  We present a new sink particle algorithm developed for the Adaptive Mesh
Refinement code RAMSES. Our main addition is the use of a clump finder to
identify density peaks and their associated regions (the peak patches). This
allows us to unambiguously define a discrete set of dense molecular cores as
potential sites for sink particle formation. Furthermore, we develop a new
scheme to decide if the gas in which a sink could potentially form, is indeed
gravitationally bound and rapidly collapsing. This is achieved using a general
integral form of the virial theorem, where we use the curvature in the
gravitational potential to correctly account for the background potential. We
detail all the necessary steps to follow the evolution of sink particles in
turbulent molecular cloud simulations, such as sink production, their
trajectory integration, sink merging and finally the gas accretion rate onto an
existing sink. We compare our new recipe for sink formation to other popular
implementations. Statistical properties such as the sink mass function, the
average sink mass and the sink multiplicity function are used to evaluate the
impact that our new scheme has on accurately predicting fundamental quantities
such as the stellar initial mass function or the stellar multiplicity function.
