The M41A Pulse Rifle wasn't seen until the 1986 sequel Aliens. It was a standard issued rifle given to the United States Colonial Marines that were sent to investigate their sudden contact with loss on the planet LV-426. The rifle was given to the ones not possessing the M-56 Smart Gun.
In the final battle against the Xenomorphs; the Marines had only a few rifles to spare with only 50 rounds each magazine. After the fight; Corporal Dwayne Hicks used this weapon on an attacking Xenomorph; which caused the acid blood to damage him.
Lt. Ellen Ripley eventually took one of these rifles and combined it with an M240 Incinerator and used it to go rescue Rebecca "Newt" Jorden. During the rescue; the weapon was fired multiple times and was used to destroy the egg sacks that were to produce more eggs.