Impact parameter and beam energy dependence for azimuthal asymmetry of direct photons and free protons in intermediate energy heavy-ion collisions

Hard photon emitted from energetic heavy ion collisions is of very interesting since it does not experience the late-stage nuclear interaction, therefore it is useful to explore the early-stage information of matter phase. In this work, we have calculated the impact parameter and beam energy dependence for azimuthal asymmetry, characterized by directed transverse flow parameter F and elliptic asymmetry coeffcient v2, of direct photons and the corresponding free protons in intermediate energy heavy-ion collisions. It is further shown the anti-correlated azimuthal asymmetry between direct photons and free protons.     

放射性束引起的重离子碰撞中敏感于对称能的几个观测量

利用同位旋与动量相关的强子输运模型，我们研究了放射性束引起的中能重离子碰撞中几个观测量的对称能效应。我们发现自由核子发射的非对称度的快度分布，中快度中－质比的横动量分布，的动能分布，以及同位旋相分化（fractionation）的时间演化都敏感于对称能。     

Observation of strong azimuthal asymmetry between slow and fast particles from high energy nuclear collisions

Evidence is presented for the strong azimuthal asymmetry between slow and fast fragments in nuclear collisions in the energy interval of 0.4 to 1 GeV per nucleon. The asymmetry gets stronger when incident energy and impact parameter decrease. The results on theA dependence of the azimuthal asymmetry are also presented.     

Quantum confinement in an asymmetric double‐well potential through energy analysis and information entropic measure

Localization of a particle in the wells of an asymmetric double‐well (DW) potential is investigated here. Information entropy‐based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phase‐space area, are utilized to explain the contrasting effect of localization‐delocalization and role of asymmetric term in such two‐well potentials. In asymmetric situation, two wells behaves like two different potentials. A general rule has been proposed for arrangement of quasi‐degenerate pairs, in terms of asymmetry parameter. Further, it enables to describe the distribution of particle in either of the deeper or shallow wells in various energy states. One finds that, all states eventually get localized to the deeper well, provided the asymmetry parameter attains certain threshold value. This generalization produces symmetric DW as a natural consequence of asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple, accurate variation‐induced exact diagonalization method. In brief, information measures and phase‐space analysis can provide valuable insight toward the understanding of such potentials.     

一种特殊的非对称量子阱中的电光效应

运用密度矩阵方法推导出了特殊非对称量子阱中电光系数的解析表达式,并以典型的GaAs/AlGaAs非对称量子阱为例进行了数字计算.计算结果表明,量子阱的非对称性随着参数a的增大而增强,随着参数V₀的增大而减小.电光系数的最大值也随着参数a的增大而增大,随着参数V₀的增大而减小,表明电光系数将随着量子阱非对称性的增大而增大.在取不同的参数a和不同的参数V₀时,电光系数和入射光子能量的关系分别被绘制成曲线图.在图中分别有三个不同的峰,而且系统的非对称性越大,峰值就越大.随着量子阱非对称性的增大,曲线中的峰向能量低的方向移动.另外,在这种量子阱中得到了比较大的电光系数,大约在10^-6m/V量级.随着近来纳米制作技术的进步,使得在实验上制作这种特殊非对称量子阱并得到较好的非线性材料成为可能.     

Azimuthal asymmetry of direct photons in intermediate energy heavy-ion collisions

Hard photon emitted from energetic heavy ion collisions is of very interesting since it does not experience the late-stage nuclear interaction, therefore it is useful to explore the early-stage information of matter phase. In this work, we have presented a first calculation of azimuthal asymmetry, characterized by directed transverse flow parameter F   and elliptic asymmetry coefficient v₂$v_2$, for proton–neutron bremsstrahlung hard photons in intermediate energy heavy-ion collisions. The positive F   and negative v₂$v_2$ of direct photons are illustrated and they seem to be anti-correlated to the corresponding free proton's flow.     

Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions

High energy heavy-ion collisions are proposed as a novel means to constrain stringently the high density (HD) behavior of nuclear symmetry energy. Within an isospin-dependent hadronic transport model, it is shown for the first time that the isospin asymmetry of the HD nuclear matter formed in high energy heavy-ion collisions is uniquely determined by the HD behavior of the nuclear symmetry energy. Experimental signatures in two sensitive probes, i.e., pi(-) to pi(+) ratio and neutron-proton differential collective flow, are also investigated.     

Liquid-drop description of the nuclear excitation energy

An extended Fermi-gas model is presented to describe volume, surface and asymmetry contributions to the nuclear excitation energy. The potential part of the nuclear energy is treated within Brueckner's energy-density formalism; appropriate corrections due to surface and asymmetry effects are included. An excited nucleus is interpreted as a metastable superheated liquid. The excitation energy as a function of the temperature is given by a sum of volume, surface and asymmetry terms. The corresponding level-density formula is in reasonable agreement with experimental values for a suitable choice of the nuclear incompressibility modulus. It is shown that the surface contribution is appreciable.     

Azimuthal asymmetry of jet production as a signal of parton energy losses in semicentral heavy-ion collisions

The question is investigated of whether an azimuthal asymmetry in the hadron-jet spectra can arise because of rescattering and energy losses of partons produced via hard processes in a dense quark-gluon matter formed in the region of the initial nuclear overlap in collisions characterized by a nonzero value of the impact parameter. Methods are discussed for determining the reaction-plane angle in ultrarelativistic heavy-ion collisions with the aid of the flux of semihard particles.     

Intra- and intergroup azimuthal correlations of particles in the interaction of gold nuclei with silver and bromine nuclei of track emulsions at the projectile energy of 10.6 GeV per nucleon

Inter- and intragroup azimuthal correlations of target and projectile fragments and of shower particles in the interactions between gold nuclei of energy 10.6 GeV per nucleon and silver and bromine nuclei of a track emulsion are studied at intermediate values of the impact parameter. The asymmetry index β′₁ and the collinearity index β′₂ of groups’ asymmetry vectors are used to study azimuthal correlations between two and three groups of particles. The interplay of effects of intra- and intergroup azimuthal particle correlations is investigated.     

Correlations between electronic energy bands spin splitting and magnetic profile symmetry of magnetic superlattice

We have theoretically investigated the energy band structures of two typical magnetic superlattices formed by perpendicular or parallel magnetization ferromagnetic stripes periodically deposited on a two-dimensional electron gas (2DEG), where the magnetic profile in the perpendicular magnetization is of inversion anti-symmetry, but of inversion symmetry in parallel magnetization, respectively. We have shown that the energy bands of perpendicular magnetization display the spin-splitting and transverse wave-vector symmetry, while the energy bands of the parallel magnetization exhibit spin degeneration and transverse wave-vector asymmetry. These distinguishing spin-dependent and transverse wave-vector asymmetry features are essential for future spintronics devices applications.     

Energy spectra and asymmetries of neutrons emitted after muon capture

Inclusive energy spectra and the energy dependence of the asymmetry parameter have been measured for neutrons emitted after muon capture in O, Si, Ca and Pb. In addition a neutron-neutron coincidence measurement has been performed for Ca. The results of these measurements confirm the exponential shape of the energy spectra and the positive asymmetry observed by Sundelin and Edelstein. The observation of neutrons with energies above 50 MeV and the observation of simultaneous emission of two high-energy neutrons suggest the importance of short-range nucleonnucleon correlations in this process.     

Isospin and symmetry energy study in nuclear EOS

This paper summarizes the isoscaling and isospin related studies in asymmetry nuclear reactions by different dynamic and statistical models. Isospin dependent quantum molecular dynamics model (IQMD) and lattice gas model (LGM) are used to study the isoscaling properties and isoscaling parameters dependence on incident energies, impact parameters, temperature and other parameters. In the LGM model, the signal of phase transition has been found in free neutron (proton) chemical potential difference Δµ_n or Δµ_p as a function of temperature, or in free neutron and proton chemical potential difference Δµ_n−Δµ_p. Density dependence of symmetry energy coefficient C _sym(ρ/ρ ₀) is also studied in the frame of LGM, with the potential parameters which can reproduce the nuclear ground state property, soft density dependence of symmetry energy is deduced from the simulation results. Giant dipole resonance (GDR) induced by isospin asymmetry in entrance channel is also studied via IQMD model, and the dynamic dipole resonance shows isospin sensitivity on the isospin asymmetry of entrance channel and symmetry energy of the nuclear equation of state (EOS). GDR can also be regarded as a possible isospin sensitive signature.

     

Twist free energy

One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two parallel limiting planes, generate an interface and a cost in free energy per unit area of the interface. For continuum symmetries the order parameter interpolates smoothly between the end planes carrying two different directions of the order parameter. The cost in free energy is then proportional to L^d-2 for a system of characteristic size L. The power of L is related to the lower critical dimension, and the coefficient of this additional free energy vanishes at the critical temperature. In this note it is shown within a loop expansion that one does find the expected behavior of this twist free energy. This is a preamble to the study of situations where the broken continuum symmetry is believed to be more complex, as in Parisi ansatz for the Edwards-Anderson spin glass. Received 11 June 2001     

Convergent polynomial expansion,energy dependence of slope parameters,scaling hypothesis and predictions forπ ± p andK + p scattering

A phenomenological representation for differential cross-section recently proposed using Mandelstam analyticity and convergent polynomial expansion (CPE) which has been found to be successful in describing scaling of the differential cross-section-ratio data for several elastic diffractive and inelastic nondiffractive processes is used to analyse the energy dependence of the slope-parameter data at high energies, extrapolate the slope parameter and predict the differential cross-section ratio as a function of |t| at higher energies forπ ^± pndK ⁺ p scattering. Following the method of Hansen and Krisch it is found that, in spite of the existence of rather widely varying data points for nearbys values, a more systematic trend in the energy dependence of the slope parameter emerges when a statistical average of the existing high-energy data is used. Extrapolating the fits to the average data ontos → ∞ provides strong evidence in favour of a model-independent result that asymptotically theπ ^± p slopes may be equal. There is also a strong indication to the effect that each of these two slopes may be equal to theK ⁺ p slope fors → ∞. Using the scaling curves generated by the existing data on differential cross-section ratio and extrapolated values of the slope parameter, the differential cross-section ratio for each of the three processes is predicted as a function of |t| for higher energies.     

Isotropic and anisotropic dark energy models

In this review we discuss the evolution of the universe filled with dark energy with or without perfect fluid. In doing so we consider a number of cosmological models, namely Bianchi type I, III, V, VI₀, VI and FRW ones. For the anisotropic cosmological models we have used proportionality condition as an additional constrain. The exact solutions to the field equations in quadrature are found in case of a BVI model. It was found that the proportionality condition used here imposed severe restriction on the energy-momentum tensor, namely it leads to isotropic distribution of matter. Anisotropic BVI₀, BV, BIII and BIDE models with variable EoS parameter ω have been investigated by using a law of variation for the Hubble parameter. In this case the matter distribution remains anisotropic, though depending on the concrete model there appear different restrictions on the components of energy-momentum tensor. That is why we need an extra assumption such as variational a law for the Hubble parameter. It is observed that, at the early stage, the EoS parameter v is positive i.e. the universe was matter dominated at the early stage but at later time, the universe is evolving with negative values, i.e., the present epoch. DE model presents the dynamics of EoS parameter ω whose range is in good agreement with the acceptable range by the recent observations. A spatially homogeneous and anisotropic locally rotationally symmetric Bianchi-I space time filled with perfect fluid and anisotropic DE possessing dynamical energy density is studied. In the derived model, the EoS parameter of DE (ω^(de)) is obtained as time varying and it is evolving with negative sign which may be attributed to the current accelerated expansion of Universe. The distance modulus curve of derived model is in good agreement with SNLS type Ia supernovae for high redshift value which in turn implies that the derived model is physically realistic. A system of two fluids within the scope of a spatially flat and isotropic FRW model is studied. The role of the two fluids, either minimally or directly coupled in the evolution of the dark energy parameter, has been investigated. In doing so we have used three different ansatzs regarding the scale factor that gives rise to a variable decelerating parameter. It is observed that, in the non-interacting case, both the open and flat universes can cross the phantom region whereas in the interacting case only the open universe can cross the phantom region. The stability and acceptability of the obtained solution are also investigated.     

Exciton-phonon interaction and energy transfer in benzene and isotopically impure deuterobenzene crystals

Absorption and fluorescence of pure and isotopically substituted benzene crystals are reported for the range 4.2–20°K. The energy of electron- and vibron-phonon interactions and the probability of respective optical transitions are determined. The pronounced asymmetry of phonon sidebands of absorption and luminescence spectra is found. The kinetic analysis of isotopically impure crystal spectra gives the trap-trap energy transfer probability and the energy dependence of the electron-phonon coupling coefficient.     

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z^2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV L 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.     

Effect of Wigner energy on the symmetry energy coefficient in nuclei

The nuclear symmetry energy coefficient(including the coefficient a_(sym)~((4)) of the I~4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei.It is found that the extracted symmetry energy coefficient a_(sym)~*(A,I) decreases with increasing isospin asymmetry I,which is mainly caused by Wigner correction,since e_(sym)~* is the summation of the traditional symmetry energy e_(sym) and the Wigner energy ew.We obtain the optimal values J = 30.25±0.10 MeV,a_(ss)=56.18±1.25 MeV,a_(sym)~((4)) = 8.33±1.21 MeV and the Wigner parameter x= 2.38 ±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with20 ≤ A ≤ 261 with an rms deviation of 23.42 keV.We also find that the volume symmetry coefficient J■ 30 MeV is insensitive to the value x,whereas the surface symmetry coefficient a_(ss) and the coefficient a_(sym)~((4)) are very sensitive to the value of x in the range 1≤x≤4.The contribution of the a_(sym)~((4)) term increases rapidly with increasing isospin asymmetry I.For very neutron-rich nuclei,the contribution of the a_(sym)~((4)) term will play an important role.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.