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Examination of the inversion of isobaric analogue states in mirror nuclei

J. Henderson and S. R. Stroberg
Phys. Rev. C 102, 031303(R) – Published 28 September 2020
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    Abstract

    A recent study by Hoff and collaborators [Nature (London) 580, 52 (2020)] presented evidence that the ground-state spin of Sr73 is different from that of its mirror, Br73, likely due to an inversion of the ground- and first-excited states. Here, we assess the likelihood of such an inversion arising from normal isospin-symmetry breaking and, more broadly, whether such phenomena challenge our understanding of charge-symmetry-breaking forces in atomic nuclei. By placing the result within the context of previous experimental and theoretical work we demonstrate that this inversion lies entirely within the bounds of normal isospin-symmetry-breaking behavior. We further note that, in the context of isospin, neither level inversions nor the nuclear ground state hold any special significance.

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    • Received 3 June 2020
    • Accepted 14 September 2020

    DOI:https://doi.org/10.1103/PhysRevC.102.031303

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Coulomb energies & analogue statesNuclear forces
    1. Properties
    59 ≤ A ≤ 89
    1. Techniques
    Nuclear structure & decaysShell model
    Nuclear Physics

    Authors & Affiliations

    J. Henderson1,* and S. R. Stroberg2,†

    • 1Lawrence Livermore National Laboratory, Livermore, California 94550, USA
    • 2Department of Physics, University of Washington, Seattle, Washington 98105, USA

    • *Present address: Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
    • †stroberg@uw.edu

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    Vol. 102, Iss. 3 — September 2020

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    • Figure 1
      Figure 1

      (Top) (a) Experimental and (b) Woods-Saxon theoretical energy splitting (E12N>Z) of the states in the N>Z nucleus plotted against δE12. The dashed lines in (a) and (b) indicate E12N>Z=−δE12. Points below the lines result in a state inversion in translating to the N<Z nucleus. (Bottom) Experimental (c) and theoretical (d) projections of (a) and (b), respectively. The experimental data are separated into like- and opposite-parity pairs. The theoretical calculations can only produce like-parity pairs. As shown schematically in the insets to (d), the effect of a negative δE12 is to compress and potentially invert the level spacing in the N<Z nucleus, whereas a positive value causes their spacing to expand.

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    • Figure 2
      Figure 2

      Calculated probability that a pair of states with energy difference E12N>Z will invert. Probabilities are shown for like- and opposite-parity pairs as well as for the shell-model results. Assuming strong correlations between states within a nucleus, relative uncertainties are calculated as Np/Np, where Np is the number of mirror systems that exhibit same- and opposite-parity pairs. Also shown are two examples of observed splittings due to isospin-symmetry-breaking phenomena: the 2− and 1− states in F16−N16, and the 1/2+ and 1/2− states in the N13−C13 mirror pair [9, 10]. The 27-keV energy splitting in Br73 is highlighted. We also indicate other likely cases for ground-state inversion but emphasize that these inversions would not provide more insight than any other mirror energy shifts with regard to isospin-symmetry breaking.

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