NLO Corrections of HTC∏^0 and ∏＋∏- Pair Production at ILC in TC2 Model

As well known, if the Higgs boson were not observed at LHC, the technicolor model would be the most favorable candidate responsible for the symmetry breaking. To overcome some defects in the previous model, some extended versions have been proposed. In the TC2 model typical signature is existence of heavy HTC and technipion ∏. A direct proof of validity of the model is to produce them at accelerator. Thus we study the production rates of e＋e^- → HTC∏^0 and e＋e^- → ∏＋∏- at ILC in the topcolor-assisted technicolor （TC2） model. In fact, there is a flood of models belonging to new physics, which can result in products with characteristics similar to HTC ＋ ∏ of the TC2 model. Therefore to distinguish this model from others one may need to investigate some details by calculating the cross section to NLO. We indeed find that the NLO corrections are significant, namely the ratio δ ≡（ σNLO - σLO）/σLO in e＋e- →HTC∏^0 exceeds 100% within a plausible parameter space.     

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.     

Collisional broadening of some 21△g ← B1∏u lines in Na2 molecules by optical-optical double resonance spectroscopy

Using the optical-optical double resonance (OODR) technique, we have studied the collisional broadening of some 21△g ← B1∏u lines in Na2 molecules. A single line Ar+ laser is used to pump the sodium dimers from thermally populated ground state X1∑g+ level to the intermediate B1∏u state. Then, a single-mode diode laser is used to probe the doubly excited 21△g state. The broadening rate coefficient is determined from the slope of the total linewidth versus Ne density curve. We obtain the average value kbr = (1.1 ± 0.5) × 10-s cm3s-1. The collisional excitation transfer between rotational levels of the B1∏u state (I.e., B1∏u(2,83/84) ← B1∏u(2, 82)) is also investigated. The rates can be determined from the relative intensities of the main peak and satellite lines, combined with a rate equation model. The rates of 1.25 × 106 and 1.07 × 106 s-1 are obtained, respectively.     

碰撞诱导振动能量转移：Cs2[B1∏u(v′=5)]+ N2→Cs2[B1∏u(v′=4，6)]+ N2

利用激光诱导荧光方法研究了Cs_2B~1Π_u[(v′=5)]与N2的碰撞能量转移.脉冲激光激发Cs_2基态至B~1Π_u[(v′=5)]态,池温保持在410 K,N_2气压在1.5×10~2 Pa～2.5×10~3 Pa之间变化.荧光中含有直接荧光和碰撞转移荧光成分,记录直接荧光B~1Πu(v′=5)→Χ~1∑~+_g(v″=0)的时间分辨强度.从荧光强度的对数值给出的直线斜率得到B~1Π_u(v′=5)→Χ~1∑~+_g(v″=0)的有效寿命,由Stern-Volmer方程,得到B~1Π_u(v′=5)→Χ~1∑~+_g(v″=0)的辐射寿命为(45±9)ns.B~1Π_u(v′=5)态与N_2碰撞的猝灭总截面为(9.8±1.5)×10~(-15)cm~2.用类似的方法得到B~1Π_u(v′=4,6)能级的辐射寿命.在不同的N_2气压下,测量B~1Π_u(v′=5,4,6)→Χ~1∑~+_g(v″=0)的时间积分荧光强度,首次得到v′=5→v′=4及v′=5→v′=6的碰撞转移截面分别为(3.9±0.8)×10~(-15) cm~2和(4.1±0.8)×10~(-15)cm~2.     

碰撞诱导振动能量转移：Cs2[B1∏u(v′=5)]+ N2→Cs2[B1∏u(v′=4，6)]+ N2

利用激光诱导荧光方法研究了Cs2[B1∏u(v′=5)]与N2的碰撞能量转移。脉冲激光激发Cs2基态至[B1∏u(v′=5)]态,池温保持在410K ,N2气压在1.5×102Pa至2.5×103Pa之间变化。荧光中含有直接荧光和碰撞转移荧光成分,记录直接荧光B1∏u(v′=5)→X1∑+g(v〞=0)的时间分辨强度。从荧光强度的对数值给出的直线斜率得到B1∏u(v′=5)→X1∑+g(v〞=0)的有效寿命,由Stern-Volmer方程,得到B1∏u(v′=5)→X1∑+g(v〞=0)的辐射寿命为（45±9）ns。B1∏u(v′=5)态与N2碰撞的猝灭总截面为（9.8±1.5）×10-15cm2。用类似的方法得到B1∏u(v′=4,6)能级的辐射寿命。在不同的N2气压下,测量B1∏u(v′=5,4,6)→X1∑+g(v〞=0)的时间积分荧光强度,首次得到v′=5→v′=4及v′=5→v′=6的碰撞转移截面分别为(3.9±0.8)×10-15cm2和(4.1±0.8)×10-15cm2。     

The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σ _u ^?1 (c ⁴Σ _u ^? ), v vibrational states of the O ₂ ⁺ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ₀ = 0.054 meV and Γ₁ = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O₂ molecule. About 99% of the O ₂ ⁺ ions in the 2σ _u ^?1 (c ⁴Σ _u ^? ), v states were found to decompose to the O(¹ D) + O⁺(⁴ S) dissociation products.     

Elastic collisions of sulfur and hydrogen in their ground states at low temperatures and spectroscopic parameters of SH（X^2∏） radical

This paper constructs the interaction potential of the SH（X^2∏） radical by using the coupled-cluster singlesdoubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, ωe, ωeχe, ae and Be values are of 3.7767eV, 0.13424nm, 2699.846 cm^-1, 47.7055 cm^-1, 0.2639cm^-1 and 9.4414 cm^-1, respectively, which are in excellent agreement with those obtained from the measure- ments. A total of 19 vibrational states has been found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH（X^2∏） potential energy curve. Over the impact energy range from 1.0×10^-11 to 1.0×10^-4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the 1 = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions.     

Analytical potential energy function for the electronic states 2^∏1/2 and 2^∏3/2 of O^x2 （x=＋1, -1）

The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.     

Perturbation Facilitated Optical-Optical Double Resonance spectroscopy of the 6Li233Σg+, 23Πg, 13Δg,b3Πu,and a3Σu+ states

The technique, Perturbation Facilitated Optical-Optical Double Resonance, has provided spectroscopic access to and molecular constants for the 3³Σ_g⁺ (v = 1–9), 2³Π_g (v = 0–24), 1³Δ_g (v = 3–14), b³Π_u (v = 0–17), and a³Σ_u⁺ (v = 0–6) states of the ⁶Li₂ molecule. Perturbation Facilitated Optical-Optical Double Resonance takes advantage of two weak spin-orbit perturbations, A¹Σ_u⁺ (v = 2, J = 33) ∼ b³Π_u (v = 9, F₁, N = 32) and A¹Σ_u⁺ (v = 9, J = 20) ∼ b³Π_u (v = 15, F₁, N = 19), to excite from X¹Σ_g⁺ (v = 0 or 1) into single rotation-vibration levels of ³Λ_u (F₁ fine structure component only) via the spin-mixed intermediate levels. The ³Λ_u (F₁ only) states are sampled in resolved fluorescence spectra from Perturbation Facilitated Optical-Optical Double Resonance-populated ³Λ_g levels.     

Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.     

Effects of pressure on structural,electronic, and mechanical properties of α,β,and γ uranium

The first-principles methods have been employed to calculate the structural, electronic, and mechanical properties of the α, β, and γ phases of uranium under pressure up to 100 GPa. The electronic structure has been viewed in forms of density of states and band structure. The mechanical stability of metal U in the α, β, and γ phases have been examined.The independent elastic constants, polycrystalline elastic moduli, as well as Poisson's ratio have been obtained. Upon compression, the elastic constants, elastic moduli, elastic wave velocities, and Debye temperature of α phase are enhanced pronouncedly. The value of B/G illustrates that α and γ phases are brittle in ground state.     

Synchronization of the fractional-order generalized augmented L u¨system and its circuit implementation

In this paper, the synchronization of the fractional-order generalized augmented Lu¨ system is investigated. Based on the predictor–corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincare′maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system parameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchronization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses,which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.     

钠分子B^1∏u与2^1∑g^＋间的碰撞激发转移

The B 1pi(u) electronic state of Na2 was excited by the 441.6 nm He-Cd laser line. The Na atomic transitions and the A 1sigma(u)+ --> X 1sigma(g)+ band of Na2 were recorded. From the intensities and spectra of the Na and Na2 fluorescence several collisional processes in the excited sodium atom-dimer system were identified. The Na atomic lines are the result of collisional energy transfer from Na2 (B 1pi(u)) to Na(3P). Predissociation process may also contribute to atomic fluorescence. The A 1sigma(u)+ --> X 1sigma(g)+ band is interpreted through a populating mechanism involving collisional transfer from B 1pi(u) to 2 1sigma(g)+ followed by a radiative transfer to the A 1sigma(u)+ state. From the decay constants and fluorescence intensities, the rate coefficient at 360 degrees C for collisional energy transfer from Na2 (B 1pi(u)) to Na2 (2 1sigma(g)+) was found to be 5.7 x 10(-10) cm3 x s(-1). The predissociation rate of the B 1pi(u) is 2.7 x 10(6) s(-1).     

强子对撞机上中性top-pion介子产生过程的研究pp（pp-）∏0t∏0t,b∏0t的研究

在TC2模型框架下研究了强子对撞机Tevatron和LHC上中性top-pion介子∏0t的产生过程pp（p-p）→∏0t∏0t和pp（p-p）→b∏0t.研究结果表明,在Tevatron上,这两个过程的产生截面都很小,通过这两个过程我们无法探测到中性top-pion介子.在LHC上,产生截面会大大增加,但通过∏0t∏0t的产生仍无法探测到中性top-pion介子.b∏0t在LHC上的产生截面能达到几百个fb甚至pb的量级,LHC每年能产生104-105个b∏0t事例.另外,味改变耦合∏0tt-c的存在,使得实验能通过背景非常干净的衰变道∏0t→t-c来探测∏0t.因此,通过b∏0t这一产生机制,未来的LHC实验应能获得足够多的可鉴别的∏0t事例.我们的研究结果,可为LHC上寻找中性top-pions介子检验TC2模型提供有价值的理论指导.     

Accurate Analytic Potential Energy Function and Spectroscopic Study for G1 ∏g State of Dimer 7Li2

The reasonable dissociation limit for the G1∏g state of dimer 7Li2 is determined. The equilibrium internuclear distance, dissociation energy, harmonic frequency, vibrational zero energy, and adiabatic excitation energy are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space in Gaussian03 program package at such numerous basis sets as 6-311 G, 6-311 G(2df, 2pd), 6-311 G(2df, p), cc-PVTZ, 6-311 G(3df, 3pd), CEP-121G, 6-311 G(2df, pd), 6-311 G(d,p),6-311G(3df,3pd), D95(3df,3pd), 6-311 G(3df, 2p),6-311 G(2df), 6-311 G(df, pd) D95V , and DGDZVP. The complete potential energy curves are obtained at these sets over a wide internuclear distance range and have least squares fitted to Murrell-Sorbie function. The conclusion shows that the basis set 6-311 G(2df, p) is a most suitable one for the G1∏g state. At this basis set, the calculated spectroscopic constants Te, De, Eo, Re, ωe, ωeXe, αe, and Be are of 3.9523 eV, 0.813 06 eV, 113.56 cm-1, 0.320 15 nm,227.96 cm-1, 1.6928 cm-1, 0.004 436 cm-1, and 0.4689 cm-1, respectively, which are in good agreement with measurements whenever available. The total 50 vibrational levels and corresponding inertial rotation constants are for the first time calculated and compared with available RKR data. And good agreement with measurements is obtained.