  Positronium in the $2^3S$ metastable state exhibits a low electrical
polarizability and a long lifetime (1140 ns) making it a promising candidate
for interferometry experiments with a neutral matter-antimatter system. In the
present work, $2^3S$ positronium is produced - in absence of electric field -
via spontaneous radiative decay from the $3^3P$ level populated with a 205nm UV
laser pulse. Thanks to the short temporal length of the pulse, 1.5 ns
full-width at half maximum, different velocity populations of a positronium
cloud emitted from a nanochannelled positron/positronium converter were
selected by delaying the excitation pulse with respect to the production
instant. $ 2^3S $ positronium atoms with velocity tuned between $ 7 \cdot 10^4
$ m/s and $ 10 \cdot 10^4 $ m/s were thus produced. Depending on the selected
velocity, a $2^3S$ production effciency ranging from $\sim 0.8 \%$ to $\sim
1.7%$, with respect to the total amount of emitted positronium, was obtained.
The observed results give a branching ratio for the $3^3P$-$2^3S$ spontaneous
decay of $(9.7 \pm 2.7) \% $. The present velocity selection technique could
allow to produce an almost monochromatic beam of $\sim 1 \cdot 10^3 $ $2^3S$
atoms with a velocity spread $ < 10^4 $ m/s and an angular divergence of $\sim$
50 mrad.
