Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2020 / Module NE4 / 2 / c

The assumption is a leading approximation for concentrated ballistic radiation damage, not an exact statement that the alpha particle displaces no atoms. The daughter has only about $m_{\alpha }/M_d$ times the alpha particle's kinetic energy, but it is much slower and loses a much larger fraction of that energy in collisions with target nuclei. Those collisions initiate closely packed recoil cascades. The alpha particle deposits most of its much larger energy into the electronic system over a path hundreds of times longer, with a less concentrated displacement contribution.

Thus the dense region susceptible to one-event loss of crystalline order can reasonably be associated chiefly with the daughter recoil. This explains why the effective damaged volume in the direct-impact amorphization model can be estimated or fitted from recoil-dominated cascades. It is the spatial density and stopping channel of the damage, not simply which particle carries more energy, that matters.

The approximation has a measurable limit. Turcotte's comparison of actinide-dioxide self-damage and external alpha irradiation found a nonzero alpha contribution, reporting about $19\%$ of total damage in the studied case. Comparison of diffraction-derived lattice changes with internal-reference measurements helps separate real radiation-induced swelling from instrument shifts, while the distinction between self-decay and external-alpha irradiation probes the omitted recoil channel.^[ref]

Consequently “all ballistic radiation damage” is useful as the stated model assumption but should not be promoted to an exact material-independent law. electronic excitation can also couple to structural change, and recovery alters what survives. The derivation in part (b) remains valid for an effective one-event volume fitted consistently to the relevant regime; it does not establish that all ceramics or spent fuels share the same $V_{\alpha }$ or the same eventual amorphous fraction.