The time-dependent generator coordinate method in nuclear physics

Abstract

The emergence of collective behaviors and the existence of large amplitude motions are both central features in the fields of nuclear structure and reactions. From a theoretical point of view, describing such phenomena requires increasing the complexity of the many-body wavefunction of the system to account for long-range correlations. One of the challenges, when going in this direction, is to keep the approach tractable within our current computational resources while gaining a maximum of predictive power for the phenomenon under study. In the Generator Coordinate Method (GCM), the many-body wave function is a linear superposition of (generally non-orthogonal) many-body states (the generator states) labeled by a few collective coordinates. Such a method has been widely used in structure studies to restore the symmetries broken by single-reference approaches. In the domain of reactions, its time-dependent version (TDGCM) has been developed and applied to predict the dynamics of heavy-ion collisions or fission where the collective fluctuations play an essential role. In this review, we present the recent developments and applications of the TDGCM in nuclear reactions. We recall the formal derivations of the TDGCM and its most common approximate treatment, the Gaussian Overlap Approximation. We also emphasize the Schrödinger Collective-Intrinsic Model (SCIM) variant focused on the inclusion of quasiparticle excitations into the description. Finally, we highlight several exploratory studies related to a TDGCM built on time-dependent generator states.

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Cited by in corpus (28)

• Future of Nuclear Fission Theory
• Theory of Nuclear Fission
• Microscopic Calculation of Fission Product Yields with Particle Number Projection
• Time-dependent generator coordinate method study of fission: dissipation effects
• Description of the multidimensional potential energy surface in fission of ${}^{252}$Cf and ${}^{258}$No
• Generalized time-dependent generator coordinate method for induced fission dynamics
• Theoretical description of fission yields: towards a fast and efficient global model
• Fission dynamics, dissipation and clustering at finite temperature
• Improvements to the macroscopic-microscopic approach of nuclear fission
• Extended time-dependent generator coordinate method study of induced fission (II): total kinetic energy distribution
• Generalized time-dependent generator coordinate method for small and large amplitude collective motion
• Generation, dynamics, and correlations of the fission fragments' angular momenta
• Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation
• Quantum fluctuations induce collective multiphonons in finite Fermi liquids
• Nuclear Quantum Many-Body Dynamics: From Collective Vibrations to Heavy-Ion Collisions (2nd edition)
• Microscopic Calculation of Fission Product Yields for Odd-Mass Nuclei
• Smoothing of one- and two-dimensional discontinuities in potential energy surfaces
• Building Surrogate Models of Nuclear Density Functional Theory with Gaussian Processesand Autoencoders
• 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
• Three-dimensional potential energy surface for fission of ${}^{236}$U within covariant density functional theory
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model
• Microscopic theory of angular momentum distributions across the full range of fission fragments
• Impact of finite-range spin-orbit and tensor terms in Gogny EDF
• Microscopic self-consistent description of induced fission: dynamical pairing degree of freedom
• A critical assessment of the current implementations of the Generator Coordinate Method
• Restoring Broken Symmetries for Nuclei and Reaction Fragments
• Microscopic Theory of Nuclear Fission