Neutrons in a reactor must be slowed down. Using the result…

Neutrons in a reactor must be slowed down. Using the result of Translational Dynamics 144, find which target slows a neutron best in a head-on elastic collision: (a) a proton ($m_p \approx m_n$), (b) an alpha particle ($m_\alpha \approx 4m_n$).

Explanation of Method

Best target for slowing neutrons.

Step 1: Energy passed to the target

\[ \frac{E_2'}{E_1} = \frac{4m_nM}{(m_n + M)^2}. \]

Step 2: The two cases

\[ \text{(a) } M = m_n: \ \frac{4}{4} = 1, \]

\[ \text{(b) } M = 4m_n: \ \frac{16}{25} = 0.64. \]

\[\begin{gathered} \text{proton: all energy lost} \\ \text{alpha: 64\% lost, 36\% kept} \end{gathered}\]

The proton (hydrogen) is the best moderator, which is why water and paraffin, rich in hydrogen, are used to slow neutrons.

$\text{proton (m)}$ $36\%$ $\text{alpha (4m)}$ $71.6\%$ $\text{carbon-12 (12m)}$ $0\% \ \text{(stops)}$ $\text{energy the neutron keeps in a head-on collision}$

Energy left to the neutron after one head-on elastic collision, $\left(\frac{m - M}{m + M}\right)^2$. A target of equal mass takes it all; heavier nuclei take less.

Result

\[\boxed{\,\begin{gathered} \text{proton: all energy lost} \\ \text{alpha: 64\% lost, 36\% kept} \end{gathered}\,}\]

Remark

Check. The original results are correct. They apply to head-on collisions; in glancing collisions less energy is transferred, but the conclusion (lighter targets slow neutrons faster) stays the same.