In Star Trek: TNG Episode "The Drumhead" (4x21) there was a breach in the dilithium chamber that caused a radiation leak that caused them to have isolation doors drop and prevent the crew access to the warp core for something like 36 hours. Since warp cores run on matter anti-matter collisions, and none of the radiation normally produced in such collisions is considered long lasting (see the accepted answer), what kind of radiation is created in this breach? And why is it created?
Antimatter Radiation is seen a few times in Star Trek, but is never really addressed in detail. Memory Alpha simply says it's a byproduct of antimatter. Some other notable examples are:
Star Trek II: The Wrath of Khan
When Spock has to realign the dilithium crystals by hand, flooding the chamber he's in with lethal levels of radiation.
Friendship One (VOY 7x21) takes place on a planet suffering from nuclear winter as a result of antimatter explosions.
One possible explanation is that the radiation comes not from the M/AM reaction, but from the dilithium crystals in the reactor.
One of the reasons why dilithium was so valuable before the late 23rd century was because dilithium gradually decrystalizes during use, and there existed no practical means of inducing recrystallization. However, during a time travel mission to 1986, Spock and Scotty developed a method of recrystallizing dilithium through exposure to gamma radiation. (Star Trek IV: The Voyage Home)
Decrystalizing dilithium resulted in certain byproducts, including illium-629 and, when used in warp cores, trilithium resin. (TNG: "Pen Pals", "Starship Mine")
(from Memory Alpha/Dilithium Crystal) If recrystallization would require bombarding it with gamma radiation, it seems possible to a layperson such a myself that the decrystalization process would involve the release of similar radiation along with the above-mentioned byproducts.
Of course, as NKCampbell pointed out, an easy answer to this question would be that "antimatter radiation" is simply a plot device for dramatic effect (devastatingly effective dramatic effect in STII!)
According to the Star Trek Encyclopedia, the most likely culprit here is gamma radiation, known to be a byproduct of faulty or damaged warp cores;
... Damage to a starship’s warp core can sometimes cause it to leak gamma radiation.
The example it gives is from VOY: Warlord. The crew encounter a ship with a damaged matter/anti-matter warp core. It's venting plasma and gamma radiation which is making the crew unwell.
TUVOK: Captain, sensor readings indicate that radiation inside the alien vessel is rising to toxic levels. The lifesigns of the passengers are growing weaker.
TORRES: Their warp core is heavily damaged. It's leaking drive plasma and gamma radiation. It could breach any time.
CHAKOTAY: Can we beam the passengers out through all that radiation?
This would also tally with what's seen in the show as compared to real life. Gamma radiation would cause significant injury to those exposed, but wouldn't cause the surrounding material to become radioactive over the longer term once the cause had been vented or contained.
Theta Radiation is the waste byproduct of warp power, even in the 23rd century. The photon collector in Star Trek IV collects any source of high energy Radiation and uses it to recrystalize the Dilithium. Antimatter Radiation and Theta Radiation are the same thing. Dilithium crystals by themselves are not radioactive, As we have seen various star trek characters handle them with their bare hands with no ill effects at all.