arXiv · 2506.21852
Universal Effective Charges in the $sd$ and $fp$ Shells
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 $πf_{7/2}\otimesνf_{5/2}$ spin-coupled multiplet, which decays to the $3^+,πf_{7/2} \otimes νp_{1/2}$ ground state. The new half-life corresponds to a pure $E2$ transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous $B(E2)$ value in the neutron-rich $fp$ region to date for a nucleus with valence protons above $Z=20$. Notably, it is roughly four times larger than the $B(E2; 1/2^{-} \rightarrow 5/2^{-})$ value in $^{55}$Ca. The results, as compared to semi-empirical and ab initio shell-model calculations, indicate (1) a weak $N=34$ sub-shell gap relative to $N = 32$, (2) a large $E2$ enhancement in Sc as compared to Ca due to $1p-1h$ 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 $e_π\approx 1.1-1.15e$ and $e_ν\approx 0.6-0.8e$ for $fp$-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 $sd$ and $fp$ shells.
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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. 2025-06-27. Universal Effective Charges in the $sd$ and $fp$ Shells. https://doi.org/10.1103/75ry-71sj
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