Antisymmetrized Molecular Dynamics Research Articles

PANDORA Project for the study of photonuclear reactions below A=60

Photonuclear reactions of light nuclei below a mass of A=60 are planned to be studied experimentally and theoretically with the PANDORA (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics) project. Two experimental methods, virtual photon excitation by proton scattering and real photo absorption by a high-brilliance gamma -ray beam produced by laser Compton scattering, will be applied to measure the photoabsorption cross sections and decay branching ratio of each decay channel as a function of the photon energy. Several nuclear models, e.g. anti-symmetrized molecular dynamics, mean-field and beyond-mean-field models, a large-scale shell model, and ab initio models, will be employed to predict the photonuclear reactions. The uncertainty in the model predictions will be evaluated based on the discrepancies between the model predictions and experimental data. The data and predictions will be implemented in the general reaction calculation code, TALYS. The results will be applied to the simulation of the photo-disintegration process of ultra-high-energy cosmic rays in inter-galactic propagation.

Examination of cluster production in excited light systems at Fermi energies from new experimental data and comparison with transport model calculations

Four different reactions, $^{32}$S+$^{12}$C and $^{20}$Ne+$^{12}$C 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 (HF$l$ 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.

Reaction dynamics and in-medium nucleon-nucleon cross section with C12+H1 at 95 MeV/nucleon

Reaction dynamics and effective in-medium nucleon-nucleon $(NN)$ cross section are studied, using the antisymmetrized molecular dynamics (AMD) model with one of the simplest heavy ion collisions, $^{12}\mathrm{C}+^{1}\mathrm{H}$. The roles of different stochastic processes are studied, which are installed in the original AMD. One is the diffusion process as a part of the quantum fluctuation originated from the Fermi motion during the time evolution of the wave packets in the mean field (AMD/D). The second is a coalescence treatment for light clusters with $A\ensuremath{\le}8$ (AMD/D-COALS). The third is the collision process, installed in AMD with different form of the in-medium $NN$ cross sections. These different processes are examined, using the experimental angular distributions and energy spectra of light charged particles and intermediate mass fragments. The effective in-medium $NN$ cross sections are evaluated from the simulated AMD events and compared with the experimentally extracted values. A good agreement is obtained between the AMD values from the $^{12}\mathrm{C}$ $+$ $^{1}\mathrm{H}$ reaction at 95 MeV/nucleon and the experimental results for nuclear matter.

Investigating the time dependence of neutron-proton equilibration using molecular dynamics simulations

Neutron-proton equilibration has previously been studied experimentally in dynamically deformed nuclei in heavy ion collisions [Phys. Rev. Lett. 118, 062501 (2017); Phys. Rev. C 95, 044604 (2017)] using the NIMROD detector array at the Cyclotron Institute at Texas A University. Results indicated the composition of the two heaviest fragments originating from the excited projectile-like fragment evolved exponential with respect to their orientation angle to be more similar. Constrained Molecular Dynamics and Antisymmetrized Molecular Dynamics simulations were performed for different formulations of the density dependence of the asymmetry energy term of the nuclear equation of state. The simulations are compared to experimental results, which indicate a better agreement with a softer interaction in the nuclear equation of state.

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.

Energy density functional for α+12C elastic scattering

In this work, the α-particle elastic scattering from 12C is studied using three different 12C densities based on the cluster model. This work aims to extend our previous analysis of α+12C system to study the energy dependence of the real double folded (DF) potential deduced from the energy density functional (EDF) α-cluster model over a wide energy range. In addition, The EDF α-cluster model is compared with other cluster models to see how reliable is this cluster model for 12C nucleus. The two α-cluster models used for comparison are based on the antisymmetrized molecular dynamics (AMD) and a cubic approximation of the nuclear equation of state (liquid drop type density-LD) models. The 12C densities based on these cluster models are used in the double folding procedure to obtain α+12C real part of the optical model potential (OMP). The imaginary part of the OMP is considered in conventional Wood-Saxon (WS) form. The obtained elastic scattering results show the reliability of the EDF α-cluster model in reproducing the experimental data on equal footing with the other two considered cluster models. Thus the EDF is reliable for studying the ground state α-cluster of the light 4mα-conjugate nuclei.

Role of spatially compact nucleon wave packets in an ab initio description of H3 within high-momentum antisymmetrized molecular dynamics

We found the important role of the spatially compact nucleon wave packets to fully describe the nucleon correlations within the framework of the high-momentum antisymmetrized molecular dynamics (HM-AMD), which is a variational method based on the antisymmetrized molecular dynamics. In HM-AMD, short-range and tensor correlations between nucleons are described by nucleon pairs with high momentum (high-momentum pairs), which are given by putting large centroids of the Gaussian wave packets in opposite signs. In this paper, we further improve momentum distribution of the high-momentum pairs by varying the width parameter of the Gaussian wave packets of nucleons. We show the reliability of this new scheme by applying it to the $^{3}\mathrm{H}$ nucleus with the bare Argonne v8' potential. It is found that the spatially compact nucleon wave packets give the important effect to lower the total energy, which brings sufficient high-momentum components in the nucleus. We also include the spin-parallel configuration of the three nucleons induced by the tensor interaction, which is necessary to converge the HM-AMD results. Finally, comparable results to the other theoretical calculations are obtained for the total energy and Hamiltonian components.

Time of Fragmentation in Heavy Ion Collisions near the Fermi Energy

We simulated 64Ni + 58Ni collisions at an incident energy of E/A = 40 MeV by using an antisymmetrized molecular dynamics (AMD) model with employing a statistical decay code. The primary fragment yields were analyzed, and a power-law distribution was shown in the mass range 1 A 30. = 2.3 was treated as the signature of the reaction system (64Ni + 58Ni) at the critical point, and suggested that the fragments formed at 55-75 fm/c while the disassembling system at/or near its critical point.

4α linear-chain state produced by Be9+Be9 collisions

The linear-chain (LC) structure provides significant insights into quantum many-body systems with geometric configurations. In this study, $4\ensuremath{\alpha}+2n$ LC was assessed in $^{18}\mathrm{O}$. The excitation energies, moment of inertia, and $\ensuremath{\alpha}$- and $^{9}\mathrm{Be}$-decay widths of the LC states were predicted using antisymmetrized molecular dynamics. We predict that there are two $4\ensuremath{\alpha}$ LC bands, ${K}^{\ensuremath{\pi}}={0}^{+}$ and ${K}^{\ensuremath{\pi}}={3}^{\ensuremath{-}}$, which exhibit different decay properties. We demonstrate that the ${K}^{\ensuremath{\pi}}={3}^{\ensuremath{-}}$ LC states can be verified by the head-on $^{9}\mathrm{Be}+^{9}\mathrm{Be}$ collision experiments because their states exhibited large decay widths in the $^{9}\mathrm{Be}+^{9}\mathrm{Be}$ channel.

New many-body method using cluster expansion diagrams with tensor-optimized antisymmetrized molecular dynamics

We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$-shell nuclei within the triple products of the correlation functions of tensor and central-types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provides the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations.

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.

Using spin alignment of inelastically excited nuclei in fast beams to assign spins: The spectroscopy of O13 as a test case

Excited states in 13O were investigated using inelastic scattering of an E/A=69.5-MeV 13O beam off of a 9Be target. The excited states were identified in the invariant-mass spectra of the decay products. Both single proton and sequential two-proton decays of the excited states were examined. For a number of the excited states, the protons were emitted with strong anisotropy where emissions transverse to the beam axis are favored. The measured proton-decay angular distributions were compared to predictions from distorted-wave born-approximation (DWBA) calculations of the spin alignment which was shown to be largely independent of the excitation mechanism. The deduced $^{13}$O level scheme is compared to ab initio no-core shell model with continuum (NCSMC) predictions. The lowest-energy excited states decay isotropically consistent with predictions of strong proton 1s1/2 structure. Above these states in the level scheme, we observed a number of higher-spin states not predicted within the model. Possibly these are associated with rotational bands built on deformed cluster configurations predicted by antisymmetrized molecular dynamics (AMD) calculations. The spin alignment mechanism is shown to be useful for making spin assignments and may have widespread use.

Manifestation of the divergence between antisymmetrized-molecular-dynamics and container pictures of 9Be via 9Be(p,pn)8Be knockout reaction

We propose a new approach to probe the spatial extension of the valence neutron orbital in the 9Be nucleus via the 9Be(p,pn)8Be knockout reaction. This property of the nuclear molecular orbital has not been established in previous experimental studies and divergence exists between the theoretical descriptions of 9Be from different perspectives, i.e., the antisymmetrized molecular dynamics and the container pictures of cluster dynamics. These pictures are represented by two different well-proven microscopic models, the antisymmetrized molecular dynamics (AMD) and Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave functions. The corresponding reduced width amplitudes (RWAs) in the 8Be+n channel are extracted from both the AMD and THSR wave functions, and they are found to describe drastically different valence-nucleon motion, which shows the theoretical ambiguity in describing the π-orbitals in 9Be. Using the RWAs as input, the physical observables of the 9Be(p,pn)8Be knockout reaction are predicted by the distorted-wave impulse approximation (DWIA) framework. The magnitudes of the triple-differential cross sections (TDX) are found to be highly sensitive to the RWA input. It is concluded that the 9Be(p,pn)8Be knockout reaction could provide a feasible probing for the subtle differences between several structure models manifesting through the spatial extension of the π-orbital in the 9Be nucleus.

Investigation of the nuclear liquid-gas phase transition in the static AMD

Nuclear liquid-gas phase transitions are investigated in the framework of static antisymmetrized molecular dynamics (static AMD) model under either a constant volume or a constant pressure. A deuteron quadrupole momentum fluctuation thermometer is applied to extract the temperature of fragmenting systems of 36Ar and 100Sn. A plateau structure of caloric curves is observed under a constant volume for those system with a density ρ ⩽ 0.03 fm−3. A clear backbending in the caloric curves, which indicates a first order phase transition, is observed under a constant pressure with all pressures studied. The similar behavior of caloric curves of 36Ar and 100Sn systems indicates that there is no strong system size effect under a constant volume or a constant pressure. Both the mass distributions and the light particle multiplicities show a strong α clusterization at low excitation energies in the static AMD simulations. The liquid-gas phase transition measures of the multiplicity derivative (dM/dT) and the normalized variance of Z max (NVZ) are applied. The experimental caloric curves are also compared with those of 100Sn of the static AMD simulations under both the constant volume and the constant pressure conditions. Discussions are presented with the available experimental results and those from the static AMD simulations. Large errors in the experimental temperature measurements and those in the reconstruction technique for the primary fragmenting source hinder to draw a conclusion whether the phase transition occurs under either a constant volume or a constant pressure. This study suggests that different measures for the liquid-gas phase transitions should be examined besides the caloric curves in order to draw a conclusion.

Cluster correlation and nuclear vorticity in low-lying 1− states of Mg24

We investigated cluster correlation and nuclear voricity in low-lying $1^-$ states of $^{24}$Mg within antisymmetrized molecular dynamics framework. We found that the toroidal and compressional dipole modes separately appear as the $K=1$ and $K=0$ states. The $1^-$ ($K=1$) state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1^-$ ($K=0$) state is the compressional dipole state having enhanced cluster structure but has the weaker vorticity.

Role of the unitary correlation operator on high-momentum antisymmetrized molecular dynamics using the bare NN interaction for 3H and 4He

Abstract We extend high-momentum antisymmetrized molecular dynamics (HMAMD) by incorporating the short-range part of the unitary correlation operator method (UCOM) as the variational method of finite nuclei. In this HMAMD+UCOM calculation of light nuclei, HMAMD is mainly in charge of the tensor correlation with up to four-body correlation, while the short-range correlation is further improved by using UCOM. The binding energies of the $^3$H and $^4$He nuclei are calculated with HMAMD+UCOM using the AV8$'$ bare nucleon–nucleon ($NN$) interaction. The different roles of the short-range and tensor correlations from HMAMD and UCOM are analyzed in the numerical results. Compared with previous calculations based on different variational methods, this newly extended HMAMD+UCOM method can almost provide consistent results with ab initio results.

Microscopic coupled-channel calculation of proton and alpha inelastic scattering to the $4^+_1$ and $4^+_2$ states of $^{24}\textrm{Mg}$

Abstract The triaxial and hexadecapole deformations of the $K^\pi=0^+$ and $K^\pi=2^+$ bands of $^{24}$Mg have been investigated by the inelastic scatterings of various probes, including electrons, protons, and alpha($\alpha$) particles, for a prolonged time. However, it has been challenging to explain the unique properties of the scatterings observed for the $4^+_1$ state through reaction calculations. This paper investigates the structure and transition properties of the $K^\pi=0^+$ and $K^\pi=2^+$ bands of $^{24}$Mg employing the microscopic structure and reaction calculations via inelastic proton and $\alpha$ scattering. In particular, the $E4$ transitions to the $4^+_1$ and $4^+_2$ states are reexamined. The structure of $^{24}$Mg was calculated employing the variation after the parity and total angular momentum projections in the framework of the antisymmetrized molecular dynamics (AMD). The inelastic proton and $\alpha$ reactions were calculated by the microscopic coupled-channel (MCC) approach by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of $^{24}$Mg. Reasonable results were obtained on the properties of the structure, including the energy spectra and $E2$ and $E4$ transitions of the $K^\pi=0^+$ and $K^\pi=2^+$ bands owing to the enhanced collectivity of triaxial deformation. The MCC+AMD calculation successfully reproduced the angular distributions of the $4^+_1$ and $4^+_2$ cross sections of proton scattering at incident energies of $E_p=40$–100 MeV and $\alpha$ scattering at $E_\alpha=100$–400 MeV. This is the first microscopic calculation to describe the unique properties of the $0^+_1\to 4^+_1$ transition. In the inelastic scattering to the $4^+_1$ state, the dominant two-step process of the $0^+_1\to 2^+_1\to 4^+_1$ transitions and the deconstructive interference in the weak one-step process were essential.

Successive variational approach with the tensor-optimized antisymmetrized molecular dynamics for the 5He nucleus

Abstract We study $^5$He variationally as the first $p$-shell nucleus in the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon–nucleon interaction without any renormalization. In TOAMD, the central and tensor correlation operators promote the AMD’s Gaussian wave function to a sophisticated many-body state including the short-range and tensor correlations with high-momentum nucleon pairs. We develop a successive approach by applying these operators successively with up to double correlation operators to get converging results. We obtain satisfactory results for $^5$He, not only for the ground state but also for the excited state, and discuss explicitly the correlated Hamiltonian components in each state. We also show the importance of the independent optimization of the correlation functions in the variation of the total energy beyond the condition assuming common correlation forms used in the Jastrow approach.

Isospin diffusion measurement from the direct detection of a quasiprojectile remnant

The neutron-proton equilibration process in 48 Ca+ 40 Ca at 35 MeV/nucleon bombarding energy has been experimentally estimated by means of the isospin transport ratio. Experimental data have been collected with a subset of the FAZIA telescope array, which permitted to determine Z and N of detected fragments. For the first time, the QP evaporative channel has been compared with the QP break-up one in a homogeneous and consistent way, pointing out to a comparable n-p equilibration which suggests close interaction time between projectile and target independently of the exit channel. Moreover, in the QP evaporative channel n-p equilibration has been compared with the prediction of the Antisymmetrized Molecular Dynamics (AMD) model coupled to the GEMINI statistical model as an afterburner, showing a larger probability of proton and neutron transfers in the simulation with respect to the experimental data.

Effects of cluster correlations on fragment emission in C12+C12 at 50 MeV/nucleon

The effects of cluster correlations have been studied in the $^{12}\mathrm{C}+^{12}\mathrm{C}$ reaction at 50 MeV/nucleon, using three antisymmetrized molecular dynamics (AMD) models, the AMD (AMD/D) without any additional cluster correlations, AMD/D-COALS with nucleon correlations based on a coalescence prescription for light cluster formations with $A\ensuremath{\le}4$, and AMD-cluster with an extended cluster correlation in two-nucleon collision processes and a special treatment for intermediate fragment formation with $A\ensuremath{\le}9$. The angular distributions and energy spectra of fragments have been simulated and compared with the available experimental data. It is found that the cluster correlations take a crucial role to describe the productions of light charged particles (LCPs) and intermediate mass fragments (IMFs), and the AMD-cluster studied here provides a consistent overall reproduction of the experimental data. It is also shown that the significant effects of the secondary decay processes are involved for the fragment production besides the dynamical productions in the AMD stage. Detailed LCP and IMF production mechanisms involved in the intermediate energy heavy ion collisions are discussed.