  We investigate encounters between giant molecular clouds (GMCs) and star
clusters. We propose a single expression for the energy gain of a cluster due
to an encounter with a GMC, valid for all encounter distances and GMC
properties. This relation is verified with N-body simulations of cluster-GMC
encounters and excellent agreement is found. The fractional mass loss from the
cluster is 0.25 times the fractional energy gain. This is because 75% of the
injected energy goes to the velocities of escaping stars, that are higher than
the escape velocity. We derive an expression for the cluster disruption time
(t_dis) based on the mass loss from the simulations, taking into account the
effect of gravitational focusing by the GMC. The disruption time depends on the
cluster mass (M_c) and half-mass radius (r_h) as t_dis=2.0 S (M_c/10^4
M_sun)(3.75 pc/r_h)^3 Gyr, with S=1 for the solar neighbourhood and inversely
proportional to the GMC density. The observed shallow relation between cluster
radius and mass gives t_dis a power-law dependence on the mass with index 0.7,
similar to that found from observations and from simulations of clusters
dissolving in tidal fields (0.62). The constant of 2.0 Gyr is about a factor of
3.5 shorter than found from earlier simulations of clusters dissolving under
the combined effect of galactic tidal field and stellar evolution. It is
somewhat higher than the observationally determined value of 1.3 Gyr. It
suggests, however, that the combined effect of tidal field and encounters with
GMCs can explain the lack of old open clusters in the solar neighbourhood. GMC
encounters can also explain the (very) short disruption time that was observed
for star clusters in the central region of M51, since there rho_n is an order
of magnitude higher than in the solar neighbourhood.
