Search

A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a superposition of Gaussian wave packets, to describe the relative motion between two colliding nuclei, which may be simplified to a problem for one particle in one dimension. In this article, how the model describes the potential-barrier transmission is investigated by paying attention to the time evolution of the phase space distribution, which in particular reveals that the behavior of the free propagation of the incoming state is not trivial, depending on the number of superposed wave packets. Passage over the barrier can occur due to the high-momentum components in the incoming state corresponding to energies above the barrier height, which is, however, of classical nature and needs to be distinguished from the true quantum tunneling. Although a transmitted wave packet in some case may end up with an energy lower than the barrier, a difficulty is noticed in guaranteeing the energy conservation when the energies of different exit channels, e.g. of transmission and reflection, are individually measured. To overcome these issues for a description of quantum tunneling is still a challenging problem. This article mainly treats the same system with the same model as in the paper Hasegawa, Hagino and Tanimura (2020) [1]. However, we reach different conclusions.

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.

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, 3H and 4He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s -shell nuclei, 3 H and 4 He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions. [ABSTRACT FROM AUTHOR]

A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a superposition of Gaussian wave packets, to describe the relative motion between two colliding nuclei, which may be simplified to a problem for one particle in one dimension. In this article, how the model describes the potential-barrier transmission is investigated by paying attention to the time evolution of the phase space distribution, which in particular reveals that the behavior of the free propagation of the incoming state is not trivial, depending on the number of superposed wave packets. Passage over the barrier can occur due to the high-momentum components in the incoming state corresponding to energies above the barrier height, which is, however, of classical nature and needs to be distinguished from the true quantum tunneling. Although a transmitted wave packet in some case may end up with an energy lower than the barrier, a difficulty is noticed in guaranteeing the energy conservation when the energies of different exit channels, e.g. of transmission and reflection, are individually measured. To overcome these issues for a description of quantum tunneling is still a challenging problem. This article mainly treats the same system with the same model as in the paper Hasegawa, Hagino and Tanimura (2020) [1]. However, we reach different conclusions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The cluster structures of the excited states in 11B are studied by analyzing the isoscalar monopole and quadrupole strengths in the reaction at . The excitation strengths are compared with the predictions by the shell-model and antisymmetrized molecular-dynamics (AMD) calculations. The large monopole strength for the state at is well described by the AMD calculation and is suggested to be an evidence for a well developed cluster structure. [Copyright &y& Elsevier]

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 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 $3/2^-_3$ state at Ex = 8.56 MeV is well described by the AMD calculation and is an evidence for a developed 2α + t cluster structure. [ABSTRACT FROM AUTHOR]

In order to calculate nuclear collisions as dynamics of quantum many-nucleon systems, we have developed a microscopic approach called antisymmetrized molecular dynamics (AMD). The original idea of AMD is to use Gaussian wave packets for nucleons with the full antisymmetrization, so that the Pauli principle is correctly treated. The simplest time evolution of the wave packet centroids is derived from the time-dependent variational principle. Furthermore, the quantum branching into many reaction channels has been taken into account by the stochasticity of dynamics. As the source of quantum branching, we have considered not only the two-nucleon collision effect but also the splitting into wave packets of the single-particle wave function evolving in the mean field. In this article, the theoretical development of AMD is reviewed, together with several applications for cluster formation reactions, including studies of the effects of the equation of state of isospin symmetric and asymmetric nuclear matter. The close relationship between the quantum statistics of AMD and the quantum branching is also emphasized. [Copyright &y& Elsevier]