Puzzling $B(E2;0^+\rightarrow 2^+)$ strength in the proton dripline nucleus $^{36}$Ca

Abstract: Recent measurements of the $E2$ transition rate from the ground state to the first 2$^+$ excited state of the proton dripline nucleus $^{36}$Ca show an unusual pattern when compared to its isotopic neighbor $^{38}$Ca: despite having a higher $E_x(2_1^+)$ excitation energy, the $B(E2; 0^+_1\rightarrow 2^+_1)$ rate in $^{36}$Ca is larger. The question that naturally arises is to what extent this observation can be attributed to the unbound character of the $2^+_1$ state. To understand the influence of the continuum space on the low-energy properties of $^{36}$Ca, we carried out Gamow shell model calculations that can account for the continuum coupling effects. We found that in the threshold $2^+$ state, $^{36}$Ca is spatially diffused, which accounts for the abnormal $B(E2)$ trend observed.