Isobaric yield ratio difference between the 140 AA MeV 58,64^{58, 64}Ni + 9^{9}Be reactions studied by antisymmetric molecular dynamics model

\item[Background] The isobaric yield ratio difference (IBD) method is found to be sensitive to the density difference of neutron-rich nucleus induced reaction around the Fermi energy. \item[Purpose] An investigation is performed to study the IBD results in the transport model. \item[Methods] The antisymmetric molecular dynamics (AMD) model plus the sequential decay model GEMINI are adopted to simulate the 140$A$ MeV $^{58, 64}$Ni + $^{9}$Be reactions. A relative small coalescence radius R$_c =$ 2.5 fm is used for the phase space at $t =$ 500 fm/c to form the hot fragment. Two limitations on the impact parameter ($b1 = 0 - 2$ fm and $b2 = 0 - 9$ fm) are used to study the effect of central collisions in IBD. \item[Results] The isobaric yield ratios (IYRs) for the large--$A$ fragments are found to be suppressed in the symmetric reaction. The IBD results for fragments with neutron-excess $I =$ 0 and 1 are obtained. A small difference is found in the IBDs with the $b1$ and $b2$ limitations in the AMD simulated reactions. The IBD with $b1$ and $b2$ are quite similar in the AMD + GEMINI simulated reactions. \item[Conclusions] The IBDs for the $I =$ 0 and 1 chains are mainly determined by the central collisions, which reflects the nuclear density in the core region of the reaction system. The increasing part of the IBD distribution is found due to the difference between the densities in the peripheral collisions of the reactions. The sequential decay process influences the IBD results. The AMD + GEMINI simulation can better reproduce the experimental IBDs than the AMD simulation.Comment: 6 pages, 5 figure

Universal scaling of the pion, kaon and proton pTp_{\rm{T}} spectra in Pb-Pb collisions at 2.76 TeV

With the experimental data collected by the ALICE collaboration in Pb-Pb collisions at a center-of-mass energy per nucleon pair 2.76 TeV for six different centralities (0-5$\%$, 5-10$\%$, 10-20$\%$, 20-40$\%$, 40-60$\%$ and 60-80$\%$), we investigate the scaling property of the pion, kaon and proton transverse momentum ($p_{\rm{T}}$) spectra at these centralities. We show that in the low $p_{\rm{T}}$ region with $p_{\rm T} \leq$ 2.75 (3.10 and 2.35) GeV/c the pion (kaon and proton) spectra exhibit a scaling behaviour independent of the centrality of the collisions. This scaling behaviour arises when these spectra are presented in terms of a suitable variable, $z=p_{\rm{T}}/K$. The scaling parameter $K$ is determined by the quality factor method and is parameterized by $a \langle N_{\rm{part}}\rangle^{b}$, where $\langle N_{\rm{part}}\rangle$ is the average value of the number of participating nucleons, $a$ and $b$ are free parameters, $b$ characterizes the rate at which $\textrm{ln} K$ changes with $\textrm{ln} \langle N_{\rm{part}}\rangle$. The values of $b$ for pions and kaons are consistent within uncertainties, while they are smaller than that for protons. In the high $p_{\rm{T}}$ region, due to the suppression of the spectra, a violation of the proposed scaling is observed going from central to peripheral collisions. The more peripheral the collisions are, the more clearly violated the proposed scaling becomes. In the framework of the colour string percolation model, we argue that the pions, kaons and protons originate from the fragmentation of clusters which are formed by strings overlapping and the cluster's fragmentation functions are different for different hadrons. The scaling behaviour of the pion, kaon and proton spectra in the low $p_{\rm T}$ region can be simultaneously explained by the colour string percolation model in a qualitative way.Comment: 15 pages, 6 figures, accepted by Nucl. Phys.

Digitizing Dunhuang Cultural Heritage: A User Evaluation of Mogao Cave Panorama Digital Library

published_or_final_versio

Generalized r-matrix structure and algebro-geometric solution for integrable systems

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure. All these nonlinear systems have {\it r}-matrices, and are completely integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure