The electric dipole polarizability α_D and the neutron-skin thickness ΔR_np of ^208Pb are two powerful and clean probes for constraining the symmetry energy at subsaturation densities. Within the framework of the antisymmetrized molecular dynamics (AMD) model, the width of the strength function and its dynamical origins are understood, and the α_D and ΔR_np data favor effective interaction parameter sets with S_0≈32-34 MeV and L=64-87 MeV. In addition, our calculations show that the sensitive densities of α_D and ΔR_np range from 0.2ρ_0 to 0.57ρ_0, and the corresponding values of the symmetry energy at the lower and upper ends of this sensitive density region are S(0.2ρ_0)=10.18± 1.10 MeV and S(0.57ρ_0)=22.31± 1.32 MeV.

The neutron-skin thickness and electric dipole polarizability are among the most sensitive probes of the symmetry energy at subsaturation densities. Motivated by the tension raised by recent analyses of PREX-II and CREX data within density-functional-based approaches, we perform a unified study of static and dynamical isovector observables within the antisymmetrized molecular dynamics (AMD) framework. Using thirty interaction parameter sets that span different values of the symmetry-energy coefficient S_0, slope parameter L, and neutron-proton effective-mass splitting Δm_np^*, we systematically analyze the neutron-skin thicknesses of nuclei from ^40Ca to ^238U together with the electric dipole polarizability α_D of ^208Pb. A combined χ^2 analysis of neutron-skin thicknesses and the electric dipole polarizability yields preferred values of L that increase with S_0, reflecting the joint constraint from the static and dynamical observables. Furthermore, we identify the density region mainly probed by these observables as 0.019 ≤ ρ/ρ_0≤0.60, where the relative narrowing strength function varies by less than 10

A Bayesian analysis aimed at tuning two parameters of the AMD model, one of them related to the in medium nucleon nucleon cross-section and the other to the clustering, has been performed. Experimental data collected with four blocks of the FAZIA setup have been compared with simulated data built with different values of the investigated parameters.

Within the TMEP, we present a detailed study of the performance of different transport models in Sn+Sn collisions at $270A$ MeV, and put particular emphasis on the production of pions and $\Delta$ resonances, which have been used as probes of the nuclear symmetry energy. We prescribe a common and rather simple physics model, and follow in detail the results of 4 BUU models and 6 QMD models. The nucleonic evolution of the collision and the nucleonic observables in these codes do not completely converge, but the differences among the codes can be understood as being due to several reasons: the basic differences between BUU and QMD models in the representation of the phase-space distributions, computational differences in the mean-field evaluation, and differences in the adopted strategies for the Pauli blocking in the collision integrals. For pionic observables, we find that a higher maximum density leads to an enhanced pion yield and a reduced $\pi^-/\pi^+$ yield ratio, while a more effective Pauli blocking generally leads to a slightly suppressed pion yield and an enhanced $\pi^-/\pi^+$ yield ratio. We specifically investigate the effect of the Coulomb force, and find that it increases the total $\pi^-/\pi^+$ yield ratio but reduces the ratio at high pion energies, although differences in its implementations do not have a dominating role in the differences among the codes. Taking into account only the results of codes that strictly follow the homework specifications, we find a convergence of the codes in the final charged pion yield ratio to a $1\sigma$ deviation of about $5\%$. However, the uncertainty is expected to be reduced to about $1.6\%$ if the same or similar strategies and ingredients, i.e., an improved Pauli blocking and calculation of the non-linear term in the mean-field potential, are similarly used in all codes.

Molecular dynamics approaches use wave packets as nucleon wave functions to simulate the time evolution of nuclear reactions. It is crucial to activate the momentum fluctuation inherent in each wave packet so that it properly affects the time evolution. In the antisymmetrized molecular dynamics (AMD) model, this has traditionally been done by splitting the wave packets, i.e., by introducing a random fluctuation to the wave packet center of each particle. The present work proposes an improved approach to activate the fluctuation in both the one-body mean-field propagation and the two-nucleon collision processes, consistently based on the gradual or sudden change of the degree of isolation, which is derived from the fragment number function used for the zero-point energy subtraction. This new method is applied to the 12C + 12C and 12C + p reactions at about 100 MeV/nucleon, focusing on the momentum distribution of the 11B fragments produced by one-proton removal from the 12C projectile. The results show that, with the momentum fluctuation suitably activated, the method correctly accounts for the recoil from the removed nucleon to the residue and the 11B momentum distribution is significantly improved, while without activating the fluctuation the distribution is too narrow compared to the experimental data. Furthermore, the AMD results indicate that the momentum distribution consists of two components; one is the high P_z component with a small shift from the beam velocity, resulting from the simple removal of a proton after an energetic collision with a target particle; the other is the low P_z component with a larger peak shift resulting from the decay of an excited 12C nucleus in a longer time scale. The activation of momentum fluctuation mainly affects the high P_z component to broaden it. The role of cluster correlations in this problem is also investigated.

This article presents an investigation of isospin equilibration in cross-bombarding $^{40,48}\mathrm{Ca}+^{40,48}\mathrm{Ca}$ reactions at 35 MeV/nucleon, by comparing experimental data with filtered transport model calculations. Isospin diffusion is studied using the evolution of the isospin transport ratio with centrality. The asymmetry parameter $\ensuremath{\delta}=(N\ensuremath{-}Z)/A$ of the quasiprojectile (QP) residue is used as isospin-sensitive observable, while a recent method for impact parameter reconstruction is used for centrality sorting. A benchmark of global observables is proposed to assess the relevance of the antisymmetrized molecular dynamics (amd) model, coupled to gemini$++$, in the study of dissipative collisions. Our results demonstrate the importance of considering cluster formation to reproduce observables used for isospin transport and centrality studies. Within the amd model, we prove the applicability of the impact parameter reconstruction method, enabling a direct comparison to the experimental data for the investigation of isospin diffusion. For both, we evidence a tendency to isospin equilibration with an impact parameter decreasing from 9 to 3 fm, while the full equilibration is not reached. A weak sensitivity to the stiffness of the equation of state employed in the model is also observed, with a better reproduction of the experimental trend for the neutron-rich reactions.

This article presents an investigation of isospin equilibration in cross-bombarding $^{40,48}$Ca$+^{40,48}$Ca reactions at $35$ MeV/nucleon, by comparing experimental data with filtered transport model calculations. Isospin diffusion is studied using the evolution of the isospin transport ratio with centrality. The asymmetry parameter $\delta=(N-Z)/A$ of the quasiprojectile (QP) residue is used as isospin-sensitive observable, while a recent method for impact parameter reconstruction is used for centrality sorting.A benchmark of global observables is proposed to assess the relevance of the antisymmetrized molecular dynamics (AMD) model, coupled to GEMINI++, in the study of dissipative collisions. Our results demonstrate the importance of considering cluster formation to reproduce observables used for isospin transport and centrality studies.Within the AMD model, we prove the applicability of the impact parameter reconstruction method, enabling a direct comparison to the experimental data for the investigation of isospin diffusion.For both, we evidence a tendency to isospin equilibration with an impact parameter decreasing from $9$ to $3$ fm, while the full equilibration is not reached.A weak sensitivity to the stiffness of the equation of state employed in the model is also observed, with a better reproduction of the experimental trend for the neutron-rich reactions.

An investigation of the quasiprojectile breakup channel in semiperipheral and peripheral collisions of $^{58,64}$Ni+$^{58,64}$Ni at 32 and 52 MeV/nucleon is presented. Data have been acquired in the first experimental campaign of the INDRA-FAZIA apparatus in GANIL. The effect of isospin diffusion between projectile and target in the two asymmetric reactions has been highlighted by means of the isospin transport ratio technique, exploiting the neutron-to-proton ratio of the quasiprojectile reconstructed from the two breakup fragments. We found evidence that, for the same reaction centrality, a higher degree of relaxation of the initial isospin imbalance is achieved in the breakup channel with respect to the more populated binary output, possibly indicating the indirect selection of specific dynamical features. We have proposed an interpretation based on different average projectile-target contact times related to the two exit channels under investigation, with a longer interaction for the breakup channel. The time information has been extracted from AMD simulations of the studied systems coupled to GEMINI++: the model calculations support the hypothesis hereby presented.

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.

We present our first results for a microscopic simulation of symmetric boost fission in terms of the antisymmetrized molecular dynamics (AMD) model. In AMD model, ground states of fissioning nuclei were prepared by a frictional cooling method and symmetrical boost momenta were given to nucleons inside to split the ground-state into fission fragments. After the simulation, we calculated the mass numbers and total kinetic energy (TKE) of the fission fragments. We also calculated orbital angular momenta of each fragment and identified them as spins, their mutual orientation and their orientation with respect to the linear momenta which defined the fission axis. Moreover, we found spin distribution of fission fragments was similar to the one given by the Fermi-gas model if spin cut-off parameter was adjusted. Finally, several ternary fission events were observed, emitting Tritium or 4He from the neck region, and average energy and angles of these ternary particles with respect to the fission axis were found to be in accord with experimental data.

Four different reactions, ^32S+^12C and ^20Ne+^12C at 25 and 50 MeV/nucleon, have been measured with the FAZIA detector capable of full isotopic identification of most forward emitted reaction products. Fragment multiplicities, angular distributions and energy spectra have been measured and compared with Monte Carlo simulations, i.e. the antisymmetrized molecular dynamics (AMD) and the heavy-ion phase space exploration (HIPSE) models. These models are combined with two different afterburner codes (HFl and SIMON) to describe the decay of the excited primary fragments. In the case of AMD, the effect of including the clustering and inter-clustering processes to form bound particles and fragments is discussed. A clear confirmation of the role of cluster aggregation in the reaction dynamics and particle production for these light systems, for which the importance of the clustering process increases with bombarding energy, is obtained.

In the paper by Hasegawa, Hagino and Tanimura (HHT) [Phys. Lett. B 808 (2020) 135693, arXiv:2006.06944], they concluded that quantum tunneling was simulated by a time-dependent generator coordinate method (TDGCM). In contrast, difficulties of TDGCM in describing quantum tunneling were pointed out by Ono in the paper [Phys. Lett. B 826 (2022) 136931, arXiv:2201.02966]. Recently, HHT submitted a comment [arXiv:2202.00513v1], by which they appear to give some counterarguments to Ono's paper. Here I examine their arguments, reviewing the main points of Ono's paper. The confusion in HHT's arguments may be mostly resolved by recognizing how the wave packets interfere with each other when they are coherently superposed.

Transport models are the main method to obtain physics information from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. Calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, and more realistic calculations of heavy-ion collisions. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. We review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known as BUU and QMD type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. We often indicate improved strategies in performing transport simulations and thus provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review.

Transport models are the main method to obtain physics information from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. Calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, and more realistic calculations of heavy-ion collisions. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. We review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known as BUU and QMD type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. We often indicate improved strategies in performing transport simulations and thus provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review.

Experimental information on fragment emissions is important in understanding the dynamics of nuclear collisions and in the development of transport model simulating heavy-ion collisions. The composition of complex fragments emitted in the heavy-ion collisions can be explained by statistical models, which assume that thermal equilibrium is achieved at collision energies below 100 MeV/u. Our new experimental data together with theoretical analyses for light particles from Sn+Sn collisions at 270 MeV/u, suggest that the hypothesis of thermal equilibrium breaks down for particles emitted with high transfer momentum. To inspect the system's properties in such limit, the scaling features of the yield ratios of particles from two systems, a neutron-rich system of ^132Sn+^124Sn and a nearly symmetric system of ^108Sn+^112Sn, are examined in the framework of the statistical multifragmentation model and the antisymmetrized molecular dynamics model. The isoscaling from low energy particles agree with both models. However the observed breakdown of isoscaling for particles with high transverse momentum cannot be explained by the antisymmetrized molecular dynamics model.

Transport models are the main method to obtain physics information from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. Calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, and more realistic calculations of heavy-ion collisions. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. We review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known as BUU and QMD type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. We often indicate improved strategies in performing transport simulations and thus provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review.

Transport models are the main method to obtain physics information from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. Calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, and more realistic calculations of heavy-ion collisions. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. We review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known as BUU and QMD type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. We often indicate improved strategies in performing transport simulations and thus provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review.

Background: The $^{44}$Ti nucleus has been known to have a $^{40}$Ca+$\alpha$ cluster structure, and inversion doublet structure has been observed; however, $\alpha$ cluster structure tends to be washed out when the breaking of the $\alpha$ cluster is allowed due to the spin-orbit interaction. Nevertheless, $\alpha$ clustering in medium-heavy nuclei is quite a hot subject recently. Purpose: The tensor interaction has been known to play an essential role in the strong binding of the $^4$He nucleus, which induces the two-particle-two-hole (2p2h) excitation. Since this excitation is blocked when another nucleus approaches, it is worthwhile to show whether the tensor effect works to keep the distance between $^4$He and $^{40}$Ca and becomes the salvation of the clustering in $^{44}$Ti. Methods: The spin-orbit effect is included in the cluster model by using the antisymmetrized quasi cluster model (AQCM) developed by the authors. We have also developed an improved version of the simplified method to include the tensor contribution ($i$SMT), which allows us to estimate the tensor effect within the cluster model. The competition of these two is investigated in the medium-heavy mass region for the first time. Results: According to AQCM, the spin-orbit interaction completely breaks the $\alpha$ cluster and restores the symmetry of $jj$-coupling shell model when the $\alpha$ cluster approaches the $^{40}$Ca core. On the other hand, $i$SMT gives a large distance between $\alpha$ and $^{40}$Ca due to the tensor effect. Conclusions: In $^{44}$Ti, because of the strong spin-orbit and tensor contributions, two completely different configurations ($jj$-coupling shell model and cluster states) almost degenerate, and their mixing becomes important.

C.Y. Tsang, 2 Yongjia Wang, M.B. Tsang, 2 J. Estee, 2 T. Isobe, M. Kaneko, 5 M. Kurata-Nishimura, J.W. Lee, Fupeng Li, 7 Qingfeng Li, 8 W.G. Lynch, 2 T. Murakami, 5 R. Wang, Dan Cozma, Rohit Kumar, Akira Ono, and Ying-Xun Zhang National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA Department of Physics, Michigan State University, East Lansing, Michigan 48824, USA School of Science, Huzhou University, Huzhou 313000, China RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan Department of Physics, Kyoto University, Kita-shirakawa, Kyoto 606-8502, Japan Department of Physics, Korea University, Seoul 02841, Republic of Korea College of Science, Zhejiang University of Technology, Hangzhou 310014, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China IFIN-HH, Reactorului 30, 077125 Mǎgurele-Bucharest, Romania Department of Physics, Tohoku University, Sendai 980-8578, Japan China Institute of Atomic Energy, Beijing 102413, China (Dated: July 30, 2021)