ states of the C_5ν molecule cyclopentadienyl thallium in various excited vibrational states. The microwave transitions in the excited A₁ states v₄ = 1, 2, 3, the excited E′ state v′₀ = 1 and the combination state v₄ = 1, v′₀ = 1 have yielded constants which are anomalous in several respects (1). Coriolis interactions between the ν₄ and ν₁₀ vibrations are shown to account for the observed anomalies.     

Relativistic calculation of atomic X-ray transition rates

The fully relativistic transition probabilities in atomic X-ray emission are calculated for a wide range of selected elements of the periodic table, fromZ=21 toZ=93. The treatment includes the effect of the retardation of the radiation field. The atomic model used is the self-consistent relativistic Hartree-Fock, with the Slater approximation for the exchange term. The formulas for EL and ML multipole transition rates are derived, and transition rates are calculated for all transitions to theK-shell,L-subshells, andM-subshells. The contributions of all multipoles, as determined by the angular momentum and parity selection rules, are included in the present work. The calculated values of (Kα ₂/Kα ₁), (Kβ ₁/Kα ₁), (Kβ ₃/Kβ ₁) and (Kβ ₂ Kβ ₁) transition rates are in good agreement with the available experimental data. Rates for the forbidden (M1) 2s _1/2→1s _1/2 transitions are also presented.     

Dipole γ-ray transition rates in 238U

M1 and E1 transition rates from the ground to excited states and between excited states in ²³⁸U are calculated within the quasiparticle-phonon nuclear model with the wave functions consisting of one- and two-phonon terms. We show that there are relatively large M1 transitions between 2⁺ states in the low-energy region. The fragmentation of the one-phonon states strongly affects M1 and E1 strength distributions. The correlation takes place between E1 and E3 transition strengths. We show that there are fast E1 and M1 transitions between large components of the wave functions differing by an octupole or quadrupole phonon.     

Accurate calculations of the 18 Λ-S states and 50 Ω states of PO+ cation: potential energy curves and spectroscopic parameters including the spin-orbit coupling effect

The potential energy curves (PECs) of 5 Ω states generated from the 18 Λ-S states (X ¹ Σ ⁺, A¹Σ^?, 1¹ Δ, 1¹ Π, 2¹Σ⁺, 2¹ Π, a ³ Σ ⁺, 1³ Δ, 1³ Π, 1³Σ^?, 2³Σ⁺, 2³ Π, 1⁵Σ⁺, 1⁵ Π 2⁵ Π, 1⁵Σ^?, 2⁵Σ⁺ and 1⁵ Δ) of PO⁺ cation are studied for the first time for internuclear separations from about 0.08 to 1.0 nm. Of these Λ-S states, only the 2⁵Σ⁺ and 1⁵ Δ are the replusive ones. The a ³ Σ ⁺, 2³Σ⁺, 1⁵Σ^?, 2³ Π, 1³ Δ, 2⁵Σ⁺ , and 1⁵ Δ are the inverted states with the spin-orbit coupling effect included. The 1¹ Π, 1³ Π, 1⁵ Π and 2³ Π states possess the double well. The 1⁵Σ^?, 2¹ Π and 2⁵ Π states and the second wells of 1¹ Π, 1³ Π, 2³ Π and 1⁵ Π states are the rather weakly bound states. The PEC calculations are performed by the CASSCF method, which is followed by the icMRCI approach with Davidson correction in combination with the aug-cc-pV6Z basis set. Core-valence correlation and scalar relativistic corrections are included at the same time. The spin-orbit coupling effect is accounted for. All the PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated for all the Λ-S and Ω bound states, and compared with the measurements and other theoretical results. Fair agreement is found between the present spectroscopic parameters and the measurements. The vibrational properties are evaluated for the weakly bound states. The effect of spin-orbit coupling on the spectroscopic parameters is discussed. The results reported in this paper can be expected to be reliable predicted ones.     

S1 ← S0 laser excitation spectra of glyoxal in a supersonic jet: Vibrational analysis

The vibrational analysis of the S₁ ← S₀ spectra from 465 to 415 nm leads to the location of 49 S₁ vibrational levels between 0 and 2000 cm⁻¹ of vibrational excitation in S₁. The origins of bands are determined after rotational analysis within 0.01 cm⁻¹. Their assignments are deduced from the analysis of the dispersed fluorescence emitted by these levels. The fundamental energies of modes 3, 10, and 11 are determined. Normal mode constants are obtained: 5 ω_i⁰ values and 21 χ_ij values (5 χ_ii and 16 cross anharmonicities χ_ij). Fermi resonance between the 4¹ and the 6¹7¹ levels is observed and deperturbed.     

Extension of the rotational analysis of the 1Π-X1Σ+ system of AsN

Rotational analysis of bands with v′ = 0 through 3, in the ¹Π-X¹Σ⁺ system as the AsN molecule, has been carried out. Rotational constants for the X¹Σ⁺ state are: B_e = 0.54551 cm^?1, α_e = 0.003366 cm^?1 and D_e = 5.3 × 10^?7cm^?1. Strong perturbations are observed in the upper levels and the resulting B_v curves are plotted against J.     

Many-body atomic potentials in Thomas-Fermi theory

Many-body atomic potentials, ?, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ?(1, 2) ≡ E(1, 2) ? E(1) ? E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (?1)ⁿ for all coordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ?'s, when truncated at the n-body terms, has the sign (?1)ⁿ⁺¹.     

Quantum electrodynamic calculation of interelectron interaction for He-like and Li-like multiply charged ions

Exact quantum-electrodynamic calculations of the interelectron interaction corrections are performed for the 1s _1/22s _1/2 ¹ S ₀, 1s _1/22p _1/2 ³ P ₀, and 1s _1/22s _1/2 ³ S ₁ configurations in He-like ions and for the (1s _1/2)²2s _1/2 and (1s _1/2)²2p _1/2 configurations in Li-like ions for all charges of nuclei 10≤Z≤92. The calculations are performed in the Coulomb calibration. The Coulomb-Coulomb and the Coulomb-Breit parts are calculated exactly, and the Breit-Breit part of the correction is calculated by neglecting the retardation. The calculations are the most exact of those available by now.     

Decay of 120Sb

Single γ spectra and K _X coincidence spectra from ¹²⁰Sb decay are measured. The total internal conversion coefficients (ICCs) and those on the K-shell are determined for slowed E1 and E2 transitions in ¹²⁰Sn. Penetration effects are observed for which the penetration parameters are found to be λ₁ (89.9 keV, E1) = 3.6 ± 1.6 and λ₁ (197.3 keV, E2) = 6 ± 2.     

Quantum algebra U q(2, 1): q analogs of the Gelfand-Graev formulas

The discrete series of unitary irreducible representations of the noncompact quantum algebra U _q(2, 1) are studied. For the negative discrete series, two bases of these irreps are considered. One of them corresponds to the reduction U _q(2, 1) → U _q(2)×U(1). The second basis is connected with the reduction U _q(2, 1) → U(1)×U _q(1, 1). The matrix elements of the U _q(2, 1) generators in both bases are calculated. For the intermediate discrete series, only first type of basis is considered and the q analogs of the Gelfand-Graev formulas are obtained. Also, the transformation brackets connecting the two bases are found for the negative discrete series.     

Solution of functional equations of restricted An−1(1) fused lattice models

Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted A_n−1⁽¹⁾ lattice models of Jimbo, Miwa and Okado. Specifically, these equations are solved analytically for the finite-size scaling spectra, central charges and some conformal weights. The results are obtained in terms of Rogers dilogarithm and correspond to coset conformal field theories based on the affine Lie algebra A_n−1⁽¹⁾ with GKO pair A_n−1⁽¹⁾ ⊕ A_n−1⁽¹⁾ ⊃ A_n−1⁽¹⁾.     

On representations of the groups Sp(n, 1) and Sp(n)

New classes of unitary irreducible representations of Sp(n, 1) which can be useful for applications in physics are obtained. The infinitesimal operators of these representations of Sp(n, 1) and of irreducible representations of Sp(n+1) with highest weights (m, m, m₃,…,m_n+1) and (m₁, m₂, 0,…,0) are expressed in terms of the simple Clebsch–Gordancoefficients for Sp(n). For Sp(3) and Sp(2, 1) they are found in an explicit form.     

Tentatively identified and predicted H- Fano resonances

Positions are calculated for the Fano resonances that are due to interactions of the discrete autoionized 1s3s, 1s3p, and 1s4p states of H^- with overlapping split-configuration continua. The two first-mentioned resonances are tentatively identified with the diffuse interstellar doublets at λλ6376,6379 and λλ5780, 5797 on the basis of the relative positions of the autoionized states and the relative intensities of the doublet components.The observed wave-numbers of the 1s2s, 1s3s, 1s2p, and 1s3p resonances seem to belong to two series that converge towards a common limit in a kind of reverse Rydberg-series fashion. The position of the limit is close to 9000 Å, in accordance with theory. An extrapolation leads to the identification of the 1s4p resonance with the diffuse λ 6614 line. A further extrapolation leads to the prediction of positions at about 7183 and 7583 Å for the 1s5p and 1s6p resonances.The half-widths calculated for the singlet components of the 1s3p and 1s4p resonances are of the order of magnetude of those observed for the diffuse lines, and of the observed distance between the probably partly mixed singlet and triplet 1s3p components. The profile of the λ 5780 resonance is calculated on the basis of an assumed helium-line value for the oscillator strength. Its shape indicates that the “λ 5778 band” may be just a misinterpretation of the asymmetric wings.Tables of Hartree functions for the 3s², 3p² and 4p² configurations of H^- are given in an appendix.     

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyB _n are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. Thek _E1- andk _M1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofk _E1 are 1.5–2 times larger and the values ofk _M1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.     

Infrared-microwave double resonance in CH3OH using a Zeeman-tuned 3.5-μm HeXe laser

Infrared microwave double resonance signals have been observed for CH₃OH using the 3.5-μm HeXe laser line. When microwave transitions in the ground vibrational state are pumped, the double resonance signals are obtained on two infrared transitions v = 1 ← 0 of ν^CH(a′); v = 1, J, K, μ = 4, 2, 1 ← v = 0, J, K, μ = 3, 2, 1, and 4, 3, 1 ← 3, 3, 1. Three weak double resonance signals are due to the collision-induced transitions. Their relative intensities have been explained successfully by using the rate constants of collision-induced transitions which are proportional to the dipole matrix elements between the states involved in the transitions.     

Semi-simple real subalgebras of non-compact semi-simple real Lie algebras IV

The investigation of the problem of embedding a semi-simple real Lie algebra $\text{L}$′ in a non-compact semi-simple real Lie algebra $\text{L}$ is extended to the case in which at least one of the real Lie algebras has a semi-simple complex extension, which consists of the direct sum of two simple complex Lie algebras. Detailed procedures are given, which together with those given previously, allow the construction of all embeddings of $\text{L}$′ in $\text{L}$ when their complex extensions are A₁, B₁, C₁, D₁ or a direct sum of any two of these. The procedures are illustrated by considering examples corresponding to complex Lie algebra embeddings A₁?(A₂⊕A₂), (A₁⊕A₁)?(A₂⊕A₂), (A₁⊕A₁)?A₃, (A₁⊕A₁)??(A₃⊕A₃) and (A₁⊕A₁)?(A₃⊕A₂). Because of its physical significanc embeddings of SL(2,C) in simple and semi-simple real Lie algebras are studied in detail.     

Reactions of excited atoms and molecules with atoms and molecules

From a He-beam excited by electron impact we eliminated the He(2¹ S) component to better than 0.5% by irradiating light from a He discharge. The quenching process ishv(2¹ P→2¹ S)+He(2¹ S)→He(2¹ P)→He(1¹ S +hv) (2¹ P 1)¹ S. By measuring the ions produced in collisions of the He-metastables with various target gases in a mass spectrometer, singlet to triplet Penning-cross section ratios were obtained. These ratios are without exception close to one, which is taken as evidence for the previously proposed electron exchange mechanism of the Penning ionization. In the case that more ions are produced in the collision of He (2¹ S) and He(2³ S) with a target gas, separate relative production cross sections are obtained for the two metastables. For the rare gases the measurements are performed at two temperatures of the He-beam, 320 and 90 °K. It is found that the cross section ratio of associative — to Penning ionization increases considerably as the temperature is decreased for both, He(2¹ S) and He(2³ S), the effect being much more pronounced for He(2¹ S). The results of this work are found to confirm conclusions drawn from measured energy distributions of the electrons ejected in the Penning process.     

Oscillator strengths for the 2s2, 2p2, 2s3s(1S)-2s2p(1P) transitions of B(II)

Accurate configuration interaction wavefunctions for the 2s²(¹S), 2p²(¹S), 2s3s(¹S) and 2s2p (¹P) states of B(II) are calculated in a single optimized orbital basis of 7s, 6p and 4d Slater-type orbitals. 95, 84, 57 and 90% of the correlation energies, respectively, are realized by these wavefunctions. Oscillator strengths for the three ¹S-¹P transitions are calculated from these and from less accurate wavefunctions in the same orbital basis. The length values obtained from our most accurate wavefunctions, in order of increasing ¹S energy, are 0.9885, 0.202 and 0.007. The degree of accuracy of these oscillator strengths is estimated by noting the convergence to final values as increasing percentages of correlation energies are included in the wavefunctions together with the increasing agreement between length and velocity formulas. The exact theoretical oscillator strength for the resonant line is projected to be 0.985 with an error almost certainly not greater than ±0.015. The theoretical oscillator strengths for the other lines are considered to be 0.21±0.02 and less than 0.007, respectively.     

Lasing conditions in recombining helium plasmas

Lasing conditions for He have been evaluated numerically. We have used a collisional radiative model to calculate overpopulation densities Δn_ij, which are defined as differences between population densities per unit statistical weight of the upper and lower excited levels i and j, respectively. Laser oscillations for the level pairs 2¹P-3¹S, 2¹P-4¹S, 2¹P-3¹D, 2¹P-4¹D, 3¹D-4¹F, 3¹P-4¹S, 3¹P-4¹D, and 3³P-4³S are possible when the electron densities are within well defined limits at low electron temperature (T_e = 0.1 eV). For level pairs of the singlet state, the inversion mechanism for He is the same as for H. Only collisional processes produce population inversion in the triplet level pair 3³P-4³S.