Energy of the First Two Excited States of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$

Owing to its importance in stellar helium burning, we have carefully remeasured the excitation energy of the second excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ with a tandem accelerator and a broad-range magnetic spectrograph. The excitation energy of this state is found to be 7655.9 ± 2.5 keV, in excellent agreement with two other recent measurements. This value lowers the calculated rate of the helium-burning process in stars by a factor of ≅3 from that previously assumed. A simultaneous measurement of the first excited state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ gives 4442.2 ± 1.5 keV. A comparison is made with recent $\gamma$-ray measurements of this state.