  Recent studies have found an unusual way of dissociation in formaldehyde. It
can be characterized by a hydrogen atom that separates from the molecule, but
instead of dissociating immediately it roams around the molecule for a
considerable amount of time and extracts another hydrogen atom from the
molecule prior to dissociation. This phenomenon has been coined roaming and has
since been reported in the dissociation of a number of other molecules. In this
paper we investigate roaming in Chesnavich's CH$_4^+$ model. During
dissociation the free hydrogen must pass through three phase space bottleneck
for the classical motion, that can be shown to exist due to unstable periodic
orbits. None of these orbits is associated with saddle points of the potential
energy surface and hence related to transition states in the usual sense. We
explain how the intricate phase space geometry influences the shape and
intersections of invariant manifolds that form separatrices, and establish the
impact of these phase space structures on residence times and rotation numbers.
Ultimately we use this knowledge to attribute the roaming phenomenon to
particular heteroclinic intersections.
