The Proton-Deuteron Transformation As a Source of Energy in Dense Stars

The rates of energy evolution due to the transformation to helium, starting with the reaction $\mathrm{H}+\mathrm{H}=\mathrm{D}+e^{+}$, in hydrogen at densities of ${10}^4$ to ${10}^8$ g/${\mathrm{cm}}^3$, were calculated on the basis of complete degeneracy, and the assumption of a crystal-like spacing of the protons. The results indicate that any considerable amount of hydrogen in white dwarf stars would lead to much higher luminosities than those observed. Thus the low effective molecular weight (1.5) as calculated for some of these stars from the accepted white dwarf model, cannot be due to a high content of hydrogen. It might be explained as due to very large content (∼100 percent) of the helium isotope ${\mathrm{He}}^3$ but it is very difficult to see how such large amounts of this isotope could be present in these stars. It appears that the paradox can be removed only by revision of the observational data concerning the white dwarf radii.