  Producing positronium (Ps) in the metastable $2^3\text{S}$ state is of
interest for various applications in fundamental physics. We report here about
an experiment in which Ps atoms are produced in this long-lived state by
spontaneous radiative decay of Ps excited to the $3^3\text{P}$ level manifold.
The Ps cloud excitation is obtained with a UV laser pulse in an experimental
vacuum chamber in presence of guiding magnetic field of 25 mT and an average
electric field of 300 V/cm. The indication of the $2^3\text{S}$ state
production is obtained from a novel analysis technique of single-shot
positronium annihilation lifetime spectra. Its production efficiency relative
to the total amount of formed Ps is evaluated by fitting a simple rate
equations model to the experimental data and found to be $ (2.1 \pm 1.3) \, \%
$.
