Measurement of the B(E2↑) strengths of Ca 36 and Ca 38

The B(E2,01+→21+) strengths of Ca36 and Ca38 are measured to be 131(20) e2fm4 and 101(11) e2fm4, respectively. The B(E2) value for Ca36 required a measurement of the p/γ branching ratio because the 2+ state is proton unbound. This branching ratio is Bp=0.087(8). These B(E2) and branching-ratio values can be reproduced in the shell-model with the ZMB2 interaction, an interaction that predicts the Z=20 sd-shell closure is incomplete with large proton pf-shell occupancies in the ground state. These occupancies are at odds with other shell-model and energy-density-functional calculations of Ca36. New data are used to provide an update on constraints of the density dependence of the symmetry energy through mirror charge-radii differences as well as to help reduce uncertainties of the astrophysical important K35(p,γ) reaction.