Intermediate mass fragment emission in Fe+Au collisions.

We study the emission of fragments in central collisions of light and heavily charged systems of 40Ar+45Sc and 84Kr+197Au, respectively, using the Quantum Molecular Dynamics (QMD) model as the primary model. The fragments are identified using an energy based clusterization algorithm, i.e., the Simulated Annealing Clusterization Algorithm (SACA). The charge distributions of intermediate mass fragments [3≤ ≤12] are fitted with power-law ( ) and exponential ( ) fits in order to extract the parameters τ and whose minimum values are also sometimes linked with the onset of fragmentation or the critical point for a liquid-gas phase transition. Other parameters such as the normalized second moment , , average size of the second largest cluster , phase separation parameter ( ), bimodal parameter (P), information entropy (H), and Zipf's law are also analyzed to find the exact energy of the onset of fragmentation. Our detailed analysis predicts that an energy point exists between 20-23.1 MeV/nucleon, which is very close to the experimentally observed value of 23.9 MeV/nucleon for the 40Ar+45Sc reaction. We also find that the critical energy deduced using Zipf's law is higher than those predicted from other critical exponents. Moreover, no minimum is found for τ values of the highly charged system of 84Kr+197Au, in agreement with experimental findings and various theoretical calculations. We observe that the QMD + SACA model calculations are in agreement with the experimental observations. This agreement supports our results regarding the energy point of the liquid-gas phase transition and the onset of fragmentation.

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. 1 General framework and motivation of this work A fully microscopical simulation of nucleon-ion and ionion collisions, at nucleon level, can be performed, among several different approaches [1], by means of Quantum Molecular Dynamics (QMD) models [2]. They are dynamical models which allow to study the phase-space evolution of the projectile-target colliding systems, from their initial mutual trajectory influence and eventually their overlap, depending on the impact parameter, to the compression phase, accompanied by a temperature and density increase, up to the following expansion stage, characterized by the formation of hot excited fragments (pre-fragments). The whole phase occurs on a time scale within a few hundreds fm/c, depending on the size of the colliding systems and the bombarding energy, and is called the “fast” stage of the reaction. Additionally, improved versions of QMD models (e.g., the CoMD one, developed by Papa et al. [3]) allow to compute the system evolution even for a longer time, up to thousands fm/c, and thus have also been used to describe pre-fragment de-excitation, at least in its initial stage. This has led to direct comparisons of the results of improved QMD simulations to experimental data concerning fragment emission distributions. On the other hand, pre-fragment de-excitation can occur on a time scale even larger (up to ∼10−15 s). Thus, a complete treatment of this slow stage can be covered by different models, generally based on statistical considerations. The underlying assumption in applying one of these statistical models to nuclear systems is that they are thermalized. While at the lowest energies the colliding ions stay close to each other for a time long enough for thermalization to occur, to define a temperature for the whole system at higher energies (several tens MeV/A) can be very problematic, since the expansion phase can begin before a global thermalization process is completed. Anyway, in the last case, at advanced time in the expansion stage pre-fragments are well separated and each of them is supposed to be thermalized. Whereas theoretical models allow to compute an excitation energy for each pre-fragment, from the experimental point of view the problem of the determination of hot fragment temperatures a Presenting author, e-mail: maria.garzelli@mi.infn.it 1e-14 1e-12 1e-10 1e-08 1e-06 1e-04 0.01 1 10

We report preliminary results from exclusive measurements on the reactions Nb + Au and Fe + Au at incident energies in the range 50 to 100 MeV/A using a detector array with large solid angle and large dynamic range. Correlations among target fragments, energetic light charged particles and projectile fragments have been measured. These results indicate that intermediate mass fragment (IMF) emission dominates the reaction cross section for all cases studied. Their cross sections, multiplicites and distributions in Z change little with bombarding energy.

The nucleon-nucleon interaction is investigated by using the improved quantum molecular dynamic (ImQMD) model with three sets of parameters IQ1, IQ2 and IQ3, in which the corresponding incompressibility coefficients of nuclear matter are different. The charge distributions of fragments are calculated for various reaction systems at different incident energies. The parameters strongly affect the charge distributions and the fragment multiplicity spectrum below the threshold energy of nuclear multifragmentation. The fragment multiplicity spectrum for 238U+197Au at 15 A MeV and the charge distributions for 129Xe+120Sn at 32 and 45 A MeV, and 197Au+197Au at 35 A MeV are reproduced by the ImQMD model with the set of parameter IQ3. It is found that: 1) The charge distribution of the fragments and the fragment multiplicity spectrum are good observables for testing the model and the parameters. 2) The Fermi energy region is a sensitive energy region for studying nucleon-nucleon interaction.

The onset of nuclear vaporisation in heavy-ion collisions is examined in the present study. For this, we perform quantum molecular dynamics (QMD) model calculations supplemented with a clusterisation algorithm for fragment identification, namely the Simulated Annealing Clusterization algorithm (SACA) approach. Our results with the very sophisticated SACA method show a good agreement with the experimental findings of vaporisation (predicted by the asymptotic behaviour of the average fragment charge) in 16O + 80Br and 16O + 107Ag collisions. Further, we predicted the energy of the onset of vaporisation for 40Ca + 40Ca, 84Kr + 84Kr, 132Xe + 132Xe and 197Au + 197Au collisions by investigating the gas/liquid content and probability of vaporisation (and its derivative) versus the incident energy behaviour. These two observables probe the critical point of nuclear vaporisation in an extremely sophisticated manner, relative to an average fragment charge. Our findings on these two novel variables to predict the energy of the onset of vaporisation is verifiable in experiments. The influence of the colliding geometry as well as the role of Coulomb interactions are also studied to understand the system size effects on nuclear vaporisation.

Predictions from the RQMD model are systematically compared to recently published charged hadron distributions of AGS Experiment 802 for central Si+Au collisions at 14.6A GeV/c, taking into account both the experimental trigger condition and acceptance. The main features of the data, including K + production, can be understood quantitatively to better than 20 % within the framework of the model, although several discrepancies are found, most importantly for the proton spectra. 1.

We have analyzed energy spectra, angular distributions, and mass and charge distributions of intermediate-mass fragments (IMFs) from the interaction of 27Al, 59Co, and 197Au with 200 MeV protons. Calculations within the modified statistical model with final-state interaction were performed using SAPTON code. Within the experimental uncertainty and constraint, SAPTON shows good agreement with the data, and suggests that the IMFs are produced after the intra-nuclear cascade stage, and during the surface coalescence, as well as the evaporation/fission stages.

We present the calculations of the mass dependence of energy of vanishing flow for the reactions with masses between 24 and 394 units using isospin-dependent quantum molecular dynamics (QMD) model. Our calculations confirm the power law dependence of the energy of vanishing flow, in accordance with earlier studies, and show a good agreement with the experimentally observed energy of vanishing flow. A detailed comparison with various theoretical models reveals that once the physics parameters are fixed, different numerical realizations as well as various transport models such as BUU, IBUU, RVUU, LV, QMD, IQMD, RQMD, AMD and optical model yield nearly same energy of vanishing flow in most of the cases.

Validation of Light–Ion Quantum Molecular Dynamics (LIQMD) model for hadron therapy

The quantum molecular dynamics (QMD) model incorporated into the general-purpose radiation transport code PHITS was revised for accurate prediction of fragment yields in peripheral collisions. For more accurate simulation of peripheral collisions, stability of the nuclei at their ground state was improved and the algorithm to reject invalid events was modified. In-medium correction on nucleon-nucleon cross sections was also considered. To clarify the effect of this improvement on fragmentation of heavy nuclei, the new QMD model coupled with a statistical decay model was used to calculate fragment production cross sections of Ag and Au targets and compared with the data of earlier measurement. It is shown that the revised version can predict cross section more accurately.

Intermediate mass fragment emission for reactions of $^{32}\text{S} +\,^{51}\text{V},\,^{109}$Ag, and $^{238}\text{U}$ has been studied. Double differential cross sections were analysed in terms of the generalised moving source model yielding charge distributions. Isotope ratios show strong fragment mass dependencies. The data were successfully reproduced by the coalescence model as well as by statistical multifragmentation model calculations. Quantum molecular dynamics model calculations were not so successful.

The dynamical cluster-decay model (DCM) is developed further for the decay of hot and rotating compound nuclei (CN) formed in light heavy-ion reactions. The model is worked out in terms of only one parameter, namely the neck-length parameter, which is related to the total kinetic energy TKE($T$) or effective $Q$ value ${\mathit{Q}}_{\mathrm{eff}}(T)$ at temperature $T$ of the hot CN and is defined in terms of the CN binding energy and ground-state binding energies of the emitted fragments. The emission of both the light particles (LP), with $A\ensuremath{\le}4,Z\ensuremath{\le}2$, as well as the complex intermediate mass fragments (IMF), with $4lAl20,Zg2$, is considered as the dynamical collective mass motion of preformed clusters through the barrier. Within the same dynamical model treatment, the LPs are shown to have different characteristics compared to those of the IMFs. The systematic variations of the LP emission cross section ${\ensuremath{\sigma}}_{\mathrm{LP}}$ and IMF emission cross section ${\ensuremath{\sigma}}_{\text{IMF}}$ calculated from the present DCM match exactly the statistical fission model predictions. A nonstatistical dynamical description is developed for the first time for emission of light particles from hot and rotating CN. The model is applied to the decay of ${^{56}\mathrm{Ni}}^{\ensuremath{\ast}}$ formed in the $^{32}\mathrm{S}+^{24}\mathrm{Mg}$ reaction at two incident energies ${E}_{\mathrm{c}\mathrm{.}\mathrm{m}\mathrm{.}}=51.6$ and 60.5 MeV. Both the IMFs and average $\stackrel{\underline{}}{\mathit{TKE}}$ spectra are found to compare resonably well with the experimental data, favoring asymmetric mass distributions. The LPs' emission cross section is shown to depend strongly on the type of emitted particles and their multiplicities.

The theoretical description of heavy-ion collisions at intermediate beam energies, 10 MeV ≲, E/A ≲ 150 MeV, is still in an unsatisfactory state. Different factors contribute to that situation. Thus, for one, the nucleon excitation energies are low and in that comparable to nucleon localization energies, indicating a likely importance of the quantal effects. With the change in the beam energy in the discussed range, the dynamics changes from that dominated by the mean field to that dominated by collisions (as evidenced in the appearance of the flow balance-energy). As excitation energies grow, they begin to exceed the average binding energies per nucleon and, within the mentioned range of E/A, a massive production of intermediate-mass fragments (IMF) takes place[1]. The production, in terms of IMF multiplicity or total mass that IMF carry, maximizes at E/A ~ 75 MeV. The description of the intermediate and light fragment production is beyond the capability of common single-particle models of collisions[2]. The single-particle models with fluctuating forces[3,4] can describe fragment production, but miss the shell effects and the discreteness of the mass and charge numbers. The involved limitation is recognized once one realizes that, in the very central Au + Au collisions at 100 MeV/nucleon, the probability for a proton to come out from the reaction as a constituent of an a particle is close[5] to 50%. Within the Boltzmann-Langevin model with the fluctuating forces[3,4], the α particle plays no distinguished role. Statistical models[6,7] account for the shell effects, but miss the reaction dynamics. The importance of the dynamics is seen, in particular, in the fact that the collective outward flow energy in the reactions is comparable to the thermal energy.

This work, concentrated on the effect of nuclear equation of state on the elliptic flow (v2) in heavy ion collision by using quantum molecular dynamics model (QMD). The elliptic flow of proton in 197Au+197Au collision at incident energy 0.25A GeV and impact parameter from 0 to 0.25 and from 0.25 to 0.45 within the quantum molecular dynamics model was studied. The theoretical calculations were performed with the nuclear equation of state (soft and hard EoS). The elliptic flow of proton as a function of the mid-rapidity (y0) was computed and compared with those from experiments. The calculated results show thet the behaviour of matter at high density and high temperature are described by a soft EoS. With the theoretical result, the elliptic flow of proton as a function of (y0) is consistent with the experimental FOPI data.

In this article, we investigate the dependence of nuclear temperature on emitting source neutron-proton () asymmetry with light charged particles (LCPs) and intermediate mass fragments (IMFs) generated from intermediate-velocity sources in thirteen reaction systems with different asymmetries, on , and , on , , , and at 40 MeV/nucleon. The apparent temperature values of LCPs and IMFs from different systems are deduced from the measured yields using two helium-related and eight carbon-related double isotope ratio thermometers, respectively. Then, the sequential decay effect on the experimental apparent temperature deduction with the double isotope ratio thermometers is quantitatively corrected explicitly with the aid of the quantum statistical model. The present treatment is an improvement compared to our previous studies in which an indirect method was adopted to qualitatively consider the sequential decay effect. A negligible asymmetry dependence of the real temperature after the correction is quantitatively addressed in heavy-ion reactions at the present intermediate energy, where a change of 0.1 units in source asymmetry corresponds to an absolute change in temperature of an order of 0.03 to 0.29 MeV on average for LCPs and IMFs. This conclusion is in close agreement with that inferred qualitatively via the indirect method in our previous studies.