Critical assessment of the current implementations of the generator coordinate method for fission and heavy-ion reactions
Phys. Rev. C 114, 024606 – Published 17 August, 2026
DOI: https://doi.org/10.1103/2z3h-12hs
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. The eGCM framework opens the possibility to evaluate time-dependent lower bounds on the entropy in nuclear reactions and induced fission in particular, and thus on the evolution toward “thermalization” or equilibration. The eGCM framework is well suited to extract in a microscopic approach the induced fission cross sections, which are notoriously difficult to model.
