On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Laser absorption spectroscopy of the A1Σu+-X1Σg+(v′, v″) bands of Na2

Laser absorption spectra of the band system A¹Σ_u⁺-X¹Σ_g⁺(v′,v″) of Na₂ in the range between 16835 and 16960 cm^?1 are analyzed. The spectra are free of first-order-Doppler broadening at low internal temperature. Rotational and vibrational assignments of 10 bands are reported. Rotational and vibrational levels, especially the (22, 1) band, are found to be perturbed by the b³Π_u state. The band origins and line frequencies calculated from previously reported constants do not reproduce the observed values. The disagreement between the calculated and observed values is discussed. More accurate constants are needed to predict the line locations.     

Far-infrared LMR spectroscopy of NF a1Δ (v = 0, 1, 2)

Far-infrared LMR spectra of NF in its a¹Δ state have been detected and assigned. Lines in two rotational transitions of both v = 0 and v = 1 states were measured for analysis. The derived constants are in excellent agreement with earlier EPR work (hyperfine parameters, v = 0) and with diode laser spectroscopy (rotational constants for v = 0 and 1). Using the optimized parameters it is shown that there is a significant decrease in the fluorine hyperfine constant on vibrational excitation. One rotational transition from $\text{v = 2}\text{NF}{}^1\text{Δ}$ has also been assigned.     

Coincidence electroproduction of single neutral pions in the resonance region at q2 = 0.5 (GeV/c)2

Data are presented for the reaction ep → epπ⁰ at a nominal four-momentum transfer squared of 0.5 (GeV/c)². The data were obtained using an extracted electron beam from NINA and two magnetic spectrometers for coincidence detection of the electron and proton. Details are given of the experimental method and the results are given for isobar masses in the range 1.19 – 1.73 GeV/c².     

High-resolution photofragment spectroscopy of the O2+b4Σg− (v′ = 3, 4, 5) ← a4Πu (v′ = 3, 4, 5) First Negative system using coaxial dye-laser and velocity-tuned ion beams

A new photofragment spectrometer employing coaxial tunable single-mode laser and velocity-tuned fast-ion beams has been used to measure transition energies in the O₂⁺b⁴Σ_g^? ← a⁴Π_u First Negative system to an accuracy and precision that are an order of magnitude better than was previously possible in Doppler-limited emission spectroscopy. The technique consists of velocity-tuning a beam of metastable O₂⁺a⁴Π_u ions such that a set of First Negative rotational transitions can be sequentially brought into resonance with the laser wavelength. The subsequent absorption transitions promote the ions to predissociating levels of the b⁴Σ_g^? state and observation of the O⁺ photofragments is the signal that denotes that each absorption transition has occurred. Repetition of the velocity tuning at different dye-laser frequencies provides a scan of the First Negative spectrum for predissociating upper-state vibrational levels, which are inaccessible to emission spectroscopy. The O⁺ photofragment ions have a kinetic energy that depends on the height of the predissociating rotational level above the separatedatom limit. The present apparatus incorporates a photofragment energy analyzer that can often be used to separately record the wavenumbers of transitions to different upper-state rotational levels, but whose wavenumbers could not otherwise be resolved. A set of 359 wavenumbers involving the (4,4), (4,5), (5,5), and (3,3) bands were recorded with an estimated accuracy of ±0.0032 cm^?1 and a precision of 0.0028 cm^?1, the latter being estimated precisely with a statistical technique. These data were fitted to ⁴Σ and ⁴Π Hamiltonians used in recent studies of the First Negative emission spectrum to determine molecular constants for the v′ = 4, 5 and v″ = 4, 5 levels. The former represent an extension of the b⁴Σ_g^? state to new levels and the latter represent substantial improvements over the constants that were available from previous moderate-resolution emission studies. These photofragment molecular constants were merged with those from the previous emission studies to yield a new consistent set of molecular constants and Dunham coefficients for the O₂⁺b⁴Σ_g^? and a⁴Π_u states. In the fit to the photofragment bands, it was found that the Hamiltonians, which were sufficient for the emission data, are inadequate to describe these states within the precision of the present measurements.     

Quenching cross sections of the B3Π+(Ou+) v′ = 14 level of I2 by H2, CO,and CH4

In this work the deexcitation of the B³Π⁺(O_u⁺), v′ = 14 level of I₂ after pulsed laser excitation has been studied. The quenching cross sections by collisions with I₂, H₂, CO, and CH₄ have been measured. The experimental results are 190 ± 14, 2.5 ± 0.3, 15.1 ± 0.4, and 18.0 ± 0.6 Ų, respectively. These values are compatible (within 30%) with the semiempirical scaling law of proportionality with the product of polarizability and the square root of reduced mass.     

Electroproduction of π0 mesons in the resonance region at q2=1.0 (GeV/c)2

Data are presented for the reaction ep → epπ⁰ at a nominal momentum transfer squared of 1.0 (GeV/c)². The data were obtained using an extracted electron beam from NINA and two magnetic spectrometers for coincidence detection of the electron and proton. Differential cross sections have been measured for isobar masses in the range 1.19–1.73 GeV/c².     

Vibrational population densities of the A3Σu+, B3Πg, W3Δu, B'3Σu-, and C3Πu states in nitrogen plasmas

Population densities of vibrational levels of triplet excited states have been calculated using a collisional-radiative model applicable to nitrogen gas discharges with a Maxwellian electron energy distribution. Relative contributions of various electron impact and radiative processes, including intrasystem cascade, to the total cross sections of the triplet excited states are investigated.     

Laser transitions among the C1Πu, 31Σg+, A1Σu+, and X1Σg+ states of Na2

Intense infrared stimulated lines at wavelengths around 2.5 μm have been observed upon excitation of Na₂ by uv radiation from a frequency-doubled narrow-band dye laser. Frequencies of these IR lines have been measured when the pump laser was tuned to C¹Π_u ← X¹Σ_g⁺ assigned transitions in the wavelength range 331–334 nm. High-resolution spectroscopy measurements of the involved rovibrational levels of both C¹Π_u and 3¹Σ_g⁺ electronic states allow the unambiguous assignment of these IR laser lines to C¹Π_u → 3¹Σ_g⁺ transitions.     

Laser magnetic resonance for the v = 1 ← 0 transition of SeO (X3Σ−) by a CO2 laser

The vibration-rotation transitions for a fundamental band of SeO (X³Σ^?) were studied by means of the infrared laser magnetic resonance (LMR) method employing a CO₂ laser. The LMR spectra arising from five SeO isotopic species except ⁷⁴SeO were detected and analyzed. Band origins for these species were determined. Molecular parameters ω_e, ω_eχ_e, B_e, and α_e, were obtained with the aid of the reduced mass relations. For ⁷⁷SeO the axial component of magnetic hyperfine interaction was obtained.     

The Hg2 (A3Ou− → X1Σg+) and (A31u → X1Σg+) fluorescence

The fine structure emission sepctrum near 5500 Å attributed to the Hg₂ (A³O_u^? → X¹Σ_g⁺) transition is shown to be strikingly similar to the HgCl (B²Σ⁺ → X²Σ⁺) emission spectrum sensitized by Hg(6³P_o) metastables. The correct Hg₂ (A³O_u^? → X¹Σ_g⁺) emission spectrum at 4850 Å was re-examined and confirmed to be a continuous one. It is suggested that the fine structure arose from the sensitization of a chlorine containing impurity.     

Molecular constants for the I1Πg and J1Δg states of the 3d complex in H2, HD,and D2

The experimental rovibronic energies of the 3dπI¹Π_g^? and 3dδJ¹Δ_g^? states of H₂ and D₂ (v = 0–4 and N = 1–11) have been fitted by rovibronic constants, including L-uncoupling through constants B_v^ΠΔ and D_v^ΠΔ. Comparison of the constants obtained for H₂ and D₂ yields information on the Born-Oppenheimer and adiabatic electronic energies T_e^BO and T_e^AD, and on the diagonal corrections for nuclear motion. T_e^BO derived from experiment for the I¹Π_g state lies 2 cm^?1 below the ab initio calculation of Ko?os and Rychlewski (J. Mol. Spectrosc., 66, 428–440 (1977). The nuclear mass dependence of the ω_e and B_e values in H₂ and D₂ deviates from simple isotope relationships but agrees with expectations based on the R-dependence of the diagonal corrections for nuclear motion through the term $\text{〈L}{}^2\text{?2}\text{Λ}{}^2\text{〉}\text{2μR}{}^2$, i.e., $\text{+2}\text{μR}{}^2$ for 3dπ and $\text{?1}\text{μR}{}^2$ for 3dδ.     

High-resolution Fourier spectrometry of 14N2 and 15N2 infrared emission spectrum: Extensive analysis of the W3Δu - B3Πg system

The infrared spectrum of the nitrogen molecule, excited in a microwave discharge, has been recorded in high resolution by Fourier spectrometry in the range 2500–15 000 cm^?1. The precision of the measurements is estimated to be about 0.003 cm^?1. We have analyzed 19 bands of the W³Δ_u-B³Π_g system of ¹⁴N₂, with 0 ≤ v′ ≤ 7, and three bands of ¹⁵N₂ lying between 2500 and 5900 cm^?1. The molecular constants of the ³Δ_u and B³Π_g states have been determined by direct approach using an iterative nonlinear least-squares procedure. It has proved convenient to describe the levels of W³Δ_u state in a case a basis although in fact they approximate those of Hund's case b. Derived values of equilibrium constants of W³Δ_u are, in cm^?1: T_e = 8875.3347 (with origin taken in A, ³Σ_u⁺v = 0 level); ω_e = 1506.4859; ω_eχ_e = 12.5469; B_e = 1.4702537; α_B = 0.0170389; D_e = 0.55958 × 10^?5. RKR potential energy curves for the two states are constructed, and the Franck-Condon factors calculated for the W-B system.     

Observation of the v = 1 ← 0 band of SH (X2Π) with a difference frequency laser

The fundamental vibration-rotation band of SH (X²Π) has been studied in absorption at Doppler-limited resolution with an estimated accuracy of 0.002 cm^?1. The band origin (ν₀ = 2598.7675 ± 0.0003 cm^?1) and the molecular constants for the excited vibrational state (v = 1), as well as improved molecular constants for the ground vibrational state, have been determined in a least-squares fit.     

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.     

On the path integral for the potential V = ar−2 + br2

A simple, alternative path integral formulation for the potential V = ar^?2 + br², r ? 0, is presented. This is achieved by mapping the problem to a two-dimensional oscillator and using the method of image paths.     

The inverse problem for the third order equation uxxx + q(x)ux + r(x)u = −iζ3u

The spectral problem u_xxx + q(x)u_x + r(x)u = ?iξ³u is considered. A set of spectral data which is sufficient for the reconstruction of the potentials q(x) and r(x) is found and the problem of this reconstruction, this inverse problem solved.     

Synthesis and magnetic properties of InM2+CrS4(M2+ = Mn,Fe,Co, Ni)

The crystallographic and magnetic properties of the compounds InM²⁺CrS₄(M = Mn, Fe, Co, Ni) were studied. Three of these compounds except MnInCrS₄ were antiferromagnetic. The Néel termperature and paramagnetic Curie temperature were determined to be 20 and 82K for InFeCrS₄, 36 and 115K for InCoCrS₄ and 22 and 26K for InNiCrS₄, respectively.     

Revised molecular constants,RKR potential,and long-range analysis for the B3Π(0u+) state of Cl2, and rotationally dependent Franck-Condon factors for Cl2 (BX1Σg+)

Literature data for the line frequencies of the B³Π(0_u⁺) ← X¹Σ_g⁺ transition of Cl₂ are fitted directly by least squares to obtain new molecular constants. The constants from individual bands are merged to obtain single-valued estimates of the rotational constants for each vibrational level of the B state. The results are combined with recent data from the B → X system in emission to obtain new RKR turning points for the B and X states, and Franck-Condon factors for the B-X system. The new constants are also used to provide revised long-range parameters for Cl₂(B) which differ from those of earlier work. In particular, the coefficient C₅ of the leading term in the inverse-power long-range potential is now found to be $\text{C}{}_5\text{= 1.16(2) × 10}{}^5\text{A}\text{?}{}^5\text{cm}{}^{\mathrm{?1}}$. Theoretical results for the variation of centrifugal distortion parameters for levels near dissociation are tested for D_v and H_v, and an extrapolation based on this behavior is used to facilitate determination of reliable B_v and G(v) values for the highest observed B-state levels.