As someone currently limerent myself, I can relate to how you feel. (My LO is a former professor, and it's a very different situation, so it wouldn't be a good idea in my case.) However, as a woman who was once someone else's LO (not an ex), I would be terrified if this guy called me out of nowhere and said he's obsessed with me. (I'd probably call the police.)

Since you did have a relationship with this woman, I think whether or not you should do this depends on how thing ended. If it was amicable, then I think it's okay to call her, but I definitely wouldn't use the word "obsessed." If it wasn't amicable, however, I would advise against it, as it might frighten her/creep her out, and she could even get a no contact order on you.