Combined chiral dynamics and MIT bag model study of strong Σ<Superscript>(*)</Superscript><Subscript>Q</Subscript>→Λ<Subscript>Q</Subscript>π decays

The strong decays of the heavy baryons Σ^(*) _Q→Λ_Qπ are studied by combining the chiral dynamics and the MIT bag model. In the charm sector, we calculate the decay widths Γ(Σ^(*) _c→Λ_cπ) and compare these with the experimental data and other theoretical estimations. In addition, we also predict the strong decay widths Γ(Σ^(*) _b→Λ_bπ).     

Perturbations in the rotational structure of the 4<Emphasis Type="Italic">p</Emphasis> complex of H<Subscript>2</Subscript> molecule terms

A statistical analysis of all the available data on the wave numbers of spectral lines related to triplet-triplet electronic-vibrational-rotational (rovibronic) radiation transitions into the H₂ molecule (1sσ2sσ) a ³Σ _g ⁺ electronic state was performed for the first time. This allowed us to check and refine the controversial identification of several spectral lines. Optimum rovibronic term values were found for 15 electronic states, including the (4pσ)f ³Σ _u ⁺, (4pπ)k ³Π _u ⁺, and (4pπ)k ³Π _u ⁻ states studied in this work. The ratios between the oscillator strengths of R- and P-branch lines with common upper levels (branching coefficients) for the f ³Σ _u ⁺ → a ³Σ _g ⁺ and k ³Π _u ⁺ → a ³Σ _g ⁺ systems of H₂ molecule bands were measured for the first time. Substantial deviations of the measured branching coefficients from the corresponding ratios between the Henl-London factors were observed. The deviations monotonically increased as the rotational quantum number N grew, which, in combination with substantial Λ-doubling in the k ³Π _u state, was evidence of an important role played by electronicrotational interaction in the 4pσ³Σ _u ⁺ and 4pπ³Π _u ⁺ adiabatic electronic states. A strong correlation was observed between the N dependences of branching coefficients for transitions from the mutually perturbed f ³Σ _u ⁺ and k ³Π _u ⁺ electronic states. The results of this work show that the measured branching coefficients are a much more sensitive and capacious channel of information about perturbation effects than rovibronic term values.     

Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .     

A Riemann–Roch Theorem¶for One-Dimensional Complex Groupoids

We consider a smooth groupoid of the form Σ⋊Γ, where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C ₀(Σ)⋊Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem of Connes and Moscovici. This involves in particular a generalisation of the Euler class constructed from the modular automorphism group of the von Neumann algebra L ^∞(Σ)⋊Γ. Received: 1 February 2000 / Accepted: 3 December 2000     

Detection by two-photon ionization and magnetic trapping of cold Rb2 triplet state molecules

We present detailed experimental spectra and accurate theoretical interpretation of resonance-enhanced two-photon ionization of ultracold rubidium molecules in the 14000–17000 cm^-1 transition energy range. The dimers are formed in a magneto-optical trap by photoassociation followed by radiative decay into the a ³Σ_u⁺ lowest triplet state. The theoretical treatment of the process, which reproduces the main features of the spectra, takes into account the photoassociation and decay steps as well as the resonant ionization through the manifold of intermediate gerade states correlated to the 5S + 4D limit. In particular, the energy of the v=1 level of the potential well has been determined for the first time. In addition, a tight constraint has been put on the position of the a ³Σ_u⁺ repulsive wall. Finally, magnetic trapping of rubidium molecules in the a ³Σ_u⁺ state is demonstrated. Electronic supplementary material Online Material     

Calculation of the spectroscopic constants for the electronic states A1Σ u+ , B1Πu, C1Πu, D1Σ u+ , and E1Σ u+ of the cesium dimer

The vibrational, rotational, and centrifugal distortion constants have been calculated for the electronic states A ¹Σ _u ⁺ , B ¹Π_u, C ¹Π_u, D ¹Σ _u ⁺ , and E ¹Σ _u ⁺ of the Cs₂ molecule. The calculation was performed on the basis of the semiempirical potential energy curves constructed in this paper. The calculated spectroscopic constants are compared with the experimental data. Original Russian Text ? A.D. Smirnov, 2007, published in Optika i Spektroskopiya, 2007, Vol. 102, No. 1, pp. 23–27.     

Calculation of spectroscopic constants and radiative parameters for A1Σ u+ -X1Σ g+ and B1Πu-X1Σ g+ electronic transitions of sodium dimer

Vibrational, rotational, and centrifugal spectroscopic constants and radiative parameters, i.e., the Einstein coefficients, oscillator strengths, and wave numbers for vibrational transitions in electronic systems of bands A ¹Σ _u ⁺-X ¹Σ _g ⁺ (0 ≤ v′ ≤ 25; 0 ≤ v″ ≤ 44), B ¹Π _u -X ¹Σ _g ⁺ (0 ≤ v′ ≤ 29; 0 ≤ v″ ≤ 47), and the radiative lifetimes for the vibrational levels of excited states of the sodium dimer, are calculated. The calculations are carried out based on semiempirical potential curves constructed in this study. The calculated spectroscopic constants and radiative lifetimes are compared to the experimental values.     

Laser excited fluorescence of Na2

Fluorescence was excited in theB ¹Γ _u −X ¹Σ _g ⁺ system of Na₂, using the 488 and 514.5 nm radiations from a cw Ar⁺ laser. The fluorescence was monitored through a double monochromator employing photoelectronic detection. In the spectrum resulting from the 488 nm excitation, apart from a large number of fluorescence series, a previously unreported series could be identified. On either side of all the members of the strongest series a large number of collisional satellites were observed and assigned.     

Radiative widths of neutral kaon excitations

We observe 147 events of the axial vector pairK ₁(1270)–K ₁(1400) produced in the Coulomb field of a Pb target and measure the radiative widths Γ(K ₁(1400)→K ⁰ + γ) = 280.8 ±23.2(stat.) ±40.4(syst.) keV and Γ(K ₁(1270) →K ⁰ + γ) = 73.2 ±6.1(stat.) ±28.3(syst.) keV. These first measurements are lower than the quark-model predictions. We also place upper limits on the radiative widths forK*(1410) andK ₂ ^* (1430) and find that the latter is very small in accord withSU(3)invariance in the naive quark model.     

Values of adsorption and surface concentrations of the components in Na-K-Cs alloys

The values of adsorption Γ _i ^(N) and surface concentration X _i ^ω of all the components in alloys of the Na-K-Cs system were determined. The adsorption of cesium Γ_Cs^(N) was found to be > 0, while that for sodium Γ_Na^(N) was < 0 in all ternary alloys. The adsorption of potassium was found to undergo inversion when passing from Γ_K^(N) > 0 in ternary alloys (the ratios being X _Na: X _Cs > 14.4 and X _Cs < 6.5 at %) to the negative value of adsorption Γ_K^(N) in the alloys with X _Na: X _Cs < 14.4 and any cesium concentrations. Using the Na-K-Cs system, it was demonstrated for the first time that conditions ΣΓ _i ^(N) = 0 and ΣX _i ^ω = 1 and are fulfilled in ternary alloys.     

Spectroscopy of the a3Σu + state and the coupling to the X1Σg + state of K2

We report on high resolution Fourier-transform spectroscopy of fluorescence to the a³Σ_u ⁺ state induced by two-photon or two-step excitation from the X¹Σ_g ⁺ state to the 2³Π_g state in the molecule K₂. These spectroscopic data are combined with recent results of Feshbach resonances and two-color photoassociation spectra for deriving the potential curves of X¹Σ_g ⁺ and a³Σ_u ⁺ up to the asymptote. The precise relative position of the triplet levels with respect to the singlet levels was achieved by including the excitation energies from the X¹Σ_g ⁺ state to the 2³Π_g state and the frequencies of the fluorescence down to the a³Σ_u ⁺ state in the simultaneous fit of both potentials. The derived precise potential curves allow for reliable modeling of cold collisions of pairs of potassium atoms in their ²S ground state. Electronic supplementary material Supplementary Online Material     

Search for and study of low-mass scalar mesons in reaction np → npπ+π? at neutron beam momentum Pn = (5.20 ± 0.12) GeV/c

We present the results of a search for and study of the resonance effects in the system of π⁺π⁻ from the reaction np → npπ⁺π⁻ at the momentum of quasi-monochromatic neutrons P _n = (5.20 ± 0.12) GeV/c from the data obtained in an exposure of the 1-m hydrogen bubble chamber of Veksler and Baldin Laboratory of High Energies, Joint Institute for Nuclear Research (VBLHE JINR). After the supplementary selection of the events where a secondary proton was emitted in the forward hemisphere in the general c.m.s. of the reaction (cosθ* _p > 0) in the effective mass spectrum of π⁺π⁻ combinations, we found nine peculiarities at the masses (350 ± 3), (408 ± 3), (489 ± 3), (579 ± 5), (676 ± 7), (762 ± 11), (878 ± 7), (1036 ±13), and (1170 ± 11) MeV/c ² with experimental widths of no more than several tens of MeV/c ². We carried out a direct measurement of the spins of resonances and also obtained other quantum numbers. All of these peculiarities have a similar set of quantum numbers I ^G (J ^PC ) = 0⁺ (0⁺⁺). We investigated a sequence of scalar-isoscalar resonances f ₀(σ₀) with masses in the range M ≤ 1200 MeV/c ². We found a phenomenological dependence of the resonance mass on its number. This dependence covered not only the resonances shown in this paper, but also those present in PDG tables with quantum numbers of f ₀(σ₀) mesons.     

Asymptotic behavior of orbits of C 0-semigroups and solutions of linear and semilinear abstract differential equations

In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t ⁿ f(t, u(t)), where A is the generator of a C ₀-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C ₀-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S ^p-A defined similarly to the case of S ^p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A _u:= A ∩ BUC(ℝ, X) if n = 0 and to t ⁿ A _u ⊕ w _n C ₀ (ℝ, X) if n ∈ ℕ, where w _n(t) = (1 + |t|)ⁿ. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan     

The quenching of nucleon yields in the nonmesonic weak decay of Λ -hypernuclei and the three-body weak decay process

Recent exclusive coincidence measurements of non-mesonic weak decays (NMWD) reported for the ratio of the partial decay width of neutron-induced-to-proton-induced NMWD, Γ_n/Γ_p , values of 0.45±0.11±0.03 and 0.51±0.13±0.04 for 5lam and ¹² _Λ C , respectively. These observations agree well with the improved theoretical Γ_n/Γ_p ratios which are in the range of 0.3-0.7. It appears that the long-standing discrepancy between the experimental and theoretical values of Γ_n/Γ_p has finally been solved. However, when compared to the results of intra-nuclear cascade (INC) calculations, the observed numbers of both single nucleons and coincident nucleon pairs are strongly quenched. The quenching of the proton yield observed previously has been interpreted as an increase of the Γ_n/Γ_p ratio. On the other hand, significant contributions from the two-nucleon-induced three-body process ΛNN → nNN are predicted. Indeed, the angular correlation of the emitted nucleon pairs in the NMWD of ¹² _Λ C showed not only decay events in back-to-back kinematics, but also events with non-back-to-back kinematics. In this paper we show that the difficulties to extract the correct Γ_n/Γ_p ratio from the proton spectra is related to the three-body weak-interaction process which strongly quenches the nucleon yields.     

Combined analysis of the PFOODR data on the a 3Σ u+ , 23Πg, 23Σ g+ , 33Πg, and 43Σ g+ states of the K2 molecule

The known and new heterogeneous spectral data on the triplet states a ³Σ _u ⁺ , 2³Π_g, 2³Σ _g ⁺ , 3³Π_g, and 4³Σ _g ⁺ of the K₂ dimer are simultaneously fitted. The data published in J. Mol. Spectrosc. 234, 41 (2005) are refined. The new information used in the analysis contains the data on the 2³Σ _g ⁺ state, which have not been considered previously. The range of internuclear distances where the potential function of the lowest triplet state a ³Σ _u ⁺ is defined is extended. Original Russian Text ? V.B. Sovkov, V.S. Ivanov, D. Li, F. Xie, Li Li, 2007, published in Optika i Spektroskopiya, 2007, Vol. 103, No. 5, pp. 747–751.     

On mechanism of population transfer to ungerade ion-pair states of I<Subscript>2</Subscript> molecule

We discuss the population transfer to the D 0 _u ⁺ and F 0 _u ⁺ ungerade ion-pair states of the I₂ molecule upon optical excitation of the E0 _g ⁺ and f 0 _g ⁺ gerade states by the optical-optical double resonance method. This effect is explained by multiphoton ionization of iodine vapor and subsequent collisions with photoelectrons.     

Non-Abelian Vortices on Compact Riemann Surfaces

We consider the vortex equations for a U(n) gauge field A coupled to a Higgs field f{\phi} with values on the n × n matrices. It is known that when these equations are defined on a compact Riemann surface Σ, their moduli space of solutions is closely related to a moduli space of τ-stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the matrix f{\phi} , we show that the vortex solutions are entirely characterized by the location in Σ of the zeros of det f{\phi} and by the choice of a vortex internal structure at each of these zeros. We describe explicitly the vortex internal spaces and show that they are compact and connected spaces.     

Hyperfine interactions in molecules through laser spectroscopy

The infrared and millimeter wave spectroscopy, laser Stark spectroscopy, and beam maser spectroscopy of CH₃CN and its isotopic species will be discussed. The beam maser spectroscopy and hyperfine structure of molecules like NCCCD, ClCCD and CH₃CCH are reviewed. The laser magnetic resonance and hyperfine structure in CF, CH and CH₂ free radicals will be discussed. The Lamb dip spectroscopy and laser-induced fluorescence in I₂ involving theB ³Π(0 _u ⁺ ) state are reviewed with special reference to its hyperfine structure. The splitting of the rotational levels of N ₂ ⁺ in itsX ²Σ _g ⁺ andB ²Σ _u ⁺ states due to hyperfine interactions (along with the hyperfine structure) in laser-induced fluorescence in theB−X transition is discussed. Recent results obtained in the laser photo-acoustic spectrum of ICl in the transitionX ¹Σ⁺ −A ³Π₁ will be presented and the possibility of the use of this technique in studying the hyperfine structure will be discussed.     

Equivariant <Emphasis Type="Italic">K</Emphasis>-Theory,Generalized Symmetric Products,and Twisted Heisenberg Algebra

 For a space X acted on by a finite group Γ, the product space X ⁿ affords a natural action of the wreath product Γ _n =Γ ⁿ ⋊S _n . The direct sum of equivariant K-groups were shown earlier by the author to carry several interesting algebraic structures. In this paper we study the K-groups of Γ _n -equivariant Clifford supermodules on X ⁿ . We show that is a Hopf algebra and it is isomorphic to the Fock space of a twisted Heisenberg algebra. Twisted vertex operators make a natural appearance. The algebraic structures on ℱ⁻ _Γ(X), when Γ is trivial and X is a point, specialize to those on a ring of symmetric functions with the Schur Q-functions as a linear basis. As a by-product, we present a novel construction of K-theory operations using the spin representations of the hyperoctahedral groups. Received: 3 February 2001 / Accepted: 17 August 2002 Published online: 10 January 2003     

Singlet molecular nitrogen in the Auroral ionosphere and under the conditions of laboratory discharge

Using the suggested model of the electron kinetics of N₂ singlet states, the population of the vibrational levels in the molecular nitrogen states (a′)¹Σ _u ⁻, a ¹Π _g , and w ¹Δ _u is calculated for the case when fast auroral electrons penetrate into the Earth’s ionosphere. It is shown for the first time that the population distribution of the vibrational levels v = 0−6 in the state a ¹Π _g in the auroral ionosphere and also in a laboratory discharge varies with atmospheric pressure insignificantly. Similar calculations for pure nitrogen atmosphere show a considerable increase in the populations of lower vibrational levels (v = 0−2) with rising pressure.