An analysis of the astrophysical $S$ factor of the proton-proton weak capture ($\mathrm{p}+\mathrm{p}\rightarrow {}^2\mathrm{H}+\mathrm{e}^++\nu_{\mathrm{e}}$) 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 $0.13~\mathrm{MeV}$ that has been unexplained until now. A model-independent parametrization of $\Lambda$ valid up to about $5~\mathrm{MeV}$ 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 $(-140-467\,\mathrm{i})~\mathrm{keV}$ 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.Comment: 13 pages, 9 figures, 43 reference

Topics:
Nuclear Theory

Publisher: 'American Physical Society (APS)'

Year: 2019

DOI identifier: 10.1103/PhysRevC.100.035805

OAI identifier:
oai:arXiv.org:1902.02324

Provided by:
arXiv.org e-Print Archive

Downloaded from
http://arxiv.org/abs/1902.02324

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