# How thick must a shield be to be better than no shield at all?

[..] For high-energy particles entering dense matter, Bremsstrahlung is joined by pair production, and both together create particle showers. [..] A known problem in radiation shielding (thin shielding might be worse than no shielding at all).

Thus,

How thick must a shield be to be better than no shield at all?

Assuming the shield is used on a trip between planets of our solar system and is intended to protect the human crew.

I'm looking for both theoretical papers / calculations as well as practical studies (if there are any).

• I'd appreciate help with tagging :) – Daniel Jour Jun 22 '17 at 18:27
• Actually Bremsstrahlung would make mostly electromagnetic ($e^+, e^-, \gamma$) showers, whereas nuclear collisions would make the $\pi$, $\mu$, neutron, proton, and lighter ions in the showers, although for the highest energies it gets messier. There will be plenty of papers and calculations, but they may disagree with each other, it's a messy problem. @kimholder has dealt with these issues, and I think there are some Q&A here with some links to some papers. If I remember correctly it's the spallation products, neutrons and protons in particular that ruin your day, and your DNA. – uhoh Jun 23 '17 at 0:05
• In addition to the ionization effects from radiation exposure, fast neutrons and protons can knock a proton (hydrogen atom) right out of your DNA molecules. The situation reminds me of Steve Martin's character in the movie The Jerk where he exclaims "It's the cans! Stay away from the cans!" It's a poor analogy, but there probably is a "worst thickness" of material that will convert cosmic rays into more damaging forms, and you would indeed prefer either less or more thickness. – uhoh Jun 23 '17 at 0:15
• different but related Is radiation dose from cosmic rays higher behind 50 cm of shielding, or lower? – uhoh Mar 18 at 1:29

First of all let's define what the radiation is:

1. alpha (helium nucleus i.e. two protons and two neutrons)
2. beta (electrons)
3. gamma (high energy photons)
4. neutrons
5. ions (bare stripped nucleus)
6. other stuff like visible light, IR, UF. X-RAY is not considered here, X-RAY is gamma.

The only thing that is important to consider is a nuclear cross section which is different for every type and every protection material.

Protection:

1. alpha is easy, it's a heavy and well-charged particle. And there is not much of them in the space. The energy of the ones from the space is low. 1 mm of a kitchen tin foil will be a good protection.
2. beta. There are lots of electrons in the space and they can have wild energy, ranging from 10 to 10^20, and this is huge. For example, the large hadron collider at CERN is able to produce just 10^13 tops. There is nothing in the world that can stop such a high energy stuff. However, the good news is that the nuclear cross section of such a high energy particles is relatively small. 3mm of the kitchen foil is enough just as a placebo shield and in order to stop some low energy ones.
3. gamma. this is simple. the heavier the stuff the better. The earth is protected by 10km of air, which has the same level of protection as 10m of water, or 1.4m of steel, or 0.9m of lead, or 0.1m of depleted uranium. Sounds scary but 0.1m of U-238 can be the best option to protect from this kind of radiation.
4. neutron. this is the most difficult one. The best shielding is the light stuff - water, hydrogen, oxygen, graphite, etc. Ideally - by other neutrons. However, the nuclear cross section raises as its energy drops! The slower neutron is the more dangerous it is! Also when a neutron is stopped by some materials like cadmium, the neutron absorption is accompanied by a strong emission of gamma which requires more gamma protection. You can easily google for neutron protection articles like this, but overall, either not protect at all or establish an earth-like level of protection. The earth is protected by ~10 km of air which has about 25% of oxygen, hydrogen, and water. I would estimate that 3m of water will be a good earth-like protection from neutrons. Water is better than other material - it is rich in hydrogen.
5. Ions, UF, IR - the same stuff as alpha

Overall, 3mm of tin foil + 3m of water + 0.1m U-238 and the Martian astronauts will be just fine.

Here is a scan from one work, it's in Russian but you should get the idea, the legend here is:

• X is the aluminum shield thickness gram/cm^2