Origin of the Light Elements

It is shown that the observed isotopic abundances of Li, Be, and B can be explained by their spallation in small, prototerrestrial bodies. Spheres of arbitrary composition and radius are irradiated by protons; approximate expressions are found for the solar-flare proton spectrum, the spallation cross sections, and neutron production. A new approximation is made for the effect of the fast neutrons. It is then found that the present day proton flux is too soft to give the desired results reasonably, and that a mean proton energy of 300 MeV is necessary to get the observed isotopic ratios. The results are not sensitive to the composition, and we can obtain the measured Li, Be, and B abundances by taking dry silicate spheres of about 140 m for the protoasteroidal bodies. In order to obtain the observed D/H ratio from the irradiation, however, it is necessary to add 10% ${\mathrm{H}}_2$O. The measured crustal abundances of Li, Be, B lead to different values for D/H and for the depletion of ${\mathrm{Gd}}^{157}$ for the earth and for asteroids, contrary to observation. These discrepancies disappear if we assume that Li, Be, and B have been concentrated tenfold in the earth's crust. The different isotopic ratios found for terrestrial and meteoritic material are consistent with this model, and enable us to calculate the ${\mathrm{Li}}^7$/${\mathrm{Li}}^6$ ratios to be expected on the other planets.