  In this paper we continue the investigations in \cite{1} concerning the
origin of the cosmological constant. First of all, we generalise the results in
\cite{1,2} by considering a continuum approximation for a radiation field in a
cosmological background. In this way, we clearly show that the bare
cosmological constant is obtained with wanishing temperature $T$ and that the
specific heat $C$ is zero at the decoherence scale $L_D$. Moreover, we address
the issue to fix the parameters present in our model. In particular, we push
forward the analogy between our expression for ${\Lambda}_L$ at a given proper
scale $L$ and the one extrapolated by the Casimir effect. As a consequence, we
can fix the decoherence scale $L_D$ at which we have the crossover to
classicality to be of the order of $\sim 10^{-5}$ meters. This implies that the
actual observed value of the cosmological constant is fixed (frozen) at this
new physical scale.
