Antisymmetrized Molecular Dynamics Calculations Research Articles

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.

Transition properties of low-lying states inSi28probed via inelastic proton andαscattering

${0}^{+}, {1}^{\ensuremath{-}}, {2}^{+}$, and ${3}^{\ensuremath{-}}$ excitations of $^{28}\mathrm{Si}$ are investigated via proton and $\ensuremath{\alpha}$ inelastic scattering off $^{28}\mathrm{Si}$. The structure calculation of $^{28}\mathrm{Si}$ is performed with the energy variation after total angular momentum and parity projections in the framework of antisymmetrized molecular dynamics (AMD). As a result of the AMD calculation, the oblate ground and prolate bands, ${0}^{+}$ and ${3}^{\ensuremath{-}}$ excitations, and the ${1}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ states of the ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$ band are obtained. Using the matter and transition densities of $^{28}\mathrm{Si}$ obtained by AMD, microscopic coupled-channels calculations of proton and $\ensuremath{\alpha}$ scattering off $^{28}\mathrm{Si}$ are performed. The proton-$^{28}\mathrm{Si}$ potentials in the reaction calculation are microscopically derived by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of $^{28}\mathrm{Si}$. The $\ensuremath{\alpha}\ensuremath{-}^{28}\mathrm{Si}$ potentials are obtained by folding the nucleon-$^{28}\mathrm{Si}$ potentials with an $\ensuremath{\alpha}$ density. The calculation reasonably reproduces the observed elastic and inelastic cross sections of proton and $\ensuremath{\alpha}$ scattering. Transition properties are discussed by combining the reaction analysis of proton and $\ensuremath{\alpha}$ scattering and structure features such as transition strengths and form factors. The isoscalar monopole and dipole transitions are focused.

Antisymmetrized molecular dynamics studies for exotic clustering phenomena in neutron-rich nuclei

We present a review of recent works on clustering phenomena in unstable nuclei studied by antisymmetrized molecular dynamics (AMD). The AMD studies in these decades have uncovered novel types of clustering phenomena brought about by the excess neutrons. Among them, this review focuses on the molecule-like structure of unstable nuclei. One of the earliest discussions on the clustering in unstable nuclei was made for neutron-rich Be and B isotopes. AMD calculations predicted that the ground state clustering is enhanced or reduced depending on the number of excess neutrons. Today, the experiments are confirming this prediction as the change of the proton radii. Behind this enhancement and reduction of the clustering, there are underlying shell effects called molecular- and atomic-orbits. These orbits form covalent and ionic bonding of the clusters analogous to the atomic molecules. It was found that this "molecular-orbit picture" reasonably explains the low-lying spectra of Be isotopes. The molecular-orbit picture is extended to other systems having parity asymmetric cluster cores and to the three cluster systems. O and Ne isotopes are the candidates of the former, while the $3\alpha$ linear chains in C isotopes are the latter. For both subjects, many intensive studies are now in progress. We also pay a special attention to the observables which are the fingerprint of the clustering. In particular, we focus on the monopole and dipole transitions which are recently regarded as good probe for the clustering. We discuss how they have and will reveal the exotic clustering.

Velocity-dependent transverse momentum distribution of fragments produced fromAr40+Be9at 95 MeV/nucleon

Transverse momentum $({P}_{\mathrm{T}})$ distributions of projectilelike fragments produced at intermediate energy are investigated. ${P}_{\mathrm{T}}$ distributions of fragments with mass ${A}_{\mathrm{F}}\phantom{\rule{4pt}{0ex}}=10--37$, produced from an $^{40}\mathrm{Ar}$ beam with $E=95\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ and a Be target, are observed as a function of fragment velocity by using the Rikagaku Kenkyusho (RIKEN) Projectile Fragment Separator at RIKEN. The width of ${P}_{\mathrm{T}}$ distribution $({\ensuremath{\sigma}}_{\mathrm{T}})$ decreases monotonically with longitudinal momentum $({P}_{\mathrm{L}})$. The decreasing trend shows a clear dependence on fragment mass. The observed ${\ensuremath{\sigma}}_{\mathrm{T}}$ is analyzed with a linear function and successfully reproduced by a parameter to characterize the decreasing trend. ${\ensuremath{\sigma}}_{\mathrm{T}}$ at the primary beam velocity shows good agreement with the Goldhaber formula, which is obtained on the basis of the contribution of the Fermi momentum. In contrast, the ${\ensuremath{\sigma}}_{\mathrm{T}}$ at the center of the ${P}_{\mathrm{L}}$ distribution as determined by using the fits and parametrized energy loss in the fragmentation process is consistent with the width, which includes an additional contribution from the orbital deflection of the projectile. The antisymmetrized molecular-dynamics calculation indicates that the contribution of impact parameters is an important factor in understanding the behavior of the ${P}_{\mathrm{T}}$ distribution. In addition, the practical formulation for ${\ensuremath{\sigma}}_{\mathrm{T}}$ obtained in the present study enables a reliable characterization of the fragments, which would be applicable to various research fields involving, for example, radioactive nuclear beams.

A Model Comparison Study of Fragment Production in 140 A MeV 58,64Ni+9Be Reactions**Supported by the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No 13HASTIT046.

The cross sections of fragments produced in the 140 A MeV58,64Ni+9 Be projectile fragmentation reactions are calculated by using the antisymmetrized molecular dynamics (AMD) model, the modified statistical abrasion-ablation (SAA) model, and the empirical EPAX2/EPAX3 formulae. The Gogny-g0 interaction is taken as the effective nucleon-nucleon interaction in the AMD calculation, and the decays of fragments obtained from the AMD results are calculated by using the GEMINI code. The calculated cross sections of fragments are compared.

Ground-state properties of neutron-rich Mg isotopes

We analyze recently measured total reaction cross sections for ${}^{24--38}$Mg isotopes incident on ${}^{12}$C targets at 240 MeV/nucleon by using the folding model and antisymmetrized molecular dynamics (AMD). The folding model well reproduces the measured reaction cross sections, when the projectile densities are evaluated by the deformed Woods-Saxon (def-WS) model with AMD deformation. Matter radii of ${}^{24--38}$Mg are then deduced from the measured reaction cross sections by fine tuning the parameters of the def-WS model. The deduced matter radii are largely enhanced by nuclear deformation. Fully microscopic AMD calculations with no free parameter well reproduce the deduced matter radii for ${}^{24--36}$Mg, but still considerably underestimate them for ${}^{37,38}$Mg. The large matter radii suggest that ${}^{37,38}$Mg are candidates for deformed halo nucleus. AMD also reproduces other existing measured ground-state properties (spin parity, total binding energy, and one-neutron separation energy) of Mg isotopes. Neutron-number ($N$) dependence of deformation parameter is predicted by AMD. Large deformation is seen from ${}^{31}$Mg with $N=19$ to a drip-line nucleus ${}^{40}$Mg with $N=28$, indicating that both the $N=20$ and 28 magicities disappear. $N$ dependence of neutron skin thickness is also predicted by AMD.

Deformation of Ne isotopes in the region of the island of inversion

The deformation of Ne isotopes in the island-of-inversion region is determined by the double-folding model with the Melbourne $g$-matrix and the density calculated by the antisymmetrized molecular dynamics (AMD). The double-folding model reproduces, with no adjustable parameter, the measured reaction cross sections for the scattering of $^{28-32}$Ne from $^{12}$C at 240MeV/nucleon. The quadrupole deformation thus determined is around 0.4 in the island-of-inversion region and $^{31}$Ne is a halo nuclei with large deformation. We propose the Woods-Saxon model with a suitably chosen parameterization set and the deformation given by the AMD calculation as a convenient way of simulating the density calculated directly by the AMD. The deformed Woods-Saxon model provides the density with the proper asymptotic form. The pairing effect is investigated, and the importance of the angular momentum projection for obtaining the large deformation in the island-of-inversion region is pointed out.

Antisymmetrized molecular dynamics and its applications to cluster phenomena

Structure and reaction studies using the antisymmetrized molecular dynamics (AMD) method are reviewed. Applications of time-independent and time-dependent versions of AMD are described. In applications of time-independent AMD to nuclear structure studies, the structures of neutron-rich nuclei such as Be, C, Ne, and Mg isotopes are described, focusing on cluster aspects. The important roles of valence neutrons are discussed. The results suggest that a variety of cluster structures appear in unstable nuclei as well as in stable nuclei. Deformation and cluster phenomena in Z ∼ N nuclei in p- and sd-shell regions are also discussed. The applications of time-dependent AMD include various topics such as fragmentation in heavy-ion collisions as well as nuclear responses. The AMD calculations successfully describe multifragmentation, which is one of the remarkable phenomena observed in heavy-ion collisions. The approach is able to link reactions and nuclear matter properties. The studies suggest the important balance between single-particle motions and correlations to form clusters and fragments.

BRUECKNER-AMD STUDY OF LIGHT NUCLEI

We applied the Brueckner theory to the Antisymmetrized Molecular Dynamics (AMD), and show the reliability of the AMD calculations based on realistic nuclear interactions. Focusing our interest on a structure dependence of the tensor force, we investigate the α-α clusterization of 8 Be .

Description of nuclear structures in light nuclei with Brueckner-AMD

We develop the new antisymmetrized molecular dynamics (AMD) method, Brueckner-AMD, which makes us perform the AMD calculations starting from the realistic nuclear force. In the Brueckner-AMD, the single-particle orbits of AMD can be applied straightforward to the Bethe-Goldstone equation in the Brueck- ner theory by using the AMD+Hartree-Fock method, and the G-matrices are determined with the single-particle energies of AMD self-consistently. In that sense, in this framework, the G-matrix in AMD can be solved theo- retically without any corrections. We present the applicability of the Brueckner-AMD to describe not only the ground states but also the excited states for some light nuclei, especially the excited 0 + state in 12 C which is not solved suffi ciently by the present shell model approaches, starting from the realistic nuclear force.

Three-body cluster state in 11B

The cluster structures of the excited states in 11B are studied by analyzing the isoscalar monopole and quadrupole strengths in the 11B(d,d′) reaction at E d = 200 MeV . The excitation strengths are compared with the predictions by the shell-model and antisymmetrized molecular-dynamics (AMD) calculations. It is found that the large monopole strength for the 3 / 2 3 − state at E x = 8.56 MeV is well described by the AMD calculation and is an evidence for a developed three-body 2 α + t cluster structure.

2α+t cluster structure in 11B

The cluster structures of the excited states in $^{11}$B are studied by analyzing the isoscalar monopole and quadrupole strengths in the $^{11}$B($d$,$d'$) reaction at $E_d=200$ MeV. The excitation strengths are compared with the predictions by the shell-model and antisymmetrized molecular-dynamics (AMD) calculations. It is found that the large monopole strength for the $3/2^-_3$ state at $E_x=8.56$ MeV is well described by the AMD calculation and is an evidence for a developed $2\alpha+t$ cluster structure.

Dilute [formula omitted] cluster structure in 11B

The cluster structures of the excited states in 11 B are studied by analyzing the isoscalar monopole and quadrupole strengths in the 11 B( d , d ′) reaction at E d = 200 MeV . The excitation strengths are compared with the predictions by the shell-model and antisymmetrized molecular-dynamics (AMD) calculations. It is found that the large monopole strength for the 3 / 2 3 − state at E x = 8.56 MeV is well described by the AMD calculation and is an evidence for a developed 2 α + t cluster structure.

2α + t cluster state in11B

The cluster structures of the excited states in11B are studied by analyzing the isoscalar monopole and quadrupole strengths in the11B (d,d′) reaction at Ed= 200 MeV . The excitation strengths are compared with the predictions by the shell-model and antisymmetrized molecular-dynamics (AMD) calculations. It is found that the large monopole strength for the [Formula: see text] state at Ex= 8.56 MeV is well described by the AMD calculation and is an evidence for a developed 2α + t cluster structure.

Delta degrees of freedom in antisymmetrized molecular dynamics and (p,p') reactions in the Delta region.

\ensuremath{\Delta} degrees of freedom are introduced into antisymmetrized molecular dynamics (AMD). This is done by increasing the number of basic states in the AMD wave function, introducing a Skyrme-type delta-nucleon potential, and including NN\ensuremath{\leftrightarrows}N\ensuremath{\Delta} reactions in the collision description. As a test of the delta dynamics, the extended AMD is applied to (p,${\mathit{p}}^{\ensuremath{'}}$) reactions at ${\mathit{E}}_{\mathrm{lab}}$=800 MeV for a $^{12}\mathrm{C}$ target. It is found that the ratio and the absolute values for delta peak and quasielastic peak (QEP) in the $^{12}\mathrm{C}$(p,${\mathit{p}}^{\ensuremath{'}}$) reaction are reproduced for angles ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{lab}}$\ensuremath{\gtrsim}40\ifmmode^\circ\else\textdegree\fi{}. For forward angles the QEP is overestimated, but generally the agreement between AMD calculations and experimental data is reasonable. The results of the AMD calculations are compared to one-step Monte Carlo (OSMC) calculations and a detailed analysis of multi-step and delta potential effects is given. Along this analysis a decomposition of the cross section into various reaction channels is presented and the reaction dynamics is discussed in detail. As important side results we present a way to apply a Galilei invariant theory for (N,${\mathit{N}}^{\ensuremath{'}}$) reactions up to ${\mathit{E}}_{\mathrm{lab}}$\ensuremath{\approxeq}800 MeV which ensures approximate Lorentz invariance and we discuss how to fix the width parameter \ensuremath{\nu} of the single particle momentum distribution for outgoing nucleons in the AMD calculation.