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Universal Effective Charges in the 𝑠⁢𝑑 and 𝑓⁡𝑝 Shells

Ogunbeku, T. H. [Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); et al.] (ORCID:0000000244427757)·Allmond, J. M. [Oak Ridge National Laboratory] (ORCID:0000000165338721)·Gray, T. J. [Oak Ridge National Laboratory; University of Tennessee] (ORCID:0000000339656130)·Ong, W.-J. [Lawrence Livermore National Laboratory] (ORCID:0000000209458654)·Brown, B. A. [Facility for Rare Isotope Beams] (ORCID:0000000261111906)·Gargano, A. [Istituto Nazionale di Fisica Nucleare] (ORCID:0000000313027387)·Grzywacz, R. [University of Tennessee]·Holt, J. D. [TRIUMF; McGill University] (ORCID:0000000348337959)·Macchiavelli, A. O. [Oak Ridge National Laboratory]·Miyagi, T. [Technische Universität Darmstadt; GSI Helmholtzzentrum für Schwerionenforschung GmbH; Max-Planck-Institut für Kernphysik; University of Tsukuba] (ORCID:0000000265294164)·Neupane, S. [Lawrence Livermore National Laboratory] (ORCID:0000000333398353)·Rasco, B. C. [Oak Ridge National Laboratory]·Schatz, H. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000316744859)·Sherrill, B. M. [Facility for Rare Isotope Beams; Michigan State University]·Tarasov, O. B. [Facility for Rare Isotope Beams] (ORCID:0000000304971421)·Arora, H. [Central Michigan University]·Ayangeakaa, A. D. [University of North Carolina at Chapel Hill; Triangle Universities Nuclear Laboratory] (ORCID:0000000316793175)·Berg, H. C. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000320901255)·Berkman, J. M. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000197530096)·Bleuel, D. L. [Lawrence Livermore National Laboratory] (ORCID:0000000327920715)·Bosmpotinis, K. [Facility for Rare Isotope Beams; Michigan State University]·Carpenter, M. P. [Argonne National Laboratory] (ORCID:0000000232375734)·Cerizza, G. [Facility for Rare Isotope Beams] (ORCID:0009000510639996)·Chester, A. [Facility for Rare Isotope Beams] (ORCID:0000000276257772)·Christie, J. M. [University of Tennessee] (ORCID:0000000286538236)·Cox, I. [University of Tennessee] (ORCID:0000000268073658)·Crawford, H. L. [Lawrence Berkeley National Laboratory]·Crider, B. P. [Mississippi State University] (ORCID:0000000171538762)·Davis, J. [Pacific Northwest National Laboratory] (ORCID:0009000701352197)·Doetsch, A. A. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:000000017223789X)·Duarte, J. G. [Lawrence Livermore National Laboratory] (ORCID:0000000287813834)·Estrade, A. [Central Michigan University]·Fijałkowska, A. [University of Warsaw] (ORCID:0000000164724284)·Frantzis, C. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000014825933)·Gaballah, T. [Facility for Rare Isotope Beams; Mississippi State University]·Good, E. C. [Pacific Northwest National Laboratory] (ORCID:0000000177656188)·Haak, K. [Facility for Rare Isotope Beams; Michigan State University]·Hanai, S. [University of Tokyo]·Harke, J. T. [Lawrence Livermore National Laboratory] (ORCID:0000000151307123)·Hartley, A. C. [Facility for Rare Isotope Beams; Michigan State University]·Hermansen, K. [Facility for Rare Isotope Beams; Michigan State University]·Hoff, D. E. M. [Lawrence Livermore National Laboratory] (ORCID:0000000308385892)·Hoskins, D. [University of Tennessee] (ORCID:0009000591278140)·Huffman, J. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000015361624)·Van Isacker, P. [Grand Accélérateur National d’Ions Lourds] (ORCID:0000000339389220)·Jain, R. [Lawrence Livermore National Laboratory] (ORCID:0000000198591512)·Karny, M. [University of Warsaw] (ORCID:0000000210506203)·King, T. T. [Oak Ridge National Laboratory] (ORCID:0000000306493275)·Kitamura, N. [University of Tennessee]·Kolos, K. [Lawrence Livermore National Laboratory] (ORCID:0000000217264171)·Laminack, A. [Oak Ridge National Laboratory] (ORCID:0000000251664523)·Liddick, S. N. [Facility for Rare Isotope Beams; Michigan State University]·Longfellow, B. [Lawrence Livermore National Laboratory]·Lubna, R. S. [Facility for Rare Isotope Beams]·Lyons, S. [Pacific Northwest National Laboratory] (ORCID:000000020194261X)·Madurga, M. [University of Tennessee] (ORCID:0000000281774328)·Mogannam, M. J. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000189514953)·Owens-Fryar, G. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000167286494)·Palomino, J. R. [Mississippi State University] (ORCID:0009000371943663)·Rajabali, M. M. [Tennessee Technological University] (ORCID:0000000210464998)·Richard, A. L. [Ohio University] (ORCID:000000018308688X)·Richardson, I. J. [Facility for Rare Isotope Beams]·Ronning, E. K. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000646725834)·Rose, G. E. [University of California] (ORCID:0000000256458905)·Ruland, T. J. [Oak Ridge National Laboratory] (ORCID:0000000333541754)·Rykaczewski, K. P. [Oak Ridge National Laboratory] (ORCID:0000000257173418)·Scielzo, N. D. [Lawrence Livermore National Laboratory] (ORCID:0000000349766552)·Scriven, D. P. [Facility for Rare Isotope Beams] (ORCID:0000000238532200)·Seweryniak, D. [Argonne National Laboratory]·Siegl, K. [University of Tennessee] (ORCID:000000027778315X)·Singh, M. [University of Tennessee] (ORCID:0000000223850492)·Spyrou, A. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000286428352)·Stepaniuk, M. [University of Warsaw] (ORCID:0000000296311713)·Stuchbery, A. E. [The Australian National University] (ORCID:0000000201989901)·Sweet, A. [Lawrence Livermore National Laboratory] (ORCID:0000000177505232)·Tripathi, V. [Florida State University] (ORCID:0000000288501357)·Tsantiri, A. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000297593476)·Uthayakumaar, S. [Facility for Rare Isotope Beams] (ORCID:0000000231540734)·Walters, W. B. [University of Maryland] (ORCID:0000000156926943)·Watters, S. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:000000026243394X)·Xu, Z. [University of Tennessee] (ORCID:0000000186261276)·Yokoyama, R. [University of Tokyo] (ORCID:0000000332983542)
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Abstract

The 247-keV state in 54 Sc, populated in the 𝛽 decay of 54 Ca, is reported here as a nanosecond isomer with a half-life of 26.0(22) ns. The state is interpreted as the 1 + member of the 𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑓 5/2 spin-coupled multiplet, which decays to the 3 + ,𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑝 1/2 ground state. The new half-life corresponds to a pure 𝐸⁢2 transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous 𝐵⁡(𝐸⁢2) value in the neutron-rich 𝑓⁡𝑝 region to date for a nucleus with valence protons above 𝑍 = 20. Notably, it is roughly 4 times larger than the 𝐵⁡(𝐸⁢2;1/2 − → 5/2 − ) value in 55 Ca. The results, as compared to semiempirical and ab initio shell-model calculations, indicate (1) a weak 𝑁 = 34 subshell gap relative to 𝑁 = 32, (2) a large 𝐸⁢2 enhancement in Sc as compared to Ca due to 1⁢𝑝 − 1⁢ℎ proton excitations across 𝑍 = 28, and (3) empirical effective proton and neutron charges 𝑒 𝜋 = 1.30⁢(8)⁢𝑒 and 𝑒 𝜈 = 0.452⁢(7)⁢𝑒, respectively, that are in contrast to reports of 𝑒 𝜋 ≈1.1–1.15⁢𝑒 and 𝑒 𝜈 ≈ 0.6–0.8⁢𝑒 for 𝑓⁡𝑝-shell nuclei near 𝑁 = 𝑍. Here, we demonstrate that these reports are erroneous and that, in fact, a universal set of effective charges can be used across the 𝑠⁢𝑑 and 𝑓⁡𝑝 shells.

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Ogunbeku, T. H. [Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); et al.] (ORCID:0000000244427757), Allmond, J. M. [Oak Ridge National Laboratory] (ORCID:0000000165338721), Gray, T. J. [Oak Ridge National Laboratory; University of Tennessee] (ORCID:0000000339656130), Ong, W.-J. [Lawrence Livermore National Laboratory] (ORCID:0000000209458654), Brown, B. A. [Facility for Rare Isotope Beams] (ORCID:0000000261111906), Gargano, A. [Istituto Nazionale di Fisica Nucleare] (ORCID:0000000313027387), Grzywacz, R. [University of Tennessee], Holt, J. D. [TRIUMF; McGill University] (ORCID:0000000348337959), Macchiavelli, A. O. [Oak Ridge National Laboratory], Miyagi, T. [Technische Universität Darmstadt; GSI Helmholtzzentrum für Schwerionenforschung GmbH; Max-Planck-Institut für Kernphysik; University of Tsukuba] (ORCID:0000000265294164), Neupane, S. [Lawrence Livermore National Laboratory] (ORCID:0000000333398353), Rasco, B. C. [Oak Ridge National Laboratory], Schatz, H. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000316744859), Sherrill, B. M. [Facility for Rare Isotope Beams; Michigan State University], Tarasov, O. B. [Facility for Rare Isotope Beams] (ORCID:0000000304971421), Arora, H. [Central Michigan University], Ayangeakaa, A. D. [University of North Carolina at Chapel Hill; Triangle Universities Nuclear Laboratory] (ORCID:0000000316793175), Berg, H. C. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000320901255), Berkman, J. M. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000197530096), Bleuel, D. L. [Lawrence Livermore National Laboratory] (ORCID:0000000327920715), Bosmpotinis, K. [Facility for Rare Isotope Beams; Michigan State University], Carpenter, M. P. [Argonne National Laboratory] (ORCID:0000000232375734), Cerizza, G. [Facility for Rare Isotope Beams] (ORCID:0009000510639996), Chester, A. [Facility for Rare Isotope Beams] (ORCID:0000000276257772), Christie, J. M. [University of Tennessee] (ORCID:0000000286538236), Cox, I. [University of Tennessee] (ORCID:0000000268073658), Crawford, H. L. [Lawrence Berkeley National Laboratory], Crider, B. P. [Mississippi State University] (ORCID:0000000171538762), Davis, J. [Pacific Northwest National Laboratory] (ORCID:0009000701352197), Doetsch, A. A. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:000000017223789X), Duarte, J. G. [Lawrence Livermore National Laboratory] (ORCID:0000000287813834), Estrade, A. [Central Michigan University], Fijałkowska, A. [University of Warsaw] (ORCID:0000000164724284), Frantzis, C. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000014825933), Gaballah, T. [Facility for Rare Isotope Beams; Mississippi State University], Good, E. C. [Pacific Northwest National Laboratory] (ORCID:0000000177656188), Haak, K. [Facility for Rare Isotope Beams; Michigan State University], Hanai, S. [University of Tokyo], Harke, J. T. [Lawrence Livermore National Laboratory] (ORCID:0000000151307123), Hartley, A. C. [Facility for Rare Isotope Beams; Michigan State University], Hermansen, K. [Facility for Rare Isotope Beams; Michigan State University], Hoff, D. E. M. [Lawrence Livermore National Laboratory] (ORCID:0000000308385892), Hoskins, D. [University of Tennessee] (ORCID:0009000591278140), Huffman, J. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000015361624), Van Isacker, P. [Grand Accélérateur National d’Ions Lourds] (ORCID:0000000339389220), Jain, R. [Lawrence Livermore National Laboratory] (ORCID:0000000198591512), Karny, M. [University of Warsaw] (ORCID:0000000210506203), King, T. T. [Oak Ridge National Laboratory] (ORCID:0000000306493275), Kitamura, N. [University of Tennessee], Kolos, K. [Lawrence Livermore National Laboratory] (ORCID:0000000217264171), Laminack, A. [Oak Ridge National Laboratory] (ORCID:0000000251664523), Liddick, S. N. [Facility for Rare Isotope Beams; Michigan State University], Longfellow, B. [Lawrence Livermore National Laboratory], Lubna, R. S. [Facility for Rare Isotope Beams], Lyons, S. [Pacific Northwest National Laboratory] (ORCID:000000020194261X), Madurga, M. [University of Tennessee] (ORCID:0000000281774328), Mogannam, M. J. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000189514953), Owens-Fryar, G. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000167286494), Palomino, J. R. [Mississippi State University] (ORCID:0009000371943663), Rajabali, M. M. [Tennessee Technological University] (ORCID:0000000210464998), Richard, A. L. [Ohio University] (ORCID:000000018308688X), Richardson, I. J. [Facility for Rare Isotope Beams], Ronning, E. K. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0009000646725834), Rose, G. E. [University of California] (ORCID:0000000256458905), Ruland, T. J. [Oak Ridge National Laboratory] (ORCID:0000000333541754), Rykaczewski, K. P. [Oak Ridge National Laboratory] (ORCID:0000000257173418), Scielzo, N. D. [Lawrence Livermore National Laboratory] (ORCID:0000000349766552), Scriven, D. P. [Facility for Rare Isotope Beams] (ORCID:0000000238532200), Seweryniak, D. [Argonne National Laboratory], Siegl, K. [University of Tennessee] (ORCID:000000027778315X), Singh, M. [University of Tennessee] (ORCID:0000000223850492), Spyrou, A. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000286428352), Stepaniuk, M. [University of Warsaw] (ORCID:0000000296311713), Stuchbery, A. E. [The Australian National University] (ORCID:0000000201989901), Sweet, A. [Lawrence Livermore National Laboratory] (ORCID:0000000177505232), Tripathi, V. [Florida State University] (ORCID:0000000288501357), Tsantiri, A. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:0000000297593476), Uthayakumaar, S. [Facility for Rare Isotope Beams] (ORCID:0000000231540734), Walters, W. B. [University of Maryland] (ORCID:0000000156926943), Watters, S. [Facility for Rare Isotope Beams; Michigan State University] (ORCID:000000026243394X), Xu, Z. [University of Tennessee] (ORCID:0000000186261276), Yokoyama, R. [University of Tokyo] (ORCID:0000000332983542). 2025-08-14. Universal Effective Charges in the 𝑠⁢𝑑 and 𝑓⁡𝑝 Shells. https://doi.org/10.1103/75ry-71sj

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