- #1

AntiElephant

- 25

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We have the reaction a(A,B)b. Before the reaction we can transfer to the centre of mass frame

[itex] v_c = \frac{\sum m_i v_i}{\sum m_i} [/itex]

and note that the total energy before the reaction is

[itex] E_{CM} = E_{masses~before} + E_{kinetic~before~in~CM} [/itex]

And the total energy after is

[itex] E_{CM} = E_{masses~after} + E_{kinetic~after~in~CM} [/itex]

The problem I'm having to understand is that these two before/after energies are often equated, but the centre of mass frame is not a constant since the masses are not constant in a nuclear reaction, so [itex] v_c [/itex] changes since the denominator [itex] \sum m_i [/itex] changes (numerator remains the same due to conservation of momentum).

Am I wrong here? If I were to guess why we can do this, it's because the change in masses is so small that we can assume the centre of mass frame is constant before/after the reaction. But then this discussion breaks down when we're considering only light particles and the fractional mass change is larger, right?