Complex-energy analysis of proton-proton fusion

Abstract

An analysis of the astrophysical $S$ factor of the proton-proton weak capture ($\mathrm{p}+\mathrm{p}\to {}^2\mathrm{H}+{\mathrm{e}}^{+}+{\nu }_{\mathrm{e}}$) 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.

arXiv comment13 pages, 9 figures, 43 references

References in corpus (23)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Construction of high-quality Nucleon-Nucleon potential models
• Solar fusion cross sections II: the pp chain and CNO cycles
• Parameter-free effective field theory calculation for the solar proton-fusion and hep processes
• Weak capture of protons by protons
• Proton-Proton Fusion in Effective Field Theory
• The proton-proton weak capture in chiral effective field theory
• Proton-Proton Fusion in Effective Field Theory to Fifth Order
• The Rate of the Proton-Proton Reaction
• Radiative corrections to low energy neutrino reactions
• Proton-proton fusion in pionless effective theory
• Radiative corrections in neutrino-deuterium disintegration
• Uncertainty quantification for proton-proton fusion in chiral effective field theory
• Connection formulas between Coulomb wave functions
• Near Threshold Proton-Proton Fusion in Effective Field Theory
• On the phase-shift parameterization and ANC extraction from elastic-scattering data
• Extrapolation of scattering data to the negative-energy region II
• Extrapolation of scattering data to the negative-energy region
• Effective-range function methods for charged particle collisions
• Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system
• Proton-proton fusion in lattice effective field theory
• Universal behavior of $p$-wave proton-proton fusion near threshold

Cited by in corpus (1)

• Solar fusion III: New data and theory for hydrogen-burning stars