A critical assessment of the current implementations of the Generator Coordinate Method

Abstract

The generator coordinate method (GCM) was introduced in nuclear physics by Wheeler and independently by Peierls and their collaborators in 1950s and it is still one of the most used approximations for treating nuclear large-amplitude collective motion. GCM was inspired by similar methods introduced in molecular and condensed-matter physics in the late 1920s, after the Schrödinger equation became the tool of choice to describe quantum phenomena. The interest in the 1983 extension of GCM suggested by Reinhard, Cusson, and Goeke, which includes the internal excitations (absent in the initial GCM formulation), was revived in recent years. Unfortunately, this newer version of the time-dependent GCM framework has flaws that prevent it from describing correctly many anticipated features, in particular interference and entanglement, which can play an important role in fission and many-nucleon transfer reactions. I present here an alternative formulation, the enhanced GCM (eGCM), which is free of the difficulties encountered in previous GCM implementations and which is relevant for fission and many-nucleon transfer in heavy-ion reactions, and which can be used in either static or time-dependent eGCM formulations. In the eGCM framework, the corresponding many-body wave functions have a much more complex structure, and this framework is equivalent to a configuration-interaction approach in the continuum for nuclear reactions. The eGCM is aimed at being used in the microscopic description of heavy-ion reactions and fission in particular. ....

published version

References in corpus (35)

• Camparison of the Hanbury Brown-Twiss effect for bosons and fermions
• Synthesis of superheavies: State of affairs and outlooks
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• The sign of the overlap of HFB wave functions
• Total Prompt Energy Release in the Neutron-Induced Fission of 235-U, 238-U, and 239-Pu
• TDHF Theory and Its Extensions for the Multinucleon Transfer Reaction: a Mini Review
• Theory of Nuclear Fission
• A 4-dimensional Langevin approach to low-energy nuclear fission of ${}^{236}$U
• Generation of fragment angular momentum in fission
• Fission fragments intrinsic spins and their correlations
• Event-by-event study of prompt neutrons from 239Pu(n,f)
• The time-dependent generator coordinate method in nuclear physics
• Study of angular momentum effects in fission
• Formation and distribution of fragments in the spontaneous fission of 240Pu
• Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength
• Measures of complexity and entanglement in fermionic many-body systems
• Entanglement entropy, single-particle occupation probabilities, and short-range correlations
• Triaxial shape fluctuations and quasiparticle excitations in heavy nuclei
• Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy
• Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories
• Generalized time-dependent generator coordinate method for induced fission dynamics
• Neck Rupture and Scission Neutrons in Nuclear Fission
• Stepping into the Sea of Instability: The New Sub-us Superheavy Nucleus 252Rf
• Generalized time-dependent generator coordinate method for small and large amplitude collective motion
• Spatial orientation of the fission fragment intrinsic spins and their correlations
• Nuclear states projected from a pair condensate
• Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation
• Nuclear Quantum Many-Body Dynamics: From Collective Vibrations to Heavy-Ion Collisions (2nd edition)
• Quantum fluctuations induce collective multiphonons in finite Fermi liquids
• Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization
• Multiconfigurational time-dependent density functional theory for atomic nuclei: Technical and numerical aspects
• Non-Markovian character and irreversibility of real-time quantum many-body dynamics
• Time-Dependent Density Functional Theory Description of ${}^{238}$U(n,f), ${}^{240,242}$Pu(n,f) and ${}^{237}$Np(n,f) Reactions
• Non-Equilibrium Aspects of Fission Dynamics within the Time Dependent Density Functional Theory