The Carbon Isotope Fusion Reactions At Deep Sub-barrier Energies

The fusion reaction¹²C+¹²C is critically important in nuclear astrophysics.The temperature of carbon burning varies from 0.15～2 GK,in which the energy range ex-tends from tens of ke V to 3 Me V.Until now,all the direct measurements have been lim-ited to the reaction energy above_c.m.=2.1 Me V.Due to the complexity in¹²C+¹²C reaction,theoretical model predictions of fusion cross sections become extremely diffi-cult.As a result,the extrapolations by different models differ by up to 2 orders of mag-nitude at_c.m.=1.5 Me V.In order to obtain the reliable reaction rate for astrophysical models,we need to depend on the indirect measurements in a wider energy region and well-constrained extrapolation models,or develop new techniques to push the detection limit.This thesis work includes two parts on studying carbon fusion reaction.The first part is the measurement of¹²C+¹³C fusion cross section.In contrast to the striking resonances of fusion cross sections in¹²C+¹²C,¹²C+¹³C reaction behaves much more smoothly and is considered to be upper limit for¹²C+¹²C.The measurement of¹²C+¹³C was performed in an activation experiment by detecting the residual nucleus24Na from¹²C(¹³C,p)²⁴Na.The¹³C beam was provided by the 3 MV Tandem of IFIN-HH,Bucharest,Romania.Thanks to the high current beam of 3 Me V Tandem and ultra-low background in theμBq underground laboratory,the measurement was first pushed down to_c.m.=2.323 Me V,at which the cross section is 0.22 nb.With a calibrated statistical model using experimental data,we obtained the total fusion cross section which rules out the prediction of the hindrance model.Our results confirm the rising trend of the S-factor predicted by other models and a more reliable upper limit is established.The second part is the direct measurement for¹²C+¹²C fusion reaction.We de-veloped a new technique to study¹²C+¹²C fusion reaction at stellar energies using a detector array consisting of time projection chamber and silicon detectors.An intense12C beam was delivered by the LEAF facility at IMP.With the excellent capabilities of tracking and particle identification and the good energy resolution of silicon detectors,we achieved a sensitivity of 1.38_-0⁺²..₈₇⁴¹×10^-17/¹²C（1）,corresponding to 4.4×10^-11b,for the¹²C(¹²C,₀)²⁰Ne channel at_c.m.=2.2 Me V.The background is less than0.45/day.The new technique makes it possible to obtain a reliable¹²C+¹²C fusion reac-tion cross section and verify the existence of the strong resonance at_c.m.=2.14 Me V.