  We examine the Weyl double copy relation for vacuum solutions of the Einstein
equations with a cosmological constant using the approach we previously
described, in which the spin-1/2 massless free-field spinors (Dirac-Weyl
fields) are regarded as basic units. Based on the exact non-twisting vacuum
type N and vacuum type D solutions, the finding explicitly shows that the
single and zeroth copies fulfill conformally invariant field equations in
conformally flat spacetime. In addition, irrespective of the presence of a
cosmological constant, we demonstrate that the zeroth copy connects Dirac-Weyl
fields with the degenerate electromagnetic fields in the curved spacetime in
addition to connecting gravity fields with the single copy in conformally flat
spacetime. Moreover, the study also demonstrates the critical significance the
zeroth copy plays in time-dependent radiation solutions. In particular, for
Robinson-Trautman ($\Lambda$) gravitational waves, unlike the single copy, we
find that the zeroth copy carries additional information to specify whether the
sources of associated gravitational waves are time-like, null, or space-like,
at least in the weak field limit.
