A transmutation function for deuterons

It has been observed (Lawrence, McMillan and Thornton 1935) that when deuterons are used as bombarding particles, and the reaction involved is of the type AXZ + 2H1→A+1XZ+1H1, (1) the continuous increase of the transmutation function with deuteron energy is not correctly represented by the Gamow factor exp[- 2πZe2/ħ (M/W)½], (2) in which 2M stands for the mass and W for the kinetic energy of the deuteron. Oppenheimer and Phillips (1935) explained this by the fact that Gamow’s familiar considerations are not applicable in this case, and the deuteron need not penetrate into the nucleus at all. Instead, what actually happens is that the deuteron on account of its large size and low binding energy gets polarized by the field of the bombarded nucleus to such an extent that its neutron is captured by the nucleus, while the proton is repelled. On the basis of these ideas the final formula obtained by them for the cross-section for transmutation differs from Gamow’s by having in the exponent of (2) an extra factor f(W/I) = (2/π)(W/I)½F(W/I)-, (3) where I is the binding energy of the deuteron and F(W/I)- is the function calculated by Oppenheimer and Phillips (1935).