Universal Effective Charges in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>s</mi><mi>d</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>f</mi><mi>p</mi></mrow></math> Shells

T. H. Ogunbeku; J. M. Allmond; T. J. Gray; W.-J. Ong; B. A. Brown; A. Gargano; R. Grzywacz; J. D. Holt; A. O. Macchiavelli; T. Miyagi; S. Neupane; B. C. Rasco; H. Schatz; B. M. Sherrill; O. B. Tarasov; H. Arora; A. D. Ayangeakaa; H. C. Berg; J. M. Berkman; D. L. Bleuel; K. Bosmpotinis; M. P. Carpenter; G. Cerizza; A. Chester; J. M. Christie; I. Cox; H. L. Crawford; B. P. Crider; J. Davis; A. A. Doetsch; J. G. Duarte; A. Estrade; A. Fijałkowska; C. Frantzis; T. Gaballah; E. C. Good; K. Haak; S. Hanai; J. T. Harke; A. C. Hartley; K. Hermansen; D. E. M. Hoff; D. Hoskins, III; J. Huffman; P. Van Isacker; R. Jain; M. Karny; T. T. King; N. Kitamura; K. Kolos; A. Laminack; S. N. Liddick; B. Longfellow; R. S. Lubna; S. Lyons; M. Madurga; M. J. Mogannam; G. Owens-Fryar; J. R. Palomino; M. M. Rajabali; A. L. Richard; I. J. Richardson; E. K. Ronning; G. E. Rose; T. J. Ruland; K. P. Rykaczewski; N. D. Scielzo; D. P. Scriven; D. Seweryniak; K. Siegl; M. Singh; A. Spyrou; M. Stepaniuk; A. E. Stuchbery; A. Sweet; V. Tripathi; A. Tsantiri; S. Uthayakumaar; W. B. Walters; S. Watters; Z. Xu; R. Yokoyama

doi:10.1103/75ry-71sj

Universal Effective Charges in the $s d$ and $f p$ Shells

T. H. Ogunbeku ¹, J. M. Allmond ², T. J. Gray ^2,3, W.-J. Ong ¹, B. A. Brown ⁴, A. Gargano ⁵, R. Grzywacz³, J. D. Holt ^6,7, A. O. Macchiavelli² et al.

T. Miyagi ^8,9,10,11, S. Neupane ¹, B. C. Rasco², H. Schatz ^4,12, B. M. Sherrill^4,12, O. B. Tarasov ⁴, H. Arora¹³, A. D. Ayangeakaa ^14,15, H. C. Berg ^4,12, J. M. Berkman ^4,16, D. L. Bleuel ¹, K. Bosmpotinis^4,12, M. P. Carpenter ¹⁷, G. Cerizza ⁴, A. Chester ⁴, J. M. Christie ³, I. Cox ³, H. L. Crawford¹⁸, B. P. Crider ¹⁹, J. Davis ²⁰, A. A. Doetsch ^4,12, J. G. Duarte ¹, A. Estrade¹³, A. Fijałkowska ²¹, C. Frantzis ^4,12, T. Gaballah^4,19, E. C. Good ²⁰, K. Haak^4,12, S. Hanai²², J. T. Harke ¹, A. C. Hartley^4,12, K. Hermansen^4,12, D. E. M. Hoff ¹, D. Hoskins, III ³, J. Huffman ^4,12, P. Van Isacker ²³, R. Jain ¹, M. Karny ²¹, T. T. King ², N. Kitamura³, K. Kolos ¹, A. Laminack ², S. N. Liddick^4,16, B. Longfellow¹, R. S. Lubna⁴, S. Lyons ²⁰, M. Madurga ³, M. J. Mogannam ^4,16, G. Owens-Fryar ^4,12, J. R. Palomino ¹⁹, M. M. Rajabali ²⁴, A. L. Richard ²⁵, I. J. Richardson⁴, E. K. Ronning ^4,16, G. E. Rose ²⁶, T. J. Ruland ², K. P. Rykaczewski ², N. D. Scielzo ¹, D. P. Scriven ⁴, D. Seweryniak²⁷, K. Siegl ³, M. Singh ³, A. Spyrou ^4,12, M. Stepaniuk ²¹, A. E. Stuchbery ²⁸, A. Sweet ¹, V. Tripathi ²⁹, A. Tsantiri ^4,12, S. Uthayakumaar ⁴, W. B. Walters ³⁰, S. Watters ^4,12, Z. Xu ³, and R. Yokoyama ²²

¹Lawrence Livermore National Laboratory, Livermore, California 94550, USA
²Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37966, USA
⁴Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA
⁵Istituto Nazionale di Fisica Nucleare, Complesso Universitario di Monte S. Angelo, Napoli I-80126, Italy
⁶TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada
⁷Department of Physics, McGill University, 3600 Rue University, Montréal, Quebec H3A 2T8, Canada
⁸Department of Nuclear Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
⁹ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
¹⁰Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
¹¹Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibraki 305-8577, Japan
¹²Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
¹³Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
¹⁴Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
¹⁵Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina 27708, USA
¹⁶Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
¹⁷Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
¹⁸Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
¹⁹Department of Physics and Astronomy, Mississippi State University, Mississippi State, Mississippi 39762, USA
²⁰Pacific Northwest National Laboratory, Richland, Washington 99354, USA
²¹Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland
²²Center for Nuclear Study, University of Tokyo, Wako, Saitama 351-0198, Japan
²³Grand Accélérateur National d’Ions Lourds, CEA/DSM-CNRS/IN2P3, Boulevard Henri Becquerel, F-14076 Caen, France
²⁴Physics Department, Tennessee Technological University, Cookeville, Tennessee 38505, USA
²⁵Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
²⁶University of California, Berkeley, Berkeley, California 94704, USA
²⁷Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
²⁸Department of Nuclear Physics and Accelerator Applications, Research School of Physics, The Australian National University, ACT 2601, Canberra, Australia
²⁹Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
³⁰Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA

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Phys. Rev. Lett. 135, 072501 – Published 14 August, 2025

DOI: https://doi.org/10.1103/75ry-71sj

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 $π f_{7 / 2} \otimes ν f_{5 / 2}$ spin-coupled multiplet, which decays to the $3^{+}, π f_{7 / 2} \otimes ν p_{1 / 2}$ 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 $B (E 2; 1 / 2^{-} \to 5 / 2^{-})$ 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 $e_{π} \approx 1.1 - 1.15 e$ and $e_{ν} \approx 0.6 - 0.8 e$ for $f p$ -shell nuclei near $N = Z$ . 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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Universal Effective Charges in the sd and fp Shells

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Universal Effective Charges in the $s d$ and $f p$ Shells