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arXiv 0911.1674nucl-th
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核过程的微观输运理论

Microscopic Transport Theory of Nuclear Processes

K. Dietrich, J. -J. Niez, J. -F. Berger

摘要:

我们制定了一个微观理论的衰变的复合核通过裂变,概括了早期的微观方法的裂变动力学的绝热假设的框架内进行。该方法基于约束Hartree-Fock-Bogoliubov方法和生成坐标方法,要求核子-核子有效相互作用作为唯一输入量。基本的假设是,缓慢演变的核形状必须明确地处理,而快速随时间变化的内禀激发可以处理的统计近似。更准确地说,我们引入了一个参考密度,它代表了缓慢演变的核形状由一个减少的密度矩阵和状态的内在激发的正则分布在每个给定的形状的核。核密度分布的形状是由参数(“生成坐标”)描述的,而不是由除了完整的核子自由度之外引入的“过剩”自由度描述的。我们首先推导出一个严格的运动方程的参考密度,随后,简化这个方程的基础上的马尔可夫近似。出现在正则分布中的温度是由这样的要求确定的,即在每个时间t,参考密度应该正确地再现给定形状参数值下的平均激发能。所得到的“局部”温度方程必须与约化密度矩阵的运动方程一起求解。

英文摘要:

We formulate a microscopic theory of the decay of a compound nucleus through fission which generalizes earlier microscopic approaches of fission dynamics performed in the framework of the adiabatic hypothesis. It is based on the constrained Hartree-Fock-Bogoliubov procedure and the Generator Coordinate Method, and requires an effective nucleon-nucleon interaction as the only input quantity. The basic assumption is that the slow evolution of the nuclear shape must be treated explicitely, whereas the rapidly time-dependent intrinsic excitations can be treated by statistical approximations. More precisely, we introduce a reference density which represents the slow evolution of the nuclear shape by a reduced density matrix and the state of intrinsic excitations by a canonical distribution at each given shape of the nucleus. The shape of the nuclear density distribution is described by parameters ("generator coordinates"), not by "superabundant" degrees of freedom introduced in addition to the complete set of nucleonic degrees of freedom. We first derive a rigorous equation of motion for the reference density and, subsequently, simplify this equation on the basis of the Markov approximation. The temperature which appears in the canonical distribution is determined by the requirement that, at each time t, the reference density should correctly reproduce the mean excitation energy at given values of the shape parameters. The resulting equation for the "local" temperature must be solved together with the equations of motion obtained for the reduced density matrix.

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