Nuclear fission: a review of experimental advances and phenomenology

Size limits and fission channels of doubly charged noble gas clusters

Small, highly charged liquid droplets are unstable with respect to spontaneous charge separation when their size drops below the Rayleigh limit or, in other words, their fissility parameter X exceeds the value 1. The absence of small doubly charged atomic cluster ions in mass spectra below an element-specific appearance size na has sometimes been attributed to the onset of barrierless fission at X = 1. However, more realistic models suggest that na marks the size below which the rate of fission surpasses that of competing dissociative channels, and the Rayleigh limit of doubly charged van der Waals clusters has remained unchartered. Here we explore a novel approach to form small dicationic clusters, namely by Penning ionization of singly charged noble gas (Ng) clusters that are embedded in helium nanodroplets; the dications are then gently extracted from the nanodroplets by low-energy collisions with helium gas. We observe Ngn2+ ions that are about 40% smaller than previously reported for xenon and krypton and about 20% for argon. These findings suggest that fission barriers have been underestimated in previous theoretical work. Furthermore, we measure the size distributions of fragment ions that are produced by collisional excitation of mass-selected dications. At lowest collision gas pressure, dicationic Kr and Xe clusters that are smaller than previously observed are found to evaporate an atom before they undergo highly symmetric fission. The distribution of fragments resulting from fission of small dicationic Ar clusters is bimodal.

Scission Deformation of the ^{120}Cd/^{132}Sn Neutronless Fragmentation in ^{252}Cf(sf)

We report on a study of the radiative decay of fission fragments populated via neutronless fission of ^{252}Cf(sf). Applying the double-energy method a perfect mass identification is achieved for these rare events. In the specific case of the ^{120}Cd/^{132}Sn cold fragmentation, we find that ^{132}Sn is produced in its ground state. We can therefore directly measure the excitation energy of the complementary fragment, ^{120}Cd. The reproduction of the γ-ray spectrum, measured in coincidence with the neutronless fission events, is sensitive to the angular momentum distribution of the studied primary fragment. The latter estimated using a time-dependent collective Hamiltonian model, allows us to constrain for the first time the deformation (β_{2}≃0.4) of the studied fission fragment at scission. The present work demonstrates the high potential of the understudied neutronless fission channel for extracting detailed information on both fission fragments and process.

Experimental Evidence for Common Driving Effects in Low-Energy Fission from Sublead to Actinides

Isotopic distributions of fragments from fission of the neutron-deficient ^{178}Hg nuclide are reported. This experimental observable is obtained for the first time in the region around lead using an innovative approach based on inverse kinematics and the coincidence between the large acceptance magnetic spectrometer VAMOS++ and a new detection arm close to the target. The average fragment N/Z ratio and prompt neutron M_{n} multiplicity are derived and compared with current knowledge from actinide fission. A striking consistency emerges, revealing the unexpected dominant role of the proton subsystem with atomic number between the Z=28 and 50 magic numbers. The origin of nuclear charge polarization in fission and fragment deformation at scission are discussed.

Angular momentum generation in nuclear fission

When a heavy atomic nucleus splits (fission), the resulting fragments are observed to emerge spinning¹; this phenomenon has been a mystery in nuclear physics for over 40 years^2,3. The internal generation of typically six or seven units of angular momentum in each fragment is particularly puzzling for systems that start with zero, or almost zero, spin. There are currently no experimental observations that enable decisive discrimination between the many competing theories for the mechanism that generates the angular momentum^4-12. Nevertheless, the consensus is that excitation of collective vibrational modes generates the intrinsic spin before the nucleus splits (pre-scission). Here we show that there is no significant correlation between the spins of the fragment partners, which leads us to conclude that angular momentum in fission is actually generated after the nucleus splits (post-scission). We present comprehensive data showing that the average spin is strongly mass-dependent, varying in saw-tooth distributions. We observe no notable dependence of fragment spin on the mass or charge of the partner nucleus, confirming the uncorrelated post-scission nature of the spin mechanism. To explain these observations, we propose that the collective motion of nucleons in the ruptured neck of the fissioning system generates two independent torques, analogous to the snapping of an elastic band. A parameterization based on occupation of angular momentum states according to statistical theory describes the full range of experimental data well. This insight into the role of spin in nuclear fission is not only important for the fundamental understanding and theoretical description of fission, but also has consequences for the γ-ray heating problem in nuclear reactors^13,14, for the study of the structure of neutron-rich isotopes^15,16, and for the synthesis and stability of super-heavy elements^17,18.

New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids

Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.

Isomer yields in nuclear fission

The generation of angular momentum in the fission process is still an open question. To shed light on this topic, we started a series of measurements at the IGISOL-JYFLTRAP facility in Finland. Highprecision measurements of isomeric yield ratios (IYR) are performed with a Penning trap, partly with the aim to extract average root-mean-square (rms) quantities of fragment spin distributions. The newly installed Phase-Imaging Ion-Cyclotron Resonance (PI-ICR) technique allows the separation of masses down to tens of keV, which is suffcient to disentangle many isomers. In this paper, we first summarize the previous measurements on the neutron and proton-induced fission of uranium and thorium, e.g. the odd cadmium and indium isotopes (119 ≤ A ≤ 127). The measurements revealed systematic trends as function of mass number, which stimulated further exploration. A recent measurement was performed at IGISIOL and several new IYR data will soon be published, for the first time. Secondly, we employ the TALYS nuclear-reaction code to model one of the newly measured isomer yields. Detailed GEF and TALYS calculations are discussed for the fragment angular momentum distribution in 134I.

Fission of ^{240}Pu with Symmetry-Restored Density Functional Theory

Nuclear fission plays an important role in fundamental and applied science, from astrophysics to nuclear engineering, yet it remains a major challenge to nuclear theory. Theoretical methods used so far to compute fission observables rely on symmetry-breaking schemes where basic information on the number of particles, angular momentum, and parity of the fissioning nucleus is lost. In this Letter, we analyze the impact of restoring broken symmetries in the benchmark case of ^{240}Pu.

Fission of Relativistic Nuclei with Fragment Excitation and Reorientation

Experimental studies of fission induced in relativistic nuclear collisions show a systematic enhancement of the excitation energy of the primary fragments by a factor of ∼2, before their decay by fission and other secondary fragments. Although it is widely accepted that by doubling the energies of the single-particle states may yield a better agreement with fission data, it does not prove fully successful, since it is not able to explain yields for light and intermediate mass fragments. State-of-the-art calculations are successful to describe the overall shape of the mass distribution of fragments, but fail within a factor of 2-10 for a large number of individual yields. Here, we present a novel approach that provides an account of the additional excitation of primary fragments due to final state interaction with the target. Our method is applied to the ^{238}U+^{208}Pb reaction at 1  GeV/nucleon (and is applicable to other energies), an archetype case of fission studies with relativistic heavy ions, where we find that the large probability of energy absorption through final state excitation of giant resonances in the fragments can substantially modify the isotopic distribution of final fragments in a better agreement with data. Finally, we demonstrate that large angular momentum transfers to the projectile and to the primary fragments via the same mechanism imply the need of more elaborate theoretical methods than the presently existing ones.

Employing TALYS to deduce angular momentum rootmean-square values, Jrms, in fission fragments

Fission fragments exhibit large angular momenta J, which constitutes a challenge for fission models to fully explain. Systematic measurements of isomeric yield ratios (IYR) are needed for basic nuclear reaction physics and nuclear applications, especially as a function of mass number and excitation energy. One goal is to improve the current understanding of the angular momentum generation and sharing in the fission process. To do so, one needs to improve the modeling of nuclear de-excitation.

In this work, we have used the TALYS nuclear-reaction code to relax excited fission fragments and to extract root-mean-square (rms) values of initial spin distributions, after comparison with experimentally determined IYRs. The method was assessed by a comparative study on 252Cf(sf) and 235U(nth,f). The results show a consistent performance of TALYS, both in comparison to reported literature values and to other fission codes. A few discrepant Jrms values were also found. The discrepant literature values could need a second consideration as they could possibly be caused by outdated models. Our TALYS method will be refined to better comply with contemporary sophisticated models and to reexamine older deduced values in literature.

Bayesian Evaluation of Incomplete Fission Yields

Fission product yields are key infrastructure data for nuclear applications in many aspects. It is a challenge both experimentally and theoretically to obtain accurate and complete energy-dependent fission yields. We apply the Bayesian neural network (BNN) approach to learn existing fission yields and predict unknowns with uncertainty quantification. We demonstrated that the BNN is particularly useful for evaluations of fission yields when incomplete experimental data are available. The BNN evaluation results are quite satisfactory on distribution positions and energy dependencies of fission yields.

First Direct Measurement of Isotopic Fission-Fragment Yields of ^{239}U

A direct and complete measurement of isotopic fission-fragment yields of ^{239}U has been performed for the first time. The ^{239}U fissioning system was produced with an average excitation energy of 8.3 MeV in one-neutron transfer reactions between a ^{238}U beam and a ^{9}Be target at Coulomb barrier energies. The fission fragments were detected and isotopically identified using the VAMOS++ spectrometer at the GANIL facility. The measurement allows us to directly evaluate the fission models at excitation energies of fast neutrons, which are relevant for next-generation nuclear reactors. The present data, in agreement with model calculations, do not support the recently reported anomaly in the fission-fragment yields of ^{239}U, and they confirm the persistence of spherical shell effects in the Sn region at excitation energies exceeding the fission barrier by a few mega-electron volts.

Nuclear and chemical characterization of heavy actinides

Recent progress in the production of heavy nuclei far from stability and in the studies of nuclear and chemical properties of heavy actinides is briefly reviewed. Exotic nuclear decay properties including nuclear fission of heavy nuclei, measurements of first ionization potentials of heavy actinides, and redox studies of heavy actinides are described. Brief history of discovery of the transuranium elements is also presented.

Collisions of Self-Bound Quantum Droplets

We report on the study of binary collisions between quantum droplets formed by an attractive mixture of ultracold atoms. We distinguish two main outcomes of the collision, i.e., merging and separation, depending on the velocity of the colliding pair. The critical velocity v_{c} that discriminates between the two cases displays a different dependence on the atom number N for small and large droplets. By comparing our experimental results with numerical simulations, we show that the nonmonotonic behavior of v_{c}(N) is due to the crossover from a compressible to an incompressible regime, where the collisional dynamics is governed by different energy scales, i.e., the droplet binding energy and the surface tension. These results also provide the first evidence of the liquidlike nature of quantum droplets in the large N limit, where their behavior closely resembles that of classical liquid droplets.

Impact of pear-shaped fission fragments on mass-asymmetric fission in actinides

Nuclear fission of heavy (actinide) nuclei results predominantly in asymmetric mass splits¹. Without quantum shell effects, which can give extra binding energy to their mass-asymmetric shapes, these nuclei would fission symmetrically. The strongest shell effects appear in spherical nuclei, such as the spherical 'doubly magic' (that is, both its atomic and neutron numbers are 'magic' numbers) nucleus ¹³²Sn, which contains 50 protons and 82 neutrons. However, a systematic study of fission² has shown that heavy fission fragments have atomic numbers distributed around Z = 52 to Z = 56, indicating that the strong shell effects in ¹³²Sn are not the only factor affecting actinide fission. Reconciling the strong spherical shell effects at Z = 50 with the different Z values of fission fragments observed in nature has been a longstanding puzzle³. Here we show that the final mass asymmetry of the fragments is also determined by the extra stability provided by octupole (pear-shaped) deformations, which have been recently confirmed experimentally around ¹⁴⁴Ba (Z = 56)^4,5, one of very few nuclei with shell-stabilized octupole deformation⁶. Using a quantum many-body model of superfluid fission dynamics⁷, we find that heavy fission fragments are produced predominantly with 52 to 56 protons, which is associated with substantial octupole deformation acquired on the way to fission. These octupole shapes, which favour asymmetric fission, are induced by deformed shells at Z = 52 and Z = 56. By contrast, spherical magic nuclei are very resistant to octupole deformation, which hinders their production as fission fragments. These findings may explain surprising observations of asymmetric fission in nuclei lighter than lead⁸.

Review on the progress in nuclear fission-experimental methods and theoretical descriptions

An overview is given on some of the main advances in the experimental methods, experimental results, theoretical models and ideas of the last few years in the field of nuclear fission. New approaches have considerably extended the availability of fissioning systems for the experimental study of nuclear fission, and have provided a full identification of all fission products in A and Z for the first time. In particular, the transition from symmetric to asymmetric fission around ²²⁶Th, some unexpected structures in the mass distributions in the fission of systems around Z  =  80-84, and an extended systematics of the odd-even effect in the fission fragment Z distributions have all been measured (Andreyev et al 2018 Rep. Prog. Phys. 81 016301). Three classes of model descriptions of fission presently appear to be the most promising or the most successful. Self-consistent quantum-mechanical models fully consider the quantum-mechanical features of the fission process. Intense efforts are presently being made to develop suitable theoretical tools (Schunck and Robledo 2016 Rep. Prog. Phys. 79 116301) for modeling the non-equilibrium, large-amplitude collective motion leading to fission. Stochastic models provide a fully developed technical framework. The main features of the fission-fragment mass distribution have been well reproduced from mercury to fermium and beyond (Möller and Randrup 2015 Phys. Rev. C 91 044316). However, limited computer resources still impose restrictions, for example, on the number of collective coordinates and on an elaborate description of the fission dynamics. In an alternative semi-empirical approach (Schmidt et al 2016 Nucl. Data Sheets 131 107), considerable progress in describing the fission observables has been achieved by combining several theoretical ideas, which are essentially well known. This approach exploits (i) the topological properties of a continuous function in multidimensional space, (ii) the separability of the influence of fragment shells and the macroscopic properties of the compound nucleus, (iii) the properties of a quantum oscillator coupled to a heat bath of other nuclear degrees of freedom, (iv) an early freeze-out of collective motion, and (v) the application of statistical mechanics for describing the thermalization of intrinsic excitations in the nascent fragments. This new approach reveals a high degree of regularity and allows the calculation of high-quality data that is relevant to nuclear technology without specifically adjusting the empirical data of individual systems.