Are there big differences in the amount of radiation if you would put the crew compartment (on the journey to Mars) inside the LOX/LH2 fuel tank? I know that there are similarities with other question, but this is only meant with its own rocket fuel.
Yes, low-Z shield would work (generally, water or polyethylene). However, LH2 is famously prone to seeping through seemingly solid walls, and making habitable space fit inside the fuel tank would put you at a disadvantage:
- Crew habitat has to be at room temperature (293K).
- LH2 has to be kept at the temperature of 20K.
- You would have to increase insulation between the habitat and the tank to reduce thermal losses (and correspondingly, hydrogen boil-off which is mass wasted, pure and simple). Instead of a cylinder with hemispherical ends, you'd have to produce a less efficient and more expensive vessel.
- Even then, the crew would be freezing cold, and thermal design would be unnecessarily bulky and risky.
- If you spend the last drops of fuel on Trans-Earth injection you'll have no protection from cosmic rays during the return voyage.
- Another important part of that disadvantage is LH2's low density: 70.85 $kg/m^3$ instead of water's 1000 or ice's 917.