Neutron-Capture Theory of Element Formation in an Expanding Universe

The neutron-capture theory of element formation by non-equilibrium processes has been extended to include explicitly the effect of the expansion of the universe, and the resulting equations have been solved on an electronic digital computing machine. Inclusion of the universal expansion is found to require an increase by a factor of five of the density of matter chosen for the start of the element-forming process over that previously found necessary to represent the observed relative abundance distribution of elements in a static universe. The following physical conditions lead to agreement in the over-all trend of theoretical with observed abundances: the element-forming process is taken to start at ∼140 sec after the "beginning" of the universal expansion; at this time the temperature is ∼1.3×${10}^9$°K≃0.11 Mev, the neutron-proton ratio is 7.33:1, and the density of matter is ∼0.9×${10}^{-6\mathrm{}}$ g/${\mathrm{cm}}^3$. This density value includes a correction made to account for the effect of groupiing together nuclear species in order to reduce the number of defferential equations required to describe the neutron-capture procss.