Nuclear Cross Sections at Low Energies

The note is concerned with estimates of the accuracy of the one-term formula for the energy dependence of the reaction cross section for charged particles. The second term in an expansion of the cross section in powers of the energy is worked out for a one-body model. Comparison with data of Sawyer and Phillips on the bombardment of Li and Be with protons and deuterons shows that the deviations from the one-term formula are of the correct order of magnitude to be accounted for by the second term. This term was compared with the effect of the 107-kev resonance on the cross section of ${\mathrm{H}}^3(d, n){\mathrm{He}}^4$. Employing a conservative central-field model the correction term to the one-body asymptotic form is found to be smaller than the effect of the resonance expected from the Breit-Wigner formula. The $f$-function generalization to $L>\mathrm{}0\mathrm{}$ which has been made by Breit is studied and a table facilitating its use for the calculation of reaction cross sections is given.