Universal Effective Charges in the $sd$ and $fp$ Shells

Abstract

The 247-keV state in ${}^{54}$Sc, populated in the $\beta$ 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 $\pi f_{7/2}\otimes \nu f_{5/2}$ spin-coupled multiplet, which decays to the $3^{+},\pi f_{7/2}\otimes \nu p_{1/2}$ 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 $B(E2;1/2^{-}\to 5/2^{-})$ 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, $e_{\pi }$ = 1.30(8)$e$ and $e_{\nu }$ = 0.452(7)$e$, respectively, that are in contrast to reports of $e_{\pi }\approx 1.1-1.15e$ and $e_{\nu }\approx 0.6-0.8e$ 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.

11 pages (including 1-page appendix), 5 figures, accepted by Physical Review Letters

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