Experimental identification of the $T=1$, ${J}^{\ensuremath{\pi}}={6}^{+}$ state of $^{54}\mathrm{Co}$ and isospin symmetry in $A=54$ studied via one-nucleon knockout reactions

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Experimental identification of the $T = 1$ , $J^{π} = 6^{+}$ state of ${}^{54}{Co}$ and isospin symmetry in $A = 54$ studied via one-nucleon knockout reactions

M. Spieker, D. Weisshaar, A. Gade, B. A. Brown, P. Adrich, D. Bazin, M. A. Bentley, J. R. Brown, C. M. Campbell, C. Aa. Diget, B. Elman, T. Glasmacher, M. Hill, B. Longfellow, B. Pritychenko, A. Ratkiewicz, D. Rhodes, and J. A. Tostevin

Phys. Rev. C 100, 061303(R) – Published 11 December 2019

Abstract

New experimental data obtained from $γ$ -ray tagged one-neutron and one-proton knockout from ${}^{55}{Co}$ are presented. A candidate for the sought-after $T = 1, T_{z} = 0, J^{π} = 6^{+}$ state in ${}^{54}{Co}$ is proposed based on a comparison to the new data on ${}^{54}{Fe}$ , the corresponding observables predicted by large-scale-shell-model (LSSM) calculations in the full $f p$ -model space employing charge-dependent contributions, and isospin-symmetry arguments. Furthermore, possible isospin-symmetry breaking in the $A = 54$ , $T = 1$ triplet is studied by calculating the experimental $c$ coefficients of the isobaric mass multiplet equation (IMME) up to the maximum possible spin $J = 6$ expected for the ${(1 f_{7 / 2})}^{- 2}$ two-hole configuration relative to the doubly magic nucleus ${}^{56}{Ni}$ . The experimental quantities are compared to the theoretically predicted $c$ coefficients from LSSM calculations using two-body matrix elements obtained from a realistic chiral effective field theory potential at next-to-next-to-next-to-leading order ( $N^{3} LO$ ).

Received 25 September 2019

DOI:https://doi.org/10.1103/PhysRevC.100.061303

Physics Subject Headings (PhySH)

Direct reactions Energy levels Nuclear reactions Nuclear structure & decays Nucleon-nucleon interactions Shell model Unstable nuclei induced nuclear reactions

59 ≤ A ≤ 89

Nuclear Physics

Authors & Affiliations

M. Spieker^1,*, D. Weisshaar¹, A. Gade^1,2, B. A. Brown^1,2, P. Adrich^1,†, D. Bazin^1,2, M. A. Bentley³, J. R. Brown³, C. M. Campbell^1,2,‡, C. Aa. Diget³, B. Elman^1,2, T. Glasmacher^1,2, M. Hill^1,2, B. Longfellow^1,2, B. Pritychenko⁴, A. Ratkiewicz^1,2,§, D. Rhodes^1,2, and J. A. Tostevin⁵

¹National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA
²Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
³Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
⁴National Nuclear Data Center, Brookhaven National Laboratory, Upton, New York 11973, USA
⁵Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom

^*Present address: Department of Physics, Florida State University, Tallahassee, Florida 32306, USA; mspieker@fsu.edu
^†Present address: National Centre for Nuclear Research, Otwock, Poland.
^‡Present address: Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
^§Present address: Lawrence Livermore National Laboratory, Livermore, California, 94550, USA.

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Vol. 100, Iss. 6 — December 2019

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Figure 1
In-beam $γ$ -ray singles spectra for ${}^{54}{Co}$ (top) and ${}^{54}{Fe}$ (bottom) in black compared to $γ$ -ray spectra obtained from a geant4 simulation (red or grey). Observed transitions are marked with dashed vertical lines and their corresponding transition energies. The background structures between 400 and 800 keV, seen on top of the smooth background, are caused by $γ$ rays emitted from stopped components and taken into account in the simulation. The structure at around 3.2 MeV, seen in the inset for ${}^{54}{Co}$ , did not unambiguously resemble a clear peak shape and was, therefore, omitted in the simulation. The placement of the transitions in the level schemes is summarized in Fig. 2.
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Figure 2
Observed level schemes of ${}^{54}{Co}$ and ${}^{54}{Fe}$ . Shown are $γ$ -ray transitions which could be identified in the $γ$ -ray spectra (compare Fig. 1). $T = 0$ states are shown with shorter horizontally dashed lines (black) and $T = 1$ with solid, horizontal lines (red). States with an uncertain isospin character are presented with longer horizontally dashed lines (grey). Tentatively placed transitions are shown with vertically dashed lines. For all states but the last two observed excited states in ${}^{54}{Co}$ , spin-parity assignments were adopted from [12]. For the latter, $J^{π}$ assignments are proposed based on a comparison to ${}^{54}{Fe}$ .
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Figure 3
Partial cross sections $σ_{part}$ determined for (a) ${}^{54}{Co}$ and (b) ${}^{54}{Fe}$ in comparison to (c) and (d) for the theoretical cross sections. Only the first three states of each spin and predicted with $σ_{part} \geq 0.03$ mb are presented. $T = 0$ states are presented in black (full circles), $T = 1$ states in red (open squares), and states with uncertain isospin character in grey (full diamonds). In addition, the partial cross sections relative to the inclusive cross section $σ_{inc}$ are shown, see second axis on the right. Only statistical uncertainties are given. No reduction factor $R_{s}$ [18, 19] has been applied for the comparison. The location of the $7_{1}^{+}$ in ${}^{54}{Co}$ [12] is indicated by a black cross in (a). As described in the text, this state was not observed because of its isomeric character. After subtraction, a partial cross section of 11(4) mb [27(11) $%]$ remains in ${}^{54}{Co}$ . This would be in very good agreement with the theoretical expectations if it is mainly concentrated in the $7_{1}^{+}$ state and also accommodates the small partial cross section expected for the ground state. For further information on the theoretical cross sections, see the Supplemental Material [20].
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Figure 4
First-order calculations for $N^{3} LO$ with the CSB part multiplied by 0.8 compared to experiment as explained in Ref. [4]. The black circles are the experimentally calculated $c$ coefficients using the latest atomic mass evaluation [31]. This evaluation was not available when [4] was published. The solid lines show the sum of the Coulomb and CSB contributions. The dashed lines show only the CSB contribution.
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Figure 5
Same as Fig. 4 but with the CSB part multiplied by 0.6.
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Physical Review C

covering nuclear physics

Experimental identification of the $T = 1$ , $J^{π} = 6^{+}$ state of ${}^{54}{Co}$ and isospin symmetry in $A = 54$ studied via one-nucleon knockout reactions

M. Spieker, D. Weisshaar, A. Gade, B. A. Brown, P. Adrich, D. Bazin, M. A. Bentley, J. R. Brown, C. M. Campbell, C. Aa. Diget, B. Elman, T. Glasmacher, M. Hill, B. Longfellow, B. Pritychenko, A. Ratkiewicz, D. Rhodes, and J. A. Tostevin

Phys. Rev. C 100, 061303(R) – Published 11 December 2019

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Physical Review C

covering nuclear physics

Experimental identification of the T=1, Jπ=6+ state of Co54 and isospin symmetry in A=54 studied via one-nucleon knockout reactions

M. Spieker, D. Weisshaar, A. Gade, B. A. Brown, P. Adrich, D. Bazin, M. A. Bentley, J. R. Brown, C. M. Campbell, C. Aa. Diget, B. Elman, T. Glasmacher, M. Hill, B. Longfellow, B. Pritychenko, A. Ratkiewicz, D. Rhodes, and J. A. Tostevin

Phys. Rev. C 100, 061303(R) – Published 11 December 2019

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Experimental identification of the $T = 1$ , $J^{π} = 6^{+}$ state of ${}^{54}{Co}$ and isospin symmetry in $A = 54$ studied via one-nucleon knockout reactions