On Majorana Representations of A6 and A7

The Majorana representations of groups were introduced in Ivanov (The Monster Group and Majorana Involutions, 2009) by axiomatising some properties of the 2A-axial vectors of the 196 884-dimensional Monster algebra, inspired by the sensational classification of such representations for the dihedral groups achieved by Sakuma (Int Math Res Notes, 2007). This classification took place in the heart of the theory of Vertex Operator Algebras and expanded earlier results by Miyamoto (J Alg 268:653–671, 2003). Every subgroup G of the Monster which is generated by its intersection with the conjugacy class of 2A-involutions possesses the (possibly unfaithful) Majorana representation obtained by restricting to G the action of the Monster on its algebra. This representation of G is said to be based on an embedding of G in the Monster. So far the Majorana representations have been classified for the groups G isomorphic to the symmetric group S ₄ of degree 4 (Ivanov et al. in J Alg 324:2432–2463, 2010), the alternating group A ₅ of degree 5 (Ivanov AA, Seress á in Majorana Representations of A ₅, 2010), and the general linear group GL ₃(2) in dimension 3 over the field of two elements (Ivanov AA, Shpectorov S in Majorana Representations of L ₃(2), 2010). All these representations are based on embeddings in the Monster of either the group G itself or of its direct product with a cyclic group of order 2. The dimensions and shapes of these representations are given in the following table:     

The A2 (n, 3px) Rydberg state of formaldehyde

Pairs of bands were observed in the absorption spectrum of H₂CO, HDCO, and D₂CO in the 1470-1430 Å region which were characterized by well-defined rotational band contours. A band contour synthesis of the observed band envelopes demonstrated that the bands are described by type C selection rules. From the observed intervals and their shifts on deuterium isotope substitution these bands were assigned to quantum additions of ν₅ and ν₆. The symmetry of the upper state was deduced to be ¹A₂ from the vibrational assignment of the bands and their polarizations, while the results from MO theory lead to the orbital assignment n → 3p_x. The electronic transition then is .     

Oxygen migration in A2B2O7 pyrochlores

Atomic scale computer simulation has been used to predict activation energies for oxygen migration. In total, 54 compounds with the A₂B₂O₇ pyrochlore structure were simulated. In each case, oxygen migration was assumed to proceed via an oxygen vacancy mechanism with oxygen ions hopping between 48f sites. For some compounds the unoccupied 8a interstitial position played an important role in the migration mechanism. The results were analyzed using a contour map of activation energy versus A cation radius along the ordinate and B cation radius along the abscissa. This identified areas of similar cation radii, which exhibit lower activation energy. Results compare favourably with available experimental data.     

The Forbidden RotationalQ-Branch of CH3CF3: Torsional Properties and (A1−A2) Splittings

The pure rotational spectrum driven by the small distortion dipole moment perpendicular to the symmetry axis has been investigated between 8 and 18 GHz for CH₃CF₃in the ground vibrational state using a pulsed Fourier transform waveguide spectrometer. This molecule has been selected as a prototype for the case of a symmetric top with small (∼500 kHz) torsional energy splittings in the ground torsional state (ν₆= 0). In this state, six (k± 3 ←k)Q-branch series have been measured for lower stateK= |k| between 3 and 8 with 27 ≤J≤ 75. For (ν₆= 1), three series with lower stateKbetween 5 and 7 with 49 ≤J≤ 66 have been observed. In two of these series, the torsional fine structure extending over ∼6.8 MHz has been fully resolved. The (A₁−A₂) splitting has been measured in the (ν₆= 0) series (K= 6 ← 3) for 37 ≤J≤ 74. The global data set of 443 frequencies included avoided-crossing molecular-beam splittings of Meerts and Ozier (1991.Chem. Phys.152, 241–259) and mm-waveR-branch measurements of Bocquetet al.(1994.J. Mol. Spectrosc.165, 494–499). In a weighted least-squares analysis, a good fit was obtained by varying 18 parameters in a Hamiltonian that represented both the torsional effects and the sextic splittings. Effective values have been determined for both rotational constants, eight torsional parameters including the barrier height, six diagonal centrifugal distortion constants, and two centrifugal distortion constants (? and ?_J) that characterize the (Δk= ±3) matrix elements. The difficulties are discussed that arise in defining a unique model for the torsional terms in the Hamiltonian when a high barrier symmetric top is investigated by distortion moment spectroscopy. The redundancies are investigated that exist in the quartic and sextic Hamiltonian for a near-spherical top such as CH₃CF₃.     

Line strength measurements of carbonyl sulfide (OCS) in the 2v3, v1+2v2+v3, and 4v2+v3 bands

To support planetary studies of the Venus atmosphere, we measured line strengths of the 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ bands of the primary isotopologue of carbonyl sulfide (¹⁶O¹²C³²S), whose band centers are located at 4101.387, 3937.427, and 4141.212 cm⁻¹, respectively. For this, infrared absorption spectra in normal carbonyl sulfide (OCS) sample gas were recorded at an unapodized resolution of 0.0033 cm⁻¹ at ambient room temperatures using a Bruker Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory. The FTS instrumental line shape (ILS) function was investigated, which revealed no significant instrumental line broadening or distortions. Various custom-made short cells and a multi-pass White cell were employed to achieve optical densities sufficient to observe the strong 2v₃ and the weaker bands in the region. Gas sample impurities and the isotopic abundances were determined from mass spectrum analysis. Line strengths were retrieved spectrum by spectrum using a non-linear curve fitting algorithm adopting a standard Voigt line profile, from which Herman–Wallis factors were derived for the three bands. The band strengths of 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ of ¹⁶O¹²C³²S (normalized at 100% of isotopologue) are observed to be 6.315(13)×10⁻¹⁹, 1.570(2)×10⁻²⁰, and 7.949(20)×10⁻²¹ cm⁻¹/molecule cm⁻², respectively, at 296 K. These results are compared with earlier measurements and the HITRAN 2004 database.     

A new family of magnetoelectric materials: A2M4O9(A = Ta, Nb; M = Mn, Co)

The existence of the magnetoelectric (ME) effect in the transition metal niobates and tantalates A₂M₄O₉(A = Ta, Nb; M = Mn, Co) has been confirmed by the observation of the electrically induced magnetic moment in these materials. Both parallel and prependicular ME susceptibilities were measured as a function of temperature in powder specimens. The transition temperatures were found to be 110 ±1 (Nb₂Mn₄O₉), 103 ±1 (Ta₂Mn₄O₉), 27.0 ±0.5 (Nb₂Co₄O₉), and 20.6 ±0.5°K (Ta₂Co₄O₉) from the ME measurements.     

High-resolution infrared study of the 2ν3 (A1, E) and ν1 + ν3 (E) bands of NF3

The 2ν₃ overtone (A₁, E) and the ν₁ + ν₃ (E) combination bands of the oblate symmetric top ¹⁴NF₃ were studied by FTIR spectroscopy with a resolution of 2.5 × 10⁻³ cm⁻¹. Nearly 500 lines up to K_max/J_max = 30/43 were observed for the weak A₁ component reaching the v₃ = 2⁰ substate (1803.1302 cm⁻¹), the majority of which corresponded to reinforced K = 3p-type transitions. For the strong E component reaching the v₃ = 2^±2 substate (1810.4239 cm⁻¹), about 3550 transitions were assigned up to K_max/J_max = 65/69, favoring a clear observation of the ℓ(4, −2) and ℓ(4, 4) splittings within the kℓ = −2 and +4 sublevels, respectively. The two v₃ = 2 substates are linked by the ℓ(2, 2)- and ℓ(2, −1)-type interactions, providing severe crossings, respectively, at K′ = 6 and near K′ = 24 on the v₃ = 2⁺² side. A model working in the D-reduction and including all these ℓ-type interactions could reproduce together 3695 nonzero weighted experimental data (NZW) through 33 free parameters with a standard deviation of σ = 0.357 × 10⁻³  cm⁻¹. As for the ν₁ + ν₃ (E) combination band, about 3690 lines were assigned up to K_max/J_max = 45/55. Its v₁ = v₃ = 1 upper state (1931.577 5 cm⁻¹) was treated using the same model recently applied to the v₃ = 1 (E, 907.5413 cm⁻¹) state. It yielded 21 free parameters through 3282 NZW experimental data, adjusted with σ = 0.344 × 10⁻³  cm⁻¹ in the D-reduction. For the two excited states, the small and unobserved ℓ(0, 6) interaction was tested as useless. To confirm the adequacy of the vibrationally isolated models used, some other reductions of the Hamiltonian were tried. For the v₃ = 2 state, the D-, L-, and LD-reductions led to similar σ’s, while the Q one was not successful. For the v₁ = v₃ = 1 state, the D- and Q-reductions gave comparable σ’s, while the QD-reduction was not as good. The corresponding unitary equivalence relations are generally more nicely fulfilled for the v₃ = 2 state than for the v₁ = v₃ = 1 state. The three derivable anharmonicity constants in cm⁻¹ are x₃₃ = −4.1528, g₃₃ = +1.8235 and x₁₃ = −7.9652.     

钪原子的自电离里德伯能级3d4s(1D2)nf2 D3/2,3d4s(1D2)nf2 F5/2和3d4s(1D2)np2 D3/2<

在多通道量子亏损理论框架下,利用相对论多通道理论,分别在冻结实近似和考虑偶极极化下计算钪原子的J^π=(3/2)^-,(5/2)^-的三个收敛于 3d4s(¹D₂)的自电离里德伯系列的能级.对3d4s(¹D₂)np²D_3/2和3d4s(^{1 关键词： 相对论多通道理论 多通道量子亏损理论 电子-电子关联 自电离里德伯系列}     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP）,建立了一种称之为相干纠缠态的两粒子体系的新表象,研究了这种新表象的性质,从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉,既具有相干态的特性,又体现了纠缠态的特征,具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

Determination of hadronic partial widths for scalar-isoscalar resonances f0(980), f0(1300), f0(1500), f0(1750) and the broad state f0(1530 ?250+90 )

Recently [see V.V. Anisovich et al., Yad. Fiz. 63, 1489 (2000)], the K-matrix solutions for the wave IJ ^PC=00⁺⁺ were obtained in the mass region 450–1900 MeV, where four resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f ₀(1530 ₋₂₅₀ ⁺⁹⁰ ) are located. Based on these solutions, partial widths are determined for scalar-isoscalar states decaying into the channels ππ, KK ηη, ηη′, ππππ and corresponding decay couplings. From Yadernaya Fizika, Vol. 65, No. 8, 2002, pp. 1583–1590. Original English Text Copyright ? 2002 by Anisovich, Nikonov, Sarantsev. This article was submitted by the authors in English.     

Electronic structures of ternary iron arsenides AFe2As2 (A = Ba, Ca, or Sr)

We have studied the electronic and magnetic structures of the ternary iron arsenides AFe₂As₂ (A = Ba, Ca, or Sr) using the first-principles density functional theory. The ground states of these compounds are in a collinear antiferromagnetic order, resulting from the interplay between the nearest and the next-nearest neighbor superexchange antiferromagnetic interactions bridged by As 4p orbitals. The correction from the spin-orbit interaction to the electronic band structure is given. The pressure can reduce dramatically the magnetic moment and diminish the collinear antiferromagnetic order. Based on the calculations, we propose that the low energy dynamics of these materials can be described effectively by a t-J _H -J ₁-J ₂-type model [2008, arXiv: 0806.3526v2].     

Measurement of the analysing powers iT11, T20, T21 and T22 in elastic deuteron-proton scattering

The analysing powers iT₁₁, T₂₀, T₂₁ and T₂₂ for the elastic scattering of polarized deuterons by protons have been measured at deuteron energies of 6, 8, 10 and 11.5 MeV with the polarized deuteron beam from a tandem accelerator. The measurements cover the c.m. angular range from 40° to 155° and show small but non-zero analysing powers at all energies.     

Self-broadening, self-shift and self-mixing in the ν2, 2ν2 and ν4 bands of NH3

Using Fourier-transform spectra (Bruker IFS 120 HR, resolution ≈0.004 cm⁻¹) of NH₃ in nine branches of the ν₂, 2ν₂ and ν₄ bands, self-broadening and self-shift as well as self-mixing coefficients have been determined at room temperature (T=295 K) for more than 350 rovibrational lines located in the spectral range 1000–1800 cm⁻¹. A non-linear least-squares multispectrum fitting procedure, including line mixing effects, has been used to retrieve successively the line parameters from 11 experimental spectra recorded at different pressures of pure NH₃. The accuracies of self-broadening coefficients are estimated to be better than 2% for most lines. The mean accuracies of line-mixing and line-shift data are estimated to be about 15% and 25%, respectively. The results are compared with previous measurements and with values calculated using a semiclassical model based upon the Robert–Bonamy formalism that reproduces rather well the systematic experimental J and K quantum number dependencies of the self-broadening coefficients.The results concerning line mixing demonstrate a large amount of coupling between the symmetric and asymmetric components of inversion doublets mainly in the ν₄ band. The line mixing parameters are both positive and negative. More than two thirds of the lines studied here have a positive shift coefficient. However, for most of them the shift coefficients are negative in the 2ν₂ band. They are positive for the R branch of the ν₂ band and for the ^PR and ^RP branches of the ν₄ band. For the other branches they are both positive and negative. Some components of inversion doublets illustrate a correlation between line mixing and shift phenomena demonstrated by a quadratic pressure dependence of line position.     

NH3 self-broadening coefficients in the ν2 and ν4 bands and line intensities in the ν2 band

Self-broadening coefficients of NH₃ in the ν₂ and ν₄ bands and absolute line intensities in the ν₂ band have been measured at room temperature for some selected lines in the P- and R-branches. Using a Fourier transform spectrometer, line intensities and collisional widths were obtained by fitting Voigt profiles to the measured shapes of the lines. The results of self-broadening coefficients are in reasonable agreement with calculated linewidths using a semiclassical model which reproduce rather well the systematic experimental J and K quantum numbers dependencies. Satisfactory agreement was also obtained for line intensities with previous measurements in the ν₂ band. From the intensity measurements, we have determined effective transition dipole moments as well as Herman–Wallis parameters for the ν₂ band.     

The Mechanism of Magnetically Tuned Singlet–Triplet Avoided Crossings in the ÃA2– A1 40 Band of Thioformaldehyde H2C=S

Magnetically tuned singlet–triplet perturbations in the 4¹Ã¹A₂–2¹3¹ã³A₂ system of thioformaldehyde, found in ortho-rotational states (I = 1, the two hydrogen spins parallel) have been identified as being caused by vibronic spin–orbit coupling. This perturbation mechanism has been confirmed in several avoided crossings observed in this work for para states (I = 0, hydrogen spins antiparallel) which are much stronger. Parametrization of the theory has led to a quantitative understanding of the experimental frequency-field relations, and to an accurate prediction of the rovibrational energies of the triplet state. This in turn permitted the detection of about 100 Doppler-limited 2¹3¹ã³A₂–0^{0 1}A₁ rovibronic transitions which led into fine structure states. The combined data was then used to determine a set of rotational, fine, and hyperfine triplet-state parameters, the term value T₀(2¹3¹ã³A₂) = (16 685.385 ± 0.002) cm⁻¹, and the spin–orbit vibronic singlet–triplet coupling constant, W_ST = (0.0691 ± 0.0016) cm⁻¹. A large number of frequency perturbations observed in the crossings, ranging from 2 to 300 MHz, can be explained with this single parameter.     

Observation of signature inversion in the πh9/2?vi13/2 oblate band

High-spin states in ¹⁹⁰Tl have been studied via the ¹⁶⁰Gd(³⁵Cl, 5nγ) reaction. The level scheme, consisting of the πh _9/2⊗vi _13/2 oblate band and a cascade with character of single particle excitations, has been established. Spin values have been firmly assigned to the oblate band in ¹⁹⁰Tl, resulting in low-spin signature inversion in the πh _9/2⊗vi _13/2 oblate band for the first time. Based on the similarity of the level structure in doubly odd Tl nuclei, spin values for the oblate bands in ^192–200Tl should be re-assigned, and a consistent low-spin signature inversion has occurred in these oblate deformed nuclei. The low-spin signature inversion phenomena can be interpreted qualitatively by using the 2-quasiparticle plus rotor model including p-n residual interactions.     

钴磷族化合物BaT2P2和BaT2As2(T=Co,Rh, Ir) 的电子结构

基于密度泛函理论(DFT)在广义梯度(GGA)下计算了钴磷族化合物BaT₂P₂和BaT₂As₂(T=Co, Rh, Ir)的电子结构.研究发现在BaCo₂P₂和BaCo₂As₂中,由于范霍夫畸点位于费米面附近使得费米能级处的态密度非常高,从而导致由斯通纳机理引起的巡游铁磁不稳定性.在从Co到 关键词： 电子结构 范霍夫畸点 斯通纳不稳定性     

Infrared fluorescence from exciting the v1 and v8 modes of CF2Cl2 with a TEA CO2 laser

Infrared fluorescence from CF₂Cl₂ molecules excited with a TEA CO₂ laser below dissociation threshold, is time resolved with a HgCdTe detector without spectral resolution in the range 1100-700 cm^-1. The signal fits well to a sum of three exponentials, which are interpreted as a bulk vibration-vibration (V-V) energy transfer between the fraction of highly excited and non-excited molecules in the irradiated volume, vibro-translation (V-T) deactivation and diffusional heat and mass transport to the surrounding. The measured V-V and V-T rates increase with vibrational excitation and the V-T deactivation is independent on the observed modes (v₁/v₆ or v₈) if v₈ or v₁ are excited respectively.     

The structure and the analytical potential energy function of NH2 （X^2B1）

This paper reports that the equilibrium structure of NH2 has been optimized at the QCISD/6-311＋＋G （3df, 3pd） level. The ground-state NH2 has a bent （C2v, X^2B1） structure with an angle of 103.0582°. The geometrical structure is in good agreement with the other calculational and experimental results. The harmonic frequencies and the force constants have also been calculated. Based on the group theory and the principle of microscopic reversibility, the dissociation limits of NH2（C2v, X^2B1） have been derived. The potential energy surface of NH2（X^2B1） is reasonable. The contour lines are constructed, the structure and energy of NH2 reappear on the potential energy surface.