Attached is a link that provides additional details concerning the biometric problems associated with cosmic rays (cancer & brain damage), as well as the different methods that have been considered to shield the travellers from GCR.
http://aoss.engin.umich.edu/Radiatio...ons/Parker.pdf
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The first thought is to surround the astronauts with sufficient mass. …As someone summarized it, the astronauts would have to be surrounded by a million gallons of water, and that works out to 4000 tons. In simple terms, the thickness H of the walls of the spacecraft should provide something of the general order of magnitude of 10^3 gm/cm^2, so that an absorber with density D requires a wall thickness such that HD approximately equals 10^3 gm/cm^2 in general order of magnitude. For water this means H =10^3 cm (10 meters or 32.8 feet), and a sphere of water of this radius has a mass of about 4000 tons.
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II Magnetic Shielding
Another protection scheme considered a magnetic field to deflect the GCR. … The magnetic field strength required is comparable to a particle accelerator 10^5 Gauss which would require cryogenic cooling and a massive power supply. A nuclear power plant would be required to power the magnetic field generator. Astronauts would require separate shielding to protect them from a 10^5 gauss field which affects biochemistry, in the brain, etc:
The above article reached the same conclusion as the Scientific Americian article, there appears to be no practical solution with 20th century physics/engineering, knowledge.
The problem does not go away when the astronauts reach the Moon or Mars. The plan was for a structure to be built with roughly 30 feet walls/ceiling on the Moon or Mars. On the Moon the base is to be located in a crater which provides shielding on three sides. A Moon base is possible due to the short duration in flight. The Mars trip does not seem possible.