Deuteron formation in expanding nuclear matter from a strong coupling BCS approach

The process of deuteron formation in intermediate heavy ion reactions is approached within the strong coupling BCS theory assuming that the final stage of the reaction can be described as an adiabatic expansion of a piece of nuclear matter. Since the gap equation in the ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$${\mathrm{-}}^3$${\mathit{D}}_1$ channel goes over into the deuteron Schrödinger equation in the low density limit, a smooth transition from the superfluid Cooper pair phase to a Bose deuteron gas is found. For a fixed entropy ranging from 0.5 to 2 units per particle the deuteron fraction, the chemical potential and temperature are reported as a function of density. For densities down to ρ=0.1 ${\mathrm{fm}}^{\mathrm{-}3}$ and lower, the deuteron-to-nucleon ratio rapidly increases from a density threshold strongly depending on the entropy. Decreasing further the density this ratio tends logarithmically to one. The possible relevance of these results for heavy ion collisions and the shortcomings of the present approach are briefly discussed.