Absolute resonance strengths in the $^{6,7}Li(\alpha, \gamma)^{10,11}B$ reactions

The absolute strengths of the keV resonance in the reaction and of the keV resonance in the reaction have been measured to meV and meV, respectively, in good agreement with previous values. These resonances can be used to measure the absolute acceptance of the recoil separator ERNA to a precision of about 10%.Received: 12 December 2003, Revised: 10 February 2004, Published online: 3 August 2004PACS: 24.30.-v Resonance reactions - 25.40.Lw Radiative capture - 26.20. + f Hydrostatic stellar nucleosynthesis     

The Finite-Size Scaling Study of the Ising Model for the Fractals

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and \(d_{f}^{\beta } =1.876(8), \,d_{f}^{\gamma } =3.747(10), \,d_{f}^{\alpha } =2.081(68), \,d_{f}^{\delta } =1.940(22)\), \(d_{f}^{\eta } =2.178(10)\), \(d_{f}^{\nu } =2.960(22)\), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and \(d_{f}^{\beta } =1.875, \,d_{f}^{\gamma } =3.75, \,d_{f}^{\alpha } =2, \,d_{f}^{\delta } =1.933, \,d_{f}^{\eta } =2.25, \,d_{f}^{\nu } =3\).     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

Laplace Sequences of Surfaces in Projective Space and Two-Dimensional Toda Equations

We find that the Laplace sequences of surfaces of period n in projective space P _n–1 have two types, while type II occurs only for even n. The integrability condition of the fundamental equations of these two types have the same form

On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y of the general linear Lie algebra . In this article, we extend some of their ideas to consider the Yangian Y of the Lie superalgebra . In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

From quantum to elliptic algebras

It is shown that the elliptic algebra at the critical level c = –2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p ^m = q ^c+2 for , they commute when in addition p = q ^2k for k integer non-zero, and they belong to the center of when k is odd. The Poisson structures obtained for t(z) in these classical limits contain the q-deformed Virasoro algebra, characterizing the structures at p q ^2k as new algebras.     

Kinetic equations for autocorrelation functions in dilute gases

We show that in the case of a dilute gas of neutral particles kinetic equations for autocorrelation functions such as $$\left\langle {\hat f\left( {r,v,t} \right)\hat f\left( {r\prime v\prime ,t\prime } \right)} \right\rangle ,where\hat f\left( {r,v,t} \right) = \sum {_{i = 1}^N } \delta \left( {r - r_i \left( t \right)} \right)\delta \left( {v - v_i \left( {tt} \right)} \right)$$ , can be obtained in a very simple manner by the use of the truncated BBGKY hierarchy. The resulting equations correspond to the low-density limit of the results of van Leeuwen and Yip. Moreover, the derivation does not make use of the Bogoliubov adiabatic approximation, and therefore includes non-Markovian effects which can be important in describing light scattering from gases and the collisional narrowing of atomic dipole radiation. The resulting equations in the long-wavelength limit correspond to the non-Markovian Boltzmann equation for the self-correlation part and the non-Markovian, linearized Boltzmann equation for the total autocorrelation function.     

Prospects for production of ultracold $\mathsf{X^{1}\Sigma^{ + }}$ RbCs molecules

Recently, we have reported photoassociation of laser-cooled Rb and Cs atoms, decay of the RbCs photoassociation resonances to high levels of the state, and reexcitation to vibronic levels of the state [Kerman et al. , Phys. Rev. Lett. 92, 033004; 153001 (2004)]. Considering the reexcitation spectrum, we report here a preliminary analysis of perturbations in the c state by high levels of the and low levels of the state. Mixing with the B state provides the singlet character needed to stimulate decay to v = 0 of the ground state. We conclude that an experimental procedure that involves photoassociation of laser-cooled atoms, radiative decay, and stimulated Raman transfer to the ground electronic state is a feasible method for producing translationally, rotationally, vibrationally and electronically cold RbCs molecules. Electronic supplementary material to this article is available at and is accessible for authorized users. Received: 1 September 2004, Published online: 23 November 2004 PACS: 33.80.Ps Optical cooling of molecules; trapping - 34.50.Gb Electronic excitation and ionization of molecules; intermediate molecular states (including lifetimes, state mixing, etc.) - 33.20.Kf Visible spectra - 34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions - 33.15.Pw Fine and hyperfine structure A supplementary table (Tab. I) is only available in electronic form at http: //www.eurphysj.org     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Gluon condensate and the effective gluon mass

Using massive gauge invariant QCD we show explicity how power like corrections to \(\Pi _{\mu v} \left( q \right) = i\int {dx} e^{iq'x} \left\langle {0\left| {j_\mu ^{em} \left( x \right)\bar j_v^{em} \left( 0 \right)} \right|0} \right\rangle \) arise. Using our result for the 1/q ⁴ contribution, a one to one correspondence is made between the gluon condensate and the effective gluon mass. By relating this mass to, \(\langle 0|\frac{{\alpha _s }}{\pi }G_{\mu v}^2 |0\rangle \) a value ofm _gluon=750 MeV is found at ?q ²=10 GeV². In addition, within the context of dimensional regularization, a new technique for evaluating two loop momentum integrals with massive propagators is introduced. This method is a derivative of the Mellin transform technique that was applied to ladder diagrams in the days of Reggeisation.     

Gleichzeitige Messung von Hyperfeinstruktur,Starkeffekt und Zeemaneffekt des23Na19F mit einer Molekülstrahl-Resonanzapparatur

An electric molecular beam resonance spectrometer has been used to measure simultaneously the Zeeman- and Stark-effect splitting of the hyperfine structure of²³Na¹⁹F. Electric four pole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman field) was superimposed to the electric field (Stark field) in the transition region of the apparatus. The observed (Δm _J=±1)-transitions were induced electrically. Completely resolved spectra of NaF in theJ=1 rotational state have been measured in several vibrational states. The obtained quantities are: The electric dipolmomentμ _el of the molecule forv=0, 1 and 2, the rotational magnetic dipolmomentμ _J forv=0, 1, the difference of the magnetic shielding (σ _⊥-σ _‖) by the electrons of both nuclei as well as the difference of the molecular susceptibility (ξ _⊥-ξ _‖), the spin rotational constantsc _F andc _Na, the scalar and the tensor part of the molecular spin-spin interaction, the quadrupol interactione q Q forv=0, 1 and 2. The numerical values are

$$\begin{gathered} \mu _{\mathfrak{e}1} = 8,152(6) deb \hfill \\ \frac{{\mu _{\mathfrak{e}1} (v = 1)}}{{\mu _{\mathfrak{e}1} (v = 0)}} = 1,007985 (7) \hfill \\ \frac{{\mu _{\mathfrak{e}1} (v = 2)}}{{\mu _{\mathfrak{e}1} (v = 1)}} = 1,00798 (5) \hfill \\ \mu _J = - 2,89(3)10^{ - 6} \mu _B \hfill \\ \frac{{\mu _J (v = 0)}}{{\mu _J (v = 1)}} = 1,020 (13) \hfill \\ (\sigma _ \bot - \sigma _\parallel )_{Na} = - 51(12) \cdot 10^{ - 5} \hfill \\ (\sigma _ \bot - \sigma _\parallel )_F = - 51(12) \cdot 10^{ - 6} \hfill \\ (\xi _ \bot - \xi _\parallel ) = - 1,59(120)10^{ - 30} erg/Gau\beta ^2 \hfill \\ {}^CNa/^h = 1,7 (2)kHz \hfill \\ {}^CF/^h = 2,2 (2)kHz \hfill \\ {}^dT/^h = 3,7 (2)kHz \hfill \\ {}^dS/^h = 0,2 (2)kHz \hfill \\ eq Q/h = - 8,4393 (19)MHz \hfill \\ \frac{{eq Q(v = 0)}}{{eq Q(v = 1)}} = 1,0134 (2) \hfill \\ \frac{{eq Q(v = 1)}}{{eq Q(v = 2)}} = 1,0135 (2) \hfill \\ \end{gathered} $$     

Do the fundamental physical constants have the same values in different regions of space-time?

An analysis of quasar spectra yields highly reliable constraints on the possible variation of the fine-structure constant a and the proton-to-electron mass ratio μ during cosmological evolution from the epoch corresponding to a cosmological red shift z≈2.8 (i.e., ∼10¹⁰ years ago) to the current epoch and . Zh. Tekh. Fiz. 69, 1–5 (September 1999)     

Near-Infrared Laser Spectroscopy of TiS: The b(1)Pi-X(3)Delta Transition

Laser-induced fluorescence spectrum of TiS in the 769-863 nm region has been recorded and analyzed. The TiS molecule was produced using the technique of laser vaporization/reaction with supersonic cooling. Twenty-one weak subbands have been assigned as being due to b(1)Pi-X(3)Delta, B(3)Pi(0)-X(3)Delta(1), and C(3)Delta-X(3)Delta transitions. Strong evidence shows that the b(1)Pi state is responsible for perturbing the v = 0, 1, and 2 levels of the C(3)Delta(1) subband. The molecular constants of the b(1)Pi state have been determined as follows: T(e) = 10 589.47 cm(-1), omega(e) = 542.14 cm(-1), omega(e)x(e) = 3.16 cm(-1), B(e) = 0.19568 cm(-1), and alpha(e) = 0.00085 cm(-1). The spin-orbit interaction between the b(1)Pi (v = 2 and 3) and C(3)Delta (v = 1 and 2) levels is discussed in terms of configuration interaction occurring between the b(1)Pi from the 11varsigma(1) 5pi(1) configuration and the (1)Pi from the 5pi(1) 1delta(1) configuration, and the C(3)Delta state from 12varsigma(1) 1delta(1) configuration. Copyright 2000 Academic Press.     

Measurement of the Time-Dependent CP Asymmetry in B;{0}-->D_{CP};{(*)}h;{0} Decays

We report a measurement of the time-dependent CP-asymmetry parameters S and C in color-suppressed B{0}-->D{(*)0}h{0} decays, where h{0} is a pi{0}, eta, or omega meson, and the decays to one of the CP eigenstates K+K-, K{S}{0}pi{0}, or K{S}{0}omega. The data sample consists of 383 x 10{6} Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. The results are S=-0.56+/-0.23+/-0.05 and C=-0.23+/-0.16+/-0.04, where the first error is statistical and the second is systematic.     

Distribution of cyclic species in network formation: Microscopic theory of branching process in Ag-R-B f−g model

The distribution of cyclic species is explored for an irreversible A_g-R-B_f-g model on the basis of the concept of the “m tree” which was introduced in a preceding report by the authors. On the assumption of equal reactivity, the explicit solution is derived; i.e., for a sufficiently concentrated solution the concentration of cyclicj-mers can be expressed as \(\left[ {R_j } \right] = \left( {k_{Rj} /k_L } \right)\left[ {\left( {f - g} \right)D_B } \right]^j \omega _j /j\) , wherek _Rj andk _L are the rate constants of cyclicj-mer formation and interconnection, respectively, and $$\omega _j = \sum\limits_{k = 0}^{[j/2]} {\left( {_{2k}^j } \right)} \alpha ^k $$ where α=(g ? 1)(f ? g ? 1)/g(f ? g) and [j/2] is the Gauss' symbol. Forg → 1, ω_j → 1, so that the solution reduces to the A-R-B_f?1 case. At a critical point one observes the strong divergence of the chances ∑ φ_j of cyclization.     

Conformal tensor discontinuities in general relativity

The postulate is made that across a given hypersurfaceN the metric and its first derivatives are continuous. This postulate is used to derive conditions which must be satisfied by discontinuities in the Riemann tensor acrossN. These conditions imply that the conformal tensor jump is uniquely determined by the stress-energy tensor discontinuity ifN is non-null (and to within an additive term of type Null ifN is lightlike). Alternatively, and [R] determine ifN is non-null. These relationships between the conformal tensor and stress-energy tensor jumps are given explicitly in terms of a three-dimensional complex representation of the antisymmetric tensors. Application of these results to perfect-fluid discontinuities is made: is of type D across a fluid-vacuum boundary and across an internal, non-null shock front. is of type I (non-degenerate) in general across fluid interfaces across which no matter flows, except for special cases.The research reported herein was supported in part by the Atomic Energy Commission under contract number AT (11-1)-34, Project Agreement No. 125, while the author was at the University of California at Berkeley, and in part by National Science Foundation Grant GU-1598-University Science Development Program.     

Ab initio calculations on the α^3∑u^＋ state properties of dimer ^7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometry of the α^3∑u^＋ state for ^7Li2 is made at numerous basis sets such as 6-311＋＋G（2df）, cc-PVTZ, 6-311＋＋G（2df, p）, 6-311G（3df,3pd）, 6-311＋＋G（2df,2pd）, D95（3df,3pd）, 6-311＋＋G, DGDZVP, 6-311＋＋G（3df,2pd）, 6-311G（2df,2pd）, D95V＋＋, CEP-121G, 6-311＋＋G（d,p）, 6-311＋＋G（2df, pd） and 6-311＋＋G（3df,3pd） in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction （SAC/SAC=CI） method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at those sets over a wide internuclear distance range from about 3.0α0 to 37.0α0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at ccopVTZ, the spectroscopic data （Te, De, D0, ωe,ωeХe, αe and Be） are computed and they are 1.006 eV, 338.71 cm^-1, 307.12 cm^-1, 64.88 cm^-1, 3.41 cm^-1, 0.0187 cm^-1 and 0.279 cm^-1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant （By） and six centrifugal distortion constants （Dr Hv, Lv, My, Nv, and Ov） are calculated. The scattering length is calculated to be -27.138α0, which is in good accord with the experimental data.     

Compactification of patterns by a singular convection or stress

A wide variety of propagating disturbances in physical systems are described by equations whose solutions lack a sharp propagating front. We demonstrate that presence of particular nonlinearities may induce such fronts. To exemplify this idea, we study both dissipative u_{t}+ partial differential_{x}f(u)=u_{xx} and dispersive u_{t}+ partial differential_{x}f(u)+u_{xxx}=0 patterns, and show that a weakly singular convection f(u)=-u;{alpha}+u;{m}, 0相似文献   

Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law

In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the following steady problem: $$v \cdot \nabla _{x}F =\frac{1}{{\rm K}_{\rm n}}Q(F,F),\qquad (x,v)\in \Omega \times \mathbf{R}^{3}, \quad \quad (0.1) $$ v · ? x F = 1 K n Q ( F , F ) , ( x , v ) ∈ Ω × R 3 , ( 0.1 ) $$F(x,v)|_{n(x)\cdot v<0} = \mu _{\theta}\int_{n(x) \cdot v^{\prime}>0}F(x,v^{\prime})(n(x)\cdot v^{\prime})dv^{\prime},\quad x \in\partial \Omega,\quad \quad (0.2) $$ F ( x , v ) | n ( x ) · v < 0 = μ θ ∫ n ( x ) · v ′ > 0 F ( x , v ′ ) ( n ( x ) · v ′ ) d v ′ , x ∈ ? Ω , ( 0.2 ) where Ω is a bounded domain in ${\mathbf{R}^{d}, 1 \leq d \leq 3}$ R d , 1 ≤ d ≤ 3 , K_n is the Knudsen number and ${\mu _{\theta}=\frac{1}{2\pi \theta ^{2}(x)} {\rm exp} [-\frac{|v|^{2}}{2\theta (x)}]}$ μ θ = 1 2 π θ 2 ( x ) exp [ - | v | 2 2 θ ( x ) ] is a Maxwellian with non-constant(non-isothermal) wall temperature θ(x). Based on new constructive coercivity estimates for both steady and dynamic cases, for ${|\theta -\theta_{0}|\leq \delta \ll 1}$ | θ - θ 0 | ≤ δ ? 1 and any fixed value of K_n, we construct a unique non-negative solution F _s to (0.1) and (0.2), continuous away from the grazing set and exponentially asymptotically stable. This solution is a genuine non-equilibrium stationary solution differing from a local equilibrium Maxwellian. As an application of our results we establish the expansion ${F_s=\mu_{\theta_0}+\delta F_{1}+O(\delta ^{2})}$ F s = μ θ 0 + δ F 1 + O ( δ 2 ) and we prove that, if the Fourier law holds, the temperature contribution associated to F ₁ must be linear, in the slab geometry.