Clusters, such as Argon gas clusters, provided by a cluster source are doped in a water pick-up cell, and subsequent electron impact ionization of the doped clusters in a mass spectrometer or gas analyzer produce ionized cluster fragments that retain water. Water is supplied under pressure to the pick-up cell disposed within a vacuum chamber, and the water pressure is metered by a metering valve and monitored by a pressure gauge. A vacuum pump is coupled to the vacuum chamber that generates a vacuum within the vacuum chamber and pick-up cell. Interaction between the gas clusters and the water in the pick-up cell produces doped clusters, some of which retain water. The electron impact ionized doped cluster fragments are analyzed using the mass spectrometer or gas analyzer permits determination (detection) of the mean cluster size of the clusters. The variation in intensity of the water-containing fragments versus water pressure in the pick-up cell exhibits a Poisson behavior, from which the cross-section and mean cluster size is derived.