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Register a new userQuantal Nucleon Diffusion I: Central Collisions of Symmetric Nuclei
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Quantal diffusion mechanism of nucleon exchange is studied in the central collisions of several symmetric heavy-ion collisions in the framework of the Stochastic Mean-Field (SMF) approach. Since at bombarding energies below the fusion barrier, di-nuclear structure is maintained, it is possible to describe nucleon exchange as a diffusion process familiar from deep-inelastic collisions. Quantal diffusion coefficients, including memory effects, for proton and neutron exchanges are extracted microscopically employing the SMF approach. The quantal calculations of neutron and proton variances are compared with the semi-classical results.
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Employing the stochastic mean-field (SMF) approach, we develop a quantal diffusion description of the multi-nucleon transfer in heavy-ion collisions at finite impact parameters. The quantal transport coefficients are determined by the occupied single-particle wave functions of the time-dependent Hartree-Fock equations. As a result, the primary fragment mass and charge distribution functions are determined entirely in terms of the mean-field properties. This powerful description does not involve any adjustable parameter, includes the effects of shell structure and is consistent with the fluctuation-dissipation theorem of the non-equilibrium statistical mechanics. As a first application of the approach, we analyze the fragment mass distribution in $^{48}mathrm{Ca}+{}^{238}mathrm{U}$ collisions at the bombarding energy $E_{text{c.m.}}=193$ MeV and compare the calculations with the experimental data.
Employing a quantal diffusion description based on the stochastic mean-field (SMF) approach, we analyze the mass distribution of the primary fragments in the collisions of ${}^{136} text{Xe}+{}^{208} text{Pb}$ system at the bombarding energy $E_text{c.m.} =526$~MeV. This quantal approach provides a good description of the primary fragment distribution without any adjustable parameter, including the effects of shell structure.
Quantal diffusion mechanism of nucleon exchange is studied in the central collisions of $^{238}$U + $^{238}$U in the framework of the stochastic mean-field (SMF) approach. For bombarding energies considered in this work, the di-nuclear structure is maintained during the collision. Hence, it is possible to describe nucleon exchange as a diffusion process for mass and charge asymmetry. Quantal neutron and proton diffusion coefficients, including memory effects, are extracted from the SMF approach and the primary fragment distributions are calculated.
As an extension of previous work, we calculate the production cross-section of heavy neutron-rich isotopes by employing the quantal diffusion description to ${}^{48} text{Ca} + {}^{238} text{U}$ collisions. The quantal diffusion is deduced from stochastic mean-field approach, and transport properties are determined in terms of time-dependent single-particle wave functions of the time-dependent Hartree-Fock (TDHF) theory. As a result, the approach allows for prediction of production cross-sections without any adjustable parameters. The secondary cross-sections by particle emission are calculated with the help of the statistical GEMINI++ code.
Symmetry breaking is an importance concept in nuclear physics and other fields of physics. Self-consistent coupling between the mean-field potential and the single-particle motion is a key ingredient in the unified model of Bohr and Mottelson, which could lead to a deformed nucleus as a consequence of spontaneous breaking of the rotational symmetry. Some remarks on the finite-size quantum effects are given. In finite nuclei, the deformation inevitably introduces the rotation as a symmetry-restoring collective motion (Anderson-Nambu-Goldstone mode), and the rotation affects the intrinsic motion. In order to investigate the interplay between the rotational and intrinsic motions in a variety of collective phenomena, we use the cranking prescription together with the quasiparticle random phase approximation. At low spin, the coupling effect can be seen in the generalized intensity relation. A feasible quantization of the cranking model is presented, which provides a microscopic approach to the higher-order intensity relation. At high spin, the semiclassical cranking prescription works well. We discuss properties of collective vibrational motions under rapid rotation and/or large deformation. The superdeformed shell structure plays a key role in emergence of a new soft mode which could lead to instability toward the $K^pi=1^-$ octupole shape. A wobbling mode of excitation, which is a clear signature of the triviality, is discussed in terms of a microscopic point of view. A crucial role played by the quasiparticle alignment is presented.
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