it's Carter Burwell's
originally he wrote it about some other lady and when he heard about twilight he saw the similarities so he did some minor changes to it (or none at all i don't remember exactly)
and yeah.
Now its Bella's Lullaby.

look in the links section and try finding the article
mandapanda uploaded it.. but it was ages ago i think..
considering how many people upload links each day

thanks

kewl