Variation of electronic transition moment with the internuclear separation for the (AO+−X1Σ+) band system of PbO

Relative integrated intensities of the (AO⁺?X¹Σ⁺) band system of PbO have been measured by photographic photometry. These have been interpreted with the aid of Franck-Condon factors (q_υ′υ″) and r-centroids ($\text{r}{}_{\mathrm{\upsilon \prime \upsilon ″}}$) to show that the variation of electronic transition moment with internuclear separation is R_e(r)=const.(0.521r?1). Arrays are shown for the band strengths S_υ′υ″.     

SPIN GAINT RESONANCE AND CORE POLARIZATION EFFECTS

The effects of the coupling term between field（Y₀σ₁）_1v and r²（Y₂σ₁）_1v coming fromtensor operator are discussed for the spin gaint dipole resonance.The effects of inclu-ding the field r^λ+1(Y_λ+1σ₁)_λv on the spin gaint multipole resonance and core polariza-tion are considered.     

Photoionization and photoelectron angular distribution for H2

Photoionization of H₂(¹Σ_g⁺) in a vibrational υ″ and rotational N″ state into H₂⁺(²Σ_g⁺) in a vibrational υ′ and rotational N′ state is studied theoretically. The differential cross section, after summing over the final states, is expressed in the well-known simple form of $\text{(}\text{σ}{}_{\mathrm{T}}\text{4π}\text{)[1 + βP}{}_2\text{(}\text{cos}\text{θ)]}$. Parallel expressions are obtained for H₂⁺ in a specific υ′ state (in terms of σ(υ′) and β(υ′)) and for H₂⁺ in a rotational fine level υ′N′ (in terms of σ(υ′N′) and β(υ′N′)). Asymmetry parameters β, β(υ′) and β υ′N′), which are expressed in terms of Racah and Clebsch-Gordan coefficients and electronic transition moments, can be reduced approximately to 2 lineary polarized light and to -1 for unpolarized light. Using single-center electronic wave functions and including partial eaves l = 1, 3, and 5, σ(υ′) and β(υ′) are computed as a function of υ′ at 584 Å. The computed σ(υ′) divided by the Frank-Condon overlap, in agreement with experimental results, increases monotonically with υ′; σ_T and β are computed in the incident photon energy range of 600–4000 Å and the results compare favorably with previous calculations.     

Strong-coupling constant in coordinate space

The coordinate-space behavior of (vector) strong-coupling constant in the background field α_B(r) is compared with that in standard perturbation theory α_v(r). The numerically calculated two-loop coupling constant α_B(r) is shown to exceed α_v(r) by 1–5% at very small distances, r?0.02 fm, and to be in agreement with lattice measurements of the static potential. At large distances, α_B(r) approaches the freezing value at r?0.5 fm. An analytic form of α_B(r) is proposed that approximates α_B(r) with a precision ?2% in the region r?0.5 fm.     

Der Einflu\ einer Spin-Spinwechselwirkung auf das magnetische Moment schwerer Atomkerne

The corrections to the magnetic moments of heavy nuclei on account of a spindependent two-body-interaction of the form (σ ₁ σ ₂)V(r ₁–r ₂) are determined in the Fermi model calculating the second order contribution for the selfenergy part. It is shown using conservation laws that this contribution is connected to the local Vertex T ^ω [σ] of Migdal's theory of finite Fermi systems.     

Interplay of Curie-type and Pauli-type magnetic susceptibilities in HCl-doped polyaniline pellets

The static magnetic susceptibility (χ) of own-made HCl-doped polyaniline pellets is investigated experimentally over the full range of the protonation level Y and in the temperature (T) range 10–300 K.The obtained results suggest that χ and the electrical conductivity σ – which is known from previous work – are interrelated.Namely, there is a weakly Y dependent crossover temperature T ^* where both χ and σ undergo notable changes.In χ, this refers to a simultaneous enhancement (reduction) of the Pauli-type susceptibility χ _P and reduction (enhancement) of the Curie constant C at T = T ^* when T increases (decreases).Below T < T ^*, where thermal effects are weak to moderate, a steep increase of χ _P(Y) around Y = 0.3 occurs together with a drop of C(Y).The above findings are consistent with a picture in which, at T ^*, spins that disappear from C reappear in χ _P, and vice versa.This model is used to address the longitudinal and transversal electron localisation lengths as functions of Y, the former being estimated to take values in the range 7–8 Åand the latter in the range 1–2 Å.     

Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

A potential hydroxyl ultraviolet laser

A strong emission band extending from 3060 to 3120 Å was observed following proton beam excitation of an Ar-H₂O mixture. This emission band was assigned to the transition of OH(A²Σ⁺)_υ=0 → OH(X²Π)_υ=0. At high argon partial pressure (> 200 torr), the precursor of this emission band is believed to be the argon excimer Ar^★₂(1_u). The fluorescence efficiency of Ar-H₂O is estimated to be a factor of 4 times that of Ar-N₂. Development of a highly efficient, tunable uv laser by e-beam pumping is promising.     

Absolute Position of the D′2g(P2) Ion-Pair State of I2 Determined by Perturbation-Facilitated Optical-Optical Double Resonance

We have reexamined the sequential two-photon absorption of I₂ from the X¹Σ_g⁺ ground state to the lowest D′2_g(³P₂) ion-pair state using the high vibrational level of the B³Π(0_u⁺) state as an intermediate. The double resonance transition to the D′2_g(³P₂) state was found to occur through the B³Π(0_u⁺)-b′2_u coupled state by hyperfine interaction, which permits to mix the different J levels of different electronic states. We elucidated the B³Π(0_u⁺)-b′2_u coupling schemes in the intermediate states. The double resonance spectra recorded for the D′2_g(³P₂) state in the range v=0-30 were used to determine the absolute energy of the D′2_g(³P₂) state. The molecular parameters of the D′2_g(³P₂) state obtained in this study are Y₀₀=40 388.783(2), Y₁₀=103.956 46(57), Y₂₀=−0.207 717(51), Y₃₀=2.199(13)×10⁻⁴, Y₀₁=0.020 528 18(62), and Y₁₁=−5.1753(48)×10⁻⁵ (all in cm⁻¹ and σ in parentheses). An RKR potential curve constructed using these constants is reported. Combined with the data on the D′2_g(³P₂)-A′³Π(2_u) transition from Zheng et al. (J. Chem. Phys.96, 4877 (1992)), we can locate the A′³Π(2_u) v=0 state at 10 096.444(6) cm⁻¹ above the ground state.     

Theoretical investigation of optical spectra and covalent effect of Cr in Y2Ti2O7 and Y2Sn2O7

In this work, the complete matrix of optical spectral levels in trigonal symmetry of 3d² (3d⁸) ions are established on basis of strong field coupling mechanism by using two spin–orbit coupling parameters model. The contribution of the spin–orbit coupling of ligand to the optical spectra has been included in these formulas. As an application, the optical spectra of Cr⁴⁺ in Y₂Ti₂O₇ and Y₂Sn₂O₇ have been studied by the complete diagonalization (energy matrix) method. The covalent effect has been studied and the difficulty about Dq parameter in explanation of optical spectra of Cr-doped Y₂Ti₂O₇ and Y₂Sn₂O₇ is removed. The theoretical results are in good agreement with observed data.     

The use of electron impact dissociation and the photon-photon cascade technique to measure the lifetime of the B2Σ+ state of CN

The lifetime of the (B³Σ⁺_{υ= 0, 1} state of the CN radical has been measured by the photon-photon delayed coincidence technique, the CN radical being produced by electron impact dissociation of acetonitrile. This is the first lifetime measurement in a free radical by this method. The optical cascade in the band spectrum of CN used for the present measurement is H²Π_r - B²Σ⁺ - X²Σ⁺. The lifetime of the (B²Σ⁺)_{υ=0, 1} state in CN has been found to be 61.1 ± 7.6 ns.     

A spectroscopic study of the D(0u+) ion-pair state of Br2 by the optical-optical double-resonance technique

An optical-optical double-resonance technique has been applied to study the D(0_u⁺) ion-pair state of Br₂ in a one-photon resonant three-photon absorption. The OODR transition proceeds through the high vibrational level of the B³Π(0_u⁺) state, which compromises a large Franck-Condon shift required for the excitation of Br₂ from the X¹Σ_g⁺ state to the D(0_u⁺) state. Dunham parameters of the D(0_u⁺) state, based on a global least-squares fit of 407 transitions (v′ = 0–16, J′ = 17–115), are Y₀₀ = 49928.443(41), Y₁₀ = 134.467(19), Y₂₀ = ?8.71(27) × 10^?2, Y₃₀ = ?3.36(10) × 10^?3, Y₀₁ = 4.2382(15) × 10^?2, Y₁₁ = ?1.061(36) × 10^?4, Y₂₁ = ?2.00(27) × 10^?6, and Y₀₂ = ?1.93(11) × 10^?8 for ⁷⁹Br₂ (all in cm^?1, and 3σ in parentheses). The single rovibronic fluorescence spectrum of the D(0_u⁺) state shows a transition terminating on the X¹Σ_g⁺ ground state, and establishes the absolute v′ numbering on the basis of the Franck-Condon factor calculations. The v′ = 2 and 3 levels of the D(0_u⁺) state are strongly perturbed due to the heterogeneous interaction with the 1_u state correlating with the same ionic products of the D(0_u⁺) state at the dissociation limit, $\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{)}$.     

The Electronic Transition Moment Function for the BΠ-XΔ System of TiO

Several vibronic bands associated with v′=0, 1, and 2 for the B³Π-X³Δ transition of TiO have been observed using a dispersed laser induced fluorescence (DLIF) technique. From intensity distributions of the DLIF spectra, the dependence of the electronic transition moment R_e(r) for the B³Π-X³Δ system was determined as a function of the internuclear distance r. For the determination of the R_e(r) function, a merged fit of the observed distributions, the reported radiative lifetimes of three vibrational levels in the B³Π state, and the reported value of R_e(r) for the (0, 0) band were performed; R_e(r) was determined as R_e(r)=1.3723(79)[1−0.316(81)(r−r₀)+2.0(10)(r−r₀)²](r₀=1.6648 Å and 1.5131 Å≤r≤1.8636 Å). The r-dependence of R_e(r) was much smaller than the reported theoretical predictions. The obtained values of R_e(r) were analyzed simultaneously with the hyperfine coupling constants for the X³Δ state and the spin-orbit constants for the X³Δ and B³Π states to assess the ionic and orbital characters. It was found that the r-dependence of R_e(r) could be accounted for by both the configuration interaction in the B³Π state and the polarization in the unpaired 9σ and 4π orbitals.     

Polarization spectroscopy of the E0g+-B0u+ band system of Br2

The E-B (0_g⁺-0_u⁺) band system of Br₂ has been investigated at Doppler-limited resolution using polarization labeling spectroscopy. Merged E state data for the three naturally occurring isotopes in the range v_E = 0–16, expressed in terms of the constants for ⁷⁹Br₂, are (in cm^?1) Y_0,0 = 49 777.962(54), Y_1,0 = 150.834(22), Y_2,0 = ?0.4182(28), Y_3,0 = 6.6(11) × 10^?4, Y_0,1 = 4.1876(28) × 10^?2, Y_1,1 = ?1.607(16) × 10^?4, and Y_0,2 = 1.39(39) × 10^?8. The bond distance is $\text{r}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.194}\text{A}\text{?}$, and the diabatic dissociation energy to $\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{) +}\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{)}\text{is 34 700 cm}{}^{\mathrm{?1}}$.     

L ∞ estimates for the space-homogeneous Boltzmann equation

This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf ₀ ? 0 with (1 + ¦υ¦²)φ₀ εL ¹ and (1 + ¦υ¦)^s f ₀ε L^∞ for somes > 2, then (1 + ¦υ¦^s'f _tεL ^∞ fort>0 and ess_υ,t sup(1 + ¦υ¦)^s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5.     

Axial-field-dependent circular susceptibility in Fe-rich amorphous wires

The longitudinal magnetic field dependence of low-frequency circular susceptibility, χ(H), is measured for (Fe_1−xCr_x)_77.5Si_7.5B₁₅ (x=0,0.05,0.1, and 0.15) amorphous wires of radius r₀=0.07 mm. In order to explain the experimental results, on the basis of the widely accepted core–shell model, we consider that there are a constant axial anisotropy K_c in the core and a radius-dependent radial anisotropy K_s∝r⁸/r₀⁸ in the shell, both K_c and K_s being functions of stress-energy constant λ_sσ₀. A formula for χ(H) is derived from this model. The experimental data fits indicate that the magnetic structure can be well described by the improved core–shell model with reasonable values of λ_s.     

Bestimmung von Moleküleigenschaften des Tl205F19 aus kombinierten Stark-Zeeman-Effekt-Messungen mit der Molekularstrahlmethode

An electric Molecular-Beam-Resonance-Spectrometer has been used to measure simultanously the Zeeman- and Starkeffect splitting of the hyperfinestructure of TlF. Electric fourpole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman-Field) was superimposed to the electric field (Stark-Field) in the transition region of the apparatus. The observedΔm _J =±1 -transitions were induced electrically. Completely resolved spectra of Tl²⁰⁵F¹⁹ in theJ=1 rotational, andυ=0 vibrational state have been measured. The obtained quantities are: The rotational magnetic momentμ _J of Tl²⁰⁵F¹⁹ in the stateJ=1,υ=0, and the difference of the magnetic shielding (σ _1,±1?σ _1,0) of both nuclei as well as the difference of the molecular susceptibility (ξ _1,±1?ξ _1,0) in the states (J, m _J)=(1,±1) and (J, m_J)=(1, 0). The sign of the rotational magnetic moment could be determined unambigously by the influence of offdiagonal matrix elements. The numerical values for Tl²⁰⁵F¹⁹ in the stateJ=1 andυ=0 are:μ _J =?29,153(21) · 10^?6 μ _Bohr (σ _1,±1?σ _1,0)^Tl=?0,002291 (33) (σ _1,±1?σ _1,0)^F=?0,000206(9) (ξ _1,±1-ξ _1,0)=+3,02(15) · 10^?30erg/Gauß² The quantities in brackets are root-mean-square deviations in units of the last digit. From these data and the known values for the spin-rotational interaction constants a number of expressions are derived which characterise the electronic charge distribution in the molecule.     

αS(KT2) versus αS(K2) in QCD jet development: Some quantitative remarks

Properties of QCD jets for two proposed choices of the variable appearing in the QCD running coupling constant, α_S(K²) or α_S(K_T²) with K_T²=z(1?z)K², have been studied in detail by the use of Monte Carlo techniques. Contrary to expectations based on approximate analytic calculations it is found that when substituting K² with K_T² in α_S the growth with energy of the multiplicity of the quanta is not sensibly altered, and it is even slowed down for extreme values of the non-perturbative cutoff, which delimits the minimum virtual mass of the quanta. It appears, therefore, that the analysis of subleading effects may be totally misleading if phase-space constraints are not taken into account exactly, which is possible to do in Monte Carlo calculations.     

Oscillator strengths from line absorption in a high-temperature furnace—II. The (0,0) band of the B2σ+—X2σ+ transition in CN*

Quantitative high-resolution absorption spectroscopy was applied to the (0,0) violet band of CN. The CN radical was prepared in a furnace at 1421°K containing pure cyanogen gas. Since the calculated CN concentration is dependent on the controversial CN heat of formation, only the relationship, f_υ = 6·84 X 10^-3exp (0·354δ), where f_υ is the excess over the initially assumed ΔH⁰_f(CN) = 100·8 kcal/mole, could be directly determined in this study with an estimated error in f_υ of ±20%. For δ = 0, our f_υ is a factor of 4·8 smaller than an average value of 0·033±0· derived from other measurements. If this latter value of f_υ is assumed, our relationship yields ΔH⁰_f(CN) = 105·3±1· kcal/mole or D₀(CN) = 7·66±0·05 eV. The rotational temperature and line widths for this band were also measured.