The Stimulated Raman Spectrum of Cyanogen

The Raman spectrum of cyanogen¹²C₂¹⁴N₂has been investigated at nearly Doppler resolution by means of the Stimulated Raman technique. The regions around theQbranches of the ν₁(2330 cm⁻¹) and ν₂(845 cm⁻¹) vibrations have been recorded. Besides the fundamentals, hot bands arising fromv₅= 1,v₅= 2, andv₄= 1 have been observed. The spectra have been analyzed, and rotational constants for the excited states have been obtained. Computer simulations of the Raman contours have been carried out as a test of the assignments.     

Deformed states of high spin in42Ca

The⁴²Ca levels at 4,715 and 6,633 keV excitation energy have been investigated using the³⁹ K(α,pγ reaction atE _α=14 and 15 MeV. From particle-γ-ray angular correlations the spin assignmentsJ(4,715)=6, 4 andJ(6,633)=8, 6, 4 have been obtained. Lifetime measurements using the Doppler-shift attenuation method yieldedτ (4,715)=120±46 fs andτ(6,633)=52±21 fs. Both levels have positive parity and decay by enhancedE2 transitions. They are interpreted as theJ ^π=6⁺ and 8⁺ members, respectively, of theK ^π=0⁺ rotational band which has theE _x =1,837, 2,423 and 3,250 keV states as further members. The enhancement of inbandE2 transitions is 50 _?16 ⁺³⁵ W.u. (6→4) and 63 W.u. (8→6) respectively. The intrinsic quadrupole moments which have been derived on the basis of the coexistence model, areQ ₀=1.13?0.16/+0.37b(8→6) andQ ₀=1.36±0.25b(6→4), respectively. TheJ ^π=10⁺ member of the rotational band has possibly been observed as a level at 8,856±5 keV excitation energy.     

Two Dimensional Rotational Temperature Measurement by Multiline Laser Induced Fluorescence of Nitric Oxide in Combustion Flame

Two-dimensional rotational temperature measurement was performed in a stable combustion flame of premixed butane and oxygen using multiline laser induced fluorescence (LIF) of nitric oxide molecules. Multiple rotational absorption lines of A²∑⁺Π;X²II(0,0) Q₁ and Q₂ lines were excited by laser light around 226 nm, and the LIF signal was observed by an image-intensified digital camera. Temperature was determined through least squares fitting correlation between LIF intensity and excitation rotational quantum number for the Boltzmann distribution function. The measured LIF intensity was approximated by the Boltzmann distribution with good accuracy, and the temperature obtained was between 500 K and 1800 K for the test flame. The measuring error of the temperature was evaluated and found to be 80 K, which corresponded to 8% of the measured fluorescence intensity. The two-line LIF scheme was evaluated by different pairs of excitation lines (Q₁(31.5)/Q₁(16.5) and Q₁(18.5)/Q₁(16.5)) for comparison with the multiline LIF approach. Temperature which was obtained by two-line LIF scheme corresponded well with multiline LIF results for Q₁(31.5)/Q₁(16.5) excitation. However, for Q₁(18.5)/Q₁(16.5) excitation, the obtained temperature did not agree with the multiline LIF result because the population of rotational states J=18.5 and J=16.5 is similar at high temperatures. We found that two-line LIF temperature measurement was reliable when excitation lines were suitably selected.     

Collision-induced 1st overtone infrared absorption band of deuterium

The collision-induced 1st overtone infrared absorption band of deuterium has been observed at room temperature. The band was studied in the pure gas and in binary mixtures with argon and nitrogen at a path length of 194.3 cm at pressures up to 800 atm. The observed absorption profiles of the band do not show any splitting of the Q branch and this indicates that the contribution of the short-range overlap forces to the intensity of the band is negligible. The enhancement absorption profiles of D₂-Ar mixtures show only single-transition quadrupolar lines, but the enhancement profiles of D₂-N₂ mixtures, in addition, show the double transitions Q₂(J) of D₂ + S₀(J) of N₂, and double vibrational transitions Q₁(J) of D₂ + Q₁(J) of N₂ which occur on the low frequency side of the pure overtone band. Major contribution to the intensity of the absorption profiles of pure deuterium comes from the double transitions Q₁(J) + Q₁(J), Q₁(J) + S₁(J) and Q₂(J) + S₀(J) in the colliding pairs of D₂ molecules. Integrated absorption coefficients were measured and binary and ternary absorption coefficients were derived.     

In-beam spectroscopy of231Pa

Information on energy levels and onE 2 andM 1 matrix elements in²³¹Pa has been obtained using conversion-electron and gamma-ray spectroscopy following the²³²Th(p, 2n)²³¹Pa reaction and Coulomb excitation of the radioactive target²³¹Pa by⁴He and³²S ions. The results are analyzed in the framework of the rotational model, applied to the rotational band built on the 1/2^?[530] Nilsson state whose 3/2^? member forms the ground state of this nucleus. The deviations of the level energies from the rigid-rotor values can be described by Coriolis couplings. The analysis of the Coulomb-excitation process shows that a constant set of rotational parameters Q₀, g_R, g_K, andb can fairly well account for the measured line intensities.     

Diode laser spectroscopy of the ν6 band of 12CH3I

The vibration-rotation spectrum of the ν₆ fundamental of methyl iodide has been recorded in the 824 to 862 cm^?1 region by using a tunable semiconductor diode laser spectrometer. The rotational analysis performed for six Q branches ^pQ(J,3), ^pQ(J,4), ^pQ(J,5), ^pQ(J,6), ^pQ(J,7), and ^qQ(J,8) led to accurate values for several molecular constants. The nuclear quadrupole splitting arising from the spin of iodine has been observed very clearly in the low J transitions and for various K values.     

Contribution to the Analysis of theA2←XA1“Wulf” Transition of Ozone by High-Resolution Fourier Transform Spectrometry

The analysis of the rotational structure of the high-resolution Fourier transform 0⁰₀absorption spectrum of the³A₂←X¹A₁band system of the “Wulf” transition of the isotopomer¹⁶O₃of ozone is reported for the first time. With a near pure case (b) coupling model for the upper triplet state, we have assigned a significant portion of the spectrum, mainly theF₁(J=N+ 1) andF₂(J=N) spin components, primarily in the lower frequency region of the band. The lines corresponding to theF₃(J=N− 1) component are weak at lower frequencies and heavily congested in the central and higher frequency regions of the spectrum. Perturbations and predissociation phenomena have reduced the effective lifetime of the metastable³A₂state and have also limited the number of transitions included in the least-squares fit of the band. Approximately 100 lines have been assigned in the range from 9100–9550 cm⁻¹. Three rotational, three centrifugal distortion, three spin–rotation, and one spin–spin constant were varied. The geometry of the molecule in the³A₂state, as determined from these constants, isr= 1.345 Å and θ = 98.9°, in good agreement withab initioresults.     

Multispectrum analysis of the ν4 band of CH3CN: Positions, intensities, self- and N2-broadening, and pressure-induced shifts

A multispectrum nonlinear least-squares fitting technique was applied to measure accurate zero-pressure line center positions, Lorentz self- and nitrogen (N₂)-broadened half-width coefficients, and self- and N₂-pressure-induced shift coefficients for over 700 transitions in the parallel ν₄ band of CH₃CN near 920 cm⁻¹. Fifteen high-resolution (0.0016 cm⁻¹) laboratory absorption spectra of pure and N₂-broadened CH₃CN recorded at room temperature using the Bruker IFS 125HR Fourier transform spectrometer located at the Pacific Northwest National Laboratory (PNNL) in Richland, Washington, USA, were analyzed simultaneously assuming standard Voigt line shapes. Short spectral intervals containing manifolds of transitions from the same value of J were fitted together. In all, high-precision line parameters were obtained for P(44)-P(3) and R(0)-R(46) manifolds. As part of the analysis, quantum assignments were extended, and the total internal partition function sum was calculated for four isotopologs: ¹²CH₃¹²CN, ¹³CH₃¹²CN, ¹²CH₃¹³CN, and ¹³CH₃¹³CN. Measurements of N₂ broadening, self-broadening, N₂-shift, and self-shift coefficients for transitions with J up to 48 and K up to 12 were measured for the first time in the mid-infrared. Self-broadened half-width coefficients were found to be very large (up to ∼2 cm⁻¹ atm⁻¹ at 296 K). Ratios of self-broadened half-width coefficients to N₂-broadened half-width coefficients show a compact distribution with rotational quantum number in both the P and R branches that range from ∼4.5 to 14 with maxima near ∣m∣=24, where m=−J″, J″, and J″+1 for P, Q, and R lines, respectively. Pressure-induced shifts for N₂ are small (few exceed ±0.006 cm⁻¹ atm⁻¹ at 294 K) and are both positive and negative. In contrast, self-shift coefficients are large (maxima of about ±0.08 cm⁻¹ atm⁻¹ at 294 K) and are both positive and negative as a function of rotational quantum numbers. The present measured half-widths and pressure shifts in ν₄ were compared with corresponding measurements of rotational transitions.     

Tunable diode laser measurements of N2- and air-broadened halfwidths: Lines in the (ν4 + ν5)0 band of 12C2H2 near 7.4 μm

Nitrogen- and air-broadened Lorentz halfwidths have been determined for 29 lines in the P and R branches of the (ν₄ + ν₅)⁰ combination band of ¹²C₂H₂ using a tunable diode laser spectrometer. Two tunable diode lasers operating in the region 1250–1380 cm^?1 were used in recording the data. For nitrogen broadening, the measured halfwidths at 296 K decrease from about 0.11 cm^?1 atm^?1 at |m| = 1 to about 0.05 cm^?1 atm^?1 at |m| = 30, where m = J″ + 1 for R-branch lines, m = ?J″ for P-branch lines, and J″ is the lower state rotational quantum number. On the average, the air-broadened halfwidths are 97% of the N₂-broadened halfwidths.     

Acetylene spectra with a tunable diode laser: (ν4 + ν5)0+−ν41fQ branches of 12C2H2 and 12C13CH2

The rotational structure of the Q branches of the (ν₄ + ν₅)⁰⁺?ν₄^1f bands of ¹²C₂H₂ and ¹²C¹³CH₂ at 13.7 μm has been observed in a natural sample of acetylene by using a tunable diode laser as a source in a high-resolution infrared grating spectrometer equipped with a precision grating drive. Altogether 23 lines from J = 6 to 28 for ¹²C₂H₂ and 15 lines from J = 6 to 20 for ¹²C¹³CH₂ have been identified. The observed full width at half maximum of the resolved lines of these Q branches is very close to the calculated Doppler width. Molecular constants ν₀ + B″, B′ ? B″ ? 2D″, D′ ? D″, and H′ ? H″ have been derived from the measured line positions of the rotational structure.     

Pressure broadening coefficients of transitions in the ν5 band of methyl bromide from fitting to Voigt and Galatry line profiles

Tuneable diode laser absorption spectroscopy has been used to measure the room temperature pressure broadening coefficients (γ) of rotational transitions in the v₅ fundamental band of methyl bromide (¹²CH₃⁷⁹Br and ¹²CH₃⁸¹Br) around 6.9 μm. Nitrogen, oxygen and self-broadening coefficients have been determined for 125 lines in the ^RQ₁, ^PQ₃, ^PQ₅, ^PQ₇ and ^PQ₈ branches and 49 P and R branch transitions. Line profiles within Q branches were recorded at incremental pressures of nitrogen and oxygen up to 15 Torr and fitted to a Voigt profile to yield the broadening coefficients. The nitrogen broadened data for 14 lines, chosen from the five Q branches, were also fitted with Galatry profiles. The line profiles of the P and R branch transitions were recorded for total nitrogen and oxygen pressures of up to 300 Torr and fitted to both Voigt and Galatry profiles. Within individual Q branches, nitrogen broadening coefficients were found to decrease monotonically with increasing J from 0.14 cm⁻¹ atm⁻¹ at low J to 0.09 cm⁻¹ atm⁻¹ at high J. The corresponding values for oxygen were approximately 25% smaller. Self-broadening coefficients were found to vary between 0.48 and 0.16 cm⁻¹ atm⁻¹ with a similar J dependence to the foreign gas broadening for J > 20. However, between J = 2 and J ≈ 20 the broadening coefficient was found to increase with J. The magnitude of the pressure broadening coefficient for P and R branch transitions was found to closely follow the J dependence measured for the Q branch lines.     

Laplace operator and hodge decomposition for quantum groups and quantum spaces

LetΓ=Γ _±,z be one of theN ²-dimensional bicovariant first order differential calculi for the quantum groups GL _q (N), SL _q (N), SO _q (N), or Sp _q (N), whereq is a transcendental complex number andz is a regular parameter. It is shown that the de Rham cohomology of Woronowicz’s external algebraΓ ^{^} coincides with the de Rham cohomologies of its leftinvariant, its right-invariant and its biinvariant subcomplexes. In the cases GL _q (N) and SL _q (N) the cohomology ring is isomorphic to the biinvariant external algebraΓ _inv ^{^} and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. It is also applicable for quantum Euclidean spheres. The eigenvalues of the Laplace-Beltrami operator in cases of the general linear quantum group, the orthogonal quantum group, and the quantum Euclidean spheres are given.     

Inelastic collision cross section of excited molecules

The (v′=6,J′=43) level in theB ¹Π _u electronic state of Na₂ has been selectively populated by excitation with the 4 880 Å line of the argon laser. Through collisions with He atoms energy is transferred to neighbouring rotational states in Na₂ and the density of these states is determined by observing fluorescence to electronic ground state. From previous measurement of the lifetime of theB ¹Π _u state and new measurements of the intensities of collision induced spectral lines as a function of He pressure, absolute collision cross sections for all rotational transitions up to ΔJ=±5 have been obtained. The total cross section for all rotational transitions observed is σ _rot ^total =65±15 Ų. Preliminary results about collision induced vibrational transitions are also presented.     

Electromagnetic contributions to proton- and neutron-4He scattering

A proper treatment of various electromagnetic contributions toN-⁴He scattering enables one to determinen(p)-⁴He observables fromp(n)-⁴He data. Several calculations ofn-⁴He observables considering different electromagnetic effects are presented. It is shown that the contribution of thep-⁴He Coulomb corrections ton-⁴He polarizations and differential cross sections dominates over other electromagnetic effects forθ _c.m.≧30°. For smaller scattering angles, neutron magnetic scattering is important and produces a divergingn-⁴He differential cross section atθ=0° and a large peak (Mott-Schwinger effect) in the polarization. The influence of thep- andn-⁴He vacuum polarizations on then-⁴He observables is found to be small.     

Mössbauer studies and nuclear quadrupole moments of186, 188, 189, 190 Os

Mössbauer transmission experiments with the 137, 155, 69 and 187 keV gamma rays of^{186, 188, 189, 190}Os, respectively, yielded the electric quadrupole splitting of these gamma resonance lines in OsO₂ and OsP₂. From the results the following ratios of quadrupole moments were derived:Q ₂ ⁺(¹⁸⁶Os, 137 keV):Q ₂ ⁺(¹⁸⁸Os, 155keV):Q ₂ ⁺(¹⁹⁰Os, 187 keV):Q _3/2 ^?(¹⁸⁹Os, g.s.)=(+1.100±0.020): 1.0:(+0.863±0.051): (?0.586±0.011) andQ _5/2 ^?(¹⁸⁹Os, 69 keV)/Q _3/2 ^?(¹⁸⁹Os, g.s.)=?0.735 ±0.012. The ratios for^{180, 188, 190}Os are, within their limits of error, in agreement with the expectation of the rotational model, indicating that the pairing-plusquadrupole model calculations of Kumar and Baranger predict too rapid a transition form rotational to vibrational nuclei. Applying this argument to¹⁸⁶Os in particular and using the measured ratios, one obtains a set of values for the quadrupole moments themselves, namelyQ ₂ ⁺ (¹⁸⁶Os)=?(1.50 ± 0.10)b,Q ₂ ⁺(¹⁸⁸Os)=?(1.36± 0.09) b,Q ₂ ⁺ (¹⁹⁰Os)=?(1.18 ± 0.08) b,Q _3/2 ^?(¹⁸⁹Os)=+ (0.80 ± 0.06) b, andQ _5/2 ^? (¹⁸⁹Os)=? (0.59 ± 0.05) b. For the electric field gradient at Os nuclei in Re metal a value ofV _zz=?(3.3 ± 0.6) · 10¹⁷ V/cm² was found. A measurement with a magnetically split source yielded δ=+ 0.685 ± 0.025 for theE2/M1 mixing parameter of the 69 keV transition of¹⁸⁹Os,g _5/2 ^?/g _3/2 ^?=0.895 ± 0.006 for the ratio of theg-factors of the 69 keV state and the groundstate, andH _i=?(1135 ± 20) kOe for the hyperfine field at Os nuclei in an iron matrix.     

Torsional Tunneling andA1–A2Splittings and Air Broadening of therQ0andpQ3Subbranches of the ν7Band of Ethane

The strong and sharp^rQ₀and^pQ₃subbranches of the ν₇perpendicular band of C₂H₆near 3000 cm⁻¹are located in atmospheric windows and have been observed in several remote monitoring measurements of ethane using infrared solar absorption spectroscopy. We report here difference-frequency laser measurements of the air broadening and shifting of theseQbranches atT= 296 and 160 K in order to improve the quantitative analysis of the atmospheric spectra. The air-broadened spectra can be fit to high accuracy by convolving the Doppler-limited spectra with single shifted Lorentzians with broadening coefficients of ∼0.67 cm⁻¹/MPa at 296 K and temperature exponents (γ ∝T⁻ⁿ) ofn∼ 1. The peculiar Doppler contours of theseQbranches are unresolved, even at the lower temperatures. Therefore, in order to model their blended contours, we have recorded their sub-Doppler fine structure using a color-center laser optothermal molecular beam spectrometer. We have resolved torsional tunneling splittings in bothQsubbranches and anomalousA₁–A₂splittings in^pQ₃with the individualJcomponents exhibiting distinctive nuclear-spin weights. These splittings are induced by high-order torsional background perturbing states with localized irregularities, making it difficult to model the spectra with simpleJ(J+ 1) power series.     

Anomalous behaviour of transition probabilities in75Kr

Two collective bands of⁷⁵Kr have been extended up to spin 21/2 using the compound reactions⁶⁴Zn(¹⁴N,p2n)⁷⁵Kr and⁵⁰Cr(²⁸Si, 2pn)⁷⁵Kr. Spins and parities were assigned from neutron-gatedγ-ray angular distributions and excitation functions using the OSIRIS anti-Compton spectrometer. The bands are interpreted to be built on the well-deformed Nilsson states: [442] 5/2 and [301] 3/2. Energies for both bands and the order of magnitude of the mixing ratios in thef _5/2 band can be reproduced within the single-particle-plus-rotor model, while the experimentalQ(I→I?1)/Q(I→I?2) ratios, deduced from mixing ratios and branching ratios, exhibit large deviations by a factor 4 to 6 from theoretical values (which are around one). An explanation of this effect may be found by treating the two rotational bands each as a result of mixing between rotational bands of oblate and prolate states; thus explaining the large difference between B(E2,I→I?1) andB(E2, I →I?2) in the bands of⁷⁵Kr.     

Diode laser spectroscopy of the ν6 band of 13CH3l and the ν″6 band of 12CH2Dl

The ν₆ band of ¹³CH₃I and the ν″₆ band of ¹²CH₂DI have been recorded under Doppler-limited resolution in the region 820–866 cm^?1 using a tunable diode laser spectrometer. For ¹³CH₃I the constants for the ν₆ band were determined by simultaneous analysis of seven ^pQ(J,K) branches and several ^pP(J,K) and ^pR(J,K) transitions. For ¹²CH₂DI, the slight asymmetry introduced by the single D atom gives rise to noticeable asymmetry effects in the spectra of some of the ^pQ(J,K) subbands. From the analysis of six such subbands, the molecular constants for the ν″₆ level were determined.     

Study of excited states in49V with the48Ti (p, γ)49V reaction

In the⁴⁸Ti(p, γ)⁴⁹V reaction gamma decays of thirteen resonances betweenE _p =960 and 1570 keV are investigated. Level energies within ±0.5–±2.0 keV andQ-value 6756.8±1.5 keV are obtained. Branching ratios for the resonance states and strongly populated bound states are given. Gamma-ray angular distribution measurements yield the followingJ(keV) assignments of⁴⁹V bound and resonance states:J(1140)=5/2,J ^π(2235)=5/2^(?),J(2264)=(3/2),J(2308)=3/2,J(3912)=3/2,J(8105,Ep=1374keV)=(1/2) andJ ^π(8289,E _p =1564keV)=3/2^(?). Multipolarity mixing ratios for all measured primary and secondary gamma rays are tabulated. Dopplershift attenuation measurements yield the mean lifetimes τ _m (keV) of the following bound states in⁴⁹V:τ _m (748)=(200± ₁₀₀ ⁴⁰⁰ )fs, τ _m (1140)=(250± ₁₀₀ ⁵⁰⁰ )fs, τ _m (1155)>400 fs, τ _m (1515)=(45± ₂₀ ³⁰ )fs, τ _m (1644)=(55± ₂₀ ³⁰ )fs, τ _m (1661)=(25±5)fs, τ _m (1994)>400 fs, τ _m (2235)=(30± ₁₅ ³⁰ )fs, τ _m (2264)=(45± ₁₅ ³⁰ )fs and τ _m (2308)=(20±10)fs.     

Moments of the spectra for rotational transitions induced by collisions or by external perturbations

Considered first is the cross sectiond σ(J′←J)/dω for the rotational transitionJ′←J of a linear rotator in collisions. The set of cross sections for a givenJ and for allJ′ defines a discrete spectral distribution as a function of the transition energy ΔE=E(J′)?E(J). In both the classical and the quantum mechanical sudden approximations the moments \(S(\mu ;J) = \sum\limits_{J'} {(\Delta {\rm E}} )^\mu d\sigma (J' \leftarrow J)/d\omega \) of ordersμ=2n andμ=2n+1 (n=0,1,...) are polynomials of degreen in the rotational energyE(J). The special cases forn=0 indicate thatS(0;J) andS(1;J) are independent ofJ. This is a theorem proved elsewhere. Explicit expressions forS(μ; J) of low orders are presented. They are derived on the assumption of equal relative velocitiesv andv′ before and after the collision. Correction onS(μ;J) for the difference betweenv andv′ is made to the lowest order in terms ofS(μ+1;J) forv=v′. The quantum mechanical results for linear rotators are extended to spherical-top and symmetric-top rotators. These results apply not only to the collision cross section but also to a physical quantity expressible in the form ¦〈Γ′¦F¦Γ〉¦² of a transition probability withany F that is independent of the initial and final rotational states ¦Γ〉 and ¦Γ′〉.