Great guesses! But no...
Next clue:
Turns out that element exists in reality, under a different name though and has different properties. I guess its discoverer wasn't a fan of StarTrek and/or didn't notice that mention, otherwise, he would have probably given it the same name. (that's some longwinded clue!)
Mudd's Women
The Lithium!
How does this tie into Day of the Dove, which I assume is the right answer by Marsden? Oh, the swordfighting?