High-resolution diode laser absorption spectroscopy of the O-H stretch overtone band (2,0,0)←(0,0,0) of the HO2 radical

The O-H stretching overtone (2ν₁) of the HO₂ radical was observed between 6603.2 to by using tunable diode laser absorption spectroscopy (TDLAS). About 1000 lines were observed in this region of which 491 transitions could be definitively assigned to the 2ν₁. The spectrum is observed to be an A/B hybrid band with band features of both a perpendicular and parallel nature. Transitions of the A-type bands with K_a^′=0-3, N^′?16 and transitions of the B-type bands with K_a^′=0,1, N^′?15 were assigned. The origin calculated from the best fit to the present spectrum is at which is ∼ higher than previously reported. The overtone spectrum is observed to be heavily perturbed, possibly by Fermi resonance with energy levels of the nearby (ν₂+5ν₃) state.     

A relativistic wave equation for the Skyrmion

We propose a relativistically invariant wave equation for the Skyrme soliton. It is a differential equation on the space R^1,3×S³ which is invariant under the Lorentz group and isospin. The internal variable valued in SU(2)≡S³ describes the orientation of the soliton. The mass of a particle of spin and isospin both equal to is predicted to be which agrees with the known spectrum for low angular momentum. The iso-scalar magnetic moment is predicted to be , where Σ is the spin.     

The high-resolution infrared spectrum of BF3 from 400 to 1650 cm

High-resolution infrared spectra of boron trifluoride, enriched to 99.5 at. % ¹¹B, have been measured from 400 to 1650 cm⁻¹. In that region we have identified and analyzed 16 absorption bands attributed to the three fundamental bands, two combination bands, 10 hot bands, and one difference band. All possible states were accessed in this region through direct transitions either from the ground state or as hot bands from thermally populated levels. The spectral resolution of the measurements varied from 0.0015 to 0.0020 cm⁻¹. An improved set of ground state rotational constants and rovibrational constants for the infrared-active fundamental vibrations have been determined from over 32 000 assigned transitions. This study resulted in the first direct characterization of the infrared-inactive ν₁ state of ¹¹BF₃ leading to values for ν₁, , and of 885.843205(24), 0.000678548(53), and 0.000337564(66) cm⁻¹, respectively. The Fermi resonance perturbation between the E′ states ν₃ and 3ν₄ (l = ±1) was further elucidated by observation of hot band transitions to both the 3ν₄ (l = ±1) and 3ν₄ (l = ±3) states. Several other resonances were also found including the weak rotational interaction, between the state 2ν₂ and the E′ state of ν₁ + ν₄.     

Anomalous thermostat and intraband discrete breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. The coupling between both parts is bilinear. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation with memory kernels and noise term for the anharmonic coordinates . For zero temperature, i.e. for , we prove that the support of the Fourier transform of and of the time averaged velocity-velocity correlation functions of the anharmonic system cannot overlap. As a consequence, the asymptotic solutions can be constant, periodic, quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy E_T transferred to the harmonic system up to time T is proportional to T^α. If equals one of the phonon frequencies ω_ν, it is α=2. We prove that there is a zero measure set L such that for in its full measure complement R?L, it is α=0, i.e. there is no energy dissipation. Under certain conditions L contains a subset L^′ such that for the dissipation rate is nonzero and may be subdissipative (0≤α<1) or superdissipative (1<α≤2), compared to ordinary dissipation (α=1). Consequently, the harmonic bath does act as an anomalous thermostat, in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation, forcing convergence to equilibrium. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a Cantor set C(k) of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing for , related to . For the small denominators do not lead to divergencies such that is a smooth and bounded function in t.     

Convergent iterative solutions for a Sombrero-shaped potential in any space dimension and arbitrary angular momentum

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with an N-dimensional radial potential and an angular momentum l. For g large, the rate of convergence is similar to a power series in g⁻¹.     

On short and semi-short representations for four-dimensional superconformal symmetry

Possible short and semi-short representations for and superconformal symmetry in four dimensions are discussed. For the well known short supermultiplets whose lowest dimension conformal primary operators correspond to -BPS or -BPS states and are scalar fields belonging to the SU(4) R-symmetry representations [0,p,0] and [q,p,q] and having scale dimension Δ=p and Δ=2q+p, respectively, are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For a -BPS multiplet need not have a protected dimension unless the primary state belongs to a [1,p,1] representation.     

Giant optical anisotropy in R-plane GaN/AlGaN quantum wells caused by valence band mixing effect

This study investigates the optical anisotropy spectrum in the R-plane (i.e., the -oriented layer plane) of GaN/Al_0.2Ga_0.8N quantum wells of different widths. The optical matrix elements in the wurtzite quantum wells are calculated using the k⋅p finite difference scheme. The calculations show that the valence band mixing effect produces giant in-plane optical anisotropy in -oriented GaN/Al_0.2Ga_0.8N quantum wells with a narrow width. The nature of the in-plane optical anisotropy is found to be dependent on the well width. Specifically, it is found that the anisotropy changes from x^′-polarization to y^′-polarization as the well width increases.     

Crystal field effect and geometric frustration in Er2Ti2O7 —an XY antiferromagnetic pyrochlore

Magnetic susceptibility of powder Er₂Ti₂O₇ (ErT) is measured between 300 K and 80 K. shows a Curie-Weiss (CW) type behaviour with   ErTiO_3.5 and . A crystal field (CF) analysis of our experimental data, g-values (g_∥=0.27 and g_⊥=7.8) and the positions of two CF levels (reported earlier from an inelastic neutron scattering study) provide CF parameters and CF levels of the ground ⁴I_15/2 and excited multiplets of ErT. The theoretical follows a CW-type behaviour, with . Single-ion magnetic anisotropy (χ_⊥−χ_∥) is 9500×10⁻⁶ emu/mol ErTiO_3.5 at 300 K, which increases by ∼54 times at 10 K and ErT resembles an XY planar system. It can be inferred from CF analysis that the earlier observed change of from −13 K to −22 K below 50 K is not due to the CF effect. Nuclear hyperfine (HF) levels of ¹⁶⁷ErT and ¹⁶⁶ErT are calculated and the theoretical curve of vs. T (K) for T<T_N matches the observed results. Mössbauer lines expected for ¹⁶⁶ErT are also predicted.     

Rovibrational spectroscopy of the Fermi-interacting ν4 = 1 and ν3 = ν6 = 1 levels of DCF3

The high-resolution infrared spectrum of deuterated fluoroform (DCF₃) was studied in the 700 and 1200 cm⁻¹ regions, with the aim of assigning and analyzing the ν₄ CF₃ asymmetric stretching vibration. The Fermi-type anharmonic coupling between the ν₄ = 1 and ν₃ = ν₆ = 1 rovibrational levels, already mentioned in an early work of Ruoff et al. [Spectrochimica Acta Part A 31A (1975) 1099-1100], was studied here for the first time under high resolution. Assignments in the ν₃ + ν₆/ν₄ band system were confirmed and extended by the identification of the ν₃ + ν₆ − ν₆ and ν₄-ν₆ bands in the 700 cm⁻¹ region, the latter being enhanced near the Fermi crossings of the studied levels. Data from both the hot and difference bands were included in the analysis. The close separation of the studied vibrational levels of about 14.8 cm⁻¹ produces a large variety of resonance crossings which involve levels with . Besides the Fermi () and Coriolis () resonances, they were accounted for by inclusion of additional higher-order ( and ) interaction terms between the vibrational states. The least-squares fit of more that 16,000 vibration-rotation transitions provides a quantitative reproduction of data in all bands.     

4-benzyl pyridinium dihydrogenmonophosphate C6H5CH2C5H4NHH2PO4 : Single-crystal structure and its conductivity in polycrystalline form

The salt 4-benzyl pyridinium dihydrogenmonophosphate is monoclinic P2₁/c with the following unit cell dimensions: ; ; ; and β=97.328(11). Also, , D_x=1.403, , F(000)=560; ; and R=0.0495 and R_w=0.0964 for 3733 independent reflections. The structure consists of infinite parallel two-dimensional planes built of H₂PO₄⁻ anions and C₆H₅CH₂C₅H₄NH⁺ cations mutually connected by strong O-H ?O and N-H ?O hydrogen bonding. There are no contacts other than the normal Van der Waals interactions between the layers. The conductivity relaxation parameters associated with some H⁺ conduction have been determined from an analysis of the spectrum measured in a wide temperature range.     

Theoretical investigation of zero-field splitting and local structure distortion for a substitution of Fe ion in CdCl2 crystal

A theoretical method for studying the inter-relation between electron and molecule structure is proposed on the basis of the complete energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for d⁵ configuration ion in a trigonal ligand-field. As an application, the local distortion structure of (FeCl₆)^3- coordination complex for Fe³⁺ ions doped into CdCl₂ is investigated. Both the second-order zero-field splitting parameter and fourth-order zero-field splitting parameter are considered simultaneously in the structural investigation. By diagonalizing the complete energy matrices, the local structure distortion parameters ΔR=−0.24 Å, Δθ=2.137° at 26 K and ΔR=−0.203 Å, Δθ=2.515° at 225 K for Fe³⁺ ions in CdCl₂ are determined. These results elucidate a microscopic origin of various ligand-field parameters which are usually used empirically for the interpretation of electron paramagnetic resonance results. It is found that the theoretical results are in good agreement with the experimental values.     

Nonperturbative equation of state of quark-gluon plasma: Applications

The vacuum-driven nonperturbative factors L_i for quark and gluon Green’s functions are shown to define the nonperturbative dynamics of QGP in the leading approximation. EoS obtained recently in the framework of this approach is compared in detail with known lattice data for μ = 0 including P/T⁴, ε/T⁴, . The basic role in the dynamics at T ? 3T_c is played by the factors L_i which are approximately equal to the modulus of Polyakov line for quark L_fund and gluon L_adj. The properties of L_i are derived from field correlators and compared to lattice data, in particular the Casimir scaling property follows in the Gaussian approximation valid for small vacuum correlation lengths. Resulting curves for P/T⁴, ε/T⁴, are in a reasonable agreement with lattice data, the remaining difference points out to an effective attraction among QGP constituents.     

The 2ν4 overtone bands of FClO3

The high resolution infrared spectrum of the mono-isotopic species F³⁵Cl¹⁶O₃ has been studied in the region of the 2ν₄ overtone, from 2560 to 2680 cm⁻¹. The perpendicular component is strong and clearly observed while the parallel component is very weak and almost completely hidden by the perpendicular one. Their origins differ by 12.6 cm⁻¹, the being located at higher wavenumbers. The band is perturbed by the anharmonic interaction between the v₄ = 2, l₄ = ?2 and v₂ = v₄ = v₅ = 1, l₄ = l₅ = ±1 excited states, both of E symmetry. In total 3157 transitions have been assigned, 83% of these to , 12% to , and 5% to . The three bands have been analyzed simultaneously, taking into account the Fermi resonance effective between the excited states of E symmetry. The ro-vibration parameters of the excited states have been obtained, including the deperturbed band origins of and , at 2628.5890(4) and 2619.3342(5) cm⁻¹, respectively. The W₂₄₅ anharmonic constant is equal to 4.0161(4) cm⁻¹. The x₄₄+g₄₄ and x₂₄+x₄₅+g₄₅ anharmonicity constants have been derived from the obtained band origins and those of ν₄ and ν₂ + ν₅.     

Jarlskog invariant of the neutrino mapping matrix

The Jarlskog Invariant J_ν-map of the neutrino mapping matrix is calculated based on a phenomenological model which relates the smallness of light lepton masses m_e and m₁ (of ν₁) with the smallness of T violation. For small T violating phase χ_l in the lepton sector, J_ν-map is proportional to χ_l, but m_e and m₁ are proportional to . This leads to . Assuming , we find J_ν-map≅1.16×10^-2, consistent with the present experimental data.     

New type shift operators for circular well potential in two dimensions

New type shift operators for circular well potential in two dimensions are identified. These so-called shift operators connect those quantum systems with the different potentials but with same energy spectrum. It should be noted that these operators depend on both the radial circular and angular variables r and φ. We find that the operators P_±=Px±Py play the role of the shift operators. The radial linear momentum , the angular momentum and the Hamiltonian form a complete set of commuting operators with the SO(2) symmetry.     

Radiative lifetimes of Zn I highly excited states

The energy levels and lifetimes of 4sns³S₁ (n=5-25), 4snd³D₁ (n=4-25) and 4snp¹P₁ (n=5-15) of Zn I have been evaluated using the multichannel quantum defect theory (MQDT). The calculated lifetimes of 4sns³S₁ and 4snd³D₁ characterized by the effective quantum ν are given by the formula and , respectively.     

High resolution rovibrational spectroscopy of pyrimidine: Analysis of the B1 modes ν10b and ν4 and B2 mode ν6b

We report the first high resolution rovibrational analysis of the infrared spectrum of pyrimidine (C₄H₄N₂) based on measurements using our Fourier transform spectrometer, the Bruker IFS 125 HR Zürich Prototype (ZP) 2001. Measurements were conducted at room temperature in a White-type cell with effective optical path lengths between 3.2 and 9.6 m and with resolutions ranging from 0.0008 to 0.0018 cm⁻¹ in the region between 600 and 1000 cm⁻¹. The spectrum was analyzed in the ν₄ (), ν_10b () and ν_6b regions of pyrimidine () using an effective Hamiltonian. A total of about 15 000 rovibrational transitions were assigned. The root mean square deviations of the fitted data are in the ranges d_rms = 0.00018-0.00024 cm⁻¹, indicating an excellent agreement of experimental line data with the calculations. The results are discussed briefly in relation to possible extensions to spectra of DNA bases and to intramolecular vibrational redistribution at higher energy. The analysis of the ν_10b and ν₄ bands will also be useful in the interstellar search for pyrimidine in the infrared region.