yup790
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Homework Statement
Homework Equations
et Em and pm be the energy and momentum of the mass m after the collision. Let p and p' be the momentum of mass M before and after the collision.
From conservation of 4 momentum:
\begin{bmatrix}E+m \\ p\end{bmatrix}=\begin{bmatrix}E_m+E' \\ p'+p_m\end{bmatrix}
We also have our invariants
E2-p2=M2, etc.
The Attempt at a Solution
Squaring the 4-vectors we get: E^2+2Em+m^2-p^2=E'^2+2E'E_m+E_m^2-p'^2-2p_mp'-p_m^2
Using our invarients, this becomes:
M^2+m^2 + 2Em=m^2+m^2+2(E'E_m-p'p_m)<br /> \implies Em=E'E_m-p'p_m<br />
now, using the conservation of energy and momentum:
E_m=E+m-E' & p_m=p-p'
Substituting these in and using our invarient again gets us:
Em=E'(E+m)-p'p-M^2
I have tried setting p=\sqrt{E^2-M^2}however its gets so algebraically heavy. Is there an easier way??