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We study semi-stable sheaves of rank $2$ with Chern class $c_1=0$, $c_2=2$and $c_3=0$ on the Fano 3-folds $V_4$ of Picard number $1$, degree $4$ andindex $2$. We show the moduli space of such sheaves is isomorphic to the modulispace of semi-stable rank $2$ even degree vector bundles on a genus $2$ curve.This provides a natural smooth compatification of the moduli space of Ulrichbundles of rank $2$ on $V_4$.

Compactification of the moduli space of minimal instantons on the Fano threefold $V_4$