Catholic Irish immigration to the USA accelerated dramatically with the Potato Famine or Great Hunger of the 1840s: app. 1 million died, 1 million emigrated not only to the United States but also to the United Kingdom, Canada, Australia, New Zealand, Argentina, Mexico, South Africa, Brazil, Peru, continental Europe, and the Caribbean.
Thus the Irish dispersal across much of the Earth may be characterized as a diaspora.
"Emigration [from Ireland] has stopped, but South Ireland has only 3.9 million inhabitants, for a total of 5.5 millions for the whole island, when estimates of the total number of the total number of Irish people in the world, the Irish Diaspora, are 60 millions." (http://irlande.web-sy.fr/ireland_history.htm)
Other estimates: 6.2 million Irish on island, 80 million in diaspora.
See also Irish diaspora at Wikipedia.