Question 5 of 7: Detection, Instrumentation and Shielding of Fission-Neutron Radiation

Question 5: Detection, Instrumentation and Shielding of Fission-Neutron Radiation (19 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The thermal-fission reaction $n+{}^{235}\text{U}\rightarrow{}^{236}\text{U}^*\rightarrow{}^{142}\text{Ba}+{}^{92}\text{Kr}+2n$.

Find. (a) the incident neutron energy of highest fission probability; (b) detectors for the incident neutrons; (c) the outgoing fission-neutron energy spectrum shape and its most probable energy; (d) a spectrometer for that spectrum; (e) how neutron dose is measured; (f) a shielding arrangement; (g) the fission-energy partition; (h)–(i) why and how the fragments decay.

Approach. Distinguish carefully between the incident neutron that causes the fission (part a) and the outgoing fission neutrons this reaction itself produces (part c) — these are two different neutron populations with very different energy scales. Use standard reaction-based detection principles for (b) and (d), the MIRD/health-physics dose-measurement chain for (e), the moderate-then-absorb-then-shield-gammas logic for (f), and the parent nucleus's fixed $N/Z$ ratio for (h)–(i).

1. Part (a) — incident neutron energy of highest fission probability. $^{235}$U's fission cross-section is enormous at low neutron energy (it follows an approximate $1/v$ law with, additionally, a large low-lying resonance) and falls off by orders of magnitude toward the fast-neutron region, so fission is most probable for $$\boxed{\text{thermal neutrons},\ E_n \approx 0.025\ \text{eV}}$$ (room-temperature thermal equilibrium energy) — this is why thermal reactors moderate their neutrons before they cause the next fission.
2. Part (b) — detectors for the incident (thermal) neutrons. $^{10}\text{BF}_3$ proportional counters (via $^{10}\text{B}(n,\alpha)^7\text{Li}$) and $^{6}$Li-loaded scintillators, e.g. $^6$LiI(Eu) or $^6$Li-glass (via $^6\text{Li}(n,\alpha)^3\text{H}$), are the standard choices — both exploit a light nuclide with a very large thermal-neutron capture cross-section that releases an energetic, easily-detected charged particle. ($^3$He proportional counters, via $^3\text{He}(n,p)^3\text{H}$, are an equally standard third option.)
3. Part (c) — energy spectrum of the produced fission neutrons. Unlike the monoenergetic ($\sim$0.025 eV) incident neutron of part (a), the 2–3 prompt neutrons released by each fission emerge with a broad, continuous Maxwellian-like ("Watt") energy distribution, $N(E)\propto\sqrt{E}\,e^{-E/a}$ with $a\approx1.29$ MeV for $^{235}$U, peaking at $E_p=a/2\approx0.65$ MeV and with mean energy $\bar E=3a/2\approx1.9$ MeV, as sketched below.

4. Part (d) — spectrometer for the fission-neutron spectrum. A proton-recoil organic/liquid scintillator (e.g. NE-213/EJ-301) with pulse-shape discrimination is standard: fast neutrons undergo elastic n-p scattering in the hydrogen-rich scintillator, each recoiling proton deposits a light pulse proportional to its energy, and pulse-shape discrimination separates these proton-recoil events from the gamma-induced electron-recoil background; unfolding the recorded pulse-height distribution (via the known response function) recovers the incident neutron energy spectrum. (A time-of-flight spectrometer, which times each neutron's flight over a known distance to get its velocity/energy directly, is an equally standard alternative.)
5. Part (e) — how neutron radiation dose is measured. Because a bare counter's response is strongly energy-dependent, personal/area neutron dose is measured with instruments whose response is deliberately shaped to track the fluence-to-dose conversion curve — classically a "rem-meter" (a thermal-neutron detector, e.g. BF$_3$, inside a moderating polyethylene sphere sized so its net response approximates the dose-equivalent-per-fluence curve over a wide energy range), a set of Bonner spheres (multiple moderator sizes, unfolded to give both spectrum and dose), or a tissue-equivalent proportional counter (TEPC), which directly simulates energy deposition in a small tissue-equivalent gas volume.
6. Part (f) — shielding arrangement. Fission-produced fast neutrons (part c, peak $\sim$0.65 MeV, mean $\sim$1.9 MeV) and prompt gammas require a layered shield: (i) a thick hydrogenous moderator — water, polyethylene, or ordinary concrete, roughly 30–40 cm — slows the fast neutrons to thermal energy through repeated elastic scattering (each scatter off hydrogen removes, on average, half the neutron's remaining energy, so $\sim$10 mean free paths/collisions brings an MeV neutron down to thermal); (ii) a thin thermal-neutron absorber, e.g. boron-loaded polyethylene or a boric-acid layer a few cm thick, captures the thermalized neutrons via $^{10}\text{B}(n,\alpha)^7\text{Li}$, a reaction chosen because it releases very little capture-gamma energy compared with, say, capture on hydrogen or cadmium; (iii) a lead layer of roughly 5–10 cm (several gamma mean-free-paths, or tenth-value layers) attenuates both the prompt fission gammas and the residual capture gammas from stage (ii). This water/polyethylene-then-boron-then-lead sequence is the standard arrangement because no single material is simultaneously an efficient moderator, a low-gamma-yield absorber, and a dense gamma attenuator.
7. Part (g) — energy distribution among the reaction products. Using standard illustrative textbook energy-partition figures for $^{235}$U thermal fission (total $\approx207$ MeV): $$\boxed{\text{Fission fragments (Kr + Ba, kinetic energy)}: 168\ \text{MeV}\approx81\%}$$ $$\boxed{\text{Neutrons (kinetic energy)}: 5\ \text{MeV}\approx2\%}$$ $$\boxed{\text{Prompt gamma rays}: 7\ \text{MeV}\approx3\%}$$ The remaining $\sim$14% (delayed beta particles, delayed gammas, and antineutrinos from subsequent fragment decay) is released later and does not appear as prompt energy from the reaction as written; the fragments dominate because, carrying nearly all the reaction's momentum between just two heavy bodies, they also carry nearly all its kinetic energy.
8. Part (h) — why $^{92}$Kr and $^{142}$Ba are unstable. $^{235}$U has a high neutron-to-proton ratio ($N/Z\approx1.55$) appropriate to a very heavy nucleus. When it splits, each fragment inherits essentially that same high $N/Z$ ratio, but a stable nucleus at the fragment's much lower mass number ($A=92$ or $142$) needs a substantially lower $N/Z$ ($\sim$1.3–1.4). Both $^{92}$Kr ($N/Z=56/36\approx1.56$) and $^{142}$Ba ($N/Z=86/56\approx1.54$) are therefore born well above the stability line for their mass — too neutron-rich — which is why essentially every fission fragment is radioactive from the instant it is created.
9. Part (i) — most likely decay mode. Being neutron-rich (not proton-rich or simply overweight), both fragments decay by $$\boxed{\beta^-\ \text{emission}\ (n\rightarrow p+\beta^-+\bar\nu)}$$ not by $\alpha$ decay, which instead characterizes very heavy nuclei near the top of the periodic table. Each $\beta^-$ decay converts one excess neutron into a proton (mass number $A$ unchanged, atomic number $Z$ increases by one), stepping the fragment along its isobaric decay chain toward the stability valley — e.g. $^{92}$Kr decays through $^{92}\text{Rb}\rightarrow{}^{92}\text{Sr}\rightarrow{}^{92}\text{Y}\rightarrow{}^{92}\text{Zr}$ (stable), and $^{142}$Ba similarly through $^{142}$La to stable $^{142}$Ce/Nd-region nuclides.