= Solution
For $m\gg M$, retain the ratio $E/m$ until a further limit is specified. Since $E\ge M$, the leading expression from <3/a> is
$$
\boxed{E'\simeq\frac{Em}{m+2E}=\frac{E}{1+2E/m}.}
$$
For an infinitely heavy target at fixed incident <energy>, $E/m\to0$ and $\boxed{E'\to E}$: the projectile reverses with negligible target recoil <energy>. If the incident particle is ultrarelativistic even relative to the target, $E\gg m\gg M$, the same leading expression instead gives $E'\sim m/2$. The mass hierarchy alone does not justify replacing $E/m$ by zero.
Back to article page
