Radiative Capture of Protons by Carbon

In previous notes we have reported results of calculations which show that the probability of $\gamma$-ray radiation is sufficiently high to make the reaction $C^{12}+{\mathrm{H}}^1\to {\mathrm{N}}^{13}+\gamma$ a probable one. It turned out that the theoretical yield is larger than that observed by a factor of roughly 1000. As in all intensity calculations the overlapping of wave functions in the initial and final states is of primary importance and the theoretical result is sensitive to this overlapping. The apparent discrepancy between calculation and experiment may be taken to indicate that the interaction between ${\mathrm{C}}^{12}$ and ${\mathrm{H}}^1$ is not represented sufficiently well by a potential function which is constant inside ${\mathrm{C}}^{12}$ and is Coulombian outside of it. In order to decrease the theoretical yield one has to change the potential in such a way as to decrease the region in which the initial and final wave functions overlap or else one must shift the region towards smaller radii. The $\gamma$-ray yield expected in the bombardment of ${\mathrm{Be}}^9$ by protons is calculated for a nuclear radius of 0.318×${10}^{-12\mathrm{}}$ cm and a well 9 MEV deep. It increases more slowly with the voltage than the observed intensity indicating a deeper nuclear well. A simple discussion of the method of complex eigenwerte is applied to the properties of wave functions near resonance.