Determination of the $^{12}$N$\to ^{11}$C+p asymptotic normalization coefficient from the indirect $^{11}$C(d,n)$^{12}$N transfer reaction.

The $^{11}$C(p,$\gamma )^{12}$N reaction has been known to be an important branch point in supermassive low-metallicity stars because it could produce CNO seed nuclei before the traditional triple-alpha process turns on. In the present work, the $^{11}$C(d,n)$^{12}$N transfer reaction was employed with a radioactive ion beam of 150 MeV $^{11}$C with 6$\times $10$^{5}$ ions/s on target from the BEARS project at the 88'' cyclotron at LBNL. Excellent agreement was obtained between the experimental cross sections ($\theta _{cm}$=10.9\r{ } to 71.5\r{ }) and DWBA calculations. The asymptotic normalization coefficient (ANC) was deduced to be $(C_{eff}^{12N} )^2=(C_{p1/2}^{12N} )^2+(C_{p3/2}^{12N} )^2=1.85\pm 0.27fm^{-1}$, which is in good agreement with the published result from $^{14}$N($^{11}$C,$^{ 12}$N)$^{13}$C. The astrophysical S-factor at zero-energy,$S(0)=0.099\pm 0.020\mbox{ }keV\mbox{ }b$, was also calculated based on the extracted ANC value. These results confirm that the $^{11}$C(p,$\gamma )^{12}$N reaction occurs at lower temperatures and densities than previously believed.