The Cross Section for the Radiative Capture of Protons byC12near 100 Kev

Abstract

A low voltage accelerator and high current ion source has been used to determine the cross section of the reaction ${\mathrm{C}}^{12}\left(p\gamma \right){\mathrm{N}}^{13}$ over the energy range from 88 to 128 kev. A counter arrangement is described which detects 26 percent of all the positrons from the decay of the ${\mathrm{N}}^{13}$ produced in the reaction and which has a low background rate of 5.5 counts per minute. With this accelerator and detector, yields of the order of ${10}^{-16\mathrm{}}$ positron per proton and cross sections as low as ${10}^{-10\mathrm{}}$ barn or ${10}^{-34\mathrm{}}$ ${\mathrm{cm}}^2$ can be measured with errors of the order of ±20 percent. The cross section for the ${\mathrm{C}}^{12}\left(p\gamma \right){\mathrm{N}}^{13}$ reaction has been found to fit the semi-empirical expression $\sigma =0.0024\mathrm{}{E}^{-1\mathrm{}}\exp [-6\mathrm{}{E}^{-\frac{1}{2}}]$ barn with $E$ in Mev over the energy range measured. This is in satisfactory agreement with the Breit-Wigner one-level dispersion formula using constants determined at the 456-kev resonance. The astrophysical implications of these results in connection with the carbon-nitrogen cycle of nuclear reactions in stellar interiors are discussed.