13C → 13N + 2e- (for 0νββ)
or
Assuming the correct notation refers to the double beta decay of Carbon-13 to Nitrogen-13: co3 0nu
However, I need to point out that there seems to be a typo in your request. The commonly studied isotopes for 0νββ decay are not CO3 but rather nuclei like Germanium-76 (76Ge), Selenium-82 (82Se), Molybdenum-100 (100Mo), and Tellurium-130 (130Te), among others.
To date, no experiments have been conducted specifically targeting the 0νββ decay of 13C. The primary reason is the extremely low expected rate and high background levels anticipated in such measurements. 13C → 13N + 2e- (for 0νββ) or
The double beta decay is a second-order process in the weak nuclear force, where two neutrons in the nucleus are converted into two protons, two electrons, and two neutrinos. The 0νββ decay, if observed, would imply that the neutrinos are Majorana particles (i.e., their antiparticles are themselves) and have mass.
While 13C could theoretically undergo 0νββ decay, there are no ongoing or planned experiments focused on this specific process due to its unfavorable characteristics. The search for 0νββ decay remains an active area of research in particle physics, with several experiments currently operating or planned to study this phenomenon in more promising nuclei. The primary reason is the extremely low expected
Carbon-13 is not commonly studied for 0νββ decay due to its relatively low atomic mass and unfavorable Q-value. The more commonly studied isotopes have higher Q-values and larger nuclear matrix elements.