Anti-Matter- Regular Matter- Pulse Collisions?

Arian

I was reading about what would happen if an Anti-Matter star and Matter star collided. What I read says the collision would make enough gamma rays to sterilize and entire eighth of a galaxy of life.
Yet, I thought about something, when the two collide, their surfaces would touch first. (Duh) So there surface's both annilate each other producing energy, that, would 'bounce' the stars back. Gravity would then take over again and pull them closer in which their surface's would annialte and the stars bounce back. So we have a kind of 'super-pulses' that would hit each other on some time scale.
Yet, since the stars are getting smaller, their collisions get smaller.
At some point the stars would not have enough gravity to pull each other together and they would drift off, rather small into space.

So the Matter- Anti-Matter Collisions would happen several time acting like a dwindling Pulse.
Thoughts?