FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation☆
Introduction
A completely microscopic description of the fission process is a major challenge for nuclear theory. Fission is a time-dependent, non-equilibrium, quantum many-body problem where more than 200 nucleons interact over large time scales (typically s) in a coherent way to break the system into two or more fragments. Of particular interest to applications of fission in either science (nucleosynthesis, superheavy science) or applications (energy production) are the properties of the fission fragments, in particular their charge and mass distributions. One of the most effective approaches to computing such observables in a quantum-mechanical framework is the Gaussian overlap approximation (GOA) of the time-dependent generator coordinate method (TDGCM) [[1], [2]]. This approach relies on the energy density functional (EDF) formalism and reduces the dynamics of the complete system to a local, collective Schrödinger-like equation involving only a few arbitrary degrees of freedom referred to as collective variables. This approach was originally introduced for the description of low-energy neutron-induced fission in the 1980s [[3], [4], [5]] but was not applied on a large scale because of computational limitations at the time. Thanks to progress in computing capabilities, the TDGCM+GOA approach to fission has been recently applied to predictions of fission fragment distributions in 2-dimensional collective space [[6], [7], [8], [9], [10]]. These studies, together with others [11], have highlighted the need to take into account additional degrees of freedom in order to increase the accuracy of calculations. The first version of FELIX was a first step towards the goal of providing the community with a numerical tool capable of solving the TDGCM+GOA equation for an arbitrary number of collective variables [12]. In this paper, we present a major upgrade of FELIX which contains both new physics features and much improved numerical performances.
In Section 2, we review the new and upgraded features of FELIX-2.0 compared to the previous version. The convergence properties of the different numerical methods implemented are benchmarked in Section 3. We also present in the same section a comparison of the performances between FELIX-2.0 and FELIX-1.0. The Section 4 is finally devoted to the practical installation and usage of the package.
Section snippets
The TDGCM+GOA with a metric
The time-dependent extension to the generator coordinate method provides an appropriate formalism to describe the slow and large amplitude motion of nuclei [[2], [13]]. In this approach, we assume that the many-body state of the fissioning system takes the generic form The set is made of known many-body states parametrized by a vector of continuous variables . Each of these is a collective variable and must be chosen based on the physics of the
Benchmarks
In this section, we investigate the convergence properties and overall performance of the numerical methods implemented in FELIX-2.0. This analysis is performed based on the results of three benchmark runs. The first one simulates an oscillating system in a 2-dimensional harmonic oscillator and its exact solution is known analytically. The other two consist in realistic calculations of the low-energy fission yields of Fm and Pu in a collective space.
Usage of FELIX-2.0
The package is composed of the following directories and files:
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README.md, AUTHORS, LICENSE: contains the basic instructions about how to build, use and distribute this package;
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Makefile: a standard GNU makefile to build the solver, the tools, the tests, and the documentation;
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src/: C++ source files of the TDGCM solver and of the tools;
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tools/: additional C++ and Python source files to handle the inputs and outputs of the TDGCM solver;
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tests/: a unitary test suite for the package as
Acknowledgments
This software is based on pugixml library (http://pugixml.org). Pugixml is Copyright (C) 2006–2015 Arseny Kapoulkine. This work was partly performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Oak Ridge Leadership Computing Facility located in
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2023, Nuclear Physics ATheory of nuclear fission
2022, Progress in Particle and Nuclear PhysicsRole of pairing correlations in the fission process
2023, Physical Review C
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This paper and its associated computer program are available via the Computer Physics Communication homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655).