2009/11/09 by K. Dietrich, J. -J. Niez, Jean-Jacques Niez +2 · 24 citations
Chemistry · Mathematics · Physics and Astronomy · #Adiabatic process #Atomic physics #Chemistry #Classical mechanics #Degrees of freedom (physics and chemistry) #Density functional theory #Density matrix #Distribution (mathematics) #Equations of motion #Excitation #Fission #Generator (circuit theory) #High-Energy Particle Collisions Research #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Neutron #Nuclear density #Nuclear fission #Nuclear matter #Nuclear physics research studies #Nucleon #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Statistical physics #Time-dependent density functional theory #nucl-th
paper · pdf · doi:10.1016/j.nuclphysa.2009.11.004
published in Nuclear Physics A 832(3-4), 249-288 (Elsevier BV) · 33 pages, accepted in Nucl. Phys. A
arxiv created 2009/11/09 · openalex publication_date 2009/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.