Least action and the maximum-coupling approximations in the theory of spontaneous fission

Abstract

We investigate the dynamics of spontaneous fission in a configuration-interaction (CI) approach. In that formalism the decay rate is governed by an effective interaction coupling the ground-state configuration and a fission doorway configuration, with the interaction strength determined by inverting a high-dimensioned CI Hamiltonian matrix that may have a block-tridiagonal structure. It is shown that the decay rate decreases exponentially with the number of blocks at a rate determined by the largest eigenvalue of a matrix in the block space for Hamiltonians with identical off-diagonal blocks. The theory is greatly simplified by approximations similar in spirit to the adiabatic and the least-action approximations in continuum representations. Here each block is replaced by a single matrix element. While the adiabatic reduction underestimates the coupling, a reduction based on a maximum-coupling approximation works well in a schematic CI model.

arXiv comment9 pages, 5 figures. To appear in Phys. Rev. C

References in corpus (12)

• Microscopic Theory of Nuclear Fission: A Review
• Dynamic versus static fission paths with realistic interactions
• Microscopic description of fission in Uranium isotopes with the Gogny energy density functional
• Least action description of spontaneous fission in fermium and nobelium nuclei based on the Gogny energy density functional
• Composite-particle decay widths by the generator coordinate method
• Scission Dynamics with K Partitions
• Decay widths at the scission point in nuclear fission
• A schematic reaction-theory model for nuclear fission
• Diabatic scission paths
• A microscopic model for spontaneous fission: validity of the adiabatic approximation
• A new approach to barrier-top fission dynamics
• Density functional theory for nuclear fission -- a proposal

Cited by in corpus (5)

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• Schematic model for induced fission in a configuration-interaction approach
• Non-equilibrium Green's function approach to low-energy fission dynamics: fluctuations in fission reactions
• Microscopic Theory of Nuclear Fission