<human>: Can you condense the text into three sentences or less?

Okay, so around March 18th, me and my girlfriend of 9 months broke off our long distance relationship. She was a little more upset than I was, because it wasn't really mutual. I'm feeling a little better about it now, but I know she's still struggling a little bit.

Now, I've met someone where I currently live (on my college campus) who I'm moderately interested in. I've asked her out to lunch, and she was all for it. I'm still a little hesitant to try anything else though because I know that what happened between me and my previous girlfriend is still pretty recent, and has yet to reach full closure. I also don't want the girl I'm interested in to get the impression that I'm not serious about a long-term relationship. So my question is: what amount of time after separating with a girlfriend is appropriate to start looking for another serious relationship? I know there is no best answer to this, but I'm looking for a range of times that the community as a whole spends between relationships, rather than one exact amount of time where dating someone else suddenly becomes okay.
<bot>: What is your minimum time spent between relationships so that you don't portray yourself as someone who constantly dates/breaks up with significant others?