Precision measurement of the $E2$ transition strength to the 2${}_1^{+}$ state of ${}^{12}$C

The form factor of the electromagnetic excitation of ${}^{12}$C to its 2${}_1^{+}$ state was measured at extremely low momentum transfers in an electron scattering experiment at the S-DALINAC. A combined analysis with the world form factor data results in a reduced transition strength $B(E2; 2^+_1\rightarrow 0^+_1) =7.63(19)$e$^2$fm$^4$ with an accuracy improved to 2.5%. In-Medium-No Core Shell Model results with interactions derived from chiral effective field theory are capable to reproduce the result. A quadrupole moment $Q(2^+_1) = 5.97(30)$efm$^2$canbeextractedfromthestrictcorrelationwiththe$B((E2)$ strength emerging in the calculations.