The Excitation Function of Lithium Under Proton Bombardment

Abstract

The yield of alpha-particles in the bombardment of lithium with protons is calculated for different depths and widths of the "potential well." It is found that agreement with experiment can be obtained either by using the part of the incident wave having an angular momentum $L=0\mathrm{}$ or the part having $L=1\mathrm{}$. For the first condition with a radius of 0.35×${10}^{-12\mathrm{}}$ cm one needs a "potential well" about 35 MEV deep. For $L=1\mathrm{}$ and the same radius a "well" about 21.5 MEV is needed. The latter depth fits in nicely with approximate estimates of this depth from nuclear binding energies. The calculations are made more carefully than is customary in the usual type of potential barrier penetration consideration. It is found that this is necessary and that even the order of magnitude of the collision cross section requires the more accurate type of calculation. The influence of the depth and width of the "potential well" is found to be pronounced and it is found possible to vary the shape of the excitation curve as well as the absolute value of the cross section by changing the depth and width of the "well." For energies sufficient to allow the proton to slip over the potential barrier classically, the collision cross section may increase or decrease with the energy depending on the "well." Thus the saturation of the yield with the voltage is not a good measure of the height of the barrier and of the nuclear radius. The position of stationary and resonance levels is found to be important for the shape of the excitation curve. The effect of the decay of the incident wave inside the nucleus is estimated and is found to be small in the present case. The asymptotic form of the dependence of the collision cross section on velocity at low velocities is $\mathrm{const}.\mathrm{}\times v^{-2\mathrm{}}\exp \{\frac{-2\mathrm{}\pi Z{Z}^{\prime }c}{137\text{'}\text{'}v\}}$ within the limitations of the present theory. Estimates of the theoretically expected variation of the yield with velocity are made for ${\mathrm{Li}}^7$+${\mathrm{H}}^2$ and compared with the experiments of Oliphant, Kinsey and Rutherford. A correspondence between different nuclear reactions is established by means of which one can use calculations for one reaction to obtain yields for another reaction with a corresponding "potential well." The "potential well" necessary for the quantitative representation of the alpha-particle reaction is compared with the mass of ${\mathrm{Be}}^8$. It is found possible to fit both requirements by attributing the alpha-particle reaction to $L=0\mathrm{}$ and the formation of ${\mathrm{Be}}^8$ from ${\mathrm{Li}}^7$ to the addition of a proton into a $p$ level.