Abstract
We review the recent progress on studying the nuclear collective dynamics by solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice Hamiltonian method treating the collision term by the full-ensemble stochastic collision approach. This lattice BUU (LBUU) method has recently been developed and implemented in a GPU parallel computing technique, and achieves a rather stable nuclear ground-state evolution and high accuracy in evaluating the nucleon-nucleon (NN) collision term. This new LBUU method has been applied to investigate the nuclear isoscalar giant monopole resonances and isovector giant dipole resonances. While the calculations with the LBUU method without the NN collision term (i.e., the lattice Hamiltonian Vlasov method) describe reasonably the excitation energies of nuclear giant resonances, the full LBUU calculations can well reproduce the width of the giant dipole resonance of $^{208}$Pb by including a collisional damping from NN scattering. The observed strong correlation between the width of nuclear giant dipole resonance and the NN elastic cross section suggests that the NN elastic scattering plays an important role in nuclear collective dynamics, and the width of nuclear giant dipole resonance provides a good probe of the in-medium NN elastic cross section.
Highlights
Transport models deal with the time evolution of the Wigner function or phase-space distribution function f (r, p, t) that arises from the Wigner representation of the Schrödinger equation [1, 2], and provide a successful semi-classical time-dependent approach to studying nuclear dynamics, especially with regard to heavy-ion collisions (HICs)
The resulting lattice BUU (LBUU) framework has the following features: (1) a smearing of the local density, which is commonly used in transport models to obtain a smooth mean field, is included self-consistently in the equations of motion through the lattice Hamiltonian (LH) method; (2) the ground state of a nucleus is obtained by varying the total energy with respect to the nucleon density distribution based on the same Hamiltonian that governs the system evolution; (3) the NN collision term in the BUU equation is implemented through a full-ensemble stochastic collision approach
In order to calculate the nuclear collective motions accurately with the BUU equation, the present LBUU framework includes the following features: (1) the smearing of the local density is incorporated in the equations of motion selfconsistently through the lattice Hamiltonian method; (2) the initialization of a ground state nucleus is carried out according to a nucleon radial density distribution obtained by varying the same Hamiltonian that governs the evolution; (3) the NN collision term in the BUU equation is implemented through a full-ensemble stochastic collision approach; (4) highperformance GPU parallel computing is employed to increase the computational efficiency
Summary
Transport models deal with the time evolution of the Wigner function or phase-space distribution function f (r, p, t) that arises from the Wigner representation of the Schrödinger equation [1, 2], and provide a successful semi-classical time-dependent approach to studying nuclear dynamics, especially with regard to heavy-ion collisions (HICs). Pauli blocking is intimately related to the collisional damping and the width of nuclear giant resonances in the transport model calculations In this sense, studying the nuclear collective motion provides an ideal way to examine and improve transport models, since the effects of several deficiencies, such as the inaccurate treatment of Pauli blocking, are more pronounced in nuclear collective dynamics with small-amplitude oscillations. The resulting LBUU framework has the following features: (1) a smearing of the local density, which is commonly used in transport models to obtain a smooth mean field, is included self-consistently in the equations of motion through the lattice Hamiltonian (LH) method; (2) the ground state of a nucleus is obtained by varying the total energy with respect to the nucleon density distribution based on the same Hamiltonian that governs the system evolution; (3) the NN collision term in the BUU equation is implemented through a full-ensemble stochastic collision approach.
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