Application of the vector ε and ρ extrapolation methods in the acceleration of the Richardson-Lucy algorithm

The vector ε and ρ extrapolation methods are applied in accelerating the convergence of the Richardson-Lucy (R-L) algorithm and its damped version. The theory and implementation are discussed in detail, and relevant numerical results are given, including the cases of noise-free images and images corrupted by the Poisson noise. The results show that the vector ε and ρ extrapolations of 9 orders can speed the convergence quite efficiently, and the ρ(9) method is more powerful than the ε(9) method for noisy degraded images. The extra computation burden due to the extrapolation is limited, and is well paid back by the accelerated convergence. The performances of these two methods are compared with the famous automatic acceleration method. For noise-free degraded images, the vector ε(9) and ρ(9) methods are more stable than the automatic method. For noisy degraded images, the damped R-L algorithm accelerated by vector ρ(9) or automatic methods is more powerful, and the instability of the automatic method is restrained by the damping strategy. We explain the instability of the method in accelerating the normal R-L algorithm by the numerical noise due to its frequent applications in the run.     

Measurement of the branching ratios for the decays J/ψ → ϱπ and J/ψ → γη′

Decays of the J/ψ (3.1) resonance into final states with two charged hadrons and two photons are investigated. Branching ratios for the decays J/ψ → ?π and J/ψ → γη′ are determined to be

$\text{Г(J/ψ → pφ)}\text{Г(J/ψ → all)}\text{= (1.0± 0.2) ·10}{}^{\mathrm{?2}}\text{,}\text{Г(J/ψ → γη′)}\text{ГJ/ψ → all)}\text{= (2.0± 0.7) ·}{}^{\mathrm{?3}}$

Upper limits for the same decay modes of ψ′ (3.7) are also determined.     

An ab Initio Study of the ÃΠ State and the ÃΠ←X?Σ Electronic Transition of MgNC

We use the RENNER program system (see, for example, P. Jensen, G. Osmann, and P. R. Bunker, in “Computational Molecular Spectroscopy” (P. Jensen and P. R. Bunker, Eds.), Wiley, Chichester, 2000, and references therein) to make a detailed calculation of the rovibronic energies in the first excited electronic state, òΠ, of the MgNC radical. This calculation is based on ab initio data (supplemented here with points for larger bending displacements from linearity) calculated at the level of MR-SDCI(+Q)/[TZ3P+f(Mg), aug-cc-pVQZ (N and C)] by T. E. Odaka, T. Taketsugu, T. Hirano, and U. Nagashima (J. Chem. Phys.115, 1349-1354 (2001)). These authors employed ab initio derived spectroscopic constants to calculate vibronic energies using perturbation expressions (J. T. Hougen and J. P. Jesson, J. Chem. Phys.38, 1524-1525 (1963)), and their results suggested that an observed vibronic band belonging to the òΠ←X?²Σ⁺ electronic transition (R. R. Wright and T. A. Miller, J. Mol. Spectrosc.194, 219-228 (1999)) should be reassigned. The present work confirms this conclusion, which is further substantiated by the rotational structures calculated in the vibronic states and by Franck-Condon theory predicting relative intensities.     

The far-infrared and microwave spectra of the CH radical in the v = 1 level of the XΠ state

Transitions between the spin-rotational levels of the ¹²CH radical in the v = 1 level of the X²Π state have been studied by the technique of laser magnetic resonance at far-infrared wavelengths. The data have been combined with a measurement of lambda-doubling transition frequencies at 7 GHz to determine an improved set of molecular parameters for CH in the v = 1 level. The parameters provide information on the effects of vibrational excitation on the structural properties of CH. Accurate predictions of the transition frequencies between the low-lying levels of the radical in the absence of a magnetic field have also been made.Small inconsistencies in the least-squares fit of the laser magnetic resonance data prompted re-measurement of three far-infrared laser frequencies, the 122.5 μm line of CH₂F₂ pumped by 9R(22), the 122.5 μm line of CH₂F₂ pumped by 9P(8) and the 554.4 μm line of CH₂CF₂ pumped by 10P(14). The new measurements differ by as much as 3.8 MHz from those made previously and are more accurate; they also remove the inconsistencies in the fit. The re-measured frequencies of the two 122.5 μm lines are identical within experimental error which suggests that the far-infrared lasing transition is the same, namely the ^rR₂₃(32) transition in the v₉=1 level of CH₂F₂.     

Axis-Switching and Coriolis Coupling in the Ã(010)-X?(000) Transitions of DCCl and HCCl

The rotationally resolved Ã(010)-X?(000) spectrum of DCCl between 12 880 and 12 964 cm⁻¹ was measured using frequency-modulated laser absorption spectroscopy of jet-cooled and ambient temperature samples. Transitions to levels with K_a′=0 and 1 were assigned, and their analysis leads to improved accuracy of both the ground state rotational constants of DCCl and, when combined with existing data for HCCl, the geometry of the radical. In addition to the expected perpendicular band structure, a number of parallel (Δ K_a=0) subbands were observed. Their intensity derives from a combination of c-type Coriolis coupling and axis-switching (J. T. Hougen and J. K. G. Watson, 1965, Can. J. Phys.43, 298) resulting from the change in geometry between the two states. The two contributions have been calculated for the (010)-(000) band of DCCl and previously recorded data for HCCl. Satisfactory agreement with experimental measurements was obtained. The Coriolis contributions are small for these transitions, but may add to or subtract from the axis-switching. For higher bending excitation in the upper state, Coriolis coupling is predicted to make larger contributions to the parallel subband intensities.     

Line mixing in the ν6Q branches of self- and nitrogen-broadened methyl bromide

Line-mixing effects are studied in the ν₆^RQ_K and ^PQ_K (K=0-6) branches of methyl bromide (CH₃Br) perturbed by nitrogen (N₂). Laboratory Fourier transform spectra have been obtained at room temperature, and for a large range of pressure values of atmospheric interest. In order to accurately model these spectra, a theoretical approach accounting for line-mixing effects is proposed. This model is based on the use of the state-to-state rotational cross-sections calculated by a statistical modified exponential-gap fitting law depending on a few empirical parameters. These parameters are deduced by adjusting the calculated diagonal elements of the relaxation matrix to the N₂-broadening coefficients, known from accurate previous measurements. Comparisons between experimental and calculated profiles for various Q branches and under various pressure conditions (0.2-1 atm) demonstrate the adequacy and consistency of the proposed model. To allow accurate laboratory measurements, line-mixing effects are also modeled in the case of self-perturbed CH₃Br.     

Photonic band structure and effect of ε and μ on the reflectivity of one-dimensional magnetic photonic crystal structure

In this paper, we study the photonic band structure and reflection properties in one-dimensional magnetic photonic crystals (MPCs). Investigation of dispersion characteristics shows that in the case of MPCs, photonic band gaps arise due to the contrast in the wave impedance, not due to the contrast in the refractive index, while contrast in the refractive index of the two layers decides the position and number of the band gaps. We also study the effect of permittivity and permeability on reflection bands, which shows that the structure that has larger values of magnetic permeability (μ) than dielectric permittivity (ε) have wider TM-reflection bands, whereas the structure for which ε is greater than μ has wider TE-reflection bands. But the gap to mid-gap frequency ratio for TM-reflection bands is larger than TE-reflection bands. Thus, magnetic permeability has greater impact on the reflectivity of MPCs than dielectric permittivity. Finally, the analysis of the omni-reflectance in MPCs has also been studied.     

Spectroscopy of AlO: Combined analysis of the AΠi → XΣ and BΣ → XΣ transitions

A combined analysis of the A²Π_i → X²Σ⁺ and B²Σ⁺ → X²Σ⁺ band systems of AlO, involving 21,500 line assignments, has been performed. The analysis indicates that the previously reported γ values of the B²Σ⁺ state are questionable. The present analysis shows that γ(B²Σ⁺) ≈ 0.014 cm⁻¹, essentially independent of the vibrational level. The positive sign is consistent with second order interaction with the higher-lying C²Π_r and lower-lying A²Π_i states. It also appears that many of the previously reported γ and γ_D values of X²Σ⁺ (v > 0) are doubtful. In fact, γ(X²Σ⁺) is observed to become increasingly negative for v″ > 1, due to second order interaction with the low-lying A²Π_i state. The present results are based on models where the hyperfine structure of the ²Σ⁺ states has been taken into account explicitly. Intensity patterns of the branches of the B²Σ⁺ → X²Σ⁺ system have been shown to be influenced by the case bβ_S coupling in the ground state v = 0,1 levels. This gives rise to intensity differences of around 10 percent in the R₁/R₂ and P₁/P₂ doublet components. The synthesized intensity patterns are fully in accord with the F₁/F₂ assignments of the present work.     

A Theoretical Study of MgNC and MgCN in the X?Σ Electronic State

The MgNC radical was the first Mg-containing species to be observed in interstellar space. This fact has stimulated considerable spectroscopic interest in this molecule, and in its isomer MgCN, but nevertheless the only rotationally resolved spectroscopic data presently available for X?²Σ⁺ MgNC comprise the rotational spectrum (K. Kawaguchi et al., 1993, Astrophys. J.406, L39-L42; K. Ishii et al., 1993, Astrophys. J.410, L43-L44; M. A. Anderson and L. M. Ziurys, 1994, Chem. Phys. Lett.231, 164-170; E. Kagi et al., 1996, J. Chem. Phys.104, 1263-1267; E. Kagi and K. Kawaguchi, J. Mol. Spectrosc. 2000, 199, 309-310) together with a few vibronic bands, all originating in the vibronic ground state and belonging to the òΠ←X?²Σ⁺ electronic transition (R. R. Wright and T. A. Miller, 1999, J. Mol. Spectrosc.194, 219-228). For MgCN, only the rotational spectrum in the vibrational ground state is known (M. A. Anderson, T. C. Steimle, and L. M. Ziurys, 1994, Astrophys. J.429, L41-L44). We report here potential energy surfaces calculated by the Averaged Coupled-Pair Functional (ACPF) method with TZ3P+f (Mg), TZ2P+f(N,C) basis sets including core-valence correlation due to the Mg 2s and 2p electrons. The ab initio results are used for determining the standard spectroscopic constants of X?²Σ⁺ MgNC and MgCN. Also, we report variational calculations of the rotation-vibration energies, and variational simulations of the lowest rotation-vibration bands, carried out with the MORBID program system (P. Jensen, 1988, J. Mol. Spectrosc.128, 478-501). We hope that our theoretical results will encourage and facilitate further characterization of X?²Σ⁺ MgNC and MgCN by high-resolution spectroscopy.     

Ab initio study of the spectroscopy of the XΠ electronic ground states of CNO and NCO

The X²Π electronic ground states of NCO and CNO have been investigated by complete ab initio methods. The dependence of the Renner-Teller parameters, ? and , on the ab initio method and on the basis set have been studied. These parameters have also been compared to experimental data for NCO. The potential energy surfaces of the X²Π state have been determined by the MRCI method and the cc-pVQZ basis set for NCO and CNO. The rovibronic levels of both isomers have been calculated variationally up to approximatively 4000 cm⁻¹ for J ? 5/2 and K ? 2, with the inclusion of the geometry dependence of the spin-orbit coupling. The agreement with experimental data obtained for NCO is remarkable. A similar accuracy for the ab initio rovibronic levels of CNO is expected since no experimental data exists for this isomer.     

Experimental studies on the Kβ/Kα intensity ratio of Zn at different thickness and pressure

Kβ/Kα intensity ratios of Zn were measured at a photon excitation energy of using a high-resolution Si(Li) detector for several thickness at different pressure. Present results were compared with theoretical data and other experimental values. The results were in good agreement theoretical values based on Hartree-Fock theory.     

KL0-KS0 transmission regeneration on deuterons and neutrons in a momentum range of 10–50 GeV/c

The energy dependence of the K_L⁰-K_S⁰ transmission regeneration amplitudes on deuterons and neutrons in the momentum region 10–50 GeV/c is determined. The moduli of the modified transmission amplitudes are momentum dependent. These dependences are fitted by the expression A_jp^?nj, where A_j and n_j (j = d, n) are constants:

$\text{A}{}_{\mathrm{<mtext>d</mtext>}}\text{=2.88 ±0.04}\text{mb}\text{, n}{}_{\mathrm{<mtext>d</mtext>}}\text{=0.546±0.030,}\text{for deuterons}\text{,}$

$\text{A}{}_{\mathrm{<mtext>n</mtext>}}\text{=1.97 ±0.14}\text{mb}\text{, n}{}_{\mathrm{<mtext>n</mtext>}}\text{=0.530±0.019,}\text{for neutrons}\text{,}$

The amplitude phases do not depend on the kaon momentum and are equal to $\text{?}{}_{\mathrm{<mtext>d</mtext>}}\text{= (?130.9 ± 2.7)°}$?_n = (?132.3 ± 1.7)°. The mean value of the ratio of the total cross-section differences for K⁰ and K⁰ interactions with neutrons and protons is determined. The residues of the partial ω and ? amplitudes, which contribute to the kaon-nucleon interaction amplitudes, are also obtained.     

Line Intensity of R(0) and R(3) of the CH4 2ν3 Band from Diode Laser Spectroscopy

We have determined the spectroscopic parameters that are necessary to describe accurately the R(0) line profile of the CH₄ 2ν₃ band from about 1 Torr to a few hundred Torr of pure CH₄. The intensities determined at each pressure are in overall agreement to better than 0.7%. The R(3) manifold of the same band has also been investigated. Relative positions and absolute intensities of the three transitions composing the triplet have been determined. The intensity distribution inside the triplet is in fair agreement with recent theoretical predictions.     

Electrical and switching properties of the Se90Te10−xAgx (0?x?6) films

Amorphous Se₉₀Te_10−xAg_x (0?x?6) films are obtained by thermal evaporation technique under vacuum from the synthesized bulk materials on pyrographite and glass substrates. X-ray analysis shows the amorphous nature of the obtained films. The dc electrical conductivity was studied for different thicknesses (165-711 nm) as a function of temperature in the range (298-323 K) below the corresponding T_g for the studied films. The obtained results show that the conduction activation energy has a single value through the investigated range of temperature which can be explained in accordance with Mott and Davis model. The I-V characteristic curves for the film compositions are found to be typical for a memory switch. The mean value of the threshold voltage increases linearly with increasing film thickness (165-711 nm), while it decreases exponentially with increasing temperature in the investigated range for the studied compositions. The results are explained in accordance with the electrothermal model for the switching process. The effect of Ag on the studied parameters is also investigated.     

Sub-Doppler laser absorption spectroscopy of the AΠi − XΣ (1, 0) band of CN: Measurement of the N hyperfine parameters in AΠ CN

Measurements of multiple rotational lines in the (1, 0) band of the A²Π_i − X²Σ⁺ “red” system of the cyanogen radical (CN) at sub-Doppler resolution are reported. The CN radical was produced by 193 nm photodissociation of NCCN (ethane dinitrile) and detected with a Ti:sapphire ring laser operating near 10 900 cm⁻¹. The sample was exposed to a weak, frequency-modulated probe beam and a strong, counterpropagating bleach laser beam. Demodulated probe laser signals display absorption and dispersion features derived from Doppler-free saturation of the hyperfine components as the laser scans across the central region of a Doppler-broadened rotational line spectrum. Hyperfine-resolved transition frequencies were combined with known ground-state X²Σ hyperfine term values to determine A²Π state hyperfine term values, which were analyzed in terms of an effective Hamiltonian for the A²Π state. All the expected hyperfine and ¹⁴N quadrupolar parameters were determined and their values analyzed in terms of a simple molecular orbital picture of the bonding in the radical. Higher sensitivity obtained with 400 kHz amplitude modulation of the bleach laser and additional phase-sensitive detection allowed hyperfine splittings in some rotational lines of ¹³C¹⁴N to be observed in natural abundance. Excited state hyperfine splittings were determined for a selection of rotational states, but not enough to determine the ¹³C hyperfine parameters.     

Sharper focal spot below λ/4 of azimuthally polarized illumination phase-encoded by the binary 0/π phase plate

The intensity distribution in the focal region for the azimuthally polarized beam phase-encoded by the binary 0/π phase plate is calculated on the basis of the vector diffraction theory. With the annular pupil aperture employed, the resolution of the focal spot will be improved remarkably. We demonstrate a sharper focal spot with full width at half maximum (FWHM) of 0.223λ (below λ/4), significantly smaller that of linear, circular and radial polarization beam under the same condition. The focusing phenomena for illumination beam with various polarization status and beam shapes are analyzed explicitly. This analysis could have potential applications in confocal microscopy and two-photo microscopy for polarization difference imaging.     

A correlation between the two ratios γ/χ(0) and |Jm|/TK in Kondo system

Using the approach based on molecular field calculations for resonant level model; a close relationship between the two ratios γ/χ(0) and |J_m|/T_K is obtained. Where γ represents the electronic contribution in the specific heat, χ(0) is the susceptibility at zero temperature, J_m is the molecular field parameter and T_K is the Kondo temperature.     

Doppler-limited spectroscopy of the AΠ1 ← XΣ system of ICl in the 0.8 μm region using a Ti:sapphire ring laser

Doppler-limited vib-rotational absorption spectra of the A ← X electronic transition of I^35/37Cl are measured in the range 11,352-13,507 cm⁻¹ using a Ti:sapphire ring laser. The P-, Q-, and R-branch lines belonging to the v ← v″ = (0-7) ← (0-7) transition in I³⁵Cl and the v ← v″ = (0-6) ← (2-6) transition in I³⁷Cl are assigned. Under Doppler-limited conditions, the P- and R-branch lines are split into doublets by the nuclear quadrupole coupling effect of the I atom. The unperturbed positions of these lines are correctly calculated, whereas splitting in the Q-branch lines was not observed. The mass-reduced Dunham expansion coefficients U_l,m of the A and X states and the spectroscopic constants , and H_v^′ of the A state are determined using a global least-squares fitting procedure.     

Absorption spectrum of the (2, 1) band in the AПi-XΣ system of CS cation

The spectrum of CS⁺ cation was recorded in the 12,235-12,600 cm⁻¹ region by employing optical heterodyne velocity modulation absorption spectroscopy. In combination with simultaneous measurement of optical heterodyne concentration modulation absorption spectroscopy, the spectral lines of CS⁺ blended with the neutral CS lines were identified and extracted from the observed spectra. One hundred and eighty-two spectral lines of CS⁺ were assigned to the (2, 1) band in the A²П_i-X²Σ⁺ system and the improved molecular constants of the upper level (υ = 2) in the A²П_i state were derived by nonlinear least squares fitting.