Mirror energy differences above the 0f7/2 shell : First γ-ray spectroscopy of the Tz=−2 nucleus 56Zn

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Mirror energy differences above the 0f7/2 shell : First γ-ray spectroscopy of the Tz=−2 nucleus 56Zn © 2021 The Author(s). Published by Elsevier B.V. Published version Fernández, A.; Jungclaus, A.; Doornenbal, P.; Bentley, M. A.; Lenzi, S. M.; Rudolph, D.; Browne, F.; Cortés, M. L.; Koiwai, T.; Taniuchi, R.; Vaquero, V.; Wimmer, K.; Arici, T.; Imai, N.; Kitamura, N.; Longfellow, B.; Lozeva, R.; Mauss, B.; Napoli, D. R.; Niikura, M.; Pereira-Lopez, X.; Pigliapoco, S.; Poves, A.; Recchia, F.; Ruotsalainen, P.; Sakurai, H.; Uthayakumaar, S.; Wadsworth, R.; Yajzey, R. Fernández, A., Jungclaus, A., Doornenbal, P., Bentley, M. A., Lenzi, S. M., Rudolph, D., Browne, F., Cortés, M. L., Koiwai, T., Taniuchi, R., Vaquero, V., Wimmer, K., Arici, T., Imai, N., Kitamura, N., Longfellow, B., Lozeva, R., Mauss, B., Napoli, D. R., . . . Yajzey, R. (2021). Mirror energy differences above the 0f7/2 shell : First γ-ray spectroscopy of the Tz=−2 nucleus 56Zn. Physics Letters B, 823, Article 136784. https://doi.org/10.1016/j.physletb.2021.136784 2021 Physics Letters B 823 (2021) 136784 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Mirror energy differences above the 0f7/2shell: First γ-ray spectroscopy of the Tz=−2 nucleus 56Zn A. Fernández a, A. Jungclaus a,∗, P. Doornenbal b, M.A. Bentley c, S.M. Lenzi d,e, D. Rudolph f, F. Browne b, M.L. Cortés e, T. Koiwai g,b, R. Taniuchi c, V. Vaquero a, K. Wimmer g,b, T. Arici h, N. Imai i, N. Kitamura i, B. Longfellow j,k, R. Lozeva l, B. Mauss b, D.R. Napoli e, M. Niikura g, X. Pereira-Lopez c, S. Pigliapoco d, A. Povesm, F. Recchia d,e, P. Ruotsalainen n, H. Sakurai g, S. Uthayakumaar c, R. Wadsworth c, R. Yajzey c,o aInstituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain bRIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan cDepartment of Physics, University of York, Heslington, York YO10 5DD, United Kingdom dDipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova and INFN Padova, I-35131 Padova, Italy eIstituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy fDepartment of Physics, Lund University, SE-22100 Lund, Sweden gDepartment of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan hGSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany iCenter for Nuclear Study, University of Tokyo, RIKEN campus, Wako, Saitama 351-0198, Japan jDepartment of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA kNational Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA lUniversité Paris-Saclay, IJCLab, CNRS/IN2P3, F-91405 Orsay, France mDepartamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid, E-28049, Madrid, Spain nDepartment of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland oDepartment of Physics, Faculty of Science, Jazan University, Jazan, Saudi Arabia a r t i c l e i n f o a b s t r a c t Article history: Received 23 August 2021 Received in revised form 19 October 2021 Accepted 15 November 2021 Available online 19 November 2021 Editor: B. Blank Excited states in 56Zn were populated following one-neutron removal from a 57Zn beam impinging on a Be target at intermediate energies in an experiment conducted at the Radioactive Isotope Beam Factory at RIKEN. Three γrays were observed and tentatively assigned to the 6+→4+→2+→0+yrast sequence. This turns 56Zn into the heaviest Tz=−2 nucleus in which excited states are known. The excitationenergy differences between these levels and the isobaric analogue states in the Tz=+2mirror partner, 56Fe, are compared with large-scale shell-model calculations considering the full pf valence space and various isospin-breaking contributions. This comparison, together with an analysis of the mirror energy differences in the A =58, Tz=±1pair 58Zn and 58Ni, provides valuable information with respect to the size of the monopole radial and the isovector multipole isospin-breaking terms in the region above doubly-magic 56Ni. ©2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction The exchange symmetry between protons and neutrons is one of the fundamental symmetries of modern physics and led to the concept of isospin in nuclear physics. Isospin symmetry is a consequence of the almost perfect charge independence and charge symmetry of the attractive strong nucleon-nucleon interaction. *Corresponding author. E-mail address: andrea.jungcla[email protected] (A. Jungclaus). However, isospin symmetry is naturally broken by the Coulomb force acting between protons. Furthermore, systematic studies of pairs of mirror nuclei, i.e. nuclei with interchanged proton and neutron numbers, over the last two decades have revealed that additional isospin-breaking (ISB) multipole effects exist (see, e.g., Refs. [1–4] and references therein). Most information has been gathered for nuclei in the 0f7/2shell, i.e. nuclei in the region between 40Ca and 56Ni [5], as summarized in Fig. 1. While many of these nuclei are rather easily accessible using heavy-ion induced fusion-evaporation reactions in conjunction with highly-efficient γ-ray spectrometers, the most neutron-deficient ones were studied https://doi.org/10.1016/j.physletb.2021.136784 0370-2693/©2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. A. Fernández, A. Jungclaus, P. Doornenbal et al. Physics Letters B 823 (2021) 136784 Fig. 1. Overview of isospin-symmetry studies in the region above 40Ca. Mirror pairs studied with fusion-evaporation reactions are shown in blue and those investigated employing in-beam γ-ray spectroscopy at intermediate energies with a 58Ni primary beam at NSCL in green [5]. The A =56, Tz=±2 mirror pair subject of the present study is shown in red. in recent years using in-beam γ-ray spectroscopy at intermediate energies at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University [6–12]. On the theoretical side, the nuclei in this region can be described with very good accuracy by the nuclear shell model (SM) when the full pf valence space is considered [2,4]. A systematic comparison between the rich experimental information and shell-model calculations allowed to establish a consistent picture with respect to several isospin-breaking contributions. In particular, it was demonstrated that in order to describe observed differences in excitation energies of states in mirror nuclei, two specific ISB contributions are required besides well-established Coulomb terms, namely the isovector multipole term, VB, and the monopole radial term, VCr [1,4,13–15]. In stark contrast, the question how these two additional ISB terms have to be treated above the 0f7/2orbital, i.e., in the Z=N=28-50 shell, is still an open question [15,16]. Isospin-symmetry studies of heavier systems therefore often depend on ad hoc assumptions and thus clearly suffer from the lack of decisive data points [15–19]. To tackle this question, we present in this Letter the first γ-ray spectroscopy of 56Zn (Z=30, N=26), which has an isospin projection of Tz=−2. An in-beam study of this nucleus is at the very limit of feasibility and became possible only recently due to the availability of a high-intensity 78Kr primary beam at the Radioactive Isotope Beam Factory (RIBF) at RIKEN. The observation of three γrays, emitted from excited 56Zn ions produced via one-neutron removal from a 57Zn beam at intermediate energies, allowed to establish the yrast sequence of this nucleus. 56Zn, as well as its Tz=+2mirror nucleus 56Fe and the Tz=±1 pair 58Zn/58Ni, has only two nucleons outside the 0f7/2shell (see Fig. 1). Therefore, the influence of the next orbital, 0g9/2, which quickly increases when more and more nucleons are added above 56Ni, is still small and these nuclei are still well described by SM calculations in the pf space. The A =56, Tz=±2 and A =58, Tz=±1mirror pairs thus offer a unique opportunity to pin down the contributions of the 1p, 0f5/2orbitals to the VBand VCr terms in the upper pf shell. 2. Experiment and results The experiment was conducted at the RIBF, operated by the RIKEN Nishina Center and the Center for Nuclear Study of the University of Tokyo. A 78Kr primary beam with an average intensity of 300 pnA and an energy of 345 MeV/nucleon underwent fragmentation on a 7-mm thick Be target. During their passage through the BigRIPS spectometer [20], the constituents of the resulting cocktail beam were identified based on their charge (Z) and mass-tocharge ratio (A/Q) by means of the Bρ-E-TOF method [21]. The magnetic rigidity, Bρ, the time-of-flight, TOF, and the energy loss, E, were determined on an event-by-event basis thus enabling a complete identification of the beam components. The 57Zn ions, which followed a central trajectory in BigRIPS, reached the 6-mm thick Be secondary reaction target placed in the final focal plane of BigRIPS with an energy of 200 MeV/nucleon, translating into a mid-target velocity of β=0.51. The secondary reaction products were identified via the measurement of Bρ, TOF, and Ein the ZeroDegree spectrometer [20], leading to an unambiguous selection of reaction residues. To detect γradiation emitted following the nuclear reactions, the reaction target was surrounded by the DALI2+ spectrometer [22] which was composed of 226 NaI crystals covering polar angles in the range θ=18◦-125◦with respect to the beam axis. The individual crystals were calibrated in the energy range of interest using 88Y, 60Co, and 137Cs sources. The response of the array to in-flight decays was simulated using the Geant4 toolkit [23]. A photo-peak efficiency of 15% and a resolution after Doppler correction of 11% (FWHM) were obtained for 1.3 MeV γrays emitted at β=0.51. Confidence intervals for the γray energies and absolute intensities were extracted by means of a χ2minimization following the maximum-likelihood method for Poisson-distributed, binned data [24], and using model responses from the Geant4 simulation. Systematic uncertainties in the deduced model parameters and the geometry of the experimental setup were characterized using well-known transitions in 52Fe and 54Ni, nuclei which were populated in the same experiment. The target position relative to the DALI2+ array deduced from the fit of known γrays emitted from excited states with negligible half-lives was found to be in good agreement with the measured physical location. The accuracy obtained for the extracted γ-ray energies was better than 0.4%. This additional uncertainty was propagated accordingly in the γ-ray energy uncertainties reported below. For more details regarding the data analysis we refer to Ref. [25]. The prompt Doppler-corrected γ-ray spectrum of 56Zn, populated via one-neutron removal from 57Zn, is presented in Fig. 2(a). The spectrum was adjusted in the range between 400 and 2500 keV including three DALI2+ response functions simulated for γray energies of 830, 1272, and 1380 keV. A smooth background was represented by a double-exponential function. Although the full-energy peaks of the 1272-keV and 1380-keV γrays were not resolved, the occurrence of a well-defined global minimum for the two transitions was verified by a χ2test in terms of the γ-ray energies and intensities of the doublet. Correlations between the model parameters were accounted for by minimizing the χ2as a function of the remaining parameters describing the doublet [25]. The resulting χ2matrix for the energies is presented in the inset of Fig. 2(a). The confidence intervals are taken as the extremes of the 1σcontour in the multi-parameter χ2surfaces. The resulting γ-ray energies for the three observed transitions are 830(5), 1272(13), and 1380(16) keV. The lifetimes of all relevant excited states in 56Zn are expected to be τ≤10 ps based on a comparison with the Tz=+2mirror nucleus 56Fe [26]. This lifetime limit translates into an uncertainty of <1 keV for the transition energy when τ=0ps is assumed in the simulations. For the relative intensities, values of 100(5), 76(19), and 58(11)%, respectively, were obtained from the χ2analysis. Independent evidence for the doublet structure of the broad peak around 1.3 MeV in Fig. 2(a) is provided by inspection of the background-corrected γ-γcoincidence spectra shown in Fig. 2(b). When selecting the left part of the doublet, the higher-energy component is observed in coincidence and vice versa. Furthermore, in both coincidence spectra a 2 A. Fernández, A. Jungclaus, P. Doornenbal et al. Physics Letters B 823 (2021) 136784 Fig. 2. (a) Prompt γ-ray energy spectrum of 56Zn populated via one-neutron removal from 57Zn. Only events in which less than five DALI2+ crystals fired were included. The red line represents the best fit of the spectrum. The simulated lineshapes composing the fit are depicted in blue. The black dashed line represents the double-exponential background. The χ2matrix for the γ-ray energies of the 12721380-keV doublet is shown in the inset. (b) Background-subtracted γ-γcoincidence spectra for the left (blue) and right (red) part of the doublet, respectively. line at 830 keV is visible. Thus, the three transitions are observed in mutual coincidence and it can be concluded that they form a γ-ray cascade. The ordering of the transitions within the cascade was established on the basis of the experimental intensities. For the resulting excited states at energies of 830(5), 2102(14), and 3482(21) keV tentative spin and parity assignments of (2+), (4+), and (6+), respectively, are proposed based on the analogy to the mirror nucleus 56Fe, which is illustrated in Fig. 3. 3. Discussion To analyze the experimental findings, large-scale shell-model calculations were performed for the A =56, Tz=±2mirror pair and the Tz=±1nuclei 58Zn and 58Ni. The latter form the only other even mirror pair with only either protons or neutrons above the N=Z=28 gap for which experimental mirror energy differences (MED) are available. In addition, the population of excited states in 56Zn via one-neutron removal from 57Zn was calculated. The shell-model code ANTOINE [27,28]was used and the full pf valence space was employed, comprising the 0f7/2, 1p3/2, 1p1/2, and 0f5/2orbitals above the 40Ca core. Due to computational limitations, the calculations for the A =57, 58 nuclei had to be constrained to t=8 particle-hole excitations across the N=Z=28 shell gaps. No restrictions were applied at A =56. The calculations were performed with the KB3GR [29]effective interaction. As compared to its precursor, the well-established KB3G interaction [30,2], KB3GR features an improved description of the interaction among the 1p3/2, 1p1/2, and 0f5/2orbitals which was derived from a fit to the energies of about 200 excited states of nuclei with Nor Z in the range 28 to 32. Due to the way it was constructed, this interaction is considered best suited for the study of the A =56, 58 nuclei under discussion in the present work. For the calculation of transition probabilities bare gfactors and effective nucleon charges εp=1.15eand εn=0.80ewere used for protons and neutrons, respectively [31]. Fig. 3shows the level scheme calculated with the isospin-conserving KB3GR interaction for the A =56, Tz=±2nuclei in comparison with experimental information. We note that Fig. 3. Partial level scheme of 56Fe [26](left), KB3GR shell-model prediction for A =56, Tz=±2 (middle), and yrast sequence of 56Zn as observed in the present work (right). the known decay pattern of the non-yrast states in 56Fe nicely agrees with the shell-model expectation based on the calculated electromagnetic decay properties. The observed relative intensities of the three γrays connecting the yrast line in 56Zn are also consistent with those estimated from the calculated branching ratios and spectroscopic factors for one-neutron removal from 57Zn assuming constant single-particle reaction cross sections. To study mirror energy differences, isospin-breaking terms have to be included in the shell-model calculations. Here, we follow the terminology and prescription of Ref. [4]. First, we add the Coulomb multipole matrix elements, VCM, to the nuclear ones and adjust the single-particle proton and neutron energies taking into account the electromagnetic spin-orbit, Vs, and orbit-orbit, V, corrections. After diagonalizing this interaction in the model space for both mirror partners, we compute the expectation value of the schematic isospin-breaking isovector term, VB. This term was originally introduced for the 0f7/2shell, where V2 B=+100 keV was applied to the J=2 coupling [1,3,4]. Later, it was shown that equivalent results are obtained applying either V2 Bto the J=2or V0 B=−V2 Bto the J=0matrix element [14]. The latter approach has the important advantage of allowing to consider this term on an equal footing for all orbitals of the valence space [15,32,19]. For the mass range A =51-54, i.e. the heaviest 0f7/2-shell nuclei, a best value of V0 B=−71(3)keV was deduced from the experimental data [14]. Here, this strength is applied to either only the 0f7/2orbital or all four orbitals of the valence space in order to investigate the contribution of the 1pand 0f5/2orbitals to this term. Finally, we add to the MED the radial term, VCr, that takes into account state-dependent changes in the nuclear radius. Since low- orbits in a shell have larger radii than higher-ones, changes in the relative occupation of these orbits modify the radius [1,4]. In the study of nuclei in the 0f7/2shell, usually only the occupancy of the 1p3/2orbital, which typically is far below one nucleon, is considered with a standard strength parameter α=200 keV [4]. Recently, however, it has been shown that when a low-orbit is occupied by more than one nucleon its radius decreases considerably [33,34]. In the case of the sd shell, the difference between the root-mean-square radii of the 1s1/2and 0dorbitals, ρs-ρd, reduces around A ≈28 by a factor of 2.5-3.0 [34]. In the nuclei under study here, the occupancy of the 1p3/2orbital is typically in the range 1.5-2.0. It is thus expected that a smaller value of α, as compared to the standard value, would be more appropriate in the present cases. Since the decrease of ρp-ρfupon filling of the 1p3/2orbital is not known, calculations were made for values of α=0, 50, 100, and 200 keV in order to derive the best value of αfor nuclei in the upper pf shell from a comparison to the experimental data. 3 A. Fernández, A. Jungclaus, P. Doornenbal et al. Physics Letters B 823 (2021) 136784 Fig. 4. Comparison of experimental MED (red dots, from Ref. [5]and the present work) with the results of shell-model calculations with the KB3GR interaction for (a) the A =58, Tz=±1and (b) the A =56, Tz=±2 mirror pair. Predictions are shown for α=0keV (green), 50 keV (black), 100 keV (blue), and 200 keV (gray) for the 1p3/2orbital and, for the A =58 pair, V0 B=−71 keV applied to either all pf orbitals (solid lines) or only to the 0f7/2(dashed lines). Panels (c) and (d) show the individual contributions to the MED. See text for details. Experimental data are taken from Ref. [5]and the present work. For the 1p1/2orbital with occupancies <0.5, the standard value α=200 keV is used [15,33,35]. The predicted MED for the two mirror pairs of interest are compared with the experimental results in Figs. 4(a) and (b), while Figs. 4(c) and (d) show the individual contributions to the calculated MED. These are the Coulomb contribution, VCM, coupled to the multipole Coulomb single-particle shifts, V and Vs, the additional isovector term, VB, and the radial term, VCr. Fig. 4(a) evidences that the A =58 pair is particularly sensitive to the contribution of the orbitals of the upper pf shell to the isovector term, VB. In these nuclei, the 0f7/2shell is nearly completely filled, so that the contribution of this orbital to VBvanishes, see Fig. 4(c). In contrast, large values of around VB≈50 keV are expected for the 2+and 4+states when this correction is applied for all orbitals of the valence space. The dependence of the MED on the value of α, on the other hand, is very small for this mirror pair as shown in Fig. 4(a). The comparison between experimental and calculated MED shown in that figure therefore clearly demonstrates that the contribution of all pf orbitals to the VBterm has to be taken into account in order to reproduce the experimental data. Having settled the correct treatment of the VBterm, we can now proceed to investigate the size of the radial term, VCr. This monopole term scales with the difference in Zof the mirror partners. The new experimental data on the A =56, Tz=±2pair therefore offer a unique opportunity to estimate the strength parameter αfor the 1p3/2orbital in the region above the 0f7/2shell, i.e. for nuclei in which the occupancy of this orbital significantly exceeds one nucleon. As seen in Fig. 4(d), the SM calculations yield only small Coulomb and VBcontributions up to the 4+state. This is expected considering the particle-hole symmetry of these nuclei having one pair of nucleons and one pair of holes with respect to 56Ni. Furthermore, VCM +V +Vsand VBhave opposite sign and nearly cancel for all states. It is thus mainly the radial term, VCr, which determines the trend of the MED curve, as observed by comparing Figs. 4(b) and (d). Best agreement between experimental and calculated MED is found for a value of αaround 50 keV or even below, a value which is significantly smaller as compared to that commonly used for nuclei in the 0f7/2shell. This finding constitutes first evidence that the radius of the 1p3/2orbital decreases considerably when it is occupied by more than one nucleon. A similar behavior of the 1s1/2orbital was recently discussed in Ref. [34]. To conclude the discussion of Fig. 4, based on the comparison between the measured and theoretical MED the magnitude of the VBand VCr terms in the region above the 0f7/2 shell could be determined and thereby the open question raised in the introduction answered. 4. Summary To summarize, we reported on the first γ-ray spectroscopic study of 56Zn which allowed to establish the yrast sequence of this Tz=−2 nucleus up to the 6+state. The mirror energy differences for the A =56, Tz=±2, and A =58, Tz=±1, pairs were compared with shell-model calculations performed using the full pf valence space and the KB3GR effective interaction. This comparison has put in evidence that the experimental data can only be reproduced when the isovector multipole term, VB, is considered on equal footing for all orbitals of the valence space, not only the 0f7/2shell. Furthermore, it has shown that the contribution of the 1p3/2orbital to the radial term, VCr, is significantly quenched due to the decrease of its radius once its occupancy exceeds one nucleon. We note that these results, which set the basis for future studies of isospin symmetry in the upper pf shell, were obtained under the presumption that for the nuclei discussed in the present work the influence of the 0g9/2orbital is negligible. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We thank the RIKEN Nishina Center accelerator staff and the BigRIPS team for providing excellent beams to the experiment. This work was supported by the Spanish Ministerio de Ciencia e Innovación under contracts FPA2017-84756-C4-2-P, PGC-2018-94583, and SEV-2016-0597, the Swedish Research Council (Vetenskapsrådet, VR 2016-3969), and the UK Science and Technology Facilities Council (STFC) under grants ST/L005727/1 and ST/P003885/1. FB is supported by the RIKEN Special Postdoctoral Researcher Program. References [1] A.P. Zuker, S.M. Lenzi, G. Martínez-Pinedo, A. Poves, Phys. Rev. Lett. 89 (2002) 142502. [2] E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, Rev. Mod. Phys. 77 (2005) 427. [3] J. Ekman, C. Fahlander, D. Rudolph, Mod. Phys. Lett. A 20 (2005) 2977. [4] M.A. Bentley, S.M. Lenzi, Prog. Part. Nucl. Phys. 59 (2007) 497. [5] https://www.nndc .bnl .gov /ensdf. [6] J.R. Brown, et al., Phys. Rev. C 80 (2009) 011306(R). [7] P.J. 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