对高重子数密度粒子发射源的干涉学分析

应用量子路径积分的方法,分析了高能重离子碰撞产生的高重子数密度粒子发射源的２K和2π干涉学（hanbury Brown Twiss,HBT关联）。利用相对论流体动力学描述源的演化,采用的状态方程包含QGP到强子相的一级相变和对强子气体的体积修正。在２π关联的计算中考虑了激发态粒子衰变和多重散射效应,并将其HBT关联半径和寿命与传统热冻结模型的结果进行了对比。计算表明,早期化学冻结产生的K介子的HBT关联半径比２π关联的HBT关联半径小。激发态粒子的衰变使HBT关联半径和寿命增加,而多重散射对HBT关联的结果几乎没有影响。Using quantum path integral formulae, we examined the two kaon and two pion Hanbury Brown Twiss (HBT) interferometry for the particle emitting source with high baryon density. The evolution of the source is described by relativistic hydrodynamics. We use an equation of state of first order transition from QGP to hadronic phase and consider a volume correction for the hadronic gas. The two pion HBT results with effects of excited particle decay and multiple scattering were investigated and compared with those for conventional thermal freeze out (TFO) model. We found that the two kaon HBT radius was smaller than those of the two pion interferometry. The particle decay increases the HBT radius and lifetime, while the effect of multiple scattering on HBT results can be neglected.     

Pion Interferometry for Hydrodynamical Expanding Source with a Finite Baryon Density

We calculate the two-pion correlation function for an expanding hadron source with a finite baryon density. The space-time evolution of the source is described by relativistic hydrodynamics and the Hanbury-Brown-Twiss (HBT) radius is extracted after effects of collective expansion and multiple scattering on the HBT interferometry have been taken into account, using quantum probability amplitudes in a path-integral formalism. We find that this radius is substantially smaller than the HBT radius extracted from the freeze-out configuration.     

Source Function Determined from Hanbury—Brown／Twiss Correlations by the Maximum Entropy Principle

We study the reconstruction of the source function in space-time directly from the measured Hanbury-Brown/Twiss (HBT) correlation function using the maximum entropy principle.We find that the problem is ill-defined without at least one additional theoretical constraint as input.Using the requirement of a finite source lifetime for the problem we find a new Gaussian parametrization of the source function directly in terms of the measured HBT radius parameters and its lifetime,where the latter is a free parameter which is not directly measurable by HBT.We discuss the implication of our results for the remaining freed om in building source models consistent with a given set of measured HBT radius parameters.     

Two-pion interferometry in heavy ion collisions at HIRFL-CSR energy

We examine the two-pion Hanbury-Brown-Twiss (HBT) interferometry for the particle-emitting source produced in heavy ion collisions at HIRFL-CSR energy. The source evolution is described by relativistic hydrodynamics with three kinds of equations of state for chemical equilibrium (CE), chemical freeze-out (CFO), and partial chemical equilibrium (PCE) models, respectively. We investigate the effects of particle decay, multiple scattering, and source collective expansion on the two-pion interferometry results. We find that the HBT radii of the evolution source for the CFO and PCE models are smaller than that for the CE model. The HBT lifetime for the CFO model is smaller than those for the PCE and CE models. The particle decay increases the HBT radius and lifetime while the source     

Nonparaxial propagation of phase-flipped Gaussian beams

This paper derives the closed-form expressions for nonparaxial phase flipped Gaussian （PFG） beams propagating in free space, through a knife edge and an aperture, which enable us to study nonparaxial propagation properties of PFG beams and to compare nonparaxial results with paraxial ones. It is found that the f parameter, offsetting distance of the knife edge and truncation parameter affect the nonparaxial beam propagation properties. Only under certain conditions the paraxial approximation is applicable. The results are illustrated by numerical examples.     

Pion transverse-momentum spectrum,elliptic flow,and Hanbury-Brown-Twiss interferometry in a viscous granular source model

We examine the evolution of quark-gluon plasma(QGP) droplets with viscous hydrodynamics and analyze the pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss(HBT) interferometry in a granular source model consisting of viscous QGP droplets. The shear viscosity of the QGP droplet speeds up and slows down the droplet evolution in the central and peripheral regions of the droplet, respectively. The effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change little for granular sources with and without viscosity. On the other hand,the influence of viscosity on HBT radius Rout is considerable. It makes Rout decrease in the granular source model.We determine the model parameters of granular sources using the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii together, and investigate the effects of viscosity on the model parameters. The results indicate that the granular source model may reproduce the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii in heavy-ion collisions of Au-Au at√s_(NN)=200 GeV and Pb-Pb at√s_(NN) =2.76 Te V in different centrality intervals. The viscosity of the droplet leads to an increase in the initial droplet radius and a decrease of the source shell parameter in the granular source model.     

Interferometry Signatures for QCD First-Order Phase Transition in High Energy Heavy Ion Collisions

Using the technique of quantum transport of the interfering pair we examine the Hanbury-Brown-Twiss （HBT） interferometry signatures for the particle-emitting sources of pions and kaons produced in heavy ion collisions at 10-30 AGeV. The evolution of the sources is described by relativistic hydrodynamics with the first-order phase transition from quark-gluon plasma （QGP） to hadronic matter. We use quantum probability amplitudes in a path-integral formalism to calculate the two-particle correlation functions, where the effects of particle decay and multiple scattering are taken into consideration. Our model-calculated results indicate that both the HBT radii of pions and kaons increase with the system initial energy density. The HBT lifetimes of the pion and kaon sources increase significantly when the initial energy density is tuned to the phase boundary between the QGP and mixed phase. This increase of HBT lifetimes will likely appear in heavy ion collisions with an incident energy between 10-30 AGeV.     

The nonparaxial property of chirped pulsed beam

The nonparaxial property of the chirped pulsed beam is analyzed both quantitatively and qualitatively. Through the qualitative investigation of the paraxial approximation condition, we show there are chirp-induced changes in the nonparaxial propagation of the chirped pulsed beam. A quantitative nonparaxial correction was developed by use of the perturbational technic and the Fourier transform for a few-cycle chirped pulsed beam with relative small chirp parameter. It was shown that the nonparaxial corrections were enhanced near the leading or trailing edge of pulse depending on weather the chirp parameter is positive or negative. An example for pulsed Gaussian beam driven by a chirped Gaussian pulse is shown in the numerical result to confirm our analysis.     

Imaging source with Gaussian proper time distribution

Making use of the maximum entropy method, we study the most probable source function in heavy ion collisions. An anisotropic Gaussian source is deduced by simply assuming that the particles are emitted within a finite proper-time. The general relations between the most probable source function and the minimal assumptions are discussed, which are instructive in constructing a self-consistent source function from observed Hanbury-Brown/Twiss（HBT） correlations.     

Two-pion interferometry for a partially coherent evolution source

We give the formulas of two-pion Hanbury-Brown-Twiss (HBT) correlation function for a partially coherent evolution pion-emitting source, using quantum probability amplitudes in a path-integral formalism. The multiple scattering of the particles in the source is taken into consideration based on Glauber scattering theory. Two-pion interferometry with effects of the multiple scattering and source collective expansion is examined for a partially coherent source of hadronic gas with a finite baryon density and evolving hydrodynamically. We do not find observable effect of either the multiple scattering or the source collective expansion on HBT chaotic parameter.     

Properties of multi-Gaussian Schell-model beams carrying an edge dislocation propagating in oceanic turbulence

Based on the theory of coherence, the model of multi-Gaussian Schell-model(MGSM) beams carrying an edge dislocation generated by the MGSM source is introduced. The analytical cross-spectral density of MGSM beams carrying an edge dislocation propagating in oceanic turbulence is derived, and used to study the evolution properties of the MGSM beams carrying an edge dislocation. The results indicate that the MGSM beam carrying an edge dislocation propagating in oceanic turbulence will evolve from the profile with two intensity peaks into a flat-topped beam caused by the MGSM source, and the beam will evolve into the Gaussian-like beam due to the influences of oceanic turbulence in the far field.As the propagation distance increases, the MGSM beam carrying an edge dislocation propagating in oceanic turbulence with the larger rate of dissipation of mean-squared temperature(χT) and ratio of temperature to salinity contribution to the refractive index spectrum(?) or the smaller rate of dissipation of kinetic energy per unit mass of fluid(ε) evolves into the flat-topped beam or a Gaussian beam faster.     

Size of the freeze-out source in high energy heavy ion collisions

Based on a hydro-inspired azimuthally symmetric emission function, we analyze the HBT radius R_s and the single-particle transverse momentum spectra in Au+Au collisions measured by the STAR Collaboration at √s_NN=200 GeV. The results show that consistent assumptions about transverse density (and/or flow profile) in the calculation of the HBT radius R_s and single-particle spectral analyses play an important role for understanding the size of the freeze-out source.     

Interferometry imaging for the evolving source in heavy ion collisions at HIRFL-CSR energy

Imaging analysis of two-pion interferometry is performed for an evolving particle-emitting source in heavy ion collisions at HIRFL-CSR energy. The source evolution is described by the relativistic hydrodynamics in (2+1) dimensions. The model-independent characteristic quantities of the source are investigated and compared with the interferometry results obtained by the usual Gaussian formula fit. It is found that the first- order source function moments can describe the source sizes. The ratio of the normalized standard deviation σ to the first-order moment R, σ/R, is sensitive to the shape of the source function.     

对光滑粒子流体动力学模型π源的视像分析

∈利用光滑粒子流体动力学模型,研究了NN=200 GeV Au+Au碰撞产生的介子发射源的视像结果。 碰撞后的演化图显示, 系统在演化过程中呈现出明显的非均匀性颗粒集团分布。 这种发射源所得到的视像分析结果表明, 即使在相同的碰撞参数下, 不同事件的相对发射源函数也会存在差异。 这种差异在大碰撞参数下表现得尤为明显。 We investigate the imaging of pion emitting source produced in NN=200 GeV Au+Au collisions with NeXSPheRIO model. The pictures of the system evolution show that there is obvious inhomogeneous structure of granular lumps. The results of imaging analysis indicate that the relative source functions for the various events of the granular sources are different even though the events are with the same impact parameter. This difference is more evident for the events with large impact parameter.     

Two-pion interferometry for viscous hydrodynamic sources

The space-time evolution of the (1+1)-dimensional viscous hydrodynamics with an initial quark-gluon plasma (QGP) produced in ultrarelativistic heavy ion collisions is studied numerically. The particle-emitting sources undergo a crossover transition from the QGP to hadronic gas. We take into account a usual shear viscosity for the strongly coupled QGP as well as the bulk viscosity which increases significantly in the crossover region. The two-pion Hanbury-Brown-Twiss (HBT) interferometry for the viscous hydrodynamic sources is performed. The HBT analyses indicate that the viscosity effect on the two-pion HBT results is small if only the shear viscosity is taken into consideration in the calculations. The bulk viscosity leads to a larger transverse freeze-out configuration of the pion-emitting sources, and thus increases the transverse HBT radii. The results of the longitudinal HBT radius for the source with Bjorken longitudinal scaling are consistent with the experimental data.     

Propagation of partially coherent beams carrying an edge dislocation through atmospheric turbulence along a slant path

This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model (GSM) beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope vert pvert and the smaller the off-axis distance vert dvert are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The GSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.     

Planar near-field acoustical holography based on equivalent source method and its experimental investigation

The current main approach to reconstruct and predict the acoustic field of a planar source is Near-field Acoustical Holography （NAH） based on FFT. But this method has some disadvantages such as wraparound error and edge Gibbs phenomena which will contaminate the results badly. A planar NAH based on equivalent source approach is developed, which has no wraparound error and edge Gibbs phenomena, and it is beneficial for engineering application. The experimental results of acoustic radiation generated by a point-driven plate with clamped boundaries validate the correctness and availability of the method.     

Dependence of Nucleon and Pion-Induced Fission Cross Sections on the Level Density Parameter in the Cascade-Exciton Model

A new method is used to compute the fission cross sections in which a change of the ratio of the level density parameter in fission to neutron emission channels is taken into account with the change of the incident energy of the projectile. It is shown that fission cross sections induced by nucleons and pions depend on the ratio of the level density parameter in the fission and evaporation modes, i,e. af /an, respectively. We are unable to describe well the cross sections for fission without using this new method. The computed values exhibit reasonable agreement with the experimental data found in the literature across a wide range of beam energies.     

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-Ⅱ beam

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometricGaussian type-Ⅱ beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre–Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.     

Accuracy and analysis of long-radius measurement with long trace profiler

The long trace profiler(LTP) is proposed to measure radius of curvature(R) and surface figure of a longradius spherical surface in an optical shop.Equipped with a motorized rotary stage and a two-dimensional tilt stage,the LTP scans the full aperture and calculates the absolute radius of curvature of each scanning line based on the least square method.Nonlinear error and manufacture error difference between center and the edge are obtained by comparing R results.The R-limit is validated and expressed as D/R,where D is the aperture of the mirror under test.A full-aperture three-dimensional figure is also reconstructed based on triangle interpolation.