The Metropolitan Opera and the English National Opera will collaborate on two productions slated for forthcoming seasons, the opera houses announced yesterday. John Adams’s “Doctor Atomic,” under the direction of Penny Woolcock, and a newly commissioned opera by composer Osvaldo Golijov and film director Anthony Minghella will be staged at both houses. Mr. Adams’s third opera, which focuses on the events leading to the first atomic bomb test explosion in New Mexico, will have its premiere in New York beginning October 13, 2008, and will open in Britain in February 2009. Messrs. Golijov and Minghella’s commission will be worked through first by ENO, and is tentatively scheduled to have its first showing there in 2010, before coming to the Met during its 2011–12 season.”Thecombined resources of our companies and schedules allow for greater artistic preparation and development that these new works demand,” the general manager of the Met, Peter Gelb, said in a statement.