  We study the Cauchy problems for the Hartree-type nonlinear Dirac equations
with Yukawa-type potential in two and three spatial dimensions. This paper
improves our previous results \cite{chohlee,cholee}; we establish global
well-posedness and scattering for large data with a certain condition. Firstly
we investigate the long-time behavior of solutions to the Dirac equation
satisfies good control provided that a particular dispersive norm of solutions
is bounded. The key of our proof relies on modifying multilinear estimates
obtained in our previous papers. Secondly, we obtain large data scattering by
exploiting the Majorana condition.
