Transport approaches for the description of intermediate-energy heavy-ion collisions

Abstract

The transport approach is a useful tool to study dynamics of non-equilibrium systems. For heavy-ion collisions at intermediate energies, where both the smooth nucleon potential and the hard-core nucleon-nucleon collision are important, the dynamics are properly described by two families of transport models, i.e., the Boltzmann-Uehling-Uhlenbeck approach and the quantum molecular dynamics approach. These transport models have been extensively used to extract valuable information of the nuclear equation of state, the nuclear symmetry energy, and microscopic nuclear interactions from intermediate-energy heavy-ion collision experiments. On the other hand, there do exist deviations on the predications and conclusions from different transport models. Efforts on the transport code evaluation project are devoted in order to understand the model dependence of transport simulations and well control the main ingredients, such as the initialization, the mean-field potential, the nucleon-nucleon collision, etc. A new era of accurately extracting nuclear interactions from transport model studies is foreseen. 2 from 50 MeV to 2 GeV, where the nucleon degree of freedom dominates the dynamics, and both the smooth nuclear potential and the hard-core nucleon-nucleon collisions become important. The central purpose of intermediate-energy heavy-ion collisions is to extract the equation of state (EOS) of the hot and dense nuclear matter formed during the collisions, while the uncertainties mostly come from the isospin-dependent part, i.e., the nuclear symmetry energy.In order to describe properly the dynamics of intermediate-energy heavy-ion collisions, transport approaches at this energy regime are mostly developed along two directions: the Boltzmann-Uehling-Uhlenbeck (BUU) approach and quantum molecular dynamics (QMD) approach. The BUU approach basically models the time evolution of the one-body phase-space distribution based on the BUU equation numerically using the test-particle method, and the QMD approach models the time evolution of nucleons under a many-body Hamiltonian with the wave function of each nucleon represented by a Gaussian wave packet. Both approaches can be derived from many-body theories with various approximations. Without nucleon-nucleon collisions, the BUU approach reduces to the Vlasov approach, which is similar to the TDHF approach. On the other hand, it is difficult to solve exactly the extended TDHF approach, which incorporates the collision contribution into the TDHF approach [3]. Both the BUU approach and the QMD approach include mainly three ingredients: the initialization of projectile and target nuclei, the mean-field potential for each nucleon, and the nucleon-nucleon collision in the dynamical evolution. The mean-field potential can be obtained from effective in-medium nucleon-nucleon interactions based on the Hartree or Hartree-Fock method, and in this way the microscopic nuclear interaction is related to the macroscopic nuclear EOS through the energy-density functional form.So far both the BUU appr...

Phase-space consideration on barrier transmission in a time-dependent variational approach with superposed wave packets

“…Heisenberg's uncertainty principle), it works in many cases without causing serious inconsistencies, mainly because 𝑇 0 is just a constant term in the Hamiltonian, so it affects neither the equation of motion nor the energy conservation. However, to the best of the author's knowledge, the models that take View B have not been extended successfully to treat coherent superposition of wave packets, though stochastic branching of wave packets or manybody states is typically considered in transport models [6][7][8][9][10][11][12][13]. It is therefore an important question whether View B can be taken in the TDGCM model, which will be addressed later in detail.…”

“…of fusion and scattering, is a general desire in time-dependent approaches for many-body systems. In some cases, stochastic extension of a model can allow channels to emerge as a consequence of time evolution, such as in transport models for heavy-ion collisions [6][7][8][9][10][11][12][13]. Tunneling further requires true quantum description for the translational motion of a nucleus, which is often not straightforward because the center-of-mass wave function is enforced to be localized in space, like a wave packet, when the nucleus is described in a mean-field model.…”

Effect of internal magnetic field on collective flow in heavy ion collisions at intermediate energies

“…As it became clear that, many physical effects (e.g., in-medium cross sections, pion dispersion relation, ∆ production and decay, etc.) may significantly affect the sensitivity of π − /π + ratio on the density-dependent symmetry energy [50][51][52][53][54][55], all these effects deserve further studies. For v n 2 -v p 2 , the effect of magnetic field is smaller than that of symmetry energy in the mid-rapidity region, especially at 0.4 GeV/nucleon, where one expect the effect of symmetry energy is more evident.…”

Analysis of the dynamical mechanism for elliptic flow production in heavy-ion collisions at intermediate energies

“…由此可见, 椭圆流能够反映重离子碰撞中被压 缩核物质演化的信息, 因此是探究高密核物质性质 的重要探针之一. 从输运模型的角度来看, 平均场和 碰撞项作为输运模型中的两个主要部分都会明显 影响椭圆流的演化, 而且随着入射能量的改变, 这两 者作用的相对强度也会发生变化 [9][10][11][20][21][22][23] . 比如, 在 能量较低时, 核子-核子间的碰撞截面虽然比较大, 但由于周围核子的作用, 大多数核子-核子碰撞被阻 止(泡利阻塞效应), 此时平均场的作用占主导.…”