The purpose of this section is to summarise the main recommendations of this report that reflect challenges facing nuclear fission theory. The high-level recommendations, addressing the general challenges facing the field of microscopic nuclear fission theory, are listed in section 9.1. More detailed recommendations, pertaining to specific subareas, are listed in section 9.2. The ordering does not imply any priority.
General recommendations relevant to the field as a whole follow below. The numbers in brackets refer to key sections pertaining to individual recommendations.
Quantitative predictions require quantified input. It is essential to develop interactions and energy density functionals that are specifically tailored for the purpose of modelling fission. Of particular importance are the interaction components responsible for nuclear deformability and the pairing interactions that control the level of adiabaticity. It would be desirable to develop several quantified interactions/functionals for fission studies for (i) benchmarking purposes and (ii) to assess statistical and systematic uncertainties. Moreover, statistical calibration of interactions for fission should be carried out that would determine the sensitivity of parameters to key experimental constraints. [6, 4]
Considering limited resources, in order to maximise progress it is important to identify the essential ingredients in fission theory that require careful microscopic treatment and more robust ingredients that are necessary for a correct description of fission dynamics, but perhaps require less sophisticated modelling at the early stage of development. An example of essential ingredient is the PES. A more robust quantity is dissipation tensor; indeed many properties of predicted fission yields are found insensitive to large variations of the dissipation strength. [4]
There exist microscopic, yet greatly unutilised, extensions of current models of non-adiabatic large-amplitude collective motion that can be adopted to modern studies of nuclear fission. Many of those techniques involve algorithmic developments and significant computational capabilities. This includes: (i) Description of fission trajectories in the full TDHFB manifold; (ii) Inclusion of non-adiabatic couplings between many-body configurations; and (iii) Consistent treatment of quantum and statistical fluctuations. [3, 4, 5, 8]
Fission is a complex phenomenon with a multitude of final channels and measured observables. In order not to be misled by a good agreement with limited classes of data, it is advisable to develop a comprehensive approach to fission observables. This is important because different elements of fission models are sensitive to different data. For instance, good reproduction of fission yields does not guarantee quality predictions of TKEs. In this context, priority should be given to modelling of measured quantities, not unobservables, which are primarily of theoretical interest. [7, 2.2]
To be able to describe fission observables, a connection between models of fission dynamics based on the intrinsic-system concept, and the symmetry-conserved observables studied experimentally (particle number, angular momentum, parity) needs to be established. There are two possible avenues to achieve this goal. One is based on a reaction-theory approach that is explicitly formulated in the laboratory reference frame. Another way is by means of projection techniques. In both cases, many foundational developments are needed. [3,7]
To model various kinds of fission, it is important to develop a unified description of initial states. At various instances of the fission phenomenon (from spontaneous fission to fission induced by fast probes; from low-energy to high-energy fission), the entrance channel should be properly described. This includes the realistic modelling of compound nucleus for neutron-induced fission as well as specific nuclear states populated in photofission or -decay. In the latter case, implementation of flexible QRPA methods (for any shape, for arbitrary multipole and charge-exchange channels, and indiscriminately for even-even, odd, and odd-odd systems) is recommended. [5]
Future exascale computing ecosystems will offer a unique opportunity for microscopic modelling of nuclear fission. To achieve this goal, this report recommends the development of specific computing capabilities and launching a library of general-purpose fission software based on novel algorithms and programming that can efficiently utilise modern computing infrastructures. To this end, collaborations with computer scientists, applied mathematicians, and data scientists will be needed to (i) develop open-source, modular nuclear solvers and (ii) leverage high-performance computing and statistical machine learning. [8.1]
Establish databases of microscopic fission output for further processing. This can include various HFB and TDHFB results (PESs, fission pathways, fission fragment yields and properties). Having computed multi-model fission data available will be essential not only for post-processing but also for benchmarking and uncertainty quantification. [8.1.3]
A number of specific recommendations are proposed in the body of this report. The numbers in brackets refer to specific sections where individual recommendations can be found.
In the studies of SF and low-energy fission, a part of collective motion proceeds through the classically-forbidden space. The most commonly used approach is that based on the CSE and a WKB approximation, in which the tunnelling rate is obtained from the collective action calculated along an effective one-dimensional trajectory. Limitations of this approach should be studied and, depending on the outcome, extensions explored. Those include: generalisation of the one-dimensional WKB treatment to several dimensions; increasing the number of collective coordinates; or other approaches to tunnelling, such as the imaginary-time method. [3.6]
Since TDHF equations emerge as a classical field theory for interacting single-particle fields, the TDDFT approach can neither describe the motion of the system in classically-forbidden regions of the collective space nor quantum fluctuations. In the context of tunnelling, one should determine the feasibility of arriving at instanton solutions to the TDDFT fission problem and develop methods to calculate the full ATDHFB collective inertia. As far as fluctuations are concerned, this problem shows up in too-narrow fission yield distributions predicted by time-dependent theories. A possible resolution to this problem lies in the Stochastic Mean-Field approach that allows larger fluctuations in collective space. [3]
Most microscopic calculations of nuclear fission pertain to even-even nuclei. It is therefore urgent to develop a consistent theoretical framework for the fission of even-even, -odd, and odd-odd nuclei. This will require going beyond the usual blocking approximation to fully consider time-reversal symmetry-breaking effects. Odd-even staggering of fission yields is an example of a quantity that can be sensitive to such effects. [3, 7]
Classical Langevin theory has been very successful in explaining many properties of fission products. To bridge it with microscopic fission frameworks, it is important to clarify the connections between microscopic TDHFB and TDGCM with dissipative theories – to make contact with Langevin-based approaches. [3.12, 7].
An approach to fission based on reaction theory is useful, because it is explicitly formulated in the laboratory reference frame, which guarantees that the important quantum numbers are conserved. One should consider assessing the feasibility of developing a practical microscopic approach to fission based on the -matrix reaction theory. It offers a completely different calculational framework for spontaneous fission as well. [3.9]
On the way from the entrance configuration to scission, the fissioning nucleus explores the continuum of trajectories in the collective space. Current approaches explore limited sectors of this space and hence it is essential to develop methods to search for optimum fission pathways in such a way that a blind exploration of the full multi-dimensional collective space is not required. [4.1]
It would be very useful to go beyond simple constraining operators for which important configurations may be overlooked. Within the large family of density constraints, the technique that constrains the entire density distribution obtained in TDDFT is promising in that it provides a tight control of the shape. It naturally localises the system in the space of nuclear configurations, as does wave function constraints such as the -partitioning. Also, constraints based on fission observables may be useful in the study of fluctuations. [3.2.2]
The ability to compute Hamiltonian matrix elements between configurations is essential for microscopic calculations of reaction theory, level crossing dynamics, and the dissipation tensor. This capability is already included for the pairing interaction in CHFB. However, the neutron-proton interaction is ignored in current codes except for its mean-field contribution. [3.9, 3.7, 3.12.3]