Antisymmetrized Molecular Dynamics Model Research Articles

Microscopic simulation of symmetric boost fission with antisymmetrized molecular dynamics

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.

Rapidity distributions of Z = 1 isotopes and the nuclear symmetry energy from Sn+Sn collisions with radioactive beams at 270 MeV/nucleon

The rapidity distributions of hydrogen isotopes emitted from central collisions of neutron-rich 132Sn+124Sn and neutron-deficient 108Sn+112Sn systems at 270 MeV/nucleon were investigated at RIKEN-RIBF. The data are compared with antisymmetrized molecular dynamics (AMD) calculations and the rapidity distributions can be reproduced after adjusting the in-medium nucleon-nucleon cross sections. The double ratios between the two reaction systems taken for the relative yields of deuteron to proton (d/p) and triton to proton (t/p) are further examined in the midrapidity domain, where the adjustments in the AMD calculations do not affect much on them. The d/p and t/p double ratios at midrapidity agree well with the ratio of the system neutron numbers and its squared value, respectively, and the rapidity dependence of these double ratios is consistent with a picture of partial mixing of colliding nuclei. By comparing with the AMD model which shows a strong symmetry energy dependence of the t/p double ratio, the experimental result in the midrapidity domain favors the calculation with a symmetry-energy slope parameter around L=46 MeV rather than L=108 MeV.

Shape analysis applied in heavy ion reactions near Fermi energy

A new method is proposed to perform shape analyses and to evaluate their validity in heavy ion collisions near the Fermi energy. In order to avoid erroneous values of shape parameters in the calculation, a test particle method is utilized in which each nucleon is represented by n test particles, similar to that used in the Boltzmann–Uehling–Uhlenbeck (BUU) calculations. The method is applied to the events simulated by an antisymmetrized molecular dynamics model. The geometrical shape of fragments is reasonably extracted when n = 100 is used. A significant deformation is observed for all fragments created in the multifragmentation process. The method is also applied to the shape of the momentum distribution for event classification. In the momentum case, the errors in the eigenvalue calculation become much smaller than those of the geometrical shape analysis and the results become similar between those with and without the test particle method, indicating that in intermediate heavy ion collisions the shape analysis of momentum distribution can be used for the event classification without the test particle method.

High-energy proton emission and Fermi motion in intermediate-energy heavy-ion collisions

An antisymmetrized molecular dynamics model (AMD-FM), modified to take into account the Fermi motion explicitly in its nucleon-nucleon collision process, is presented. Calculated high-energy proton spectra are compared with those of $^{40}\mathrm{Ar}+^{51}\mathrm{V}$ at 44 MeV/nucleon from Coniglione et al. [Phys. Lett. B 471, 339 (2000)] and those of $^{36}\mathrm{Ar}+^{181}\mathrm{Ta}$ at 94 MeV/nucleon from Germain et al. [Nucl. Phys. A 620, 81 (1997)]. Both of the experimental data are reasonably well reproduced by the newly added Fermi boost in the nucleon-nucleon collision process without additional processes, such as a three-body collision or a short-range correlation. The production mechanism of high-energy protons in intermediate-energy heavy-ion collisions is discussed.

One-dimensionality in atomic nuclei: A candidate for linear-chainαclustering inC14

The clustering of $\ensuremath{\alpha}$ particles in atomic nuclei results in the self-organization of various geometrical arrangements at the femtometer scale. The one-dimensional alignment of multiple $\ensuremath{\alpha}$ particles is known as linear-chain structure, evidence of which has been highly elusive. We show via resonant elastic and inelastic $\ensuremath{\alpha}$ scattering of a radioactive $^{10}\mathrm{Be}$ beam that excited states in the neutron-rich nucleus $^{14}\mathrm{C}$ agree with recent predictions of linear-chain structure based on an antisymmetrized molecular dynamics model.

Freezeout concept and dynamical transport model in intermediate-energy heavy-ion reactions

For the central collision events of ${}^{40}\mathrm{Ca}\phantom{\rule{4pt}{0ex}}+{\phantom{\rule{0.16em}{0ex}}}^{40}\mathrm{Ca}$, generated by an antisymmetrized molecular dynamics model in the intermediate energy range of 35 to 300 MeV/nucleon, the density and temperature of a fragmenting source have been extracted using a self-consistent method with the modified Fisher model. Rather flat density values, $\ensuremath{\rho}/{\ensuremath{\rho}}_{0}\ensuremath{\sim}0.65$ to 0.7, are evaluated at the incident energies studied, even though the maximum density of the system achieved during the collisions increases monotonically from $\ensuremath{\rho}/{\ensuremath{\rho}}_{0}\ensuremath{\sim}1.3$ at 35 MeV/nucleon to 1.8 at 300 MeV/nucleon. Flat temperature values of $T\ensuremath{\sim}5.9$ to 6.5 MeV are also extracted in this incident energy range. These extracted values indicate that, in average, intermediate mass fragments are formed at a later stage when the hot nuclear matter reaches at a ``freezeout'' volume by the expansion, which is not assumed in any transport models, but assumed generally in statistical multifragmentation models. This is the first time to demonstrate quantitatively a direct connection between the freezeout concept and transport model simulations in a multifragmenting regime of heavy ion collisions.

Reconstructed primary fragments and symmetry energy, temperature and density of the fragmenting source in Zn64+Sn112 at 40 MeV/nucleon

Symmetry energy, temperature and density at the time of the intermediate mass fragment formation are determined in a self-consistent manner, using the experimentally reconstructed primary hot isotope yields and anti-symmetrized molecular dynamics (AMD) simulations. The yields of primary hot fragments are experimentally reconstructed for multifragmentation events in the reaction system $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. Using the reconstructed hot isotope yields and an improved method, based on the modified Fisher model, symmetry energy values relative to the apparent temperature, $a_{sym}/T$, are extracted. The extracted values are compared with those of the AMD simulations, extracted in the same way as that for the experiment, with the Gogny interaction with three different density-dependent symmetry energy terms. $a_{sym}/T$ values change according to the density-dependent symmetry energy terms used. Using this relation, the density of the fragmenting system is extracted first. Then symmetry energy and apparent temperature are determined in a self consistent manner in the AMD model simulations. Comparing the calculated $a_{sym}/T$ values and those of the experimental values from the reconstructed yields, $\rho /\rho_{0} = 0.65 \pm 0.02 $, $a_{sym} = 23.1 \pm 0.6$ MeV and $T= 5.0 \pm 0.4$ MeV are evaluated for the fragmenting system experimentally observed in the reaction studied.

Investigation of equation of state and in-mediumNNcross sections through nuclear stopping

By using an antisymmetrized molecular dynamics model (AMD), the data of kinematically complete events are compared with the experimental INDRA data through nuclear stopping in $\text{Xe}+\text{Sn}$ collisions at 10 to $100A$ MeV. The sensitivity of the nuclear stopping is studied through interactions with different equations of state (EOSs) (soft and stiff) and in-medium $NN$ cross sections in different energy domains. Above $25A$ MeV, both EOSs and different $NN$ cross sections can affect the nuclear stopping, but none of these parameters used in the AMD model can reproduce the experimental data at 20 to $30A$ MeV. On the other hand, below $25A$ MeV, nuclear stopping is not sensitive to both of the EOSs and the $NN$ cross sections because of complete nuclear stopping. This indicates that some important mechanisms may be missing in AMD or that the selection of central collision events may be significantly different between the experiments and the simulations at this energy range.

Dynamics aspect of subbarrier fusion reaction in light heavy ion systems

Subbarrier fusion of the 7Li+12C reaction is studied using an antisymmetrized molecular dynamics model (AMD) with an after burner, GEMINI. In AMD, 7 Li shows an α + t structure at its ground state and it is significantly deformed. Simulations are made near the Coulomb barrier energies, i.e., Ecm = 3 — 8MeV. The total fusion cross section of the AMD + GEMINI calculations as a function of incident energy is compared to the experimental results and both are in good agreement at Ecm > 3MeV. The cross section for the different residue channels of the AMD + GEMINI at Ecm = 5MeV is also compared to the experimental results.

Nuclear Electro-disintegration with Antisymmetrized Molecular Dynamics

The extended antisymmetrized molecular dynamics (AMD) wave function is used to study the two-body nuclear electro-disintegration. The final-state interactions are included using the Glauber multiple scattering approximation. Non-relativistic nuclear charge and current operators are employed when calculating longitudinal and transverse nuclear response functions. It is found that the AMD model gives a very good description of experimental data for the 4He response functions.

Investigation of transverse collective flow of intermediate mass fragments

The transverse flow of intermediate mass fragments (IMFs) has been investigated for the 35 MeV/u ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ systems. A transition from the IMF transverse flow strongly depending on the mass of the system, in the most violent collisions, to a dependence on the charge of the system, for the peripheral reactions, is shown. This transition was shown to be sensitive to the density dependence of the symmetry energy using the antisymmetrized molecular-dynamics model. The results present an observable, the IMF transverse flow, that can be used to probe the nuclear equation of state. Comparison with the simulation demonstrated a preference for a stiff density dependence of the symmetry energy.

Isobaric yield ratios and the symmetry energy in heavy-ion reactions near the Fermi energy

The relative isobaric yields of fragments produced in a series of heavy-ion-induced multifragmentation reactions have been analyzed in the framework of a modified Fisher model, primarily to determine the ratio of the symmetry energy coefficient to the temperature, ${a}_{\mathrm{sym}}/T$, as a function of fragment mass $A$. The extracted values increase from 5 to $~$16 as $A$ increases from 9 to 37. These values have been compared to the results of calculations using the antisymmetrized molecular dynamics (AMD) model together with the statistical decay code gemini. The calculated ratios are in good agreement with those extracted from the experiment. In contrast, the values extracted from the ratios of the primary isobars from the AMD model calculation are $~$4 to 5 and show little variation with $A$. This observation indicates that the value of the symmetry energy coefficient derived from final fragment observables may be significantly different than the actual value at the time of fragment formation. The experimentally observed pairing effect is also studied within the same simulations. The Coulomb coefficient is also discussed.

Short timescale behavior of colliding heavy nuclei at intermediate energies

Noncentral collisions of $^{114}\mathrm{Cd}$ projectiles with $^{92}\mathrm{Mo}$ target nuclei at $E/A=50$ MeV are explored with an antisymmetrized molecular dynamics model. These collisions are found to be essentially binary in character with formation of an excited projectile-like fragment (PLF${}^{*}$) and targetlike fragment (TLF${}^{*}$). The average excitation energy deduced for the PLF${}^{*}$ and TLF${}^{*}$ saturates for midcentral collisions, $3.5\ensuremath{\le}b\ensuremath{\le}6$ fm, with its magnitude depending on the cluster recognition time. For short cluster recognition times $(t=150\phantom{\rule{0.3em}{0ex}}\mathrm{fm}/c)$, an average excitation energy as high as \ensuremath{\approx}6 MeV is determined, indicating a short statistical lifetime for the fragments produced. Evidence for such a rapid deexcitation is observed in the present calculations.

Structure of light exotic nuclei studied with AMD model

Study of the structure of Li, Be, B, and C isotopes with the antisymmetrized molecular dynamics (AMD) is reported. It is emphasized that the AMD study reveals large and characteristic structure changes of these isotopes with the increase of the neutron number. Around neutron drip lines, clustering structure is predicted for Be and B, while large oblate deformation with neutron skin is predicted for C. AMD wave functions which show large change of structure reproduce well various observed data especially magnetic moments and electric quadrupole moments. AMD prediction of opposite sign between neutron deformation and proton deformation in some exotic nuclei is shown to be supported by the observed data of electric moments and transition rates in mirror nuclei.

Statistical properties of anti-symmetrized molecular dynamics

We study the statistical equilibrium properties of the recently developed anti-symmetrized molecular dynamics model for heavy-ion reactions. We consider A non-interacting fermions in one dimension, either bound in a common harmonic potential or moving freely within an interval, and perform a Metropolis sampling of the corresponding parameter space. Generally the average excitation and the specific heat, considered as functions of the imposed temperature, behave in a classical manner when the canonical weight is calculated in the mean-field approximation. However, it is possible to obtain results that are much closer to the quantal behavior by modifying the weight to take approximate account of the energy fluctuations within the individual wave packets.