  We construct approximate solutions $ (\psi_*, n_*)$ of the critical 4D
Zakharov system which collapse in finite time to a singular renormalization of
the solitary bulk solutions $ (\lambda e^{i \theta}W, \lambda^2 W^2)$ . To be
precise for $ N \in \mathbb{Z}_+,\;N \gg1 $ we obtain a magnetic envelope/ion
density pair of the form
  $$ \psi_*(t, x)= e^{i\alpha(t)}\lambda(t) W(\lambda(t)x) + \eta(t, x),
\;n_*(t,x) = \lambda^2(t) W^2(\lambda(t) x) + \chi(t,x), $$
  where $ W(x) = (1 + \frac{|x|^2}{8})^{-1}$, $\alpha(t) = \alpha_0 \log(t)$,
$\lambda(t)= t^{-\frac{1}{2}-\nu}$ with large $\nu > 1 $ and further
  $$
  i \partial_t \psi_* + \Delta \psi_* + n_* \psi_* = \mathcal{O}(t^N),\; \Box
n_* - \Delta (|\psi_*|^2) = \mathcal{O}(t^N),\;\;\eta(t) \to \eta_0, \chi(t)
\to \chi_0,
  $$
  as $ t \to 0^+$ in a suitable sense. The method of construction is inspired
by matched asymptotic regions and approximation procedures in the context of
blow up solutions introduced by the first author jointly with W. Schlag and D.
Tataru, as well as the subsequently developed methods in the Schr\"odinger
context by G. Perelman et al.
