Electroweak bremsstrahlung from neutron-neutron scattering

Abstract

Background: Nucleon-nucleon ($\mathit{NN}$) bremsstrahlung processes $\mathit{NN}\ensuremath{\gamma}$ ($\mathit{nn}\ensuremath{\gamma}$, $\mathit{np}\ensuremath{\gamma}$, and $\mathit{pp}\ensuremath{\gamma}$) have been extensively investigated. Neutrino-pair bremsstrahlung processes from nucleon-nucleon scattering $\mathit{NN}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ ($\mathit{nn}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, $\mathit{np}\ensuremath{\nu}\overline{\ensuremath{\nu}}$, and $\mathit{pp}\ensuremath{\nu}\overline{\ensuremath{\nu}}$) have recently attracted attention in studies of neutrino emission in neutron stars. The calculated $\mathit{NN}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ cross sections (or emissivities) are found to be sensitive to the two-nucleon dynamical model used in the calculations. Purpose and Method: A realistic one-boson-exchange (ROBE) model for $\mathit{NN}$ interactions is used to construct the electroweak bremsstrahlung amplitudes using the well-known nucleon electromagnetic and weak interaction vertices. The constructed $\mathit{nn}\ensuremath{\gamma}$ and $\mathit{nn}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ amplitudes are investigated by applying them to calculate $\mathit{nn}\ensuremath{\gamma}$ and $\mathit{nn}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ cross sections, respectively. Results: (i) The 190-MeV ROBE $\mathit{nn}\ensuremath{\gamma}$ cross sections agree well with those calculated using the TuTts amplitude, but they are in disagreement with those calculated using the Low amplitude. (ii) The calculated $\mathit{nn}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ cross sections using the ROBE amplitude at the neutrino-pair energy $\ensuremath{\omega}$ $=$ 1 MeV are in quantitative agreement with those calculated by Timmermans et al. [Phys. Rev. C 65, 064007 (2002)], who used the leading-order term of the soft neutrino-pair bremsstrahlung amplitude. Conclusions: The $\mathit{nn}\ensuremath{\gamma}$ amplitude in the ROBE approach, which obeys the soft-photon theorem, has a predictive power similar to that of the TuTts amplitude. The $\mathit{nn}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ amplitude in the ROBE approach, which is consistent with the soft neutrino-pair bremsstrahlung theorem, has a predictive power similar to that of the soft neutrino-pair bremsstrahlung amplitude of Timmermans et al. in the low neutrino-pair energy region.