Investigating $13C+12C$ reaction by the activation method. Sensitivity tests

We have performed experiments to check the limits of sensitivity of the activation method using the new 3 MV Tandetron accelerator and the low and ultra-low background laboratories of the “Horia Hulubei” National Institute of Physics and Nuclear Engineering (IFIN-HH). We have used the $12C+13C$ reaction at beam energies E_lab= 6, 7 and 8 MeV. The knowledge of this fusion cross section at deep sub-barrier energies is of interest for astrophysical applications, as it provides an upper limit for the fusion cross section of $12C+12C$ over a wide energy range. A $13C$ beam with intensities 0.5–2 particleμA was provided by the accelerator and used to bombard graphite targets, resulting in activation with $24Na$ from the $12C$(⁠$13C$⁠,p) reaction. The 1369 and 2754 keV gamma-rays from $24Na$ de-activation were clearly observed in the spectra obtained in two different laboratories used for measurements at low and ultralow background: one at the surface and one located underground in the Unirea salt mine from Slanic Prahova, Romania. In the underground laboratory, for E_lab = 6 MeV we have measured an activity of 0.085 ± 0.011 Bq, corresponding to cross sections of 1–3 nb. This demonstrates that it is possible to measure $12C$ targets irradiated at lower energies for at least 10 times lower cross sections than before β–γ coincidences will lead us another factor of 10 lower, proving that this installations can be successfully used for nuclear astrophysics measurements.