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1.Problem: An electron with energy ##E## which is much higher than its restmass collides with a much much heavier particle "A" of mass ##m## which is at rest. Find the maximal transfer of four-momentum. (Elastic collision)

1.Problem: An electron with energy ##E## which is much higher than its restmass collides with a much much heavier particle "A" of mass ##m## which is at rest. Find the maximal transfer of four-momentum. (Elastic collision)

**2. Conservation of four momentum**

**3. Everything in natural units. So I go look at the particle A in its restframe and go look at this particle before and after the collision. The square of the four-momentum transfer is then:**

##q^{2}=(p_{A1}-p_{A2})^{2}##

Working this out gives me:

##q^{2}=2m_{A}^{2}-2E_{A2}m_{A}##

When ##E_{A2}## is minimal, namely just ##m_{A}##, ##q^{2}=0##. This means that for any real collision the square of the momentum transfer will be negative. I assume the question is asking when this value is the most negative? In that case, it's obvious, when ##E_{A2}## is maximal.

Now I tried to find some expression for a maximal ##E_{A2}## but not really succeeded yet.

##q^{2}=(p_{A1}-p_{A2})^{2}##

Working this out gives me:

##q^{2}=2m_{A}^{2}-2E_{A2}m_{A}##

When ##E_{A2}## is minimal, namely just ##m_{A}##, ##q^{2}=0##. This means that for any real collision the square of the momentum transfer will be negative. I assume the question is asking when this value is the most negative? In that case, it's obvious, when ##E_{A2}## is maximal.

Now I tried to find some expression for a maximal ##E_{A2}## but not really succeeded yet.