We study the phase-space dependence of 2p-2h excitations in neutrino
scattering using the relativistic Fermi gas model \cite{Rui14}. We
follow a similar approach to Refs. \cite{Pace03,Ama10}, but focusing
in the phase-space properties, comparing with the non-relativistic
model of \cite{Van81}. A careful mathematical analysis of the angular
distribution function for the outgoing nucleons is performed. Our
goals are to optimize the CPU time of the 7D integral to compute the
hadronic tensor in neutrino scattering, and to conciliate the
different relativistic and non relativistic models by describing
general properties independently of the two-body current. For some
emission angles the angular distribution becomes infinite in the Lab
system, and we derive a method to integrate analytically around the
divergence. Our angular distribution is the same as the
one obtained in the Monte Carlo generators by a boost from the CM
isotropical distribution. Our formalism is applied to neutrino
scattering from C-12, in the particular case of the seagull MEC
diagrams. Our results show that the frozen approximation, obtained by
neglecting the momenta of the two initial nucleons inside the integral
of the hadronic tensor, reproduces fairly the exact response
functions.
\begin{thebibliography}{expo92}
\bibitem{Rui14}
I. Ruiz Simo, C. Albertus, J.E. Amaro,
M.B. Barbaro, J.A. Caballero, T.W. Donnelly,
arXiv:1405.4280 [nucl-th].
\bibitem{Pace03}
A. De pace, M. Nardi, W.M. Alberico, T.W. Donnelly, A. Molinari,
\bibitem{Ama10} J.E. Amaro, C. Maieron, M.B. Barbaro, J.A. Caballero,
T.W. Donnelly, Phys. Rev. C 82, 044601 (2010).
\bibitem{Van81}
J.W. Van Orden, T.W. Donnelly,
Published in Annals Phys. 131 (1981) 451.
\end{thebibliography}
