  The production of $\Sigma^{0}$ baryons in the nuclear reaction p (3.5 GeV) +
Nb (corresponding to $\sqrt{s_{NN}}=3.18$ GeV) is studied with the detector
set-up HADES at GSI, Darmstadt. $\Sigma^{0}$s were identified via the decay
$\Sigma^{0} \rightarrow \Lambda \gamma$ with subsequent decays $\Lambda
\rightarrow p \pi^{-}$ in coincidence with a $e^{+}e^{-}$ pair from either
external ($\gamma \rightarrow e^{+} e^{-}$) or internal (Dalitz decay
$\gamma^{*}\rightarrow e^{+} e^{-}$) gamma conversions. The differential
$\Sigma^0$ cross section integrated over the detector acceptance, i.e. the
rapidity interval $0.5 < y < 1.1$, has been extracted as
$\Delta\sigma_{\Sigma^{0}} = 2.3 \pm (0.2)^{stat} \pm
\left(^{+0.6}_{-0.6}\right)^{sys} \pm (0.2)^{norm}$ mb, yielding the inclusive
production cross section in full phase space $\sigma^{total}_{\Sigma^{0}} = 5.8
\pm (0.5)^{stat} \pm \left(^{+1.4}_{-1.4}\right)^{sys} \pm (0.6)^{norm} \pm
(1.7)^{extrapol}$ mb by averaging over different extrapolation methods. The
$\Lambda_{all}$/$\Sigma^{0}$ ratio within the HADES acceptance is equal to 2.3
$\pm$ $(0.2)^{stat}$ $\pm$ $(^{+0.6}_{-0.6})^{sys}$. The obtained rapidity and
momentum distributions are compared to transport model calculations. The
$\Sigma^{0}$ yield agrees with the statistical model of particle production in
nuclear reactions.
