Neutron shielding

Neutrons are the part of radiation protection where intuition fails most often. Lead, the default shield for gamma rays, does almost nothing to slow fast neutrons. A thin sheet of cadmium or a few centimetres of borated plastic can stop slow neutrons completely, yet produce penetrating gamma rays as it does so. And the best neutron shield of all is ordinary water. This lesson gives Hana's class the physics to make sense of that, with the shielding around reactors and around the neutron sources used to calibrate instruments as the main examples.

Where neutron doses come from

At a power station, neutrons come mainly from the reactor core during operation and leak through the reactor shielding in small numbers; from spent fuel, through spontaneous fission of curium and other actinides and through (α,n) reactions in the oxide fuel; and from sealed neutron sources used for instrument calibration, reactor start-up and well logging. Common sealed sources are americium-241 mixed with beryllium, in which alpha particles knock neutrons out of beryllium, and californium-252, which emits neutrons by spontaneous fission.

Neutrons carry no charge and interact only with nuclei, so their behaviour depends on the energy. Fast neutrons, above about 0.1 MeV, lose energy mainly by elastic scattering. Slow or thermal neutrons, near 0.025 eV at room temperature, are readily captured by many nuclei. Shielding therefore works in two stages: slow the fast neutrons down, then absorb them, and finally deal with the gamma rays that capture produces.

Slowing down: why hydrogen wins

In an elastic collision, a neutron loses the most energy when it hits a nucleus of similar mass, as one billiard ball stops another. A head-on collision with hydrogen can transfer all of the neutron's energy; a collision with lead, about 200 times heavier, removes at most about 2 %. The average logarithmic energy loss per collision, \(\xi\), is 1 for hydrogen, about 0.16 for carbon and about 0.01 for lead, so a neutron slows from 2 MeV to thermal energy in about 18 collisions with hydrogen but more than 1000 with lead. Hydrogen-rich materials, water, polyethylene, paraffin and the water bound in concrete, are therefore the backbone of neutron shields.

Heavy and medium elements still help. Fast neutrons above about 1 MeV can scatter inelastically from iron or lead, leaving the nucleus excited and losing a large step of energy at once; the excited nucleus then emits a gamma ray. A layer of iron in front of a hydrogenous shield is therefore effective at degrading the highest-energy neutrons, which hydrogen handles less well because its scattering cross section falls at high energy.

Absorbing slow neutrons

Once thermal, neutrons diffuse until they are captured. Ordinary hydrogen captures them with a cross section of about 0.33 barn and emits a 2.2 MeV gamma ray. Boron-10, with a cross section of about 3840 barns, captures them far more readily in the reaction \(^{10}\text{B}(n,\alpha)^{7}\text{Li}\), which releases mostly an alpha particle and a lithium nucleus, both stopped immediately, with a soft 0.48 MeV gamma ray in most reactions. Adding boron to polyethylene or concrete therefore removes thermal neutrons quickly and greatly reduces the hard 2.2 MeV capture gamma rays from hydrogen. Cadmium also absorbs thermal neutrons strongly but emits energetic capture gamma rays; gadolinium is used in some fuel and pool applications.

Removal cross sections

Full neutron transport calculations are done with computer codes. For hand estimates of thick shields, engineers use the removal cross section \(\Sigma_R\). The idea is that in a thick hydrogenous shield, any fast neutron that has one significant collision is effectively removed from the penetrating fast flux, because it is quickly slowed down and absorbed. The fast neutron dose behind the shield then falls roughly exponentially:

The removal method only works when there is enough hydrogen in or behind the shield to finish the slowing down; a pure iron or lead shield cannot be treated this way. Concrete's neutron performance depends on its bound water, which is why concrete in high-temperature regions near a reactor may be specified with extra hydrogen or boron, and why its water content is checked over the life of the plant.

# Neutron shielding estimates (approximate data, rounded).
import math
XI = {'hydrogen': 1.0, 'carbon': 0.158, 'iron': 0.0353, 'lead': 0.00963}
E0, Eth = 2.0e6, 0.025          # eV
for el, xi in XI.items():
    print(f"collisions to thermalize in {el:8s}: {math.log(E0/Eth)/xi:7.0f}")

# Unshielded Am-Be source: fluence rate and dose rate at 1 m
A_GBq = 37.0
S = 6.0e4 * A_GBq               # neutrons per second
r = 100.0                       # cm
phi = S / (4 * math.pi * r**2)  # n/(cm2 s)
h = 390e-12                     # Sv cm2, approximate ambient dose equivalent coefficient for Am-Be
Hdot = phi * h * 3600 * 1000    # mSv/h
print(f"S = {S:.2e} n/s, fluence rate at 1 m = {phi:.1f} n/cm2/s, dose rate = {Hdot:.3f} mSv/h")

# Removal attenuation for a thick hydrogenous shield
SIGMA_R = {'water': 0.10, 'polyethylene': 0.12, 'concrete': 0.085}   # 1/cm
target = 0.001                  # mSv/h at 1 m
for m, sr in SIGMA_R.items():
    x = math.log(Hdot / target) / sr
    print(f"{m:12s}: {x:5.1f} cm to reach {1000*target:.0f} uSv/h")

# Thermal versus fast neutrons: same fluence, very different dose
for name, coeff in (('thermal', 10e-12), ('1 MeV', 420e-12)):
    print(f"{name:8s}: {coeff*1e12:4.0f} pSv cm2 -> {coeff*1e4*3600*1e3:.3f} mSv/h at 1e4 n/cm2/s")

collisions to thermalize in hydrogen:      18
collisions to thermalize in carbon  :     115
collisions to thermalize in iron    :     516
collisions to thermalize in lead    :    1890
S = 2.22e+06 n/s, fluence rate at 1 m = 17.7 n/cm2/s, dose rate = 0.025 mSv/h
water       :  32.1 cm to reach 1 uSv/h
polyethylene:  26.8 cm to reach 1 uSv/h
concrete    :  37.8 cm to reach 1 uSv/h
thermal :   10 pSv cm2 -> 0.360 mSv/h at 1e4 n/cm2/s
1 MeV   :  420 pSv cm2 -> 15.120 mSv/h at 1e4 n/cm2/s

From neutron fluence to dose

Neutron dose is not measured in the same way as gamma dose. Instruments and calculations convert neutron fluence, the number of neutrons crossing unit area, into dose with energy-dependent conversion coefficients. For ambient dose equivalent, the coefficient is roughly 10 pSv·cm² for thermal neutrons, rising to about 400 pSv·cm² near 1 MeV and higher at a few MeV. A fast neutron is therefore about forty times more effective per neutron than a thermal one, which is why thermalizing neutrons inside the shield matters so much even before they are absorbed.

For an unshielded point source emitting \(S\) neutrons per second, the fluence rate at distance \(r\) follows the inverse square law, and the dose rate is the fluence rate times the conversion coefficient for the source spectrum. The program in this lesson uses this to check the 0.03 mSv/h quoted for the Am-Be source.

Reactor neutron shielding

In a CANDU reactor, the calandria vessel is surrounded by a steel shield tank filled with light water, and the end shields at each face of the reactor are steel boxes containing steel balls and water. Together with the heavy water moderator, they reduce the neutron leakage to levels that the concrete reactor vault walls can then handle. Heavy water itself is a good moderator but a poor absorber, which is why the reactor needs separate shielding outside the moderator.

Penetrations through reactor shields are designed with special care because neutrons stream along gaps far more readily than photons through the same gaps. Cable trays and pipes crossing the biological shield use bent or stepped paths, and joints between shield blocks are offset. Even small gaps in a neutron shield can create local doses many times the design value, as surveys during commissioning regularly reveal.

Activation

Neutrons that are captured leave behind radioactive nuclei. Cobalt-59 in steel becomes cobalt-60; sodium in concrete becomes sodium-24; europium and cobalt traces in concrete become long-lived europium-152 and cobalt-60, which matter at decommissioning. Shield and structural materials near the core are therefore selected with low levels of cobalt and other activating impurities, and activation is one of the main sources of the dose that workers receive during maintenance. Source reduction, discussed in lesson 3, begins with these material choices.

In CANDU reactors, tritium is produced by neutron capture in the deuterium of the heavy water moderator and coolant. That activation product is the main reason tritium is the dominant internal dose hazard at Canadian stations, as lesson 7 explains.

Protecting people from neutrons

For workers, neutron exposures are uncommon outside reactor buildings at power and areas around spent fuel casks and neutron sources. Where they occur, neutron dosimeters, such as bubble detectors, track-etch dosimeters or albedo dosimeters, are worn alongside photon dosimeters, and area surveys use moderated neutron survey meters (remmeters), both covered in NUC-310. Because neutron dosimetry is less accurate than photon dosimetry, protection programs often apply conservative correction factors and keep neutron doses especially low.

Spent fuel and transport casks

Spent fuel combines the two shielding problems of lessons 5 and 6. Its gamma radiation is intense, and its neutron emission, from spontaneous fission of curium-242 and curium-244 and from (α,n) reactions in the oxide, grows with burnup. Dry storage and transport casks therefore use layered designs: thick steel or a steel and lead body for gamma shielding, a layer of borated resin or concrete for neutrons, and often fins or air channels for heat removal, since the fuel still produces decay heat. Cask surface dose rates are limited by transport regulations, and storage pads are arranged so that the casks shield one another and the site boundary dose stays low.

CANDU fuel is natural uranium with low burnup, so its neutron source is weaker than that of light water reactor fuel, and dry storage modules at Canadian stations are concrete structures holding baskets of fuel bundles after years of cooling in the pools.

For the calibration source store in the example, the class also checks the gamma dose. Americium-241 emits a 60 keV gamma ray, easily stopped by a few millimetres of lead, but the hydrogen capture in the polyethylene adds 2.2 MeV photons that the lead barely touches. That is why the outer layer is borated: boron absorbs the neutrons before hydrogen can, and the remaining capture gamma dose is checked with a gamma survey meter alongside the neutron measurement. A neutron shield that is checked only with a neutron meter is only half checked.