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 Schr\"odinger 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.
Highlights
Since the early days of nuclear physics, the variety of shapes that atomic nuclei can take is a core notion of our interpretation of nuclear processes
Goeke et al studied the 16O+16O collision in the framework of the quantized adiabatic time-dependent Hartree-Fock approach which yields a collective equation of motion identical to the one of Time-Dependent Generator Coordinate Method (TDGCM)+GAUSSIAN OVERLAP APPROXIMATION (GOA) [60]
Other techniques, such as the Schrödinger Collective-Intrinsic Model (SCIM) and TDGCM based on time-dependent generator states, are promising avenues that we discuss in this review
Summary
Since the early days of nuclear physics, the variety of shapes that atomic nuclei can take is a core notion of our interpretation of nuclear processes. The TDGCM in Nuclear Physics of the fragment distribution produced by fission The incorporation of these fluctuations into a quantum description leads to a many-body wave function describing the system that is a mixture of states with different shapes. The GCM proceeds with an alternative approach that introduces collective deformations DoFs without relying on a transformation of the set of nucleons DoFs. The first step of the method consists in building a family of many-body states { φ(q) } parameterized by a vector of labels q = q0 · · · qm−1. A standard procedure to handle nuclear deformations consists in the definition of the generator states as the solutions of a constrained Hartree-Fock-Bogoliubov equation In this approach, each collective coordinate is typically associated with a multipole moment observable
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