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Nuclear level densities and γ-ray strength functions in Sn120,124 isotopes: Impact of Porter-Thomas fluctuations

M. Markova, A. C. Larsen, P. von Neumann-Cosel, S. Bassauer, A. Görgen, M. Guttormsen, F. L. Bello Garrote, H. C. Berg, M. M. Bjørøen, T. K. Eriksen, D. Gjestvang, J. Isaak, M. Mbabane, W. Paulsen, L. G. Pedersen, N. I. J. Pettersen, A. Richter, E. Sahin, P. Scholz, S. Siem, G. M. Tveten, V. M. Valsdottir, and M. Wiedeking
Phys. Rev. C 106, 034322 – Published 27 September 2022; Erratum Phys. Rev. C 109, 019901 (2024)
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  • INTRODUCTION
  • DETAILS OF THE EXPERIMENT AND DATA…
  • NUCLEAR LEVEL DENSITIES
  • PORTER-THOMAS FLUCTUATIONS AND γ-RAY…
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Nuclear level densities (NLDs) and γ-ray strength functions (GSFs) of Sn120,124 have been extracted with the Oslo method from proton-γ coincidences in the (p,p′γ) reaction. The functional forms of the GSFs and NLDs have been further constrained with the Shape method by studying primary γ-transitions to the ground and first excited states. The NLDs demonstrate good agreement with the NLDs of Sn116,118,122 isotopes measured previously. Moreover, the extracted partial NLD of 1− levels in Sn124 is shown to be in fair agreement with those deduced from spectra of relativistic Coulomb excitation in forward-angle inelastic proton scattering. The experimental NLDs have been applied to estimate the magnitude of the Porter-Thomas (PT) fluctuations. Within the PT fluctuations, we conclude that the GSFs for both isotopes can be considered to be independent of initial and final excitation energies, in accordance with the generalized Brink-Axel hypothesis. Particularly large fluctuations observed in the Shape-method GSFs present a considerable contribution to the uncertainty of the method and may be one of the reasons for deviations from the Oslo-method strength at low γ-ray energies and low values of the NLD (below ≈1×103–2×103MeV−1).

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    • Received 8 April 2022
    • Revised 4 August 2022
    • Accepted 9 September 2022

    DOI:https://doi.org/10.1103/PhysRevC.106.034322

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electromagnetic transitionsEnergy levelsLevel densitiesNuclear decayNuclear structure & decaysNucleon induced nuclear reactions
    1. Properties
    90 ≤ A ≤ 149
    Nuclear Physics

    Erratum

    Erratum: Nuclear level densities and γ−ray strength functions in Sn120,124 isotopes: Impact of Porter-Thomas fluctuations [Phys. Rev. C 106, 034322 (2022)]

    M. Markova, A. C. Larsen, P. von Neumann-Cosel, S. Bassauer, A. Görgen, M. Guttormsen, F. L. Bello Garrote, H. C. Berg, M. M. Bjørøen, T. K. Eriksen, D. Gjestvang, J. Isaak, M. Mbabane, W. Paulsen, L. G. Pedersen, N. I. J. Pettersen, A. Richter, E. Sahin, P. Scholz, S. Siem, G. M. Tveten, V. M. Valsdottir, and M. Wiedeking
    Phys. Rev. C 109, 019901 (2024)

    Authors & Affiliations

    M. Markova1,*, A. C. Larsen1,†, P. von Neumann-Cosel2, S. Bassauer2, A. Görgen1, M. Guttormsen1, F. L. Bello Garrote1, H. C. Berg1, M. M. Bjørøen1, T. K. Eriksen1, D. Gjestvang1, J. Isaak2, M. Mbabane1, W. Paulsen1, L. G. Pedersen1, N. I. J. Pettersen1, A. Richter2, E. Sahin1, P. Scholz3,4, S. Siem1, G. M. Tveten1, V. M. Valsdottir1, and M. Wiedeking5,6

    • 1Department of Physics, University of Oslo, N-0316 Oslo, Norway
    • 2Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
    • 3Institut für Kernphysik, Universität zu Köln, D-50937 Köln, Germany
    • 4Department of Physics, University of Notre Dame, Indiana 46556-5670, USA
    • 5Deptartment of Subatomic Physics to SSC Laboratory, iThemba LABS, Somerset West 7129, South Africa
    • 6School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa

    • *maria.markova@fys.uio.no
    • †a.c.larsen@fys.uio.no

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    Vol. 106, Iss. 3 — September 2022

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    Images

    • Figure 1
      Figure 1

      Experimental E−ΔE spectrum measured for the Sn124 isotope. The proton channel used for the data analysis is marked with the red solid line. The ground and first excited states of Sn124 in the proton channel and the ground state of Sn122 in the triton channel, used for the calibration of the particle telescope, are marked with yellow circles.

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    • Figure 2
      Figure 2

      (a), (d) Experimental raw p−γ coincidence, (b), (e) unfolded and (c), (f) primary matrices for Sn120,124 obtained in the (p,p′γ) experiments. Yellow dashed lines indicate the neutron separation energies. Red and green dashed lines in panels (c) and (f) confine transitions to the ground (region 1) and the first excited Jπ=2+ (region 2) states. Blue solid lines (region 3) indicate the areas of the primary matrices used further in the Oslo method. Bin sizes are 64keV×64keV and 80keV×80keV for Sn120 and Sn124, respectively. Blue arrows mark the sequence of the analysis steps.

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    • Figure 3
      Figure 3

      (a) Experimental systematics for the average total radiative width for Sn isotopes. (b) Experimental systematics for the NLD at the neutron separation energy. The estimated values of 〈Γγ〉 and ρ(Sn) for Sn124 are marked with stars, the experimental 〈Γγ〉 values are taken from Ref. [52], and the level densities are obtained from the D0 values given in Ref. [52]. Arrows mark ρ(Sn) values shifted by the neutron pair-gap values for the χ2 fit.

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    • Figure 4
      Figure 4

      Experimental nuclear level densities for (a) Sn120 and (b) Sn124. The NLDs at Sn are marked with crosses, discrete states are shown as shaded areas. For the Sn124 isotope both the total and reduced NLDs are shown. The first two vertical arrows at lower Ex energies on each figure constrain the lower excitation energy fit region, while the last two arrows at higher Ex energies mark the lower and upper limits for the higher excitation energy fit region.

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    • Figure 5
      Figure 5

      Experimental total nuclear level densities for Sn116 [35], Sn117 [35], Sn118 [36], Sn118 [36], Sn120, Sn121 [37], Sn122 [37], Sn124.

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    • Figure 6
      Figure 6

      Experimental nuclear level densities for 1± states for Sn124 obtained with the Oslo method (blue data points) and the (p,p′) data [65] (orange data points). The prediction of the CT model used for the normalization of the Oslo method data is shown by the dashed blue line. A fit with the BSFG through all data and with the composite formula [54] are shown by the dashed magenta and solid cyan lines. Predictions of the microscopic Hartree-Fock-BCS method [67] and Hartree-Fock-Bogolyubov + Gogny force calculations [68] are marked by the dashed light and dark-gray lines, respectively.

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    • Figure 7
      Figure 7

      Relative fluctuations of the GSF r(Eγ,Ei) for different initial excitation energies for (a) Sn120 and (b) Sn124. All initial Ei and final energies Ei−Eγ lie within the quasicontinuum region. The excitation and γ-ray energy bins are 128 keV for Sn120 and 160 keV for Sn124.

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    • Figure 8
      Figure 8

      Relative fluctuations of the GSF r(Eγ,Ef) for different final excitation energies for (a) Sn120 and (b) Sn124. All initial energies Ei−Eγ lie within the quasicontinuum region. The same applies to the different final energies Ef represented by blue lines. The red dashed line corresponds to the ground state as the final state, the green one corresponds to the first excited 2+ state as the final state, and the yellow one corresponds to several discrete final low-lying states. The excitation-energy bins and γ-ray energy bins are 128 keV for Sn120 and 160 keV for Sn124.

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    • Figure 9
      Figure 9

      GSFs for Sn120 at initial excitation energies (a) 5.82 MeV, (b) 6.46 MeV, (c) 7.10 MeV, (d) 7.74 MeV and final excitation energies (e) ground state, (f) first excited state, (g) 2.50 MeV, (h) 3.26 MeV compared with the Oslo method strength (blue shaded band). For each strength the statistical error band is shown together with the error due to the PT fluctuations. Dark gray regions correspond to the areas of expected infinite PT fluctuations, light gray area marks energies for which the fluctuations of the strength were not determined. The γ-ray and excitation energy bin widths are both 128 keV.

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    • Figure 10
      Figure 10

      GSFs for Sn124 at initial excitation energies (a) 5.52 MeV, (b) 6.16 MeV, (c) 6.96 MeV, (d) 7.76 MeV and final excitation energies (e) ground state, (f) first excited state, (g) 2.80 MeV, (h) 3.44 MeV compared with the Oslo method strength (blue shaded band). For each strength the statistical error band is shown together with the error due to the PT fluctuations. Dark gray regions correspond to the areas of expected infinite PT fluctuations, light gray area marks energies for which the fluctuations of the strength were not determined. The γ-ray and excitation energy bin widths are both 160 keV.

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    • Figure 11
      Figure 11

      Shape-method GSFs of Sn120 for γ rays (a) feeding the ground state and (b) the first excited state compared with the Oslo method result (blue band). The Shape method results are shown together with the statistical error propagated through the method, shown as a band (significantly smaller in width than the size of the data points), and the error bars due to the PT fluctuations. The Oslo method GSF is shown with the total (stat.+syst.) error band.

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    • Figure 12
      Figure 12

      Same as Fig. 11, but for Sn124.

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