Direct and Indirect Techniques for Determining Reaction Rates

Astrophysically important reactions have been studied through indirect techniques for many years due to their prohibitively small cross sections at Gamow window energies. Indirect techniques, such as $\alpha$-transfer reactions, constrain the reaction cross section of interest in the astrophysically relevant energy range. Recently, we determined the contribution of the 3$^{-}$ state at 6.4 MeV in $^{18}$O to the $^{14}$C($\alpha,\gamma$) reaction rate through the indirect $\alpha$-transfer reaction $^{14}$C($^{7}$Li,t) at the John D. Fox Superconducting Accelerator Laboratory at FSU. Using the same experimental data we were able to determine the asymptotic normalization coefficient (ANC) of the 1$^{-}$ state at 6.2 MeV in $^{18}$O. This state is a mirror of the 6.15 MeV state in $^{18}$Ne, which dominates the $^{14}$O($\alpha$,p) reaction rate at temperatures of Novae and X-ray bursters. An experimental apparatus which will allow for direct measurements of the astrophysically important ($\alpha$,p) reaction rates in the Gamow window, the LSU-FSU Array for Nuclear Astrophysics Studies with Exotic Nucelei (ANASEN), is now under construction. I will discuss our recent results on the $^{14}$C($\alpha$,$\gamma$) and $^{14}$O($\alpha$,p) reaction rates and the current status of the ANASEN project.