The following weapons can be seen in the film The Core:
When the FBI raids Taz "Rat" Finch's apartment, at least one of the Agents can be seen wielding an unknown shotgun fitted with spare shell holders on the left side of the receiver.
Probably a Benelli of some sort. The real FBI has an affinity for it, so it's likely.
Browning M2HB Heavy Machine Gun
When Doctors Josh Keyes (Aaron Eckhart) and Serge Leveque (Tchéky Karyo) first meet Lt. General Thomas Purcell (Richard Jenkins) in the makeshift military morgue, several military vehicles in the large room can be seen fitted with Browning M2HB heavy machine guns.
Several U.S. military personnel can be seen with M16A2 rifles throughout the film, mostly at the site of the makeshift morgue.