Solution
= Solution
With $M\gg m$ and $Em\gg M^2$, one also has $E\gg M^2/m\gg M$. The denominator in <3/a> is then dominated by $2Em$, and the numerator by $EM^2$:
$$
\boxed{E'\sim\frac{M^2}{2m}.}
$$
This residual total <energy> is still much larger than the incident particle's <rest energy> $M$, but is a small fraction of its incident <energy> $E$. The target acquires most of the available <energy> in this high-energy, heavy-projectile limit.