Precision measurement of the E 2 transition strength to the 2 1 + state of C 12

The form factor of the electromagnetic excitation of $^{12}\mathrm{C}$ to its ${2}_{1}^{+}$ state was measured at extremely low momentum transfers in an electron-scattering experiment at the Superconducting Darmstadt Electron Linear Accelerator (S-DALINAC). A combined analysis with the world form-factor data results in a reduced transition strength $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=7.63(19)\phantom{\rule{4pt}{0ex}}{e}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{4}$ with an accuracy improved to 2.5%. In-medium no-core shell-model results with interactions derived from chiral effective field theory are able to reproduce the result. A quadrupole moment $Q({2}_{1}^{+})=5.97(30)\phantom{\rule{4pt}{0ex}}e\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{2}$ can be extracted from the strict correlation with the $B(E2)$ strength emerging in the calculations.