Tetrahedron Equation and Quantum R Matrices for Spin Representations of {B^{(1)}_n}, {D^{(1)}_n} and {D^{(2)}_{n+1}}

It is known that a solution of the tetrahedron equation generates infinitely many solutions of the Yang-Baxter equation via suitable reductions. In this paper this scheme is applied to an oscillator solution of the tetrahedron equation involving bosons and fermions by using special 3d boundary conditions. The resulting solutions of the Yang-Baxter equation are identified with the quantum R matrices for the spin representations of ${B^{(1)}_n}$ , ${D^{(1)}_n}$ and ${D^{(2)}_{n+1}}$ .     

A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of $$\varvec{U_ q(A^{(1)}_n)}$$U q(An(1))

We construct a q-boson representation of the Zamolodchikov-Faddeev algebra whose structure function is given by the stochastic R matrix of \(U_q(A^{(1)}_n)\) introduced recently. The representation involves quantum dilogarithm type infinite products in the \(n(n-1)/2\)-fold tensor product of q-bosons. It leads to a matrix product formula of the stationary probabilities in the \(U_q(A_n^{(1)})\)-zero range process on a one-dimensional periodic lattice.     

Lasing of optically pumped XeF and analysis of the spectrum of the laser transitionB^2 \sum _{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^ + - X^2 \sum _{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^ +

The operating principle of a photodissociation XeF laser (λ?350 nm) is discussed. A laser operating on the gas mixture XeF₂:N₂(SF₆):Ar pumped by radiation from an open high-current discharge is described. The maximum lasing duration is 5 μsec, the maximum output energy is 0.15 J. The vibrational structure of the XeF-molecule transition B²Σ_1/2 ⁺ ? X²Σ_1/2 ⁺, observed in absorption, luminescence, and stimulated emission, is investlgated. The vibrational quantum and the anharmonicity in the upper and lower states are measured: ω_e ^' = 308.7 cm^-1, ω_e ^'x_e ^' = 1.44 cm^-1, ω_e ^'' = 225.7 cm^-1, ω_e ^''x_e ^'' = 11.0 cm^-1. The difference between the equilibrium internuclear distances of the XeF molecule is determined for the excited (B) and ground (X) states, namely r_e ^' - r_e ^'' = 0.33 +- 0.01 Å.     

Theoretical study of collision and collision-free radiative lifetimes of {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right)

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the $ {B^3}\Sigma_u^{-} $ and $ {X^3}\Sigma_g^{-} $ states of the collision-free S₂ molecule and the T-shape collision complex S₂?CHe using cc-pVQZ basis sets. We obtain the transition dipole moments of the $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) $ and the Franck?CCondon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S₂ laser pumped by a transverse fast discharge.     

High-speed planar laser-induced fluorescence of the CH radical using the C^{ 2} \varSigma ^{ + } {-}X^{ 2} \varPi \left( {0,0} \right) band

The potential for kHz-rate or high-speed planar laser-induced fluorescence (PLIF) of the Methylidyne (CH) radical using its \(C^{ 2} \varSigma ^{ + } {-}X^{ 2} \varPi\) (v′ = 0, v′′ = 0) band was investigated. We show that due to its strength and the excitation wavelength (~314 nm), which is conveniently generated by a dye laser operating with a red dye, the C–X(0,0) band is a good choice for CH LIF studies wherein suppression of background scattering is not required. While interference from polycyclic aromatic hydrocarbons is small, that caused by hydroxyl (OH) can be significant. Nonetheless, the OH lines can be avoided, and we observe good CH image fidelity. Most importantly, we show that due to the favorable properties of the CH C–X band (i.e., good signal strength and convenient wavelength), it can be used for PLIF at kHz acquisition rates using a continuously pulsing laser system. This is demonstrated in laminar and turbulent CH₄-air flames with a laser system operating at 10 kHz and delivering ~0.2 mJ/pulse at 314 nm.     

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.     

Hyperfine splitting constants in the optical transition \boldsymbol{{4{f}^{7}} {6{s}^{2}} \;{^{8}{\rm S}_{7/2}} \to {4{f}^{7}} {6{s}6{p}}\; {^{6}{\rm P}_{5/2}} \ {\rm of} \ {^{151-155}{\rm Eu}}} isotopes and hyperfine anomaly

Using the method of laser-induced fluorescence in an atomic beam we have measured the hyperfine splitting constants, A and B, of the ground and excited states of the optical transition 4f ⁷6s ^{2 8}S $_{1/2}\to 4f^{7}$ 6s6p ⁶P_5/2 (564.58 nm) for ^151???155Eu isotopes. For all isotopes, the magnetic dipole constants of the ⁶P_5/2 atomic level are determined to a precision better than 0.04%. The A and B constants for the ground state ⁸S_7/2 of the radioactive ^152,154,155Eu were obtained for the first time with a precision better than 0.5%. Our data along with previous ground state hyperfine structure measurements for the stable europium isotopes allow us to determine the hyperfine anomaly for mentioned Eu isotopes.     

The Cubic Dirac Equation: Small Initial Data in {{H^{\frac{1}{2}}} (\mathbb{R}^{2}})

Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space \({{H^{\frac{1}{2}}} (\mathbb{R}^{2}}\)) is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein–Gordon equation in dimension n = 2, which is captured by constructing an adapted systems of coordinate frames.     

Measurement of Cross Sections for the Reactions $${}^{{232}}{\textrm{Th}}({{}^{3}}{\textrm{He}}{,p4n})^{{230}}$$ Pa, $${}^{{232}}{\textrm{Th}}({{}^{3}}{\textrm{He}}{,p2n})^{{232}}$$ Pa,and $${}^{{232}}{\textrm{Th}}({{}^{3}}{\textrm{He}}{,2p+pn})^{{233}}$$ Pa Induced by the Irradiation of a ThO $${}_{2}$$ Target with $${}^{3}$$ He Nuclei

Physics of Atomic Nuclei - The efficiency of employing a beam of intermediate-energy $${}^{3}$$ He particles for the production of the radionuclide $${}^{230}$$ Pa on natural-thorium targets, which...     

The Dynamics of Relativistic Strings Moving in the Minkowski Space $$\mathbb{R}^{1+n}$$

In this paper we investigate the dynamics of relativistic (in particular, closed) strings moving in the Minkowski space . We first derive a system with n nonlinear wave equations of Born-Infeld type which governs the motion of the string. This system can also be used to describe the extremal surfaces in . We then show that this system enjoys some interesting geometric properties. Based on this, we give a sufficient and necessary condition for the global existence of extremal surfaces without space-like point in with given initial data. This result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in . We also present an explicit exact representation of the general solution for such a system. Moreover, a great deal of numerical analyses are investigated, and the numerical results show that, in phase space, various topological singularities develop in finite time in the motion of the string. Finally, some important discussions related to the theory of extremal surfaces of mixed type in are given.     

Self-Consistent Calculations of Probabilities for Transitions between $${3}_{1}^{{-}}$$ and $${2}_{1}^{{+}}$$ One-Phonon States in Tin Isotopes

Physics of Atomic Nuclei - For the first time, a self-consistent method for studying second-order anharmonic effects within quantum many-body theory is applied to calculating probabilities for...     

Quantum and quasiclassical dynamics of C($^{3} P$) + H$_{2}(^{1} \varSigma_{\text{g}}^+)\rightarrow H(^{2} S)$ + CH($^{2} \varPi$) reaction: Coriolis coupling effects and stereodynamics

The dynamics of ${\rm C}+{\rm H_2}\rightarrow {\rm H}+{\rm CH}$ reaction is theoretically studied using the quasiclassical trajectory and quantum mechanical wave packet methods. The analysis of reaction probabilities, integral cross sections, and rate coefficients reveal the essential Coriolis coupling effects in the quantum mechanical wave packet calculations.The calculated polarization-dependent differential cross section, $P$($\theta_r$) and $P$($\phi_r$) show that the $\bm j'$ of product rotational angular momentum is not only aligned along the $y$ axis and the direction of the vector $\bm x+\bm z$, but also strongly oriented along the positive $y$ axis.