Universal Effective Charges in the 𝑠𝑑 and 𝑓𝑝 Shells
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 ⊗ 𝜈𝑓 5/2 spin-coupled multiplet, which decays to the 3 + ,𝜋𝑓 7/2 ⊗ 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 4 times larger than the 𝐵(𝐸2;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 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 ≈1.1–1.15𝑒 and 𝑒 𝜈 ≈ 0.6–0.8𝑒 for 𝑓𝑝-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 𝑠𝑑 and 𝑓𝑝 shells.