Dynamics of clusters and fragments in heavy-ion collisions

A review is given on the studies of formation of light clusters and heavier fragments in heavy-ion collisions at incident energies from several tens of MeV/nucleon to several hundred MeV/nucleon, focusing on dynamical aspects and on microscopic theoretical descriptions. Existing experimental data already clarify basic characteristics of expanding and fragmenting systems typically in central collisions, where cluster correlations cannot be ignored. Cluster correlations appear almost everywhere in excited low-density nuclear many-body systems and nuclear matter in statistical equilibrium where the properties of a cluster may be influenced by the medium. On the other hand, transport models to solve the time evolution have been developed based on the single-nucleon distribution function. Different types of transport models are reviewed putting emphasis both on theoretical features and practical performances in the description of fragmentation. A key concept to distinguish different models is how to consistently handle single-nucleon motions in the mean field, fluctuation or branching induced by two-nucleon collisions, and localization of nucleons to form fragments and clusters. Some transport codes have been extended to treat light clusters explicitly. Results indicate that cluster correlations can have strong impacts on global collision dynamics and correlations between light clusters should also be taken into account.Comment: review article, 64 pages, 27 figure

Multifragmentation and Symmetry Energy Studied with AMD

The antisymmetrized molecular dynamics (AMD) simulations suggest that the isospin composition of fragments produced dynamically in multifragmentation reactions is basically governed by the symmetry energy of low-density uniform nuclear matter rather than the symmetry energy for the ground-state finite nuclei. After the statistical secondary decay of the excited fragments, the symmetry energy effect still remains in the fragment isospin composition, though the effect in the isoscaling parameter seems a very delicate problem.Comment: Proceedings for VI Latin American Symposium on Nuclear Physics and Applications, Iguazu, Argentina (2005). To be published in Acta Phys. Hung.

Improvement of the nucleon emission process and the statistical property in molecular dynamics

We propose to introduce a new stochastic process in molecular dynamics in order to improve the description of the nucleon emission process from a hot nucleus. We give momentum fluctuations originating from the momentum width of the nucleon wave packet to the nucleon stochastically when it is being emitted from the nucleus. We show by calculating the liquid gas phase equilibrium in the case of antisymmetrized molecular dynamics, that with this improvement, we can recover the quantum mechanical statistical property of the nucleus for the particle emission process.Comment: 10 pages, LaTeX with revtex and epsf, uuenocded postscript figures, postscript version available at http://pearl.scphys.kyoto-u.ac.jp/~ono

Probing neutron-proton dynamics by pions

In order to investigate the nuclear symmetry energy at high density, we study the pion production in central collisions of neutron-rich nuclei ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at 300 MeV/nucleon using a new approach by combining the antisymmetrized molecular dynamics (AMD) and a hadronic cascade model (JAM). The dynamics of neutrons and protons is solved by AMD, and then pions and $\Delta$ resonances in the reaction process are handled by JAM. We see the mechanism how the $\Delta$ resonance and pions are produced reflecting the dynamics of neutrons and protons. We also investigate the impacts of cluster correlations as well as of the high-density symmetry energy on the nucleon dynamics and consequently on the pion ratio. We find that the $\Delta^-/\Delta^{++}$ production ratio agrees very well with the neutron-proton squared ratio $(N/Z)^2$ in the high-density and high-momentum region. We show quantitatively that $\Delta$ production ratio, and therefore $(N/Z)^2$, are directly reflected in the $\pi^-/\pi^+$ ratio, with modification in the final stage of the reaction.Comment: 14 pages, 10 figures; Figures 3-8 are updated with corrected numerical results. No change in the main conclusion

Viruses and Lipids

As obligatory intracellular pathogens, viruses exploit various cellular molecules and structures, such as cellular membranes, for their propagation. Enveloped viruses acquire lipid membranes as their outer coat through interactions with cellular membranes during morphogenesis within, and egress from, infected cells. In contrast, non-enveloped viruses typically exit cells by cell lysis, and lipid membranes are not part of the released virions. However, non-enveloped viruses also interact with lipid membranes at least during entry into target cells. Therefore, lipids, as part of cellular membranes, inevitably play some roles in life cycle of viruses. [...

Statistical properties of antisymmetrized molecular dynamics for non-nucleon-emission and nucleon-emission processes

Statistical properties of the antisymmetrized molecular dynamics (AMD) are classical in the case of nucleon emission processes, while they are quantum mechanical for the processes without nucleon emission. We first clarify that there coexist mutually opposite two statistics in the AMD framework: One is the classical statistics of the motion of wave packet centroids and the other is the quantum statistics of the motion of wave packets which is described by the AMD wave function. We prove the classical statistics of wave packet centroids by using the framework of the microcanonical ensemble of the nuclear system. We show that the quantum statistics of wave packets emerges from the classical statistics of wave packet centroids. It is emphasized that the temperature of the classical statistics of wave packet centroids is different from the temperature of the quantum statistics of wave packets. We then explain that the statistical properties of AMD for nucleon emission processes are classical because nucleon emission processes in AMD are described by the motion of wave packet centroids. When we improve the description of the nucleon emission process so as to take into account the momentum fluctuation due to the wave packet spread, the AMD statistical properties for nucleon emission processes change drastically into quantum statistics. Our study of nucleon emission processes can be conversely regarded as giving another kind of proof of the fact that the statistics of wave packets is quantum mechanical while that of wave packet centroids is classical.Comment: 20 pages, LaTeX with revtex and epsf, uuenocded postscript figures, postscript version available at http://pearl.scphys.kyoto-u.ac.jp/~ono

Collision integral with momentum-dependent potentials and its impact on pion production in heavy-ion collisions

The momentum dependence of the nucleon mean-field potential in a wide momentum range can be an important factor to determine the $\Delta$ resonance and pion production in intermediate-energy heavy-ion collisions. In particular, in neutron-rich systems such as ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions, we need to carefully treat the momentum dependence because the neutron and proton potentials can have different momentum dependence, as characterized at low momenta by effective masses. In the present work, we rigorously calculate the collision terms of $NN \leftrightarrow N \Delta$ and $\Delta \leftrightarrow N \pi$ processes with the precise conservation of energy and momentum under the presence of momentum-dependent potentials for the initial and final particles of the process. The potentials affect not only the threshold condition for the process but also the cross section in general as a function of the momenta of the initial particles, which is treated in a natural way in the present work. Calculations are performed by combining the nucleon dynamics obtained by the antisymmetrized molecular dynamics (AMD) model with a newly developed transport code which we call sJAM. The calculated results for central ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions at 270 MeV/nucleon clearly show that the momentum dependence of the neutron and proton potentials has a significant impact on the $NN \to N \Delta$ process, and this information is strongly reflected in the charged pion ratio ($\pi^-/\pi^+$). We also investigate the effects of the high-density symmetry energy and the isovector part of the potential of $\Delta$ resonances on pion production, which we find are relatively small compared to the effect of the momentum dependence of the neutron and proton potentials.Comment: 18 pages, 13 figures, 1 tabl

Relevance of equilibrium in multifragmentation

The relevance of equilibrium in a multifragmentation reaction of very central $^{40}Ca+^{40}Ca$ collisions at 35 MeV/nucleon is investigated by using simulations of Antisymmetrized Molecular Dynamics (AMD). Two types of ensembles are compared. One is the reaction ensemble of the states at each reaction time $t$ in collision events simulated by AMD, and the other is the equilibrium ensemble prepared by solving the AMD equation of motion for a many-nucleon system confined in a container for a long time. The comparison of the ensembles is performed for the fragment charge distribution and the excitation energies. Our calculations show that there exists an equilibrium ensemble which well reproduces the reaction ensemble at each reaction time $t$ for the investigated period $80\leq t\leq300$ fm/$c$. However, there are some other observables which show discrepancies between the reaction and equilibrium ensembles. These may be interpreted as dynamical effects in the reaction. The usual static equilibrium at each instant is not realized since any equilibrium ensemble with the same volume as that of the reaction system cannot reproduce the fragment observables.Comment: 13 pages and 12figures; added a few sentences and corrected typos, accepted in Phys. Rev.