Abstract
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 years2,3. 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 momentum4,5,6,7,8,9,10,11,12. 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 reactors13,14, for the study of the structure of neutron-rich isotopes15,16, and for the synthesis and stability of super-heavy elements17,18.
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Data availability
All data from which the conclusions of this paper are drawn are contained within this manuscript. All other data can be made available on reasonable request. The large quantities of raw data (approximately 120 Tb) are shared within the ν-Ball Collaboration on servers at the CNRS-IN2P3 Centre de Calcul in Lyon (https://cc.in2p3.fr). The ALTO facility of the IJC Laboratory has a transparent data management policy that complies with the relevant European directives on open data (https://ec.europa.eu/digital-single-market/en/european-legislation-reuse-public-sector-information). Raw data from the ν-Ball Collaboration will be made publicly available after a period of 5 years. Source data are provided with this paper.
Code availability
All codes used in the data analysis can be made available on reasonable request.
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Acknowledgements
We thank the staff of the ALTO facility of the IJC Laboratory, Orsay, for providing the intense, precisely focused 7Li primary beams for very long periods, thus permitting the collection of large datasets with the ν-Ball spectrometer. We thank W. Nazerewicz, S. Åberg and O. Serot for discussions of fission theory; we also thank S. Åberg and O. Serot for assistance with the theoretical interpretation of our experimental results. We thank G. Kessedijan for assistance with variance−covariance calculations. Finally, we thank the Gammapool international consortium for the loan of the germanium clover detectors used to construct the spectrometer. This work was supported by the IN2P3/CNRS, France, the STFC UK Nuclear Data Network, the STFC (grants ST/L005743/1 and ST/P005314) (PHR), the Marion Redfearn Trust (RCL). P.H.R., M.B., A. Boso and P.I. acknowledge support from the UK Department of Business, Energy and Industrial Strategy (BEIS) via the National Measurement System. P.K., P.-A.S. and J.W. acknowledge the support from BMBF under grant NuSTAR.DA 05P15RDFN1. Funding from the HORIZON2020 programme of the European Commission is acknowledged for Transnational Access to the ALTO facility under the Integrated Infrastructure Initiative, European Nuclear Science and Applications Research 2 (ENSAR2), grant agreement number 654002. A. Blazhev, R.-B.G. and N.W. acknowledge support by the German Research Foundation (DFG grant BL 1513/1-1). L.F., V.V., J.B. and V.S.-T. acknowledge funding from the Spanish MINECO via FPA2015-65035-P and RTI2018-098868-B-I00. A.A. acknowledges funding Spanish MINECO via FPA2017-83946-C2-1-P and Ministerio de Ciencia e Innovacion grant PID2019-104714GB-C21. B.F. acknowledges funding from the Polish National Science Centre under contracts 2014/14/M/ST2/00738 and 2013/08/M/ST2/00257. M.P. acknowledges funding from the Polish National Science Centre under contracts UMO-2019/33/N/ST2/03023, UMO-2020/36/T/ST2/00547 and A.K., K.M. and E.A. under contract UMO-2015/18/E/ST2/00217. D.G. acknowledges funding from the Norges Forskningsråd (Research Council of Norway) 263030. S.L., G.B., C.P., S.Z., L.W.I, A.G. and S.B. acknowledge funding from the Italian Istituto Nazionale di Fisica Nucleare (INFN).
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J.N.W. participated in the construction of the ν-Ball spectrometer, contributed to the experimental data taking, organised the ν-Ball international collaboration, performed the analysis work presented here and wrote the main body of the paper. D.G. helped with experimental and theoretical discussions, interpretation of results, manuscript preparation and resubmissions, calculations, plots and bibliography. D.T. constructed the spectrometer, calibrated and optimized the spectrometer, kept the spectrometer running, contributed to the experimental data taking, performed data processing of the large quantities of triggerless data and helped distribute it to the collaboration. M.L. organized the ν-Ball project, led the construction of the spectrometer, organised the experimental campaign, kept the spectrometer running, contributed to the experimental data taking and measured ν-Ball performances. M.R., N.J., R.C., G.H., R.L. and R.-B.G. helped with the cabling of the ν-Ball spectrometer, supported the running of the spectrometer (filling with liquid nitrogen, monitoring detectors, and so on), calibrated and optimized the spectrometer, contributed to the experimental data taking and performed offline data analysis. D.E. developed and helped deploy the digital electronics used for the ν-Ball Data Acquisition System). L.G. developed and deployed the 252Cf ionization chamber. S.O., C.S., T.K., P.H.R., A. Blazhev, N.W., S.L., B.F., A.A., M.F., L.F. and others contributed to the theoretical discussions and interpretation of results. S.S. helped with organization, discussions and interpretation, bibliography and manuscript preparation. F.Z. carried out fragment decay simulations using the RAINIER code. All listed collaborators helped keep the experiment, the spectrometer and the data acquisition systems running over the period of 7 weeks during which the data were collected.
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Extended data figures and tables
Extended Data Fig. 1 γ-ray coincidence spectra for 140Xe.
Spectra are gated by the 2+→0+ transition for the three different fissioning systems studied in this work. The spins of states emitting the yrast sequence of transitions are marked. Strong γ-rays from the binary partner fragments are indicated. γ-rays from fragment partners in 252Cf(SF), such as 112Ru, were detected in flight and are thus not visible owing to Doppler broadening. The 252Cf(SF) spectrum has many fewer counts, but similar experimental sensitivity is achieved owing to the elimination of backgrounds from other processes by direct detection of the fission fragment in the ionization chamber with the γ−γ coincidences.
Extended Data Fig. 2 Coincident γ-ray spectra from the 238U(n, f) reaction gated on transitions from 140Xe emitted from states of increasing spin.
The fits to transitions decaying out of specific states of the partner nucleus 96Sr are shown in red. The 492-keV transition from the 6+ state in 96Sr in the third panel is deduced from its neighbours rather than fitted, owing to contamination. The intensity pattern is not observed to vary and the average spins in 96Sr show no notable changes. The relationships between partner spins for several more nuclei are shown in Fig. 2.
Extended Data Fig. 3 Monte Carlo simulations of events with correlated spins at scission.
Placing conditions on the minimum spin at yrast of events in fragment 2 affects the yrast distributions of event spins in fragment 1.
Extended Data Fig. 4 Examples of experimental spin distributions for a range of nuclei observed in the 238U(n, f) reaction.
Statistical uncertainties are shown. To eliminate the odd−even staggering effect and facilitate easy visualization, side-feedings of odd spins are redistributed equally between the two neighbouring even spins. The red curves are fits to the experimental data with one free parameter and are used to extract 0+ side-feedings via an iterative procedure
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Wilson, J.N., Thisse, D., Lebois, M. et al. Angular momentum generation in nuclear fission. Nature 590, 566–570 (2021). https://doi.org/10.1038/s41586-021-03304-w
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DOI: https://doi.org/10.1038/s41586-021-03304-w
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