Below an answer to a recent question about shielding against radiation on a trip to Mars, there was this comment from dubu (emphasis mine):
[..] 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).
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).