B(E2) strength in $^{36,38}$Ca and in mirror nuclei 36S, 38Ar

Abstract: Recently, $B(E2, 0^+_1 \to 2^+_1)$ transition strength have been measured in $^{36}$Ca and $^{38}$Ca. Surprisingly, the measured value in $^{36}$Ca: $B(E2\ \uparrow) = 131(20)$ e$^2$fm$^4$, is significantly larger than in $^{38}$Ca, where $B(E2\ \uparrow) = 101(11)$ e$^2$fm$^4$, whereas an opposite tendency of $B(E2)$ values is seen in the mirror nuclei $^{36}$S and $^{38}$Ar. The resonance $2^+_1$ in $^{36}$Ca lies 465 keV above the proton emission threshold and its description requires inclusion of the coupling to the continuum. In this work, we are analyzing $B(E2\ \uparrow)$ values in $^{36}$Ca, $^{36}$S, $^{38}$Ca, and $^{38}$Ar using the real-energy continuum shell model, the so-called shell model embedded in the continuum, in the $(1s_{1/2}\, 0d_{3/2}\, 0f_{7/2}\, 1p_{3/2})$ model space with the monopole adjusted effective interaction ZBM-IO.