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Neutron Absorption Probability
Neutron absorption probability is the likelihood that a neutron will be absorbed rather than scattered or leaking. It is the ratio of the macroscopic absorption cross‑section to the total cross‑section. Absorption leads to fission (in fissile materials) or to neutron capture (producing new isotopes). This probability is important for determining the effectiveness of control rods, burnable poisons, and fuel depletion.
Neutron AbsorptionCross‑SectionFuel
Neutron Absorption Probability
Nuclear Engineering · Reactor Physics
Pa = Σa / Σt
Pa =
Σa /
Σt
·
Pa = absorption probability ·
Σa = absorption XS ·
Σt = total XS
Neutron absorption probability is the likelihood that a neutron will be absorbed
rather than scattered or leaking. It is the ratio of the macroscopic absorption cross‑section
(Σa) to the total cross‑section (Σt). Absorption can lead to fission
(in fissile materials) or neutron capture (producing new isotopes). This probability is crucial
for control rod design, burnable poison effectiveness, and fuel depletion analysis.
Typical values: fuel ~0.3–0.5, control rods ~0.9, moderator ~0.01–0.05.
Presets:
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Cross‑section unit:
Solve for:
Calculation Steps
Ready| Step | Operation | Value |
|---|---|---|
| Enter values and press Calculate | ||
Typical Cross‑Sections (thermal neutrons, 0.0253 eV)
Approximate macroscopic values
| Material | Σa (1/m) | Σt (1/m) | Pa |
|---|
Pa = Σa / Σt · Fuel: 0.3–0.5 · Control rod: 0.8–0.95
· Moderator: 0.01–0.05 · Higher Pa → more absorption
P_a = Σ_a / Σ_t
Neutron Absorption Probability
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| P_a | Absorption Probability | dimensionless |
| Σ_a | Macroscopic Absorption Cross‑Section | 1/m |
| Σ_t | Total Cross‑Section | 1/m |
What it means
The absorption probability indicates how likely a neutron is to be absorbed in a given medium. High absorption leads to strong neutron capture.
Worked example
Neutron Absorption Probability (Pa = Σa / Σt)
Reactor Physics
Scenario: A reactor physicist evaluates the neutron absorption probability in a PWR control rod. The control rod material (B₄C) has a macroscopic absorption cross‑section (Σa) of 45.0 m⁻¹ and a total cross‑section (Σt) of 50.0 m⁻¹ (including scattering). The absorption probability determines how effectively the control rod captures neutrons, which is critical for reactor shutdown and reactivity control.
| Parameter | Value |
|---|---|
| Macroscopic Absorption Cross‑Section (Σa) | 45.0 m⁻¹ |
| Total Cross‑Section (Σt) | 50.0 m⁻¹ |
| Absorption Probability (Pa = Σa / Σt) | 0.90 (90%) |
1Obtain the macroscopic absorption cross‑section (Σa) from nuclear data or material composition.
2Determine the total macroscopic cross‑section (Σt) = Σa + Σs (absorption + scattering).
3Calculate the absorption probability using Pa = Σa / Σt — a value close to 1 indicates a strong absorber.
Absorption Probability
Pa = 0.90
The control rod has a 90% absorption probability, making it highly effective for neutron capture and reactivity control.
Common mistakes
- Using Σa instead of Σt: The total cross‑section Σt includes scattering and absorption; forgetting scattering leads to Pa > 1.
- Confusing probability with cross‑section: Pa is a dimensionless probability, not the cross‑section itself.
- Ignoring resonance absorption: At thermal energies, absorption is mostly 1/v; in resonances, the probability becomes energy‑dependent.
Applications
- Fuel selection: Compares absorption probabilities of different fuel isotopes (e.g., U‑235 vs. Pu‑239).
- Control material evaluation: Determines how effectively a material absorbs neutrons for control rods or burnable poisons.
- Moderator choice: Ensures that the moderator has a low absorption probability to maximise neutron economy.