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.     

Duality in random matrix ensembles for all β

Gaussian and Chiral β  -Ensembles, which generalise well-known orthogonal (β=1$\beta =1$), unitary (β=2$\beta =2$), and symplectic (β=4$\beta =4$) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like {β,N,n}⇔{4/β,n,N}$\{\beta ,N,n\}\iff \{4/\beta ,n,N\}$ for all β>0$\beta >0$, where N and n respectively denote the number of eigenvalues and products of characteristic polynomials. At the edge of the spectrum, matrix integrals of the Airy (Kontsevich) type are obtained. Consequences on the integral representation of the multiple orthogonal polynomials and the partition function of the formal one-matrix model are also discussed. Proofs rely on the theory of multivariate symmetric polynomials, especially Jack polynomials.     

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.     

First search for double β decay of dysprosium

A search for double β decay of dysprosium was realized for the first time with the help of an ultra-low background HP Ge γ detector. After 2512 h of data taking with a 322 g sample of dysprosium oxide limits on double beta processes in ¹⁵⁶Dy and ¹⁵⁸Dy have been established on the level of T_1/2?¹⁰¹⁴–¹⁰¹⁶ yr$T_{1/2}?{10}^{14}\text{–}{10}^{16}\text{yr}$. Possible resonant double electron captures in ¹⁵⁶Dy and ¹⁵⁸Dy were restricted on a similar level. As a by-product of the experiment we have measured the radioactive contamination of the Dy₂O₃ sample and set limits on the α   decay of dysprosium isotopes to the excited levels of daughter nuclei as T_1/2?¹⁰¹⁵–¹⁰¹⁷ yr$T_{1/2}?{10}^{15}\text{–}{10}^{17}\text{yr}$.     

H2-broadening coefficients in the ν2 and ν4 bands of PH3

H₂-broadening coefficients are measured for 41 transitions of PH₃ in the QR branch of the ν₂ band and the PP, RP, and PQ branches of the ν₄ band, using a tunable diode-laser spectrometer. The recorded lines with J values ranging from 2 to 16 and K from 0 to 11 are located between 995 and . The collisional widths are determined by fitting each spectral line with a Voigt profile, a Rautian profile, and a speed-dependent Rautian profile. The latter model provides larger broadening coefficients than the Voigt model. These coefficients γ₀(J,K) are found to decrease slightly on the whole as J increases and they decrease significantly for K values approaching or equal to J(J?4). The H₂-broadenings are also calculated on the basis of a semiclassical model of interacting linear molecules, using an atom-atom Lennard-Jones potential in addition to the weak electrostatic contributions. The theoretical results are in satisfactory agreement with the experimental data and reproduce the J and K dependencies of the broadenings, but the decrease observed for the QR(J,K) transitions with K=J is notably overestimated.     

Line shifts in the ν2, 2ν2, and ν4 bands of NH3 perturbed by O2

Pressure-induced line shift coefficients have been measured for more than 200 rovibrational lines of NH₃ perturbed by O₂ at room temperature (T = 295 K) in some branches of the ν₂, 2ν₂, and ν₄ bands. These lines with J values ranging from 1 to 13 are located in the spectral range 800-1800 cm⁻¹. Experiments were made with a high-resolution Fourier transform spectrometer. The treatment of vibration-rotation lines includes interference effects caused by the overlapping of lines. The O₂ pressure-induced shift coefficients have been derived from the non-linear least-squares multi-pressure fitting technique. The results illustrate a vibrational dependence of line shifts with vibrational quantum number. Most of the measured shifts are negative in the ν₄ band. They are positive for the ν₂ and 2ν₂ bands. The measured shift coefficients are compared with previous measurements and with those calculated from a semiclassical theory based upon the Robert-Bonamy formalism extended to the case of symmetric top molecule with inversion motion. The predictions are generally in satisfactory agreement with the experimental data. Analyses of measured and predicted results illustrate that these shifts mainly originate from the isotropic part of the intermolecular potential.     

First assignment of the 5ν4 and ν2+4ν4 band systems of CH4 in the 6287-6550 cm region

This paper reports the first assignment of rovibrational transitions of the 5ν₄ and ν₂+4ν₄ band systems of ¹²CH₄ in the 6287-6550 cm⁻¹ region, which is usually referred to as part of the 1.58 μm methane transparency window. The analysis was based on two line lists previously obtained in Grenoble by cavity ring down spectroscopy at T=297 and 79 K completed by three long-path Fourier transform spectra recorded in Reims (at 290 K, L=1603 m, P=1-34 mbar). In order to determine the dipole transition moment parameters and quantify the intensity borrowing due to the resonance interactions, we had to include in the fit of the effective Hamiltonian model some lines of the stronger ν₁+3ν₄ and ν₂+4ν₄ bands. For this purpose, intensities of 179 additional lines were retrieved from FTS spectra above 6550 cm⁻¹ though the analysis of these higher bands is not complete. About 1955 experimental line positions and 1462 line intensities were fitted with RMS standard deviations of 0.003 cm⁻¹ and 13.1%, respectively. A line list of 8029 calculated and observed transitions which are considered as dominant was constructed for ¹²CH₄ in the 6287-6550 cm⁻¹ region. This is the first high-resolution analysis and modelling of 5-quanta band systems of ¹²CH₄.     

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.     

A deformed relativity with the quantum ℏ

Quantum relativity as a generalized, or rather deformed, version of Einstein relativity may offer a new framework to think about the structure of space–time at the true microscopic/quantum level. The approach typically gives some picture of a noncommutative (quantum) space–time. We propose a formulation with two deformations implemented on the Poincaré symmetry, using the independent Planck mass and Planck length as the invariant constraints. Together, they give the quantum ?  . The scheme leads to SO(2,4)$\mathit{SO}(2,4)$ as the relativity symmetry. We present a linear realization on a classical six-geometry beyond the familiar setting of space–time. Two extra coordinates to be considered as neither space nor time are needed. The last deformation step implementing the Planck length invariant constraines the six-geometry, as an extension of 4D space–time, giving it the structure of a AdS hypersurface. The resulted quantum world hence does not admit coordinate translation symmetries, which terminates further extension to an unstable symmetry. The quantum world is shown to be parallel to the “conformal universe”, but not scale invariant.     

Analysis of the hot bands in the 2ν9 band region of propyne-d3

The rovibrational spectrum of 2ν₉ band of CD₃CCH is overlapped by two prominent hot bands identified as (2ν₉⁰+ν₁₀^±1)(E)←ν₁₀^±1(E) and 3ν₉^±1(E)←ν₉^±1(E), where ν₁₀ and ν₉ are the degenerate CCC and CCH bending fundamental vibrations, respectively. Assignment of lines to the transitions of these hot bands were carried out with the help of the high-resolution spectra recorded at ∼195 K and at room temperature. Molecular parameters for these hot bands have been obtained from the rotational analysis of the partially resolved K-structure lines. Only Q-head of the third hot band , originating from the lower 2ν₁₀ state could be identified.     

High-resolution study of the ν1/ν5 and 2ν1/ν1+ν5 P-H stretching bands of PH2D

The P-H stretching bands ν₁/ν₅ and 2ν₁/ν₁+ν₅ were recorded using a Bruker 120 HR interferometer with a resolution of 0.0042 and 0.0088 cm⁻¹, respectively, and analyzed. From the fits 33 and 50, respectively, vibrational, rotational, centrifugal distortion, and resonance interaction parameters were obtained. These reproduce 668 and 497 rovibrational energies of the pairs of states ν₁/ν₅ and 2ν₁/ν₁+ν₅ with experimental accuracies, rms=0.00016 and , respectively. “Local mode” behavior of the PH₂ fragment is established and discussed in detail.     

The overtone spectrum of carbonyl sulfide in the region of the ν1+4ν3 and 5ν3 bands by ICLAS-VECSEL

The high-resolution overtone spectrum of OCS has been recorded in the region of the ν₁+4ν₃ and 5ν₃ bands by intracavity laser absorption spectroscopy based on an optically pumped vertical external cavity surface emitting laser (VECSEL). The extremely weak ν₁+4ν₃ band at was found to be isolated. The 5ν₃ band at is accompanied by two weaker bands at 9933.53 and assigned to the 12⁰4-00⁰0 and 04⁰4-00⁰0 bands, respectively. In addition, the 01¹5-01¹0 hot band was detected together with the extremely weak band heads of the R branch of the 02^0,25-02^0,20 hot bands. Finally, the 5ν₃ band of the ¹⁶O¹²C³⁴S minor isotopomer, present in natural abundance in the sample, was also observed and rotationally analyzed. Effective state parameters could be retrieved by standard band-by-band rotational fitting of the line positions, leading to a typical rms of . The observed line positions were compared to the predictions of the global model described by Rhaibi et al. [J. Mol. Spectrosc. 191 (1998) 32-44]. In general, the agreement is excellent, close to the experimental uncertainty () thus confirming the high predictive ability of this effective Hamiltonian model. Weak but significant deviations up to were, however, identified for two rotational levels of the highly excited 2,16⁰,0 dark state, observed through a local interaction with the 00⁰5 state. In the case of the ¹⁶O¹²C³⁴S isotopomer, the predicted line wavenumbers of the 5ν₃ band were globally overestimated by about . The new data have been included in the corresponding global model, leading to almost unchanged values of the molecular parameters and a statistical agreement with the experiment.     

Rovibrational analysis of the ν2 and 2ν2 P-D stretching bands of PH2D

The infrared spectral regions of the P-D stretching fundamental band ν₂ and the first overtone band 2ν₂ of PH₂D were recorded with a resolution of 2.7×10⁻³ and , respectively. In the analysis about 710 and 440 transitions were assigned to the ν₂ and 2ν₂ bands. These provided 358 and 268 upper rovibrational energy terms, respectively. Resonance interactions between the states (010000) and (000200) were taken into account in the Hamiltonian used to fit upper energies of the (010000) state. The rovibrational energies of the (020000) state were fitted with a Hamiltonian for an isolated vibrational state.     

High-resolution infrared and theoretical study of the fundamental bands ν2, ν4 and ν9 and the c-Coriolis interacting dyad ν5, ν14 of 1,3,4-thiadiazole

The Fourier transform gas-phase IR spectrum of 1,3,4-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 800-1500 cm⁻¹ spectral region. Five fundamental bands ν₂(A₁; 1391.9 cm⁻¹), ν₄(A₁; 964.4 cm⁻¹), ν₅(A₁; 894.6 cm⁻¹), ν₉(B₁; 821.5 cm⁻¹), and ν₁₄(B₂; 898.4 cm⁻¹) have been analysed using the Watson model. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from fits. The ν₄ and ν₉ bands are unperturbed while a strong c-Coriolis resonance perturbs the close-lying ν₅ and ν₁₄ bands. This dyad system has been analysed by a model including first and second order c-Coriolis resonance using the theoretically predicted Coriolis coupling constant . The ν₂ band is strongly perturbed by a local resonance, and we obtain a set of spectroscopic parameters using a model including second order a-Coriolis resonance with the inactive ν₁₀ + ν₁₄ band. Ground state rotational and quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational α-constants predicted by quantum chemical calculations using a cc-pVTZ basis and B3LYP methodology, have been compared with the present experimental data, where there is generally good agreement.     

Simultaneous analysis of the 2ν2, 2ν5, and ν2 + ν5 vibration-rotation bands of CH3Br

Previous studies of the parallel bands 2ν₂ and $\text{2ν}{}_5{}^0$ of CH₃Br by the two first authors have been completed by the analysis of the weaker perpendicular band ν₂ + ν₅, centered near 2745 cm^?1. It is well known that the v₂ = 1 and v₅ = 1 states of methylbromide are linked by an x-y-type Coriolis interaction. Therefore, in the 2500–2900-cm^?1 range, the levels

$\text{(v}{}_2\text{=2), (v}{}_5\text{2, l}{}_5\text{=0), (v}{}_5\text{=2, l}{}_5\text{±2), (v}{}_5\text{=v}{}_2\text{=1, l=5±1)}$

are linked by a similar interaction. Least-squares and prediction programs have been written to treat this kind of problems and they have been satisfactorily applied to both isotopic species, CH₃⁷⁹Br and CH₃⁸¹Br. A localized resonance in the K = 0 subband of ν₂ + ν₅ has been shown to be due to the 3ν₃ + ν₆ band. No evidence for a strong Fermi resonance between ν₁ and $\text{2ν}{}_5{}^0$ has been found.     

The 10.4 μm CO2 laser Stark spectra of the ν4 and the ν9 bands of 1,1 difluoroethylene

The ν₄ and the ν₉ bands of CF₂CH₂ have been studied using coincidences with the 10.4 μm band of the CO₂ laser and the 10.9 μm band of the N₂O laser. These resonances have been analyzed, together with recent microwave results, to give the following vibration-rotation parameters and dipole moments in the ν₄ and ν₉ states

     

18.

A new analysis of the ν₄(E) rovibrational band of the symmetric top molecule PF₃     

Hicham Msahal  Siham Hmimou 《Journal of Molecular Spectroscopy》2010,264(1):37-42

The high-resolution Fourier transform infrared spectrum of phosphorus trifluoride PF₃ have been reinvestigated in the ν₄ perpendicular band region around 347 cm⁻¹. Thanks to recent pure rotational measurements, 595 new infrared transitions of the ν₄ band have been assigned extending the rotational quantum number values up to K_max = 66 and J_max = 67. As a consequence of this extension, a sophisticated model containing a large number of parameters and interaction constants was adopted for the analysis of the IR transitions of the ν₄ fundamental band of PF₃. A merge of the IR transitions and the reported MW/MM/RF data within the v₄ = 1 excited level yielded an accurate rotational ground state C₀ value, 0.159970436 (69) cm⁻¹, which was used to determine an improved GS structure, r₀(P-F) = 1.56324405 (11) Å and ?(FPF) = 97.752232 (29)°. All experimental data have been refined applying various reduction forms of the effective rovibrational Hamiltonian developed for an isolated degenerate state of a symmetric top molecule. The v₄ = 1 excited state of the PF₃ oblate molecule was treated with models taking into account ?- and k-type intravibrational resonances. Parameters up to sixth order have been accurately determined and the unitary equivalence of the derived parameter sets in different reductions was demonstrated.     

19.

Generating μ and Bμ in models with Dirac gauginos     

Karim Benakli  Ann-Kathrin Maier 《Nuclear Physics B》2011,851(3):445-461

     

20.

The 2ν₁, 2ν₂ and 2ν₃ overtones of FClO₃     

E. Cané  G. Pawelke 《Journal of Molecular Spectroscopy》2007,244(1):24-32

The infrared spectra of the 2ν₁, 2ν₂ and 2ν₃ overtones of perchloryl fluoride, FClO₃, have been recorded at high resolution using monoisotopic pure samples. Four symmetric top species have been investigated: F³⁵Cl¹⁶O₃, F³⁷Cl¹⁶O₃, F³⁵Cl¹⁸O₃ and F³⁷Cl¹⁸O₃. The v_i = 2, i = 1, 2, 3 vibrationally excited states are totally symmetric, so these overtones correspond to parallel bands of medium/weak intensity, centered from 2010 to 2120 cm⁻¹ (2ν₁), from 1390 to 1430 cm⁻¹ (2ν₂) and from 1070 to 1100 cm⁻¹ (2ν₃). Most of the bands are unperturbed and their analysis was straightforward. The band origins, the rotational and centrifugal molecular constants in the v₁ = 2, v₂ = 2 and v₃ = 2 states have been determined, with standard deviations of the fits from 0.00024 to 0.00067 cm⁻¹. The 2ν₁ overtones of F³⁵Cl¹⁶O₃ and F³⁷Cl¹⁶O₃ are perturbed by an A₁/E Coriolis resonance between the v₁ = 2 state and one E component of the v₄ = 1, v₆ = 2 manifold. The 2ν₂ of F³⁷Cl¹⁸O₃ is perturbed by the same kind of interaction involving the v₁ = v₆ = 1 (E) state, at about 1396 cm⁻¹. In these bands the resonance is localized on rotational levels with specific J and K values. As a consequence, a few transitions of the perpendicular bands involving the interacting levels could be identified in the spectra. A simultaneous fit of the transitions assigned to the dyads has been performed and the parameters of the excited states have been determined, including the high order Coriolis interaction coefficient . The anharmonic constants x₁₁, x₂₂, x₃₃ of all the studied isotopologues of FClO₃, x₄₆ of F³⁵Cl¹⁶O₃, x₄₆ + g₄₆ of F³⁷Cl¹⁶O₃ and x₁₆ of F³⁷Cl¹⁸O₃, have been derived.     

	$\text{ν}{}_4$ CF2CH2	$\text{ν}{}_9$ CF2CH2
$\text{ν}{}_0$	925.7692 (2)	953.8057 (2)	cm?1
$\text{A}$	10 971.99 (2)	11 026.918 (6)	MHz
$\text{B}$	10 414.98 (2)	10 436.381 (6)	MHz
$\text{C}$	5328.48 (2)	5346.100 (6)	MHz
μ	1.382 (1)	1.382 (1)	D
$\text{μ - μ}{}_0$	0.014 (2)	0.004 (1)	D

A new analysis of the ν4(E) rovibrational band of the symmetric top molecule PF3

The high-resolution Fourier transform infrared spectrum of phosphorus trifluoride PF₃ have been reinvestigated in the ν₄ perpendicular band region around 347 cm⁻¹. Thanks to recent pure rotational measurements, 595 new infrared transitions of the ν₄ band have been assigned extending the rotational quantum number values up to K_max = 66 and J_max = 67. As a consequence of this extension, a sophisticated model containing a large number of parameters and interaction constants was adopted for the analysis of the IR transitions of the ν₄ fundamental band of PF₃. A merge of the IR transitions and the reported MW/MM/RF data within the v₄ = 1 excited level yielded an accurate rotational ground state C₀ value, 0.159970436 (69) cm⁻¹, which was used to determine an improved GS structure, r₀(P-F) = 1.56324405 (11) Å and ?(FPF) = 97.752232 (29)°. All experimental data have been refined applying various reduction forms of the effective rovibrational Hamiltonian developed for an isolated degenerate state of a symmetric top molecule. The v₄ = 1 excited state of the PF₃ oblate molecule was treated with models taking into account ?- and k-type intravibrational resonances. Parameters up to sixth order have been accurately determined and the unitary equivalence of the derived parameter sets in different reductions was demonstrated.     

The 2ν1, 2ν2 and 2ν3 overtones of FClO3

The infrared spectra of the 2ν₁, 2ν₂ and 2ν₃ overtones of perchloryl fluoride, FClO₃, have been recorded at high resolution using monoisotopic pure samples. Four symmetric top species have been investigated: F³⁵Cl¹⁶O₃, F³⁷Cl¹⁶O₃, F³⁵Cl¹⁸O₃ and F³⁷Cl¹⁸O₃. The v_i = 2, i = 1, 2, 3 vibrationally excited states are totally symmetric, so these overtones correspond to parallel bands of medium/weak intensity, centered from 2010 to 2120 cm⁻¹ (2ν₁), from 1390 to 1430 cm⁻¹ (2ν₂) and from 1070 to 1100 cm⁻¹ (2ν₃). Most of the bands are unperturbed and their analysis was straightforward. The band origins, the rotational and centrifugal molecular constants in the v₁ = 2, v₂ = 2 and v₃ = 2 states have been determined, with standard deviations of the fits from 0.00024 to 0.00067 cm⁻¹. The 2ν₁ overtones of F³⁵Cl¹⁶O₃ and F³⁷Cl¹⁶O₃ are perturbed by an A₁/E Coriolis resonance between the v₁ = 2 state and one E component of the v₄ = 1, v₆ = 2 manifold. The 2ν₂ of F³⁷Cl¹⁸O₃ is perturbed by the same kind of interaction involving the v₁ = v₆ = 1 (E) state, at about 1396 cm⁻¹. In these bands the resonance is localized on rotational levels with specific J and K values. As a consequence, a few transitions of the perpendicular bands involving the interacting levels could be identified in the spectra. A simultaneous fit of the transitions assigned to the dyads has been performed and the parameters of the excited states have been determined, including the high order Coriolis interaction coefficient . The anharmonic constants x₁₁, x₂₂, x₃₃ of all the studied isotopologues of FClO₃, x₄₆ of F³⁵Cl¹⁶O₃, x₄₆ + g₄₆ of F³⁷Cl¹⁶O₃ and x₁₆ of F³⁷Cl¹⁸O₃, have been derived.