  We describe the generation and properties of a cryogenic beam of $^7$Li$_2$
dimers from sublimation of a neon matrix where lithium atoms have been
implanted via laser ablation of solid precursors of metallic lithium or lithium
hydride (LiH). Different sublimation regimes lead to pulsed molecular beams
with different temperatures, densities and forward velocities. With laser
absorption spectroscopy these parameters were measured using the molecular
$^7$Li$_2$ (R) transitions A$^1\Sigma_u^+(v'=4,J'=J''+1)\leftarrow
$X$^1\Sigma_g^+ (v''=0,J''=0,1,3)$. In a typical regime, sublimating a matrix
at 16 K, translational temperatures of 6--8 K with a drift velocity of 130
m$\,$s$^{-1}$ in a free expanding pulsed beam with molecular density of 10$^9$
cm$^{-3}$, averaged along the laser axis, were observed. Rotational
temperatures around 5--7 K were obtained. In recent experiments we were able to
monitor the atomic Li signal -- in the D2 line -- concomitantly with the
molecular signal in order to compare them as a function of the number of
ablation pulses. Based on the data and a simple model, we discuss the
possibility that a fraction of these molecules are being formed in the matrix,
by mating atoms from different ablation pulses, which would open up the way to
formation of other more interesting and difficult molecules to be studied at
low temperatures. Such a source of cryogenic molecules have possible
applications encompassing fundamental physics tests, quantum information
studies, cold collisions, chemistry, and trapping.
