We present here the system size dependence of balance energy for semi-central and peripheral collisions using quantum molecular dynamics model. For this study, the reactions of $Ne^{20}+Ne^{20}$, $Ca^{40}+Ca^{40}$, $Ni^{58}+Ni^{58}$, $Nb^{93}+Nb^{93}$, $Xe^{131}+Xe^{131}$ and $Au^{197}+Au^{197}$ are simulated at different incident energies and impact parameters. A hard equation of state along with nucleon-nucleon cross-sections between 40 - 55 mb explains the data nicely. Interestingly, balance energy follows a power law $\propto{A^{\tau}}$ for the mass dependence at all colliding geometries. The power factor $\tau$ is close to -1/3 in central collisions whereas it is -2/3 for peripheral collisions suggesting stronger system size dependence at peripheral geometries. This also suggests that in the absence of momentum dependent interactions, Coulomb's interaction plays an exceedingly significant role. These results are further analyzed for nuclear dynamics at the balance point.
Dynamical dipole γ-ray emission in heavy-ion collisions is explored in the framework of the quantum molecular dynamics model. The studies are focused on systems of 40Ca bombarding 48Ca and its isotopes at different incident energies and impact parameters. Yields of γ rays are calculated and the centroid energy and dynamical dipole emission width of the γ spectra are extracted to investigate the properties of γ emission. In addition, sensitivities of dynamical dipole γ-ray emission to the isospin and the symmetry energy coefficient of the equation of state are studied. The results show that detailed study of dynamical dipole γ radiation can provide information on the equation of state and the symmetry energy around the normal nuclear density.
We examine the model dependence of the phase diagram of inhomogeneous nulcear matter in supernova cores using the quantum molecular dynamics (QMD). Inhomogeneous matter includes crystallized matter with nonspherical nuclei - "pasta" phases - and the liquid-gas phase separating nuclear matter. Major differences between the phase diagrams of the QMD models can be explained by the energy of pure neutron matter at low densities and the saturation density of asymmetric nuclear matter. We show the density dependence of the symmetry energy is also useful to understand uncertainties of the phase diagram. We point out that, for typical nuclear models, the mass fraction of the pasta phases in the later stage of the collapsing cores is higher than 10-20 %
Nucleon-ion and ion-ion collisions at non relativistic bombarding energies can be described by means of Monte Carlo approaches, such as those based on the Quantum Molecular Dynamics (QMD) model. We have developed a QMD code, to simulate the fast stage of heavy-ion reactions, and we have coupled it to the de-excitation module available in the FLUKA Monte Carlo transport and interaction code. The results presented in this work span the projectile bombarding energy range within 200 - 600 MeV/A, allowing to investigate the capabilities and limits of our non-relativistic QMD approach.
An experimental study of nuclear reactions between 28Si nuclei at 200 and 300 MeV/nucleon and hydrogen or deuterium target nuclei was performed at the CELSIUS storage ring in Uppsala, Sweden, to collect information about the reactions responsible for single-event effects in microelectronics. Inclusive data on 28Si fragmentation, as well as data on correlations between recoils and spectator protons or α particles are compared to predictions from the Dubna cascade model and the Japan Atomic Energy Research Institute version of the quantum molecular dynamics model. The comparison shows satisfactory agreement for inclusive data except for He fragments where low-energy sub-barrier fragments and recoiling fragments with very large momenta are produced much more frequently than predicted. The yield of exclusive data are also severely underestimated by the models whereas the charge distributions of recoils in these correlations compare well. The observed enhancement in He emission, which may well be important for the description of single-event effects, is most likely to be attributed to α clustering in 28Si nuclei.
Signatures of isospin effects were investigated for neutron-rich (124Sn+64Ni) and neutron-poor (112Sn+58Ni) systems at 35 MeV/nucleon for noncentral collisions. The centrality dependence of these signatures was tested for several impact parameter estimators. Our main observations are (i) the yields of 1H and 3He particles in the neutron-poor system are strongly enhanced with respect to the neutron-rich system, and the yields of 3H, 6He, and 7,8Li are suppressed at all impact parameters, (ii) the yields of 2H, 4He, and 6Li particles are almost the same for both systems, (iii) the N/Z ratio of intermediate mass fragments is correlated with the neutron richness of the system and is weakly dependent on the centrality of the collision, and (iv) the neutron richness of the detected fragments increases strongly with decreasing rapidity in the range from that of the projectile-like fragment to the c.m. region. The gross features of experimental data are reproduced by quantum molecular dynamics model calculations. A comparison between model calculations and the data indicates that the fragments produced in the c.m. regions are weakly excited.
The sigma meson production in p + 12C and p + 40Ca reactions at the incident energy Ep = 1.5 GeV is investigated within the Quantum Molecular Dynamics model. The simulation results indicate a distinctive A dependence of the sigma production, that is, the increase of A is followed by an increase of the production cross sections. We find that the σ meson production in proton-induced reactions is strongly medium-dependent, and the produced σ mesons decaying in a denser medium experience a stronger mass shift towards lower masses. This mass shift is an experimentally accessible observable in the final state pion pairs, which do not suffer from reabsorption by the surrounding nucleons. It is pointed out that the ratio of measured sigma cross sections as a function of the sigma invariant-mass from various reactions is a good probe to explore the existence of the σ meson in a dense nuclear environment.
Anisotropic flows ($v_1$, $v_2$, $v_3$ and $v_4$) of light fragments up till the mass number 4 as a function of rapidity have been studied for 25 MeV/nucleon $^{40}$Ca + $^{40}$Ca at large impact parameters by Quantum Molecular Dynamics model. A phenomenological scaling behavior of rapidity dependent flow parameters $v_n$ (n = 1, 2, 3 and 4) has been found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, $v_4/{v_2}^2$ keeps almost independent of rapidity and remains a rough constant of 1/2 for all light fragments
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.
Quantum Molecular Dynamics models (QMD) are Monte Carlo approaches targeted at the description of nucleon–ion and ion–ion collisions. We have developed a QMD code, which has been used for the simulation of the fast stage of ion–ion collisions, considering a wide range of system masses and system mass asymmetries. The slow stage of the collisions has been described by statistical methods. The combination of both stages leads to final distributions of particles and fragments, which have been compared to experimental data available in the literature. A few results of these comparisons, concerning neutron double-differential production cross-sections for C, Ne and Ar ions impinging on C, Cu and Pb targets at 290–400 MeV/A bombarding energies and fragment isotopic distributions from Xe + Al at 790 MeV/A, are shown in this paper.
We present the theoretical study of fragmentation at low excitation energies within dynamical microscopic theory namely, simulated annealing clusterization algorithm (SACA) and quantum molecular dynamics (QMD) model. For low excitation energy reactions, we choose the balance energies for a large number of reactions throughout the periodic table. We see that SACA gives multiplicities in terms of power law. For light fragments, it is close to 1/3, whereas, for heavier fragments it is nearly mass independent suggesting their origin in terms of participant-spectator picture.
Anisotropic flows (v1, v2, v3 and v4) of light fragments up to the mass number 4 as a function of rapidity are studied for 25MeV/nucleon 40Ca + 40Ca at large impact parameters by a quantum molecular dynamics model. A phenomenological scaling behaviour of rapidity dependent flow parameters vn (n = 1, 2, 3 and 4) is found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, v4v22 keeps to be almost independent of rapidity and remains a rough constant of 1/2 for all light fragments.
Elliptic flow (v2) and hexadecupole flow (v4) of light clusters have been studied in detail for 25 MeV/nucleon 86Kr + 124Sn at large impact parameters by using a quantum molecular dynamics model with different potential parameters. Four sets of parameters including soft or hard equation of state (EOS) with or without symmetry energy term are used. Both number-of-nucleon (A) scaling of the elliptic flow versus transverse momentum (pt) and the scaling of v4/A2 versus (pt/A)2 have been demonstrated for the light clusters in all above calculation conditions. It is also found that the ratio of v4/v22 maintains a constant of ? which is independent of pt for all the light fragments. Comparisons among different combinations of the EOS and the symmetry potential term show that the above scaling behaviours are sound and independent of the details of potential, while the strengths of flows are sensitive to the EOS and the symmetry potential term.
Anisotropic flows (v1, v2, v3 and v4) of light fragments up to the mass number 4 as a function of rapidity are studied for 25 MeV/nucleon 40Ca + 40Ca at large impact parameters by a quantum molecular dynamics model. A phenomenological scaling behaviour of rapidity dependent flow parameters vn (n = 1, 2, 3 and 4) is found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, v4/v22 keeps to be almost independent of rapidity and remains a rough constant of 1/2 for all light fragments.
Information about the Equation of State (EOS) of asymmetric matter improves our understanding of the properties of neutron star such as stellar radii and moments of inertia, maximum masses, crustal vibration frequencies, and neutron star cooling rates
The $\eta$-meson photoproduction cross sections have been measured on the C and Cu targets for the photon energies between 600 and 1100 MeV to investigate the behavior of the $S_{11}$(1535) resonance in a nucleus. The excitation functions of the cross section as well as the angular and momentum distributions of $\eta$-mesons are in quantitative agreement with the Quantum Molecular Dynamics (QMD) model calculations in which the $\eta$-meson emission processes other than the $S_{11}$(1535) resonance are also incorporated as proposed in the $\eta$-MAID model. It is shown that the excitation of the $D_{15}$(1675) resonance might play an important role for $E_{\gamma}>900$ MeV.
We studied the fragmentation of colliding nuclei at the energy of vanishing flow and evaluated its mass dependence throughout the periodic table. This study was performed within the framework of the quantum molecular dynamics model, which has been reported to reproduce the experimental data at low incident energies quite nicely. We simulated as many as 11 reactions for which the balance energy had been measured experimentally. Our observations at the energy of vanishing flow clearly suggest the existence of a power law system mass dependence for various fragment multiplicities. The power factor τ(∝Aτ) is close to (-1/3), as has also been reported for the mass dependence of the energy of vanishing flow. Experiments are needed to verify these predictions.
Using the quantum molecular dynamics model, we aim to investigate the emission of light complex particles, and degree of stopping reached in heavy-ion collisions. We took incident energies between 50 and 1000 MeV/nucleon. In addition, central and peripheral collisions and different masses are also considered. We observe that the light complex particles act in almost similar manner as anisotropic ratio. In other words, multiplicity of light complex particles is an indicator of global stopping in heavy-ion collisions. We see that maximum light complex particles and stopping is obtained for heavier masses in central collisions.
We propose to identify the new “intermediate” morphology in subsaturation nuclear matter observed in a recent quantum molecular dynamics simulation with the ordered bicontinuous double-diamond structure known in block copolymers. We estimate its energy density by incorporating the normalized area-volume relation given in a literature into the nuclear liquid drop model. The resulting energy density is higher than the other five known morphologies.
Proton productions from proton induced reactions have been investigated for target nuclei of 12C, 27Al, and 93Nb at 300 and 392 MeV. Proton inelastic continua over a broad energy range were measured at laboratory angles from 20° to 105°. The differential cross sections were compared with two theoretical models, the quantum molecular dynamics (QMD) and the intranuclear cascade (INC) model in terms of the multistep direct process. We demonstrated that consistencies of these models can be improved using a realistic ground state of target nucleus, and that the INC model developed presently has a fairly good consistency and a higher predictive ability than the QMD.
Double-differential cross sections of neutron production at angles from 0 to 110 degrees from many reactions induced by light and medium nuclei on targets from 12-C to 208-Pb, at several incident energies from 95 to 600 MeV/A have been measured recently at the Institute of Physical and Chemical Research (RIKEN) Ring Cyclotron in Japan and at the Heavy-Ion Medical Accelerator of the National Institute of Radiological Science in Chiba, Japan using the time-of-flight technique. We have analyzed all these new measurements using the Quantum Molecular Dynamics (QMD) model, the Oak Ridge intranuclear cascade model HIC, the ISABEL intranuclear cascade model from LAHET, and the Los Alamos version of the Quark-Gluon String Model code LAQGSM03. On the whole, all four models used here describe reasonably well most of the measured neutron spectra, although different models agree differently with data from specific reactions and some serious discrepances are observed for some reactions. We present here some illustrative results from our study, discuss possible reasons for some of the observed discrepancies and try to outline ways to further improve the tested codes in order to address these problems.
Within a quantum molecular dynamics model we calculate the largest Lyapunov exponent (LLE), density fluctuation and mass distribution of fragments for a series of nuclear systems at different initial temperatures. It is found that the $LLE$ peaks at the temperature ("critical temperature") where the density fluctuation reaches a maximal value and the mass distribution of fragments is best fitted by the Fisher's power law from which the critical exponents for mass and charge distribution are obtained. The time-dependent behavior of the LLE and density fluctuation is studied. We find that the time scale of the density fluctuation is much longer than the inverse LLE, which indicates that the chaotic motion can be well developed during the process of fragment formation. The finite-size effect on "critical temperature" for nuclear systems ranging from Calcium to superheavy nuclei is also studied.
We study the mass dependence of various quantities (like the average and maximum density, collision rate, participant-spectator matter, temperature as well as time zones for higher density) by simulating the reactions at the energy of vanishing flow. This study is carried out within the framework of Quantum Molecular Dynamics model. Our findings clearly indicate an existence of a power law in all the above quantities calculated at the balance energy. The only significant mass dependence was obtained for the temperature reached in the central sphere. All other quantities are rather either insensitive or depend weakly on the system size at balance energy. The time zone for higher density as well as the time of maximal density and collision rate follow a power law inverse to the energy of vanishing flow.
基于量子分子动力学模型,系统地研究了从48Ca到298114一系列核素在不同温度下的最大Lyapunov指数、密度涨落以及体系多重碎裂之间的关系.发现最大Lyapunov指数随温度变化有一峰值出现(该峰值所对应的温度为"临界温度"),在该临界温度时体系的密度涨落达到最大,碎块的质量分布能够给出较好的PowerLaw指数.通过对最大Lyapunov指数与密度涨落随时间变化行为的研究,发现密度涨落的时间尺度要大于混沌的时间尺度,意味着混沌的概念可以用来研究体系的多重碎裂过程.最后还给出了有限体系相变的临界温度随体系大小变化的规律.(Within a quantum molecular dynamics model we calculate the largest Lyapunov exponent (LLE), the density fluctuation, and the mass distribution of fragments for a series of nuclear systems at different initial temperatures. It is found that the LLE peaks at the temperature ("critical temperature") where the density fluctuation reaches a maximal value and the mass distribution fragments is fitted best by the Fisher's power law from which the critical exponents for mass and charge distribution are obtain...)
The role of neutron-Halo special structure on the momentum dissipation was studied as the increase of colliding system mass by using the quantum molecular dynamics model. In order to protrude the role of special structure of neuron-halo nuclei 11Li, 14Be and 19B on the momentum dissipation we also calculated the mo-
Using the quantum molecular dynamics model coupled with the minimum spanning tree clusterization algorithm, we investigate the system-size effects in the production of light mass fragments (with mass <~10). This was achieved by simulating the collision of symmetric nuclei like Ca+Ca, Ni+Ni, Nb+Nb, Xe+Xe, Er+Er, Au+Au, and U+U at incident energies between 50 MeV/nucleon and 1 GeV/nucleon and over full range of impact parameter. Our detailed analysis shows that the triggering of the multifragmentation and its saturation is delayed in heavier systems. The striking result, which is independent of the incident energy as well as of the impact parameter, is that the mass dependence of the multiplicity of any kind of fragment exhibits a power law behavior ∝Atotτ, where “Atot” is the mass of the composite system. Similar mass dependencies have already been reported in the literature for the fusion process at low incident energy as well as for the production of kaon and collective flow (and its disappearance) at intermediate energies. As reported for the production of kaons, the parameter τ depends on the colliding geometry as well as on the incident energy. No unique dependence of τ (such as, in the case of disappearance of flow) exists. The value of the parameter τ in central low energy collisions is close to 2/3, which suggests the dominance of the mean field. On the other hand, a linear dependence occurs at higher incident energies. Similar trends can also be seen in the preliminary reports of the FOPI experiments.
The transverse flow of positive charged kaons from heavy-ion collisions at intermediate energy is investigated within the framework of the quantum molecular dynamics model. The calculated results show that the experimental data are only consistent with the ones including the kaon mean-field potential from the chiral Lagrangian. This indicates that the transverse flow pattern of kaons is an useful probe of the kaon potential in a nuclear medium.
【摘要】 应用量子分子动力学模型 ,从原子核发生碎化时的碎块质量分布、密度涨落以及混沌动力学中描述混沌程度的最大Lyapunov指数等 3个方面 ,对原子核的液气相变及其在临界点附近的行为进行较为全面的探讨 .通过研究 ,发现在临界温度附近原子核发生最大的液气共存、密度涨落达到极大以及产生最大混沌构型. 【英文摘要】 Based on the quantum molecular dynamics model, the dynamical behaviors of the Liquid gas phase transition in nuclei are investigated. In order to explore the characters of the Liquid gas phase transition in the vicinity of the "critical point", the Maximum Lyapunov exponent (MLE) is employed and the method of calculation of the MLE is developed. The dependence of the mass distribution of fragments, density fluctuation and the MLE on temperature has been studied for nuclear systems 124 Sn an...
The transverse flow of positively charged kaons from heavy-ion collisions at intermediate energy is investigated within the framework of the quantum molecular dynamics model. The calculated results show that the experimental data are only consistent with those including the kaon mean-field potential from the chiral Lagrangian. This indicates that the transverse flow pattern of kaons is a useful probe of the kaon potential in a nuclear medium
中高能质子入射重金属靶产生散裂中子是加速器驱动洁净核能系统的一个关键部分 .利用量子分子动力学 (QMD)模型研究入射质子能量在 3 0 0MeV—1 .5GeV ,散裂靶为2 0 8Pb的 (p ,xn)核反应的双微分截面 ,QMD计算结果很好再现了实验数据 ,且QMD的计算结果明显优于HETC和LAHET .QMD在较宽的能区和核区满足加速器驱动洁净核能系统散裂靶物理计算的要求(The spallation neutron source induced by high energy protron nucleus interaction is an important link for acceralator driven system. The quantum molecular dynamics (QMD) model is applied to analize the high energy proton induced reactions on 208 Pb. The QMD simulations of the double differential cross section of 208 Pb (p, x n) reactions with incident energies of 590,800 and 1500MeV are in good agreement with the experimental data,and the results of QMD calculations are better than that of HETC a...)
We report, for the first time, the dependence of the multiplicity of different fragments on the system size employing a quantum molecular dynamics model. This dependence is extracted from the simulations of symmetric collisions of Ca+Ca, Ni+Ni, Nb+Nb, Xe+Xe, Er+Er, Au+Au and U+U at incident energies between 50 A MeV and 1 A GeV. We find that the multiplicity of different fragments scales with the size of the system which can be parameterized by a simple power law.
We discuss what the presently collected data tell us about the mechanism of multifragmentation by comparing the results of two different models, which assume or show an opposite reaction scenario, with the recent high statistics $4\pi$ experiments performed by the INDRA collaboration. We find that the statistical multifragmentation model and the dynamical Quantum Molecular Dynamics approach produce almost the same results and agree both quite well with experiment. We discuss which observables may serve to overcome this deadlock on the quest for the reaction mechanism. Finally we proof that even if the system is in equilibrium, the fluctuation of the temperature due to the smallness of the system renders the caloric curve useless for the proof of a first order phase transition.
We have measured the double-differential cross sections for neutron production from C, Ne, and Ar projectiles at E/A=290–600MeV on C, Cu, and Pb targets. Neutron energies were measured at laboratory angles between 5° and 80°. The measured neutron spectra have three components. At forward angles, a prominent peak originating from the projectile-fragmentation process was observed. The velocity of neutrons corresponding to the peak was about the same as that of the projectile. In addition to the peak, two components of Maxwellian-shape distributions corresponding to the preequilibrium and equilibrium processes were observed. By fitting with a moving-source model having three components, the neutron spectra were fairly well described. The parameters obtained for each component are consistent with a picture of the projectile fragmentation, preequilibrium, and equilibrium processes. By integrating the fitted functions with respect to the neutron energies and solid angles, the angular distributions and total cross sections for the neutron production were determined. The neutron spectra, angular distributions, and total cross sections were compared with those calculated by the quantum molecular dynamics and heavy-ion codes. We found that neither of the codes could reproduce the measured cross sections for all combinations of the projectiles and targets.
Intermediate-energy nucleon-nucleus interactions were investigated in order to achieve a more comprehensive understanding of spallation reactions. Inclusive 12C(p,p′) spectra at 300 MeV were measured in a wide energy range and compared with two theoretical calculations: the quantum molecular dynamics model and the intranuclear cascade model. The calculations are in good agreement with the experimental results in the quasifree region. In the lower energy domain, however, the calculations underestimated the experimental results by a factor of about 2. The cause of the discrepancy was discussed in terms of a collective excitation process.
We discuss the importance of momentum dependent interactions in explaining the multifragmentation in asymmetric reactions by comparing the results with 16O-induced emulsion data. The reactions are simulated within a quantum molecular dynamics model and the clusterization is performed with the minimum spanning tree method. Our results clearly indicate that the inclusion of momentum dependent forces improves the agreement with the measured atomic number distribution. The simple static interaction fails to explain the experimental data. We also discuss the universal dependence of the effect of momentum dependent interactions on the asymmetry of a reaction.
Multifragmentation resulting from an expanding nuclear matter is investigated on the basis of quantum molecular dynamics. In particular, the dependence of the fragment mass distribution on the initial temperature (Tinit) and the radial flow velocity (h) is studied. When h is large, the distribution shows exponential shape, whereas for small h, it obeys the power law. Although the power law is what Fisher’s droplet model predicts, the fragmentation mechanism in an expanding system is found to be different from the one in a thermally equilibrated system.
We present a comparison of different clusterization methods based on simple spatial correlation, spatial-momentum correlation and energy minimization (simulated annealing) by simulating the reactions of O + Ag/Br within the quantum molecular dynamics model. We find that the response of different clusterization algorithms depends on the asymmetry of the reaction. The momentum correlation methods recognize the fragments between 60-100 fm c-1, whereas the simple spatial-correlation method needs a much longer time. The response of a larger nucleon-nucleon cross section as well as of momentum-dependent interaction depends on the clusterization algorithm one is using. It is maximal with the spatial correlation method, whereas it is minimal with the energy minimization method. Interestingly, in the presence of a larger nucleon-nucleon cross section, the momentum cut and energy minimization methods yield a similar evolution. This is true at higher incident energies where the frequency of nucleon-nucleon collisions is very large.
采用量子分子动力学(QMD)和统计衰变模型(SDM)分析计算了中能中子入射锕系核素引起裂变的瞬发裂变中子数和裂变中子谱。同时给出了用于本计算的一个简单的半经验的能级密度参数公式。这样,仅需要很少的输入参数便可得到合理的结果。(The quantum molecular dynamics (QMD), statistical decay model(SDM) and the statistical fission theory were used to analyze the mass distribution of the fission products, the prompt fission neutron spectrum (x(E)) and theprompt fission neutron multiplicities ( vpf(E) ) caused by the intermediate energynucleon-induced fission. The semi-empirical formula of energy level density parameter used in the statistical process was also studied. Very few adjustable parameters were included in the present method. By som...)
The role of spatial correlations (i.e., the range of clusterization) along with the role of the range of interaction is analyzed in multifragmentation within a quantum molecular dynamics model. We find that the effect of different ranges of clusterization and interactions depends on the physical conditions and excitation energy of the system. The impact of different clusterization ranges is more than marginal in the presence of a momentum dependent interaction which is different than that obtained with a static equation of state.
The relative role of the momentum-dependent interactions and larger nucleon-nucleon cross section is discussed in multifragmentation using quantum molecular dynamical model. We find that the sensitivity of the larger cross section towards multifragmentation reduces in the presence of momentum-dependent interactions which makes it difficult to extract the magnitude of nucleon-nucleon cross section from multifragmentation. However, a large effect of different cross sections can be seen if a simple static equation of state is used.
The reactions 12C+116Sn, 22Ne+Ag, 40Ar+100Mo, and 64Zn+89Y have been studied at 47A?MeV projectile energy. For these reactions the most violent collisions lead to increasing amounts of fragment and light particle emission as the projectile mass increases. This is consistent with quantum molecular dynamics (QMD) model simulations of the collisions. Moving source fits to the light charged particle data have been used to gain a global view of the evolution of the particle emission. Comparisons of the multiplicities and spectra of light charged particles emitted in the reactions with the four different projectiles indicate a common emission mechanism for early emitted ejectiles even though the deposited excitation energies differ greatly. The spectra for such ejectiles can be characterized as emission in the nucleon-nucleon frame. Evidence that the 3He yield is dominated by this type of emission and the role of the collision dynamics in determining the 3H/3He yield ratio are discussed. Self-consistent coalescence model analyses are applied to the light cluster yields, in an attempt to probe emitter source sizes and to follow the evolution of the temperatures and densities from the time of first particle emission to equilibration. These analyses exploit correlations between ejectile energy and emission time, suggested by the QMD calculations. In this analysis the degree of expansion of the emitting system is found to increase with increasing projectile mass. The double isotope yield ratio temperature drops as the system expands. Average densities as low as 0.36ρ0 are reached at a time near 100?fm/c after contact. Calorimetric methods were used to derive the mass and excitation energy of the excited nuclei which are present after preequilibrium emission. The derived masses range from 102 to 116 u and the derived excitation energies increase from 2.6 to 6.9 MeV/nucleon with increasing projectile mass. A caloric curve is derived for these expanded A～110 nuclei. This caloric curve exhibits a plateau at temperatures near 7 MeV. The plateau extends from ～3.5 to 6.9 MeV/nucleon excitation energy.
We study one- and two-neutron transfer reactions in 11Be+208Pb by using the quantum molecular dynamics model. We find that lowering about 1-2 MeV of the potential barrier of 208Pb for fusion is gained when two neutrons separated from 11Be enter into 208Pb. Whereas no significant change of potential barrier is found when only the halo neutron separated from 11Be enters into 208Pb. The dynamical interplay between suppression and enhancement effects on the fusion probability in reaction 11Be+208Pb stemming from the easy separation of halo neutron and the long extending of neutron distribution is discussed.
Based on the quantum molecular dynamics model, we investigate the dynamical behaviors of the excited nuclear system to simulate the latter stage of heavy ion reactions, which associate with a liquid-gas phase transition. We try to search a microscopic way to describe the phase transition in real nuclei. The Lyapunov exponent is employed and examined for our purpose. We find out that the Lyapunov exponent is one of good microscopic quantities to describe the phase transition in hot nuclei. Coulomb potential and the finite size effect may give a strong influence on the critical temperature. However, the collision term plays a minor role in the process of the liquid-gas phase transition in finite systems.
利用量子分子动力学分析中高能质子轰击薄靶的物理过程研究结果表明 ,当入射质子能量小于 1.5GeV时 ,主要是直接、级联和蒸发 3个过程的竞争和转化 .3个反应过程相应的时间区间分别小于 30fm/c,30— 10 0fm/c和大于10 0fm/c .量子分子动力学分析 (p ,xn)反应的双微分截面能较好地再现实验数据(The reactions for intermediate energy protons bombarding 208 Pb have been analyzed by the quantum molecular dynamics model (QMD). It is found that the whole reaction process can be divided into three stages, i.e. the direct, the cascade and the evaporation stage. The time scale of the change of reaction mechanism in the process of reaction is investigated. The corresponding time scales of the direct, the cascade and the evaporation stage are about<30 fm/ c , 30—100fm/ c and >100fm/ c , respect...)
利用量子分子动力学和裂变理论 ,统一计算了入射能量为 3 2 2 ,660和 80 0MeV的p+ 2 0 8 Pb散裂产物的质量和电荷分布 .计算结果能较好地再现实验测量数据 .(We have studied the fragment mass distribution of the spallation reaction induced by 322MeV, 660MeV and 800MeV protons bombarding 208 Pb by using quantum molecular dynamics model (QMD) plus empirical fission model. The details of the empirical fission model is described. The calculation results are in good agreement with the experimental measurements.)
We compare in detail central collisions Xe(50A MeV) + Sn, recently measured by the INDRA collaboration, with the Quantum Molecular Dynamics (QMD) model in order to identify the reaction mechanism which leads to multifragmentation. We find that QMD describes the data quite well, in the projectile/target region as well as in the midrapidity zone where also statistical models can be and have been employed. The agreement between QMD and data allows to use this dynamical model to investigate the reaction in detail. We arrive at the following observations: a) the in medium nucleon nucleon cross section is not significantly different from the free cross section, b) even the most central collisions have a binary character, c) most of the fragments are produced in the central collisions and d) the simulations as well as the data show a strong attractive in-plane flow resembling deep inelastic collisions e) at midrapidity the results from QMD and those from statistical model calculations agree for almost all observables with the exception of ${d^2 \sigma \over dZdE}$. This renders it difficult to extract the reaction mechanism from midrapidity fragments only. According to the simulations the reaction shows a very early formation of fragments, even in central collisions, which pass through the reaction zone without being destroyed. The final transverse momentum of the fragments is very close to the initial one and due to the Fermi motion. A heating up of the systems is not observed and hence a thermal origin of the spectra cannot be confirmed.
The production of d′ dibaryons in heavy-ion collisions due to the elementary process NN → d′π is considered. The NN → d′π cross section is estimated using the vacuum d′ width Γd′ ≈ 0.5 MeV extracted from data on the double charge exchange reactions on nuclei. The d′ production rate per single collision of heavy ions is estimated at an incident beam energy of 1 A GeV within the framework of the Quantum Molecular Dynamics transport model. We suggest to analyse the invariant mass spectrum of the NNπ system in order to search for an abundance of events with the invariant mass of the d′ dibaryon. The d′ peak is found to exceed the statistical fluctuations of the background at a 6σ level for 2 × 105 · A central collisions of heavy ions with the atomic number A.
We analyze the role of different equations of state and momentum dependent interactions in fragmentation. Heavy ion collisions are simulated using a quantum molecular dynamics model and fragments are constructed with the minimum spanning tree method. A detailed study is carried out for Xe+Sn reactions at incident energies E=100 and 400 MeV/nucleon and over a wide range of impact parameters. Our analysis indicates that the light mass fragments in central collisions are sensitive towards different static equations of state whereas the heavy fragments are insensitive towards different static equations of state. The results with momentum dependent interactions are quite different. Now, the heavy fragments are also sensitive towards different equations of state. The momentum dependence of the equation of state is able to break the spectator matter into a large number of fragments at peripheral collisions whereas a simple static equation of state fails to produce any fragments. As a result, the properties of fragments (such as transverse flow, rapidity distribution, etc.) are also affected by the momentum dependence of the interaction.
Several models have been proposed to simulate heavy ion reactions beyond the mean field level. The lack of data in phase space regions which may be sensitive to different treatments of fluctuations made it difficult to judge these approaches. The recently published high energy proton spectra, measured in the reaction 94 AMeV Ar + Ta, allow for the first time for a comparison of the models with data. We find that these spectra are reproduced by Quantum Molecular Dynamics (QMD) and Boltzmann Uehling Uhlenbeck (BUU) calculations. Models like Boltzmann Langevin (BL) in which additional fluctuations in momentum space are introduced overpredict the proton yield at very high energies. The BL approach has been successfully used to describe the recently measured very subthreshold kaon production assuming that the fluctuations provide the necessary energy to overcome the threshold in two body collisions. Our new findings suggest that the very subthreshold kaon production cannot be due to two body scattering and thus remains a open problem.
Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic interactions on a large variety of observables and phenomena occurring in heavy ion collisions at relativistic energies.It is shown that the same predictions can be obtained with several -- numerically completely different and independently written -- programs as far as the same model parameters are employed and the same basic approximations are made. Many observables are robust against variations of the details of the model assumptions used. Some of the physical results, however, depend also on rather technical parameters like the preparation of the initial configuration in phase space. This crucial problem is connected with the description of the ground state of single nuclei,which differs among the various approaches. An outlook to an improved molecular dynamics scheme for heavy ion collisions is given.
The importance of a isospin dependent nuclear mean field (IDMF) in regard to the pion production mechanism is studied for the reaction $Au+Au$ at 1 GeV/nucleon using the Quantum Molecular Dynamics (QMD) model. In particular, the effect of the IDMF on pion spectra and the charged pion ratio are analyzed. It is found that the inclusion of a IDMF considerably suppresses the low$-p_t$ pions, thus, leading to a better agreement with the data on pion spectra. Moreover, the rapidity distribution of the charged pion ratio appears to be sensitive to the isospin dependence of the nuclear mean field.
Coulomb final-state interaction of positive charged kaons in heavy ion reactions and its impact on the kaon transverse flow and the kaon azimuthal distribution are investigated within the framework of QMD (Quantum Molecular Dynamics) model. The Coulomb interaction is found to tend to draw the flow of kaons away from that of nucleons and lead to a more isotropic azimuthal distribution of kaons in the target rapidity region. The recent FOPI data have been analyzed by taking into accout both the Coulomb interaction and a kaon in-medium potential of the strong interaction. It is found that both the calculated kaon flows with only the Coulomb interaction and with both the Coulomb interaction and the strong potential agree within the error bars with the data. The kaon azimuthal distribution exhibits asymmetries of similar magnitude in both theoretical approaches. This means, the inclusion of the Coulomb potential makes it more difficult to extract information of the kaon mean field potential in nuclear matter from the kaon flow and azimuthal distribution data
The properties of the high energy pions observed in heavy ion collisions, in particular in the system Au on Au at 1 GeV/nucleon are investigated. The reaction dynamics is described within the Quantum Molecular Dynamics (QMD) approach. It is shown that high energy pions freeze out early and originate from the hot, compressed matter. $N^*$--resonances are found to give an important contribution toward the high energy tail of the pion. Further the role of in-medium effects in the description of charged pion yields and spectra is investigated using a microscopic potential derived from the Brueckner G-matrix which is obtained with the Reid soft-core potential. It is seen that the high energy part of the spectra is relatively more suppressed due to in-medium effects as compared to the low energy part. A comparision to experiments further demonstrates that the present calculations describe reasonably well the neutral (TAPS) and charged (FOPI) pion spectra. The observed energy dependence of the $\pi^-/\pi^+$ ratio, i.e. deviations from the isobar model prediction, is due to Coulomb effects and again indicate that high energy pions probe the hot and dense phase of the reaction. These findings are confirmed independently by a simple phase space analysis.
The impact parameter dependence of the disappearance of nuclear flow is examined within the framework of the quantum molecular dynamics model. We confront the model with recent experimental findings of He et al. who measured the balance energy at different impact parameters for the reaction 64Zn+27Al. We simulate the heavy ion collisions with different nucleon-nucleon cross sections which includes the energy-dependent cross section, in-medium cross section (G matrix), and several constant and isotropic cross sections. Our calculations show that the balance energy in central collisions can be explained nicely with standard energy-dependent cross section whereas one needs a larger cross section to explain the balance energy at peripheral collisions
We discuss the stability of fragments formed in central heavy ion collisions at intermediate energies using a quantum molecular dynamics model as an event generator. To address the question of stability of fragments, we employ three different methods of clusterization. (i) The standard minimum spanning tree (MST) method which is based on simple spatial correlations. (ii) A modified version of MST where we first identify the prefragments using MST and then check the binding energy of each fragment explicitly. If any fragment fails to meet the binding energy check, all nucleons of that prefragment are treated as free nucleons. (iii) Our newly advanced algorithm based on energy minimization criteria. This algorithm finds the most bound fragment structure using the simulated annealing technique. Our analysis shows that the fragments created with the MST method are not stable even at 200fm/c and an additional binding energy check helps (to a great extent) to discard the unbound fragments and, as a result, the modified MST (with binding energy check) identifies the fragments quite early.
We present a systematic study of the dependence of the fragment production on the nucleon-nucleon cross section using the quantum molecular dynamics model as an event generator. We employ constant energy-dependent and in-medium cross sections. In our analysis, fragments are formed using a minimum spanning tree description. The fragment distribution with different cross sections at low energy is nearly the same. At higher energies, different nucleon-nucleon (NN) cross sections have small effects on fragment production for central collisions, whereas the fragment production is strongly influenced at semicentral and peripheral collisions. A larger NN cross section results in more intermediate mass fragments at peripheral collisions with a shift of the peak towards larger impact parameters. As a result, the rapidity distribution of fragments and the fragment flow is also affected by the choice of the cross section. This influence is reduced if fragments are constructed with a sophisticated algorithm such as the simulated annealing clusterization algorithm which searches for the most bound configuration of nucleons and fragments.
We study the role of momentum cuts in fragment formation. The time evolution of nucleons is followed using the quantum molecular dynamics model. The fragments are formed within a minimum spanning tree description which allows two nucleons to be in the same fragment if their centriods are less than 4 fm. We introduce an additional condition by imposing a restriction in momentum space. Our analysis indicates that the effect of the cut (in momentum space) on fragment formation is stronger if the cut in the relative momentum of two nucleons is <~150MeV/c. For higher values of the cut in the relative momentum of two nucleons (>~200MeV/c), fragment production with and without the momentum cut is the same. A cut of the order of the Fermi momentum (in the relative momentum of two nucleons) has a strong influence on the fragment distribution in central collisions whereas its effect is least in peripheral collisions. The fragment multiplicities and rapidity distributions obtained for central collisions with a cut of the order of the Fermi momentum (=150MeV/c) matches at asymptotic times (after 120fm/c) with the most bound fragment structure obtained using a recently advanced simulated annealing clusterization algorithm.
The incomplete fusion, onset of multifragmentation and vaporization is studied in Ca-Ca collisions at bombarding energies between 20–1000AMeV and at impact parameters between b=0 and bmax. The simulations of Ca-Ca are performed using the quantum molecular dynamics (QMD) model. We find incomplete fusion events at E/A=20–30MeV. With an increase in the bombarding energy, the multiplicity of fragments first increases to a maximum value and then decreases for central and semi-central collisions. This peak in the multiplicity of fragments shifts towards higher energies for light mass fragments compared to intermediate mass fragments. The peak in the fragment production can be related to a critical point where onset of the fragmentation starts. The light mass fragment production at a given incident energy does not show any rise and fall in the multiplicity with a change in the impact parameter. The IMF production at higher energies (>~150A MeV), however, has a clear rise and fall in their multiplicity.
The importance of a isospin dependent nuclear mean field (IDMF) in regard to the pion production mechanism is studied for the reaction $Au+Au$ at 1 GeV/nucleon using the Quantum Molecular Dynamics (QMD) model. In particular, the effect of the IDMF on pion spectra and the charged pion ratio are analyzed. It is found that the inclusion of a IDMF considerably suppresses the low$-p_t$ pions, thus, leading to a better agreement with the data on pion spectra. Moreover, the rapidity distribution of the charged pion ratio appears to be sensitive to the isospin dependence of the nuclear mean field.
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the description of light fragments with the correlations. Utilizing either type of Gaussian wave functions, with or without correlations, however, we find that we cannot describe fragment formation in a dynamic situation. Composite fragments are only produced in simulations if these fragments are present as clusters in the substructure of original nuclei. The difficulty is traced to the delocalization of wave functions during emission. Composite fragments are produced abundantly in the Gaussian molecular dynamics in the limit hbar -> 0.
Using quantum molecular dynamics simulations, we investigate the formation of fragments in symmetric reactions between beam energies of E=30AMeV and 600AMeV. After a comparison with existing data we investigate some observables relevant to tackle equilibration: dsigma/dErat, the double differential cross section dsigma/pt.dpz.dpt,... Apart maybe from very energetic E>400AMeV and very central reactions, none of our simulations gives evidence that the system passes through a state of equilibrium. Later, we address the production mechanisms and find that, whatever the energy, nucleons finally entrained in a fragment exhibit strong initial-final state correlations, in coordinate as well as in momentum space. At high energy those correlations resemble the ones obtained in the participant-spectator model. At low energy the correlations are equally strong, but more complicated; they are a consequence of the Pauli blocking of the nucleon-nucleon collisions, the geometry, and the excitation energy. Studying a second set of time-dependent variables (radii, densities,...), we investigate in details how those correlations survive the reaction especially in central reactions where the nucleons have to pass through the whole system. It appears that some fragments are made of nucleons which were initially correlated, whereas others are formed by nucleons scattered during the reaction into the vicinity of a group of previously correlated nucleons.
To know the space time evolution of a heavy ion reaction is of great interest, especially in cases where the measured spectra do not allow to ascertain the underlying reaction mechanism. In recent times it became popular to believe that the comparison of Hanbury-Brown Twiss correlation functions obtained from classical or semiclassical transport theories, like Boltzmann Uehling Uhlenbeck (BUU), Quantum Molecular Dynamics (QMD), VENUS, RQMD or ARC, with experiments may provide this insight. It is the purpose of this article to show that this conjecture encounters serious problems. The models which are suited to be compared with the experiments at CERN and Brookhaven are not able to predict a correlation function. Any agreement with existing data has to be considered as accidental. The models suited for lower energies can in principle predict correlation functions. The systematic error may be too large to be of use as far as quantitative conclusions are concerned.
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the description of light fragments with correlations. Utilizing either type of Gaussian wave functions, with or without correlations, however, we find that we cannot describe fragment formation in a dynamic situation. Composite fragments are only produced in simulations if they are present as clusters in the substructure of original nuclei. The difficulty is traced to the delocalization of wave functions during emission. Composite fragments are produced abundantly in the Gaussian molecular dynamics in the limit .
We investigate the influence of the real part of the in-medium pion optical potential on the pion dynamics in intermediate energy heavy ion reactions at 1 GeV/A. For different models, i.e. a phenomenological model and the $\Delta$--hole model, a pionic potential is extracted from the dispersion relation and used in Quantum Molecular Dynamics calculations. In addition with the inelastic scattering processes we thus take care of both, real and imaginary part of the pion optical potential. A strong influence of the real pionic potential on the pion in-plane flow is observed. In general such a potential has the tendency to reduce the anticorrelation of pion and nucleon flow in non-central collisions.
Quantum Molecular Dynamics (QMD) calculations of central collisions between heavy nuclei are used to study fragment production and the creation of collective flow. It is shown that the final phase space distributions are compatible with the expectations from a thermally equilibrated source, which in addition exhibits a collective transverse expansion. However, the microscopic analyses of the transient states in the intermediate reaction stages show that the event shapes are more complex and that equilibrium is reached only in very special cases but not in event samples which cover a wide range of impact parameters as it is the case in experiments. The basic features of a new molecular dynamics model (UQMD) for heavy ion collisions from the Fermi energy regime up to the highest presently available energies are outlined.
Quantum Molecular Dynamics (QMD) calculations are used to study the expansion phase in central collisions between heavy nuclei. The final state of such a reaction can be understood as the result of a entropy conserving expansion starting from a compact source. The properties of this hypothetic source, however, are in conflict with the assumptions used in fireball models. Moreover, this hypothetical source is not formed in the dynamical evolution of the system.
The production cross sections of various fragments from proton-induced reactions on $^{56}$Fe and $^{27}$Al have been analyzed by the Quantum Molecular Dynamics (QMD) plus Statistical Decay Model (SDM). It was found that the mass and charge distributions calculated with and without the statistical decay have very different shapes. These results also depend strongly on the impact parameter, showing an importance of the dynamical treatment as realized by the QMD approach. The calculated results were compared with experimental data in the energy region from 50 MeV to 5 GeV. The QMD+SDM calculation could reproduce the production cross sections of the light clusters and intermediate-mass to heavy fragments in a good accuracy. The production cross section of $^{7}$Be was, however, underpredicted by approximately 2 orders of magnitude, showing the necessity of another reaction mechanism not taken into account in the present model.
In order to treat low-energy heavy-ion reactions, we make an extension of quantum molecular dynamics method. A phenomenological Pauli potential is introduced into effective interactions to approximate the nature of the fermion many-body system. We treat the widths of nucleon wave packets as time-dependent dynamical variables. With these modifications, our model can well describe the ground-state properties in wide mass range. Improvements due to the extension are also obtained in the low and medium-low energy nucleus-nucleus collision calculations. ? 1996 The American Physical Society.
Collisions between 48Ti + 93Nb at 19.1 MeV/nucleon were studied using two 4π detection systems. A reconstruction procedure was developed to determine the mass, kinetic, and excitation energies of the primary projectile and targetlike fragments. The results show a broad range of mechanisms. These results were compared with predictions of the quantum-molecular dynamics model. ? 1996 The American Physical Society.
The time scale required to reach thermal equilibrium in intermediate-energy nucleon-induced preequilibrium reactions was investigated by quantum molecular dynamics (QMD). The average kinetic energy of two colliding particles in their center-of-mass system was taken to be the measure of such thermal equilibration. The corresponding time was found to be of the order of 20 fm/c (～7 × 10-23 sec), a time scale that is much shorter than the time believed for the compound reaction, i.e., ～10-18 sec. An interpretation of the reason why the kinetic energy brought by the projectile is dumped so fastly to thermal equilibrium is discussed. The equilibration time of 20 fm/c gives a justification of our ‘‘hybrid’’ approach of using the QMD plus the statistical decay model (SDM) which are connected at a time scale of ～100 fm/c. ? 1996 The American Physical Society.
The energy at which the collective transverse flow in the reaction plane disappears, the balance energy Ebal, is found to increase linearly as a function of impact parameter for 40Ar+45Sc reactions. Comparison of our measured values of Ebal(b) with predictions from quantum molecular dynamics (QMD) model calculations agrees better with an approach incorporating momentum dependence in the nuclear mean field. ? 1996 The American Physical Society.
The fragmentation pattern of central multifragmentation events observed in the collision of heavy systems can be recognized at a time when the system is still dense and the particles are still interacting with each other. This is the result obtained by applying simulated annealing algorithms to molecular dynamics simulations. We employ this algorithm to central and peripheral reactions of heavy nuclei simulated by the quantum molecular dynamics model (QMD). We see that in central collisions the fragments can already be identified when the density is still close to normal nuclear matter density and hence the fragment nucleons never pass through a density sufficiently low to allow for a liquid gas phase transition. In peripheral reactions, however, we observe that shortly after the nuclei have passed each other a division of the spectator matter into several medium-size clusters would yield the highest binding energy. However, the spectator matter does not break into these clusters but approaches thermal equilibrium.
The impact parameter dependence of the disappearance of directed transverse flow has been investigated for 40Ar+45Sc reactions using the Michigan State University 4π Array upgraded with the High Rate Array (HRA). The energy at which collective transverse flow in the reaction plane disappears, the balance energy (Ebal), is found to increase approximately linearly as a function of impact parameter. Comparison of our measured values of Ebal(b) shows agreement with predictions of Quantum Molecular Dynamics (QMD) model calculations.
We propose a model based on quantum molecular dynamics (QMD) incorporated with a statistical decay model (SDM) to describe various nuclear reactions in a unified way. In this first part of the work, the basic ingredients of the model are defined and the model is applied systematically to the nucleon- (N-)induced reactions. It has been found that our model can give a remarkable agreement in the energy-angle double differential cross sections of (N,xN′) type reactions for incident energies from 100 MeV to 3 GeV with a fixed parameter set. A unified description of the three major reaction mechanisms of (N,xN′) reactions, i.e., compound, preequilibrium, and spallation processes, is given with our model.
Spectra of various particle species have been calculated with the Quantum Molecular Dynamics (QMD) model for very central collisions of Au+Au. They are compatible with the idea of a fully stopped thermal source which exhibits a transversal expansion besides the thermal distribution of an ideal gas. However, the microscopic analyses of the local flow velocities and temperatures indicate much lower temperatures at densities associated with the freeze-out. The results express the overall impossibility of a model-independent determination of nuclear temperatures from heavy ion spectral data, also at other energies e.g. CERN or for other species (i.e. pions, kaons, hyperons)!
The covariant and non-covariant Quantum Molecular Dynamics models are applied to investigate possible relativistic effects in heavy ion collisions at SIS energies. These relativistic effects which arise due to the full covariant treatment of the dynamics are studied at bombarding energies E$_{lab.}$ = 50, 250, 500, 750, 1000, 1250, 1500, 1750 and 2000 MeV/nucl.. A wide range of the impact parameter from b = 0 fm to b = 10 fm is also considered. In the present study, five systems $^{12}$C-$^{12}$C, $^{16}$O-$^{16}$O, $^{20}$Ne-$^{20}$Ne, $^{28}$Si-$^{28}$Si and $^{40}$Ca-$^{40}$Ca are investigated. The full covariant treatment at low energies shows quite good agreement with the corresponding non-covariant approach whereas at higher energies it shows less stopping and hence less thermal equilibrium as compared to the non-covariant approach. The collisions dynamics is less affected. The density using RQMD rises and drops faster than with QMD. The relativistic effects show some influence on the resonance matter production. Overall, the relativistic effects at SIS energies ($\leq$ 2000 MeV/nucl.) are less significant.
A systematic study of energy spectra for light particles emitted at midrapidity from Au+Au collisions at E=0.25-1.15 A GeV reveals a significant non-thermal component consistent with a collective radial flow. This component is evaluated as a function of bombarding energy and event centrality. Comparisons to Quantum Molecular Dynamics (QMD) and Boltzmann-Uehling-Uhlenbeck (BUU) models are made for different equations of state.
We use the quantum molecular dynamics model to investigate the formation mechanism of protons and composite fragments in intermediate-energy heavy-ion collisions. We demonstrate that dynamical correlations result in the production rate for final state nucleon clusters (and hence composite fragments) being higher than would be expected if statistics and the properties of the available phase space were dominant in determining composite formation. This finding contradicts assumptions which underlie models based on either the one-body phase-space density or on statistical equilibrium. Hybrid models which treat the initial violent collisions in an intranuclear cascade or a Boltzmann-ühling-Uhlenbeck approach and then change to a statistical model may be used for central collisions at higher energy (e.g., 600A MeV) but fail for semiperipheral reactions and for all impact parameters at lower beam energies.
Charge, velocity, and angular correlations between intermediate mass fragments (IMF) are presented for 50 and 100 MeV/nucleon Fe bombardments of Ta, Au, and Th targets. Correlation functions generated as a function of the relative velocity and the opening angle between two IMF’s are qualitatively independent of the projectile energy and target mass and show a suppression at small relative velocities and opening angles due to the Coulomb repulsion between the fragments. The correlations are consistent with IMF’s emitted primarily from a highly excited target residue following a rapid preequilibrium cascade. The correlation data are compared to model calculations using the event generator meneka and the quantum molecular dynamics (QMD) code with a statistical deexcitation of residual fragments utilizing the multifragmentation code smm. All data are consistent with a simultaneous multifragmentation at a freeze-out density of 0.1–0.3 times normal nuclear matter density or a more sequential emission with time constant τ≤500 fm/c.
The multifragment emission for central collisions of 40Ar (25–150 MeV/nucleon) on 27Al was studied via the quantum molecular dynamics model. The distribution of intermediate mass fragments (IMFs) can be described by a power-law function with the parameter τ or an exponential function with the parameter λ. By increasing the beam energy, the mean multiplicity of IMFs and relative cross sections emitting multifragment first increase to their maximum values and then decrease; while the extracted τ, λ parameters and relative cross section for single IMF emission show the converse tendency. The calculation and relevant experiment suggest that the reactions have a critical energy point where the onset of multifragmentation takes place.
The 4π multidetector AMPHORA has been used to measure yield distributions and energy spectra for products of the collisions in the reactions of 40Ca with 40Ca at 35 MeV/nucleon. Events of high multiplicity (≥10) for which ≥85% of the total entrance channel atomic number is detected have been isolated and found to result from the most violent collisions which lead to excitation energies near 6 MeV/nucleon. A large fraction of these collisions lead to multifragment final states. A detailed comparison of the experimental data with results of various models indicates that statistical models which allow for expansion of the system or treat the multifragmentation process as a simultaneous disassembly are more successful than normal sequential binary models at reproducing the yield data and the event complexity inherent in the multifragment events. Quantum molecular dynamic (QMD) calculations are found to provide generally good agreement with the data but overestimate the proton and neutron emission. The agreement is significantly improved if an appropriate afterburner is used to deexcite the separated primary QMD fragments. The sensitivity of such hybrid calculations to the assumed matching time between the dynamical calculation and the afterburner has been explored. The experimentally filtered QMD calculations which provide good agreement with the experimental observables suggest that the most complex events observed in this work come not from the most central collisions, which decay more by light particle emission, but from a region of impact parameter b/bmax=0.5. This suggests that angular momentum effects play an important role in the multifragment decay modes. A comparison of the present results with those for projectile fragmentation in intermediate impact parameter collisions of 600 MeV/nucleon 197Au with Cu indicates that a similar multifragmenting system is produced in the two very different reaction systems.
The properties of pions from the hot and dense reaction stage of relativistic heavy ion collisions are investigated with the Quantum Molecular Dynamics model. Pions originating from this reaction stage stem from resonance decay with enhanced mass. They carry high transverse moments. The calculation shows a direct correlation between high pt pions, early freeze-out times, and high freeze-out densities. A measurement of the mass distributions of p-π correlations (e.g., the Δ++) in different pt bins is proposed to distinguish different reaction stages.
We consider the reaction 36Ar+197Au at incident 36Ar energies of 35, 50, 80, and 110A MeV, comparing calculations of precompound decay using the Boltzmann master equation (BME) and quantum molecular dynamics (QMD) models. We then estimate quasiequilibrated nuclei and excitations using the BME, and use these values as input into statistical multifragmentation models. For the latter we compare sequential binary decay as an extension of the Weisskopf-Ewing evaporation model, and a simultaneous multifragmentation for an expanded low density gas. The exclusive multiplicities predicted by these models are compared with experimental results.
Peripheral collisions for 20Ne+20Ne system at 25 MeV/A were analysed in detail by means of quantum molecular dynamics model. Its characteristics, coexistences and competitions between deep inelastic collision and fragmentation were discussed, the rnechanism giving rise to intermediate mass fragments were also explored.
Experimental results are presented on the charge, velocity, and angular distributions of intermediate mass fragments (IMFs) for the reaction Fe+Au at bombarding energies of 50 and 100 MeV/nucleon. Results are compared to the quantum molecular dynamics (QMD) model and a modified QMD which includes a Pauli potential and follows the subsequent statistical decay of excited reaction products. The more complete model gives a good representation of the data and suggests that the major source of IMFs at large angles is due to multifragmentation of the target residue.
A quasiclassical Pauli potential is used to simulate the Fermi motion of nucleons in a molecular dynamical simulation of heavy ion collisions. The thermostatic properties of a Fermi gas with and without interactions are presented. The inclusion of this Pauli potential into the quantum molecular dynamics (QMD) approach yields a model with well defined fermionic ground states, which is therefore also able to give the excitation energies of the emitted fragments. The deexcitation mechanisms (particle evaporation and multifragmentation) of the new model are investigated. The dynamics of the QMD with Pauli potential is tested by a wide range of comparisons of calculated and experimental double-differential cross sections for inclusive p-induced reactions at incident energies of 80 to 160 MeV. Results at 256 and 800 MeV incident proton energy are presented as predictions for completed experiments which are as yet unpublished.
Inclusive neutron spectra were measured at 0°, 15°, 30°, 50°, 70°, 90°, 120°, and 160° from Ne-Pb collisions at 790 MeV/nucleon. A peak that originates from neutron evaporation from the projectile appears in the spectra at 0°. The shapes and magnitudes of the spectra are compared with those calculated from models of nucleus-nucleus collisions. The Boltzmann-Uehling-Uhlenbeck (BUU), intranuclear cascade (INC), and firestreak models agree generally with the measured double-differential cross sections and particularly at 50° and beyond; however, none of the models can reproduce the peaks at small angles (θ≤15°). The quantum molecular dynamics (QMD) model underestimates the spectra of the double-differential cross sections at all angles and energies for this asymmetric system. Also, the predictions of the INC model agrees with the angular distribution of the differential cross sections except that it underestimates the cross section at 0°; the BUU prediction overestimates the differential cross section at 0° and 90°; firestreak overpredicts at 15° and 30° and underpredicts at 70° and 90°; and the QMD model underpredicts the measured angular distribution and the energy spectra at forward angles.
We study the transition from fusion-fission phenomena at about 20 MeV/nucleon multifragmentation at 100–200 MeV/nucleon in the reaction 16O+80Br employing the quantum molecular dynamics model. The time evolution of the density and mass distribution, the charged-particle multiplicity, and spectra as well as angular distributions of light particles are investigated. The results exhibit the transition of the disassembly mechanism, but no sharp change is found. The results are in good agreement with recently measured 4π data.
The quantum molecular dynamic method is used to study multifragmentation and fragment flow and their dependence on in-medium cross sections, momentum dependent interactions, and the nuclear equation of state, for collisions of 197Au+197Au and 93Nb+93Nb in the bombarding energy regime from 100 to 800A MeV. Time and impact parameter dependence of the fragment formation and their implications for the conjectured liquid-vapor phase transition are investigated. We find that the inclusive fragment mass distribution is independent of the equation of state and exhibits a power-law behavior Y(A)～A-τ with an exponent τ?-2.3. True multifragmentation events are found in central collisions for energies Elab～30–200 MeV/nucleon. The associated light fragment (d,t,α) to proton ratios increase with the multiplicity of charged particles and decrease with energy, in agreement with recent experiments. The calculated absolute charged particle multiplicities, the multiplicities of intermediate mass (A>4) fragments, and their respective rapidity distributions do compare well with recent 4π data, but are quite insensitive to the equation of state. On the other hand, these quantities depend sensitively on the nucleon-nucleon scattering cross section, and can be used to determine σ experimentally. The transverse momentum flow of the complex fragments increases with the stiffness of the equation of state. Reduced (in-medium) n-n scattering cross sections reduce the fragment flow. Momentum dependent interactions increase the fragment flow. It is shown that the measured fragment flow at 200A MeV can be reproduced in the model. We find that also the increase of the px/A values with the fragment mass is in agreement with experiments. The calculated fragment flow is too small as compared to the plastic ball data, if a soft equation of state with in-medium corrections (momentum dependent interactions plus reduced cross sections) is employed. An alternative, most intriguing resolution of the puzzle about the stiffness of the equation of state could be an increase of the scattering cross sections due to precritical scattering in the vicinity of a phase transition.
We present a detailed microscopic quantum molecular dynamic analysis of fragment formation in the reaction Ne(1.05 GeV/nucleon) + Au. The theoretical predictions of the total mass yield, the multiplicity distribution of clusters, their average momentum, and their angular distribution agree well with the available data. We find a rather localized hot participant zone, which predominantly emits protons and neutrons. The multiplicity of light clusters depends strongly on the impact parameter whereas the heavier fragments A≥40 result from the decay of spectator residues. Their yield can provide a good measure for the impact parameter. The hypothesis of a compound system of AP and AT nucleons which is globally heated and equilibrated is not supported by our results. Light and massive fragments occupy different regions in phase space. Semiperipheral reactions do not lead to a stopping of the projectile. We observe a power law behavior of the inclusive mass yield distribution. Its form, however, is caused by averaging over different impact parameters. This rules out inclusive mass yield distributions as candidates for revealing a possible liquid gas phase transition. Light and intermediate mass fragments are formed during the early compressional stage of the reaction. We find that the projectile causes a high density wave to travel through the target. It causes the target to fragment and transfers transverse momentum to the intermediate mass fragments. Lighter fragments receive additional momentum transfer due to n-n collisions