The Formation of Deuterons by Proton Combination

Abstract

The probability of the astrophysically important reaction $\mathrm{H}+\mathrm{H}=\mathrm{D}+{\ensuremath{\epsilon}}^{+}$ is calculated. For the probability of positron emission, Fermi's theory is used. The penetration of the protons through their mutual potential barrier, and the transition probability to the deuteron state, can be calculated exactly, using the known interaction between two protons. The energy evolution due to the reaction is about 2 ergs per gram per second under the conditions prevailing at the center of the sun (density 80, hydrogen content 35 percent by weight, temperature 2\ifmmode\cdot\else\textperiodcentered\fi{}${10}^{7}$ degrees). This is almost but not quite sufficient to explain the observed average energy evolution of the sun (2 ergs/g sec.) because only a small part of the sun has high temperature and density. The reaction rate depends on the temperature approximately as ${T}^{3.5}$ for temperatures around 2\ifmmode\cdot\else\textperiodcentered\fi{}${10}^{7}$ degrees.