Proton and neutron contributions to the quadrupole transition strengths in Ca39 and K39 studied by lifetime measurements of mirror transitions

The $E2$ transition matrix elements of isobaric multiplets are expected to follow a linear trend as a function of isospin projection. However, measurements of the $2^{+}\to 0^{+}$ transitions in the $A=38$ triplet of Ca, K, and Ar show a deviation from this trend with an enhanced transition strength in ${}^{38}\mathrm{Ca}$ with respect to its mirror ${}^{38}\mathrm{Ar}$. We have studied analogue $11/2^{-}\to 7/2^{-} E2$ transitions in ${}^{39}\mathrm{Ca}$ and its mirror partner ${}^{39}\mathrm{K}$ to determine if this enhancement persists in neighboring Ca isotopes. Recoil-distance lifetime measurements of ${}^{39}\mathrm{Ca}$ and ${}^{39}\mathrm{K}$ were performed utilizing a ${}^{42}\mathrm{Sc}$ secondary beam, the TRIPLEX plunger, the GRETINA array, and the S800 spectrograph. Our data provide a lifetime measurement of the ($11/2^{-}$) state in ${}^{39}\mathrm{Ca}$ as well as an improved lifetime result for the ($9/2^{-}$) state, while the ${}^{39}\mathrm{K}$ data are used to validate the present analysis. A comparison of the present data to shell-model calculations suggests an enhanced transition strength in ${}^{39}\mathrm{Ca}$, pointing to both proton and neutron contributions to core excitations across the $Z=N=20$ shell gaps in close proximity to ${}^{40}\mathrm{Ca}$.