A Coupled AKNS-Kaup-Newell Soliton Hierarchy

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup-Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures.Comment: 15 pages, late

Pion-photon and photon-pion transition form factors in light-cone formalism

We derive the minimal Fock-state expansions of the pion and the photon wave functions in light-cone formalism, then we calculate the pion-photon and the photon-pion transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma$ and $\gamma ^{\ast}\gamma \to \pi ^{0}$ processes by employing these quark-antiquark wave functions of the pion and the photon. We find that our calculation for the $\gamma ^{\ast}\gamma \to \pi ^{0}$ transition form factor agrees with the experimental data at low and moderately high energy scale. Moreover, the physical differences and inherent connections between the transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma$ and $\gamma ^{\ast}\gamma \to \pi ^{0}$ have been illustrated, which indicate that these two physical processes are intrinsically related. In addition, we also discuss the $\pi ^{0}\to \gamma \gamma$ form factor and the decay width $\mathit{\Gamma}(\pi \to \gamma \gamma)$ at $Q^{2}=0$.Comment: 20 pages, 2 figure

Scaling of Anisotropic Flows and Nuclear Equation of State in Intermediate Energy Heavy Ion Collisions

Elliptic flow ($v_2$) and hexadecupole flow ($v_4$) of light clusters have been studied in details for 25 MeV/nucleon $^{86}$Kr + $^{124}$Sn at large impact parameters by Quantum Molecular Dynamics model with different potential parameters. Four parameter sets which include soft or hard equation of state (EOS) with/without symmetry energy term are used. Both number-of-nucleon ($A$) scaling of the elliptic flow versus transverse momentum ($p_t$) and the scaling of $v_4/A^{2}$ versus $(p_t/A)^2$ have been demonstrated for the light clusters in all above calculation conditions. It was also found that the ratio of $v_4/{v_2}^2$ keeps a constant of 1/2 which is independent of $p_t$ for all the light fragments. By comparisons among different combinations of EOS and symmetry potential term, the results show that the above scaling behaviors are solid which do not depend the details of potential, while the strength of flows is sensitive to EOS and symmetry potential term.Comment: 5 pages, 5 figure

Isovector Giant Dipole Resonance of Stable Nuclei in a Consistent Relativistic Random Phase Approximation

A fully consistent relativistic random phase approximation is applied to study the systematic behavior of the isovector giant dipole resonance of nuclei along the $\beta$-stability line in order to test the effective Lagrangians recently developed. The centroid energies of response functions of the isovector giant dipole resonance for stable nuclei are compared with the corresponding experimental data and the good agreement is obtained. It is found that the effective Lagrangian with an appropriate nuclear symmetry energy, which can well describe the ground state properties of nuclei, could also reproduce the isovector giant dipole resonance of nuclei along the $\beta$-stability line.Comment: 4 pages, 1 Postscript figure, to be submitted to Chin.Phys.Let

Heavy quarkonium 2S states in light-front quark model

We study the charmonium 2S states $\psi'$ and $\eta_c'$, and the bottomonium 2S states $\Upsilon'$ and $\eta_b'$, using the light-front quark model and the 2S state wave function of harmonic oscillator as the approximation of the 2S quarkonium wave function. The decay constants, transition form factors and masses of these mesons are calculated and compared with experimental data. Predictions of quantities such as Br$(\psi' \to \gamma \eta_c')$ are made. The 2S wave function may help us learn more about the structure of these heavy quarkonia.Comment: 5 latex pages, final version for journal publicatio

Statistical nature of cluster emission in nuclear liquid-vapour phase coexistence

The emission of nuclear clusters is investigated within the framework of isospin dependent lattice gas model and classical molecular dynamics model. It is found that the emission of individual cluster which is heavier than proton is almost Poissonian except near the transition temperature at which the system is leaving the liquid-vapor phase coexistence and the thermal scaling is observed by the linear Arrhenius plots which is made from the average multiplicity of each cluster versus the inverse of temperature in the liquid vapor phase coexistence. The slopes of the Arrhenius plots, {\it i.e.} the "emission barriers", are extracted as a function of the mass or charge number and fitted by the formula embodied with the contributions of the surface energy and Coulomb interaction. The good agreements are obtained in comparison with the data for low energy conditional barriers. In addition, the possible influences of the source size, Coulomb interaction and "freeze-out" density and related physical implications are discussed

Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy

Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite dimensional integrable systems and the general involutive system engendered by binary nonlinearization is reduced to a specific involutive system generated by mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento