Critical mass of a fissionable material: which measure most effectively reduces it for a given isotope and geometry?

Introduction / Context:
Critical mass is the minimum amount of fissile material needed to sustain a chain reaction. Designers and safety engineers must understand how geometry, density, moderation, and surrounding materials change neutron economy and therefore the critical size or mass.

Given Data / Assumptions:

• Same fissile isotope and core shape.
• No change to enrichment; focus on boundary conditions and environment.
• Standard fast or thermal spectrum as implied by the configuration.

Concept / Approach:
A chain reaction requires that each fission produces, on average, at least one neutron that causes another fission (k_eff ≥ 1). A reflector (e.g., beryllium, graphite, steel, or heavy water in thermal systems) returns escaping neutrons back into the core, increasing the effective neutron utilization and lowering the mass needed for criticality.

Step-by-Step Solution:
Identify loss channels: leakage, absorption in non-fuel, and non-fission captures.Place reflector: returning leaked neutrons reduces net leakage probability.Improved economy: more neutrons available for causing fission ⇒ lower critical mass.Other effects (e.g., cooling) modestly help via density increases but less than reflectors; absorbers do the opposite.

Verification / Alternative check:
Diffusion-theory and Monte Carlo models both show a substantial reduction in critical size with thick reflectors; published data sets list “bare” versus “reflected” critical masses, the latter being significantly lower.

Why Other Options Are Wrong:
Heating: thermal expansion lowers density, usually increasing the critical mass.Cooling: can reduce critical mass slightly by raising density, but effect is smaller than a reflector.Neutron absorber shell: increases critical mass by removing neutrons.Dilution with inert metal: lowers fissile density, raising critical mass.

Common Pitfalls:
Assuming temperature changes dominate; boundary neutron economy is far more impactful.Confusing moderators with reflectors; not all moderators are good reflectors in every spectrum.

Final Answer:
Surrounding it with a neutron-reflecting material (reflector)