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Theoretical description of fission yields: Toward a fast and efficient global model

Jhilam Sadhukhan, Samuel A. Giuliani, and Witold Nazarewicz
Phys. Rev. C 105, 014619 – Published 20 January 2022
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  • INTRODUCTION
  • FORMALISM
  • RESULTS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Background: A quantitative microscopic understanding of the fission-fragment yield distributions represents a major challenge for nuclear theory as it involves the intricate competition between large-amplitude nuclear collective motion and single-particle nucleonic motion.

    Purpose: A recently proposed approach to global modeling of fission fragment distributions is extended to account for odd-even staggering in charge yields and for neutron evaporation.

    Method: Fission trajectories are obtained within the density functional theory framework, allowing for a microscopic determination of the most probable fission prefragment configurations. Mass and charge yield distributions are constructed by means of a statistical approach rooted in a microcanonical ensemble.

    Result: We show that the proposed hybrid model can reproduce experimental mass and charge fragment yields, including the odd-even staggering for a wide range of fissioning nuclei. Experimental isotopic yields can be described within a simple neutron evaporation scheme. We also explore fission fragment distributions of exotic neutron-rich and superheavy systems and compare our predictions with other state-of-the art global calculations.

    Conclusion: Our paper suggests that the microscopic rearrangement of nucleons into fission fragments occurs well before the scission and that the subsequent dynamics is mainly driven by the thermal excitations and bulk features of the nuclear binding. The proposed simple hybrid approach is well suited for large-scale calculations involving hundreds of fissioning nuclei.

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    • Received 10 June 2021
    • Revised 14 December 2021
    • Accepted 11 January 2022

    DOI:https://doi.org/10.1103/PhysRevC.105.014619

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    FissionNuclear astrophysicsNuclear bindingNuclear density functional theory
    Nuclear Physics

    Authors & Affiliations

    Jhilam Sadhukhan1,2, Samuel A. Giuliani3,4,5, and Witold Nazarewicz6

    • 1Physics Group, Variable Energy Cyclotron Centre, Kolkata 700064, India
    • 2Homi Bhabha National Institute, Mumbai 400094, India
    • 3FRIB Laboratory, Michigan State University, East Lansing, Michigan 48824, USA
    • 4European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*-FBK), Trento, I-38123, Italy
    • 5Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom
    • 6Department of Physics and Astronomy, FRIB Laboratory, Michigan State University, East Lansing, Michigan 48824, USA

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    Issue

    Vol. 105, Iss. 1 — January 2022

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    Images

    • Figure 1
      Figure 1

      Schematic of energy sharing and its evolution along the fission pathway for spontaneous fission (adapted from Ref. [38]). In thermal fission, the excess energy (∼6MeV) is shared among the prescission collective kinetic energy of the fragments Epresc and the residual thermal energy Er. EC and Edef are the Coulomb and deformation energies, respectively, and TKE is the total kinetic energy of the fragments. See the text for details.

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    • Figure 2
      Figure 2

      Calculated mass (left panels) and charge (right panels) distributions of fission fragments using the model described in this paper (dark bands), the SkM* mass table (light band), and AME2020 experimental masses (blue pattern). Experimental yields are marked by circles [6, 52]. Widths in the calculated results come from two-particle uncertainty [36].

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    • Figure 3
      Figure 3

      Pu239(nth,f) mass (left panels) and charge (right panels) fission fragment distributions calculated using the model described in this paper for different values of heavy fragment (β2H) and light fragment (β2L) deformations. These are obtained without two-particle uncertainties.

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    • Figure 4
      Figure 4

      Calculated mass (left panels) and charge (right panels) fission fragment distributions using our model for Ermax=20MeV (solid blue band), 30 MeV (horizontal pattern), and 40 MeV (vertical pattern). Experimental yields are marked by circles [6, 52].

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    • Figure 5
      Figure 5

      Fission properties of Fm264. Nucleon localization functions for (a) neutrons and (b) protons calculated at the prescission configuration. Dashed lines mark the prefragment centers. The predicted mass and charge fragment distributions are shown in panels (c) and (d), respectively.

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    • Figure 6
      Figure 6

      Total neutron multiplicities ν¯tot for different fissioning systems as a function of Ermax. Dashed and dash-dotted lines are ν¯tot obtained from the talys code [55] for Enth=1eV using the Hauser-Feshbach formalism and the gef fission yields model [56], respectively. The values of Ermax corresponding to measured values of ν¯tot [57] are indicated by arrows.

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    • Figure 7
      Figure 7

      Calculated secondary (postneutron emission) mass (left panels) and charge (right panels) fission fragment distributions using our model (blue bands), the BSM [18] (gray dashed lines), and the SPM [51] (black dashed lines) models. Red (circle) and blue (triangle) symbols show experimental data: (a) and (b) [6]; (c) and (d) [52]; (e) [58], (f) [7]; (g) and (h) [59]; (i) and (j) [60, 61]; (k) and (l) [62]; (m) and (n) [59]. Only light-fragment data are available for (a)–(f).

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    • Figure 8
      Figure 8

      Odd-even difference δY in charge yields for α=0.31 (blue band), 0.41 (vertical pattern), and 0.51 (horizontal pattern) as a function of the Coulomb factor Z2/A1/3. Red dots show experimental data [6, 52, 59]. The dashed line is δY obtained from the SPM [51].

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    • Figure 9
      Figure 9

      Distribution of heavy fragments on the N−Z plane calculated in our model.

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    • Figure 10
      Figure 10

      Predicted charge polarization of U235(nth,f) heavy fragment from our model (solid line), BSM model (dashed line), and SPM (dashed-dot line). Open circles show experimental data [6].

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    • Figure 11
      Figure 11

      Partial fragment yields for fission of Pu240 induced by thermal neutrons, Pu239(nth,f), for different fragment isotopes. Secondary (following neutron evaporation) yields calculated for a single Ermax=32MeV (light gray lines and horizontal patterns), average 〈Ermax〉=32MeV (gray lines and vertical patterns), and subsequent Gaussian convolution with σ=1 (black lines and bands) are compared with experimental data (symbols) [67].

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    • Figure 12
      Figure 12

      Fission-fragment mass (left panels) and charge (right panels) yields calculated for Ermax=40MeV. Primary yields are obtained with (short-dashed lines) and without (long-dashed lines) the pairing term, and secondary yields (dashed-dot lines) are obtained with the pairing term.

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    • Figure 13
      Figure 13

      Fragment charge distributions of Pu254, Fm290, and Og294 obtained in this paper (blue bands) and predicted in Ref. [36] by neglecting OES (red dashed bands). Predictions of BSM [18] and SPM [51] models are shown by dashed and dashed-dot lines, respectively.

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