  We prove the existence of a liquid-gas phase transition for continuous Gibbs
point process in $\mathbb{R}^d$ with Quermass interaction. The Hamiltonian we
consider is a linear combination of the volume $\mathcal{V}$, the surface
measure $\mathcal{S}$ and the Euler-Poincar\'e characteristic $\chi$ of a halo
of particles (i.e. an union of balls centred at the positions of particles). We
show the non-uniqueness of infinite volume Gibbs measures for special values of
activity and temperature, provided that the temperature is low enough. Moreover
we show the non-differentiability of the pressure at these critical points. Our
main tool is an adaptation of the Pirogov-Sina\"i-Zahradnik theory for
continuous systems with interaction exhibiting a saturation property.
