??C(n,?) ??C as a Test Case in the Evaluation of a New Method to Determine Spectroscopic Factors Using Asymptotic Normalization Coefficients

Abstract

With new radioactive isotope accelerators coming online in the next decade, the problem of extracting reliable nuclear structure information from reactions with unstable nuclei deserves considerable attention. A method has been proposed to determine spectroscopic factors (SFs) using the asymptotic normalization coefficient (ANC) to fix the external contribution of a nonperipheral reaction, reducing the uncertainty in the SF. The ??C[left right arrow]??C+n system was chosen as a test case for this new method. The direct neutron capture rate on ??C is important for a variety of topics of interest in astrophysics, and the ANC for ??C[left right arrow]??C+n was also used to calculate this reaction rate. The objective of the first part of this work was to find the ANC for ??C[left right arrow]??C+n. This was done in two independent experiments. First, the heavy ion neutron transfer reaction ??C(??C,??C)??C was measured at 12 MeV/nucleon. Second, the inverse kinematics reaction d(??C,p)??C was measured using the new Texas Edinburgh Catania Silicon Array (TECSA). The next phase of the experimental program was to measure a reaction with a non-negligible interior contribution, for which ??C(d,p)??C at 60 MeV deuteron energy was used. This reaction turned out to be more peripheral than anticipated, and as a result, the ANC for the ground state was extracted from this measurement as well. The final results for the three measurements are C?2s1/2 = 1.96?0.16 fm?? for the ground state and C?1d5/2 = (4.23?0.38)?10?? fm?? for the first excited state. Because the 60 MeV ??C(d,p)??C reaction turned out to have a very weak dependence on the interior, the SF could not be determined for the ??C+n ground state in ??C using the new method. A lower limit of 1.05 was found for the first excited state. It is possible that other reactions might turn out to be more suitable for this method, however, the difficulty encountered at this relatively high deuteron energy highlights a substantial problem likely to be seen in other applications. Using the ANCs determined in this work, the astrophysical ??C(n,?)??C reaction rate was calculated. The resulting value for the cross section for capture to the ground state at 23 keV was ?gs(23 keV)=5.1?0.4 ?b and to the first excited state was ?exc(23 keV)=0.2?0.02 ?b.