Complex-energy analysis of proton-proton fusion

An analysis of the astrophysical S factor of the proton-proton weak capture (p + p -> H-2 + e(+) nu(e) ) is performed on a large energy range covering solar-core and early Universe temperatures. The measurement of S being physically unachievable, its value relies on the theoretical calculation of the matrix element Lambda. Surprisingly, Lambda reaches a maximum near 0.13 MeV that has been unexplained until now. A model-independent parametrization of Lambda valid up to about 5 MeV is established on the basis of recent effective-range functions. It provides an insight into the relationship between the maximum of Lambda and the proton-proton resonance pole at (-140 - 467i) keV from analytic continuation. In addition, this parametrization leads to an accurate evaluation of the derivatives of Lambda, and hence of S, in the limit of zero energy.