Microscopic Theory of Nuclear Fission

TL;DR

This work surveys how microscopic, EDF-based approaches can describe nuclear fission from first principles, emphasizing the large-amplitude deformation and scission stages with a focus on actinide systems. It details static (HFB) and dynamic (TDDFT, GCM+GOA, ATDHFB) methods, the role of symmetry breaking and projection, and how PES, collective inertia, and scission configurations determine fission observables. The paper highlights spontaneous fission via WKB, fragment properties (particle numbers, deformations, spins, TXE), and fragment distributions predicted by TDGCM+GOA, including improvements from particle-number and angular momentum projections. It argues for integrating these approaches to predict cross sections and fragment yields, and outlines future directions such as uncertainty quantification, functional development, and combining TDDFT with projection methods to unify structure and reaction descriptions.

Abstract

Nuclear fission represents the ultimate test for microscopic theories of nuclear structure and reactions. Fission is a large-amplitude, time-dependent phenomenon taking place in a self-bound, strongly-interacting many-body system. It should, at least in principle, emerge from the complex interactions of nucleons within the nucleus. The goal of microscopic theories is to build a consistent and predictive theory of nuclear fission by using as only ingredients protons and neutrons, nuclear forces and quantum many-body methods. Thanks to a constant increase in computing power, such a goal has never seemed more within reach. This chapter gives an overview both of the set of techniques used in microscopic theory to describe the fission process and of some recent successes achieved by this class of methods.

Figures (8)

• Figure 1: Schematic illustration of the main physics concepts at play in fission. Potential energy surfaces (in one dimension like here: a potential energy curve) play a key role in determining the spontaneous fission probabilities, as well as the identities of the fission fragments and their distribution. The level structure above the ground state (first minimum) and the fission isomer (second minimum) will impact the fission cross sections. What is called the descent from saddle to scission involves a very slow, diabatic motion characterized by multiple level crossings and conversion between collective and intrinsic energy.
• Figure 2: Real-time evolution of the one-body density of the $^{240}$Pu asymmetric fission from TDHF+BCS calculations. The 3D surface highlights the half-saturation density (0.08 fm$^{-3}$) isosurface whereas the projected color map corresponds to a localization function of the nucleons. Figures reproduced with permission from Scamps2018 courtesy of Scamps;
• Figure 3: Logarithm of the spontaneous fission half-lives of heavy and superheavy even-even nuclei with the D1S Gogny functional. Nuclides where fission is the dominant decay mode are represented by filled symbols, those were $\alpha$ decay is dominant by open symbols. Squares indicate reflection-symmetric fission while diamonds indicate reflection-asymmetric fission. Figures reproduced with permission from Baran2015 courtesy of Warda; copyright 2015 by Elsevier.
• Figure 4: Left: Effective fission paths from the outer-turning line (brown dashed line) to scission (black dashed-dotted line) in $^{240}$Pu. Right: Contribution to the fission fragment distribution of each effective fission path Figures reproduced with permission from Sadhukhan2017 courtesy of Sadhukhan; copyright 2017 by APS.
• Figure 5: Probability distribution $\mathbb{P}(Z_{\rm R}| Z, \mathbf{q})$ of Eq. (\ref{['eq:probaZ']}) that a single scission configuration $\mathbf{q}$ contains $Z_{\rm R}$ protons. Each curve corresponds to different scission configuration for the thermal fission of $^{235}$U(n,f). Figures reproduced with permission from Verriere2021a courtesy of Verriere; copyright 2021 by APS.