Microscopic Transport Theory of Nuclear Processes

Abstract

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.

33 pages, accepted in Nucl. Phys. A

References in corpus (1)

• Structure properties of ${}^{226}$Th and ${}^{256,258,260}$Fm fission fragments: mean field analysis with the Gogny force

Cited by in corpus (13)

• Microscopic Theory of Nuclear Fission: A Review
• Future of Nuclear Fission Theory
• Theory of Nuclear Fission
• Microscopic and non-adiabatic Schrödinger equation derived from the Generator Coordinate Method based on 0 and 2 quasiparticle HFB states
• From Asymmetric to Symmetric Fission in the Fermium Isotopes within the Time-Dependent GCM Formalism
• Description of Induced Nuclear Fission with Skyrme Energy Functionals: II. Finite Temperature Effects
• Microscopic Calculation of Fission Product Yields with Particle Number Projection
• Time-dependent generator coordinate method study of fission: dissipation effects
• Fission dynamics, dissipation and clustering at finite temperature
• Generalized time-dependent generator coordinate method for small and large amplitude collective motion
• Multiconfigurational time-dependent density functional theory for atomic nuclei: Technical and numerical aspects
• Time-dependent density functional theory study of induced-fission dynamics of ${}^{226}$Th
• Microscopic Theory of Nuclear Fission