The shape of the Tz = +1 nucleus 94Pd and the role of proton-neutron interactions on the structure of its excited states

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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/ The shape of the Tz = +1 nucleus 94Pd and the role of proton-neutron interactions on the structure of its excited states © 2024 the Authors Published version Yaneva, A.; Jazrawi, S.; Mikołajczuk, M.; Górska, M.; Regan, P.H.; Das, B.; Albers, H.M.; Alhomaidhi, S.; Arici, T.; Banerjee, A.; Benzoni, G.; Cederwall, B.; Chishti, M.M.R.; Dao, D.D.; Davinson, T.; Gargano, A.; Gerl, J.; Hall, O.; Hubbard, N.; Jolie, J.; Kojouharov, I.; Mistry, A.K.; Nowacki, F.; Polettini, M.; Rudigier, M.; Şahin, E.; Schaffner, H.; Sharma, A.; Armstrong, M.; Wollersheim, H.J.; Boutachkov, P.; Dickel, T.; Haettner, E.; Heggen, H.; Hornung Ch.; Knöbel, R.; Kostyleva, D.; Kurz, N.; Kuzminchuk, N.; Mukha, I.; Pietri, S.; Plass, W.R.; Podolyák Zs.; Scheidenberger, C.; Tanaka, Y.K.; Vesic, J.; Weick, H.; Ahmed, U.; Aktas, Ö.; Algora, A.; Appleton, C.; Benito, J.; Blazhev, A.; Bracco, A.; Bruce, A.M.; Brunet, M.; Canavan, R.; Esmaylzadeh, A.; Fraile, L.M.; Häfner, G.; Hucka, K.P.; John, P.R.; Kahl, D.; Karayonchev, V.; Kern, R.; Košir, G.; Lozeva, R.; Napiralla, P.; Nara Singh, B.S.; Page, R.; Petrache, C.M.; Pietralla, N.; Régis, J.-M.; Rösch, H.; Ruotsalainen, P.; Sanchez-Temble, V.; Sexton, L.; Shearman, R.; Si, M.; Werner, V.; Wiederhold, J.; Wimmer, K.; Witt, W.; Woods, P.; Zimba, G. Yaneva, A., Jazrawi, S., Mikołajczuk, M., Górska, M., Regan, P.H., Das, B., Albers, H.M., Alhomaidhi, S., Arici, T., Banerjee, A., Benzoni, G., Cederwall, B., Chishti, M.M.R., Dao, D.D., Davinson, T., Gargano, A., Gerl, J., Hall, O., Hubbard, N., . . . Zimba, G. (2024). The shape of the Tz = +1 nucleus 94Pd and the role of proton-neutron interactions on the structure of its excited states. Physics Letters B, 855, Article 138805. https://doi.org/10.1016/j.physletb.2024.138805 2024 Phys. Lett. B 855 (2024) 138805 Available online 19 June 2024 0370-2693/© 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Letter The shape of the 𝑇𝑧=+1nucleus 94Pd and the role of proton-neutron interactions on the structure of its excited states A. Yanevaa,b,, S. Jazrawic,d, M. Mikołajczukb,e, M. Górskab,∗, P.H. Reganc,d, B. Dasb,f, H.M. Albers b, S. Alhomaidhib,g,h,i, T. Arici b, A. Banerjeeb, G. Benzonik, B. Cederwallf, M.M.R. Chishtic, D.D. Daoj, T. Davinsonl, A. Garganom, J. Gerlb, O. Halll, N. Hubbardb,g,h, J. Jolie a, I. Kojouharov b, A.K. Mistry b,h, F. Nowacki j, M. Polettinik,n,1,2, M. Rudigierh, E. Şahinb,g,h, H. Schaffnerb, A. Sharmao, M. Armstrong a,b, H.J. Wollersheim b, P. Boutachkovb, T. Dickelb, E. Haettnerb, H. Heggenb, Ch. Hornungb, R. Knöbelb, D. Kostyleva b, N. Kurz b, N. Kuzminchukb, I. Mukhab, S. Pietri b, W.R. Plassb, Zs. Podolyákc, C. Scheidenbergerb, Y.K. Tanakap, J. Vesicq, H. Weickb, U. Ahmedg,h, Ö. Aktasf, A. Algora r,s, C. Appletonl, J. Benitot, A. Blazheva, A. Bracco k,n, A.M. Bruceu, M. Brunetc, R. Canavanc,d, A. Esmaylzadeha, L.M. Frailet, G. Häfnera,v, K.P. Huckai, P.R. Johnh, D. Kahll, V. Karayoncheva,3, R. Kern h, G. Košir q,w, R. Lozeva v, P. Napirallai, B.S. Nara Singhx, R. Pagey, C.M. Petrachev, N. Pietrallah, J.-M. Régisa, H. Röschh, P. Ruotsalainenz, V. Sanchez-Temblet, L. Sextonl, R. Shearmand, M. Siv, V. Wernerg,h, J. Wiederholdh, K. Wimmerb, W. Witth, P. Woodsl, G. Zimbaz aInstitut für Kernphysik der Universität zu Köln, D-50937 Köln, Germany bGSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt, Germany cSchool of Mathematics and Physics, University of Surrey, Guildford, GU2 7XH, UK dNational Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK eFaculty of Physics, University of Warsaw, Warsaw 00681, Poland fKTH Royal Institute of Technology, Stockholm, Sweden gHelmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Darmstadt, 64289 Darmstadt-Arheilgen, Germany hInstitut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany iKing Abdulaziz City for Science and Technology (KACST), P.O. Box 6086, Riyadh 11442, Saudi Arabia jUniversité de Strasbourg, IPHC, 23 rue du Loess 67037 Strasbourg, France kINFN, Sezione di Milano, Milano, Italy lSchool of Physics and Astronomy, University of Edinburgh, Edinburgh H9 3FD, UK mIstituto Nazionale di Fisica Nucleare, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy nDipartimento di Fisica, Universita degli Studi di Milano, Milano, Italy oDepartment of Physics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India pHigh-Energy Nuclear Physics Laboratory, RIKEN, 351-0198 Saitama, Japan qJozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia rInstituto de Fisica Corpuscular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain sInstitute for Nuclear Research (ATOMKI), Bem ter 18/c, H-4026 Debrecen, Hungary tGrupo de Física Nuclear and IPARCOS, Universidad Complutense de Madrid, CEI Moncloa, E-28040 Madrid, Spain uSchool of Computing Engineering and Mathematics, University of Brighton, BN2 4AT Brighton, UK vUniversité Paris-Saclay, IJCLab, CNRS/IN2P3, F-91405 Orsay, France wFaculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia xSchool of Computing, Engineering and Physical Sciences, University of the West of Scotland, PA1 2BE Paisley, UK yDepartment of Physics, Oliver Ladge Laboratory, University of Liverpool, Liverpool L69 7ZE, UK zUniversity of Jyväskylä, Seminaarinkatu 15, 40014 Jyväskylän yliopisto, Finland * Corresponding author. E-mail addresses: [email protected] (A. Yaneva), [email protected] (M. Górska). 1Present adress: Universitá degli Studi di Padova, Italy 2Present adress: INFN Sezione di Padova, Italy 3Present adress: Argonne National Laboratory, Argonne IL 60439, USA https://doi.org/10.1016/j.physletb.2024.138805 Received 18 January 2024; Received in revised form 16 May 2024; Accepted 12 June 2024 Physics Letters B 855 (2024) 138805 2 A. Yaneva, S. Jazrawi, M. Mikołajczuk et al. A R T I C L E I N F O A B S T R A C T Editor: B. Blank Keywords: 𝛾spectroscopy Fast-timing 𝛾-ray coincidences 𝑝𝑛 interaction Isovector vs. isoscalar pairing Shell model Reduced transition probabilities have been extracted between excited, yrast states in the 𝑁=𝑍+2nucleus 94Pd. The transitions of interest were observed following decays of the 𝐼𝜋=14 +, 𝐸𝑥= 2129-keV isomeric state, which was populated following the projectile fragmentation of a 124Xe primary beam at the GSI Helmholtzzentrum für Schwerionenforschung accelerator facility as part of FAIR Phase-0. Experimental information regarding the reduced E2 transition strengths for the decays of the yrast 8+and 6+states was determined following isomerdelayed 𝐸𝛾1−𝐸𝛾2−△𝑇2,1coincidence method, using the LaBr3(Ce)-based FATIMA fast-timing coincidence gamma-ray array, which allowed direct determination of lifetimes of states in 94Pd using the Generalized Centroid Difference (GCD) method. The experimental value for the half-life of the yrast 8+state of 755(106) ps results in a reduced transition probability of B(E2:8+→6+) = 205+34 −25 e2fm4, which enables a precise verification of shellmodel calculations for this unique system, lying directly between the 𝑁=𝑍line and the 𝑁=50neutron shell closure. The determined 𝐵(𝐸2) value provides an insight into the purity of (𝑔9∕2)𝑛configurations in competition with admixtures from excitations between the (lower) 𝑁=3𝑝𝑓 and (higher) 𝑁=4𝑔𝑑𝑠 orbitals for the first time. The results indicate weak collectivity expected for near-zero quadrupole deformation and an increasing importance of the 𝑇=0proton-neutron interaction at 𝑁=48. 1. Introduction The 𝑁=𝑍=50100Sn is the heaviest self-conjugate doubly-magic nucleus that is stable with respect to particle emission. Nuclear structure of hole states in the region “south-west” of the shell closure between the 𝑁=50, 𝑍=40and the 𝑁=𝑍lines is dominated by the 0𝑔9∕2 intruder orbital from the 𝑁=4harmonic oscillator shell. It is well separated from the 𝑁=3𝑝𝑓 -shell orbitals, both energetically and by its parity, contributing only with even-particle even-hole excitations into the intruder orbital. This makes the region “south-west” of 100Sn the subject of increased focus for both experimental and theoretical investigation [1,2]. In particular, 𝑔9∕2 is the first valence high-spin orbit, where seniority breaking is discussed extensively in the literature. [3–9]. In addition, the strong spatial overlap of proton- and neutron-hole wave functions causing strong proton-neutron (𝑝𝑛) interaction gives rise to unique structural features such as spin-gap isomers and seniority induced symmetries. Remnants of the seniority level scheme in the open 𝜋𝜈(𝑔9∕2)orbitals have also been addressed in reference [10]. Experimental work directly related to this topic includes the yrast spectroscopy of 92Pd [11]and the decay of the 𝐼𝜋=16 +spin trap isomer and yrast sequence in 96Cd [12–14]. The strength of the 𝑝𝑛 interaction in the 𝜋𝜈(𝑔9∕2)orbitals manifests itself best in the stronglybinding 𝑇=0 (𝑔9∕2)2, 𝐼𝜋=9 +isoscalar two-body matrix element (TBME), which is comparable with the 𝑇=1isovector pairing, as introduced in early works [15–18]using empirical interactions employing the 𝜋𝜈(1𝑝1∕20𝑔9∕2)model space. They are reviewed in Ref. [1]together with calculations in the full 𝜋𝜈(𝑓5∕2𝑝𝑔9∕2)model space using empirical [19]and realistic [20] interactions. Subsequently, Large Scale Shell Model (LSSM) calculations were presented for the upper 𝜋𝜈(𝑔𝑑𝑠)shell using the Nowacki-Sieja interaction in Ref. [12]. Following the discovery of excited states in 92Pd [11], a series of multi-step shell-model and Interacting Boson Model (IBM) studies investigated the role of 𝜋𝜈(𝑔9∕2)proton-neutron pairs with maximum aligned spins of 9+in the 𝑁=𝑍nuclei 96Cd, 94Ag and 92Pd with particular interest on the dependence of the controlling 9+-TBME [11,21–23,5]. The content of the various 𝑝𝑛-pairs within the nuclear wave functions in the three nuclei with increasing spin was discussed. However, overlap of the aligned 9+-𝑝𝑛-boson wave functions with the exact shell-model diagonalization could only be established for low- and high-spin states, and little overlap was found for intermediate spin [5]. These conclusions are subject to modifications when excitations in the full 𝜋𝜈(𝑓5∕2𝑝𝑔9∕2)and 𝜋𝜈(𝑔𝑑𝑠)space are considered in the LSSM calculations as presented in this work. In Ref. [24], predictions in these model spaces were compared with a pure (𝑔9∕2)𝑛approach for 𝐵(𝐸2) values and spectroscopic quadrupole moments in 92Pd and 96Cd. In the low-spin range (𝐼≤6), the three approaches are equivalent for excitation energy and 𝐵(𝐸2) values, but exhibit large differences in the (presently experimentally inaccessible) spectroscopic quadrupole moments. Moreover, the lower-Z nuclei in the 𝑔9∕2 orbital exhibit signs of significant quadrupole deformation [25]. This is expected to evolve for higher spins and for nuclei closer to the 𝑁=𝑍=50doubly-magic closure due to model space exhaustion, resulting in a gradual reduction in collectivity. The 𝑇𝑧=+1nucleus 94Pd, with its 2 neutron and 4 proton holes in 𝑔9∕2 orbital below 100Sn, is situated at a crucial point of this evolution. It is the neighbour of the even-even 𝑁=𝑍systems 92Pd and 96Cd, and represents the 𝑇=1 isospin partner for states in the oddodd 𝑁=𝑍system 94Ag. In particular, the detailed structure of the 8+ seniority remnant state in 94Pd will reveal the interplay between the isovector and isoscalar coupling of the 𝑝𝑛 pairs. Moreover, the structure of 94Pd in terms of seniority-mixed states may provide a first indication of emerging collectivity when nucleons are removed from the doublymagic system 100Sn. The emergence of deformation is also supported by the prediction that favoured 𝑝𝑛 𝑇 =0pairs arrange themselves in a spin-aligned configuration to form shears blades in the Anti-Magnetic Rotational (AMR) behaviour for the yrast band of 92Pd [26]. A recent theoretical publication using the EXVAM (Excited VAMPIR) approach [27]notes the relation of 𝑇=0𝑝𝑛-pairing component to the emergence of prolate deformation and shape coexistence in 94Pd. The experimental information on excited states in 94Pd is presently available up to spin-parity 𝐼𝜋= (20+) and originates from experiments in which decays of the isomeric states with spin-parity 𝐼𝜋=14 +and (19−) were studied [28–30], and from high-spin 𝛽-decay studies of 94Ag [31,32]. Only states fed by delayed transitions are known and no prompt 𝛾-ray radiation from states in 94Pd has so far been observed. This letter presents results on electromagnetic transition rates between yrast states in 94Pd. This allows a direct comparison between the predictions of various approaches of shell-model interactions and valence spaces. Special interest is put on 𝑝𝑛 interaction treatment for this 𝑇𝑧=+1nucleus intermediate between the 𝑁=𝑍line and the 𝑁=50 closed neutron shell. 2. Experimental details The decay of the isomeric, yrast 𝐼𝜋=14 +state in 94Pd [30]was studied through its production via the projectile fragmentation of a 124Xe primary beam at 982 MeV/u from the SIS18 synchrotron at GSI Helmholtzzentrum für Schwerionenforschung accelerator facility, Darmstadt, Germany. The secondary cocktail beam, resulting from reactions between the primary beam and a 4 g/cm2thick 9Be target, was separated in terms of mass-to-charge ratio (A/Q) and atomic number (Z) in the FRagment Separator (FRS) [33]. The fragmentation products were identified on an event-by-event basis using the standard 𝐵𝜌 −△𝐸−𝐵𝜌 and 𝑇𝑜𝐹 −𝐵𝜌 −△𝐸identification methods [34]. The ions reaching Physics Letters B 855 (2024) 138805 3 A. Yaneva, S. Jazrawi, M. Mikołajczuk et al. the final focal plane of the FRS were implanted in the Advanced Implantation Detector Array (AIDA) [35]in the center of the DEcay SPEC- troscopy (DESPEC) setup [36]. The 𝛾rays emitted in the deexcitation of the 14+isomeric state (𝑇1∕2 = 515(1) ns) in 94Pd were registered using 6 triple-cluster High Purity Germanium (HPGe) detectors (GALILEO) [37,38]and 36 LaBr3(Ce) detectors, constituting the FAst TIMing Array (FATIMA) [39,40]. Each detector subsystem was equipped with an independent data acquisition system. The synchronization of the different subsystems was achieved using White Rabbit (WR) time stamp [41], which is driven by a 125 MHz clock with time accuracy of up to ∼1ns. A preliminary analysis of these data on excited states transition rates in 96Pd has been reported by the collaboration [42]. 3. Data analysis and results To extract nuclear excited-state mean lifetimes, the energy and timing data recorded by the FATIMA array were used to construct 𝐸𝛾1−𝐸𝛾2−△𝑇2,1coincidence cubes, where a delayed coincidence with implanted 94Pd ions was applied. The delayed time distribution was obtained under the condition that the feeding transition provides the start signal and the decay -the stop signal. The 𝛾-ray spectrum obtained as total projection of the matrix is shown in Fig. 1(a) along with a resulting coincidence spectrum with the 1092-keV 𝛾ray in Fig. 1(b). A time alignment was performed for all FATIMA detectors using coincidences between the 344- and 779-keV transitions from 152Eu source data. The centroid of the delayed time distribution [43–45] 𝐶(𝐷)= ∫∞ −∞ 𝑡𝐷(𝑡)𝑑𝑡 ∫∞ −∞ 𝐷(𝑡)𝑑𝑡 ,(1) where 𝐷(𝑡)is the measured time distribution, was calculated for each detector pair. The centroid of the anti-delayed time distribution was obtained in an analogous way, where in contrast to the delayed distribution the feeding transition provides the stop signal and the decay -the start signal. The generalized centroid difference (△𝐶) was obtained by subtracting the two centroids. In the Generalized Centroid Difference (GCD) method [44,45]△𝐶is directly related to the mean lifetime 𝜏 according to the expression: △𝐶(△𝐸𝛾)=𝑃𝑅𝐷(△𝐸𝛾)+2𝜏, (2) where 𝑃𝑅𝐷(△𝐸𝛾) =𝑃𝑅𝐷(𝐸𝑓𝑒𝑒𝑑𝑒𝑟) −𝑃𝑅𝐷(𝐸𝑑𝑒𝑐𝑎𝑦)is the Prompt Response Difference and the symmetry condition with respect to feederdecay inversion [43]is: △𝐶(△𝐸𝛾)𝑑𝑒𝑐𝑎𝑦 =−△𝐶(− △𝐸𝛾)𝑓𝑒𝑒𝑑𝑒𝑟 𝑃𝑅𝐷(△𝐸𝛾)𝑑𝑒𝑐𝑎𝑦 =−𝑃𝑅𝐷(− △𝐸𝛾)𝑓𝑒𝑒𝑑𝑒𝑟. (3) Here △𝐸𝛾=𝐸𝑓 𝑒𝑒𝑑𝑒𝑟 −𝐸𝑑𝑒𝑐𝑎𝑦 is the energy difference between the feeding and decaying 𝛾rays. The PRD is energy dependent and was calibrated using various coincident transitions from 152Eu source data. The values were adjusted to the 344-keV reference energy and fitted using the equation [44]: 𝑃𝑅𝐷(𝐸𝛾)= 𝑎 √𝐸𝛾+𝑏+𝑐𝐸𝛾+𝑑, (4) where a, b, c, d are the parameters for the fit presented in Fig. 1(c). The fit residuals in Fig. 1(d) allow the systematic error of the PRD to be evaluated. This analysis method is sufficiently accurate to measure excitedstate half-lives in the range from of tens of picoseconds to nanoseconds, therefore a careful background treatment is essential. To minimize the influence of the Compton background underneath the full-energy peaks (FEP), the experimental centroid difference △𝐶𝑒𝑥𝑝 was corrected using [46]: △𝐶𝐹𝐸𝑃 =△𝐶𝑒𝑥𝑝 +𝑡𝑐𝑜𝑟𝑟(𝑑𝑒𝑐𝑎𝑦)+𝑡𝑐𝑜𝑟𝑟(𝑓 𝑒𝑒𝑑𝑒𝑟) 2(5) Fig. 1. (a) Total projection of 𝛾−𝛾matrix for isomer-delayed 𝛾rays obtained from FATIMA and correlated to implantation of 94Pd ions. The matrix includes 𝛾 rays registered within 5 ns from each other. (b) Background-subtracted energy spectrum of 𝛾rays measured in coincidence with the 1092-keV transition, as marked by the dashed red lines in (a). (c) PRD calibration and (d) residuals for the PRD fit. 𝑡𝑐𝑜𝑟𝑟 = △𝐶𝑒𝑥𝑝 −△𝐶𝐵𝐺 𝑃∕𝐵,(6) where △𝐶𝐵𝐺 is the centroid difference of the background time distribution, obtained for peak-background coincidences for both the decay and the feeding transition background, and P/B is the peak-to-background ratio. The △𝐶𝐹𝐸𝑃 values derived in this way along with the PRD values for the feeder-decay energy combinations obtained from the PRD curve were used in Eq. (2)to calculate the final mean lifetimes. To determine the half-lives of the yrast 𝐼𝜋=6 +and 8+states in 94Pd, the direct and indirect feeder-decay coincidences were used to produce delayed and anti-delayed time distributions. Direct coincidence is defined as the coincidence between consecutive transitions populating and depopulating a state of interest. Indirect coincidences are when more than one state is present between the feeding and decaying transitions. However, the use of indirect coincidences for intrinsic state half-life measurements in 94Pd is only possible assuming a prompt decay of the 𝐼𝜋=2 +, 4+, 10+and 12+states with respect to the state under investigation. In the present work it was assumed that the lifetimes of other states were shorter than 20 ps. To determine the half-life of the 𝐼𝜋=6 +, the direct coincidence between the 324- and 660-keV transitions, as well as indirect coincidences between the 324- and 905-keV, and 324- and 814-keV transitions ware used. Similarly, for the half-life of the yrast 𝐼𝜋=8 +state coincidences between the direct 1092- and 324-keV transitions was used in the first instance. In view of its long lifetime, the half-life of this state was determined also using the indirect coincidences between the transitions 1092 and 660 keV, 994 and 324 keV, 994 and 660 keV, 994 and 905 keV, 96 and 324 keV, 96 and 660 keV, 96 and 905 keV, 96 and 814 keV. For each coincidence, the delayed and anti-delayed time difference distributions were produced and their centroids determined. As an example, the time distributions of the direct coincidences for the 6+ and 8+states in 94Pd are shown in Fig. 2(a) and (b), respectively. After treating the background according to the procedure explained above, and accounting for the PRD shift correction for the particular coincidence, the mean-lifetime (𝜏) and half-life (𝑇1∕2 =𝜏𝑙𝑛2) of the state of interest were obtained according to Eq. (2). The experimentally-derived half-life for the 𝐼𝜋=6 +yrast state at 𝐸𝑥= 2379 keV was obtained from a weighted average of all determined excited-state half-lives (both from direct and indirect feeder-decay coincidences), resulting in the limit of 𝑇1∕2(6+) ≤40 ps. The analysis of the coincidence between the direct feeder-decay transitions of the 𝐼𝜋=8 + state at 𝐸𝑥= 2703 keV yields a half-life value of 755(106) ps. The weighted average of individually measured half-lives for indirect coincidences resulted in the value of 𝑇1∕2 = 825(50) ps, which corresponds to the effective values with embedded half-lives of intermediate states. Physics Letters B 855 (2024) 138805 4 A. Yaneva, S. Jazrawi, M. Mikołajczuk et al. Fig. 2. Delayed and anti-delayed time distributions for coincidences between the (a) 324- and 660-keV, as well as the (b) 1092- and 324-keV transitions in 94Pd. 4. Discussion The experimental results presented in this work are discussed within the shell-model framework. In Fig. 3the experimentally-established level energies together with the known 𝛾rays are shown in comparison to the two most advanced shell-model calculations in the full diagonalization of the nuclear Hamiltonian. The first one uses the JUN45 interaction [47]in the full 𝜋𝜈(𝑓5∕2𝑝𝑔9∕2)model space, while the second one is a LSSM calculation employing the GDS interaction [12]with 𝜋𝜈(𝑔𝑑𝑠)as the model space. Both calculations reproduce the experimental yrast level energies very well up to the highest known spins. In order to access the structure of involved states, and the associated nuclear deformation using the 𝜋𝜈(𝑔𝑑𝑠)valence space and effective GDS Hamiltonian, the potential energy surface (PES) of 92,94,96Pd were obtained from Discrete Nonorthogonal Shell Model (DNO-SM) calculations in the same way as introduced in Ref. [48,49]. As shown in Fig. 4, 94Pd exhibits a non-spherical shallow minimum at moderate prolate deformation. The ground-state wave function contains dominant contributions around 𝛽∼0.1 −0.2to high spins for the yrast and yrare states with no other coexisting minimum found in the PES. This is at variance with the claim made in Ref. [27]. The predicted (𝛽, 𝛾)distributions in the wave functions evolve from a spherical regime in 96Pd towards a more axiallydeformed prolate shape in the 𝑁=𝑍system 92Pd (see Fig. 4), with 𝑇𝑧=+194Pd being the transitional nucleus between these two extremes. This trend is particularly noticeable in the 𝐼𝜋=0 +ground states. For the 𝐼𝜋=8 +state in 96Pd the shape remains spherical, whereas the deformation pattern in the two other nuclei shifts towards sphericity and maintains as such up to higher spins, in particular for the 14+state in 94Pd. It should be noted that in 92Pd, where the development of an axial prolate shape in the ground state is the most pronounced, there is no indication of other shape-coexisting minima within the configuration space. The experimentally-obtained half-lives for the 6+and 8+states in 94Pd from the current work were used to determine reduced 𝐸2tran- sition strengths. The deduced 𝐵(𝐸2) values, together with the value for the decay of the 𝐼𝜋=14 +isomeric state reported in Ref. [50], are summarized and compared to the two aforementioned shell-model approaches (JUN45, GDS) in Table 1and Fig. 5. The values from Ref. [27] are provided in the table for a cross comparison. Effective charges of 𝑒𝜋=1.5𝑒and 𝑒𝜈=1.1𝑒according to Ref. [47]were used for the JUN45 interaction [47]as determined by the least-squares fit to the experimental data. This well-known phenomenologically-tuned realistic interaction, which has reproduced many nuclear properties from the 𝑁=3 harmonic oscillator shell and the region of 56Ni approaching 100Sn, is based on the Bonn-C potential. The calculated 𝐵(𝐸2) values are overestimated when compared to the experimental data (see Fig. 5) and do not allow a simultaneous reproduction of the 8+and the 14+states in Fig. 3. Experimental level scheme of excited states in 94Pd [28–32]as well as shell-model calculations, employing the JUN45 [47]and GDS [12]interactions (see text for details). 94Pd within the experimental uncertainties for any charge state combination. This is most probably a consequence of the strong mixing of the upper 𝑓𝑝 shell with the 𝑔9∕2 orbital, characteristic for this interaction and required for lighter nuclei to substitute the missing 𝑓7∕2 orbital in the corresponding model space. The agreement between the experimental results and the most challenging LSSM calculation, which employs the GDS interaction [12]with effective charges of 𝑒𝜋=1.1𝑒and 𝑒𝜈=0.84𝑒, extracted from 102Sn and 98Cd [51], is excellent. The involvement of core excitations (up to 5p5h) in the 𝜋𝜈(𝑔𝑑𝑠)model space, exhibits an almost exact reproduction of high-spin states (see Fig. 3) as well as of the reduced transition rates (see Fig. 5). On the other hand, the AMR calculations shown in Fig. 5(denoted by solid line) reproduce the transition rates measured in the current work very well. Ref. [26] demonstrates a good reproduction of the energy levels in 92Pd using the AMR coupling scheme. For 94Pd, the calculation is based on a similar 4 quasiparticle configuration as for the ground state of 92Pd, where the shears closing behaviour takes over beyond 𝐼𝜋=8 +. This may indicate that the 𝑇=1proton-proton and neutron-neutron pairs in the g9∕2 orbitals rearrange themselves to form two oppositely aligned 𝑇=0𝑝𝑛 shears blades, the closing mechanism of which takes over in generating the higher-spin states of 94Pd and continues until the shears blades are maximally aligned at 𝐼𝜋=16 +. This supports the Physics Letters B 855 (2024) 138805 5 A. Yaneva, S. Jazrawi, M. Mikołajczuk et al. Fig. 4. Potential energy surface (PES) plots for 96,94,92Pd nuclei for the ground state as well as for the first 𝐼𝜋=8 +states. Additionally, the PES for the 𝐼𝜋= 14+state in 94Pd is shown indicating a shallow prolate minimum (see text for details). dominance of the isoscalar (𝑇=0) phase beyond 𝐼𝜋=8 +. It is worth noting that the 4 quasiparticle AMR configuration for the spin states 𝐼𝜋<8+(denoted by dotted line in Fig. 5) is expected to mix with those of 2 quasiparticle one. With the aim of examining further the interplay of the isoscalar (𝑇=0) versus isovector (𝑇=1) components of the 𝑝𝑛 shell-model interaction on the structure of 94Pd, the excited-state lifetimes were analysed within the single-0𝑔9∕2 model. Although shell-model results presented in the current work indicate that a multi-orbital space including cross shell 𝑁, 𝑍=50excitations are needed to describe 94Pd quantitatively, the restriction to this rather simple model is justified by the spherical or slightly-deformed nature of Pd nuclei evidenced by these results as well as by the prominent role played by the 0𝑔9∕2 orbital in the low-lying states of nuclei around 𝑁, 𝑍=50[12,11,21–23]. Indeed, the wavefunction overlap of all 94Pd states with the (𝜋0𝑔9∕2)−4 ⊗(𝜈0𝑔9∕2)−2 configuration, as calculated within the LSSM approach, exceeds 95%. Therefore, based on this overwhelming dominance, the calculations in the single 0𝑔9∕2 model were performed by using the two-body effective interaction derived within the framework of the many-body perturbation theory starting from the high-precision CD-Bonn 𝑁𝑁 potential [52]. Details of the calculation are described in Ref. [53]. In addition, two subsets of interactions were obtained by separately removing the 𝑇=0and 𝑇=1𝑝𝑛 matrix elements. Similar to the 𝑁=𝑍case of 92Pd discussed in [53], the energies of the yrast levels of 94Pd are reasonably-well reproduced when using the full interaction. A spectrum with the same structure is obtained only if the pure 𝑇=0𝑝𝑛 component is considered, while the inclusion of only the 𝑇=1component leads to excited states compressed in a smaller energy interval, although the effect is smaller than the 𝑁=𝑍system 92Pd. These findings are in line with those reported in Ref. [11,1], indicating that the evolution from the seniority to vibrational-type spectrum from 96Pd to 92Pd, with 94Pd exhibiting an intermediate character is related to the 𝑇=0𝑝𝑛 interaction. This is the first time when such an analysis has been performed for 𝐵(𝐸2) transition strengths. Considering the significant restrictions of using a single-𝑗space, this analysis is not intended to reproduce the experimental values, but only to investigate the relevance of the isovector Table 1 Experimental half-lives expressed in ns and 𝐵(𝐸2) strengths in e2fm4for excited states in 94Pd compared to various shellmodel approaches. The experimental half-life value for the yrast 𝐼𝜋=14 +state is taken from Ref. [50]. Quantity [ns/e2fm4]𝐼𝜋 𝑖−𝐼𝜋 𝑓 14+→12+8+→6+6+→4+ 𝑇1∕2 515(1) 0.755(106) ≤0.04 𝐵𝑒𝑥𝑝(𝐸2) 52.1(1) 205+34 −25 ≥113 𝐵𝐽𝑈𝑁45(𝐸2) 101 252 453 𝐵𝐺𝐷𝑆 (𝐸2) 49 192 548 𝐵𝑔9∕2 (𝐸2) 112 144 398 𝐵𝑔9∕2 𝑇=0(𝑝𝑛)(𝐸2) 82 191 398 𝐵𝑔9∕2 𝑇=1(𝑝𝑛)(𝐸2) 9115 𝐵𝐸𝑋𝑉 𝐴𝑀 (𝐸2) [27] 56 165 336 Fig. 5. Experimental and shell-model calculated B(E2)1∕2 values, using different effective interactions and model spaces, for states in 94Pd (see text for details). with respect the isoscalar component of the 𝑝𝑛 interaction. The same effective charges of 𝑒𝜋=1.5𝑒and 𝑒𝜈=1.1𝑒as for the JUN45 calculation, were used. The 𝐵(𝐸2) corresponding to the full interaction and to the pure 𝑇=0∕1component are reported in Table 1, while in Fig. 5the results of the full interaction are compared with the experimental and other shell-model values. The overall behaviour is similar to that predicted by the JUN45 as well as the LSSM (GDS) approaches. However, the precision of the LSSM calculation when compared to the experimental values provides the best match, indicating again the relevance of core excitations. Furthermore, as shown in Table 1, the exclusion of the 𝑇=1𝑝𝑛 component from the single-j interaction does not change significantly the calculated 𝐵(𝐸2) values with respect to the full interaction for the decay of the yrast 𝐼𝜋=6 +, 8+and 14+states. In contrast, when considering a pure 𝑇=1force, considerably longer predicted half-lives are obtained. This finding demonstrates the effect of the different structure of the wave functions resulting from the 𝑇=1force, which is in general unable to produce a sufficient fragmentation of the basis states arising from the (𝜋0𝑔9∕2)−4 ⊗(𝜈0𝑔9∕2)−2 configuration. 5. Conclusion The half-life and transitions rates for decays of intermediate-spin states in 94Pd have been established using the FATIMA array. A range of restricted-basis model spaces and interactions were used to reproduce level energies and experimentally deduce 𝐵(𝐸2) values. The LSSM approach with a 𝜋𝜈(𝑔𝑑𝑠)model space provides the best agreement with the experimental results. This model indicates no development of deformation for Pd isotopes, which is predicted at the 𝑁=𝑍line following a parallel potential energy surface analysis. Based on this conclusion, the 𝑇=0contribution of the 𝑝𝑛 interaction is manifested as the dominant one in the transition strengths of the 8+seniority remnant state and the 14+isomeric state. Physics Letters B 855 (2024) 138805 6 A. Yaneva, S. Jazrawi, M. Mikołajczuk et al. 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. Data availability Data will be made available on request. Acknowledgements The authors thank A.O. Macchiavelli for a valuable discussion. The authors would like to thank the staff of the FRS and the GSI accelerator, for their excellent support. The results presented here are based on the experiment S480, which was performed at the DESPEC decay station at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt (Germany) in the frame of FAIR Phase-0. This work was supported by the Swedish Research Council under Grants No. 621-2014-5558 and No. 2019-04880. Support by the STFC under Grants No. ST/G000697/1, No. ST/P005314, and No. ST/P003982/1 and No. ST/P004598/1 and No. ST/V001027/1; by the UK Department for Business, Energy and Industrial Strategy via the National Measurement Office; by the BMBF under Grants No. 05P19RDFN1, No. 05P21RDFN1 and No. 05P21RDFN9; by the Helmholtz Research Academy Hesse for FAIR (HFHF); by the GSI F&E Grant No. KJOLIE1820; and by BMBF grant 05P19PKFNA and 0P21PKFN1 are also acknowledged. This work was supported by the Slovenian Research and Innovation Agency under Grants No. I0-E005 and No. P1-0102. P.H.R. and R.S. acknowledge support from the National Measurements System Programmes Unit of the UK’s Department for Science, Innovation and Technology (DESIT). G.H., M.S., and R.L. acknowledge IN2P3-GSI agreements, ADI-IDEX, and CSC-UPS grants. L.M.F. acknowledges the Spanish MICINN via Project No. RTI2018- 098868-B-100. 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