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How the number of binary collisions increases with centrality faster than the number of participant in heavy ion collisions at different particle colliders?

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It's combinatorics, a variant of the "handshake problem." Suppose you are at a party with $N$ other people and you want to shake everyone's hand: you're going to give $N$ handshakes. But so is everyone else, so the total number of binary interactions handshakes will be $\frac12N(N+1)\approx N^2/2$. You can do this by hand for small parties:

  • 1 person: no handshakes
  • 2 people: 1 handshake
  • 3 people: 3 handshakes (AB, AC, BC)
  • 4 people: 6 handshakes (AB, AC, AD, BC, BD, CD)
  • 5 people: 10 handshakes

In collisions you have the additional complication of pair creation in some binary collisions increasing the number of participants as well.

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  • $\begingroup$ I have appreciated your answer. But I wonder, for the case of inelastic collisions the parent particle will loose its own identity by forming some lighter particles. So, how can you relate this phenomena with the "handshake problem", where if you shake hand with other for the first time, then you will loose your identity. $\endgroup$ – Sushanta Tripathy Oct 19 '15 at 9:11

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