 Solution

For $m\gg M$, retain the ratio $E/m$ until a further limit is specified. Since $E\ge M$, the leading expression from a isFor an infinitely heavy target at fixed incident energy, $E/m\to 0$ and $\boxed{E^{\prime }\to E}$: 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 $E^{\prime }\sim m/2$. The mass hierarchy alone does not justify replacing $E/m$ by zero.