This is a biology answer, not a physics answer, but you must not look to direct modifications of DNA by cosmic rays as a source of mutations. This is a ridiculous idea, and it is basically unsupported, and I am certain that it is completely wrong (although among biologists, I might be in the minority).
Generally, the cell has error correcting features, and mutation is not simple cleaving of DNA and rejoining with a point error. This type of mutation is rare. The idea that this is the origin of mutation comes from the 1950s, when it was noticed that stressing organisms with ionizing radiation both breaks DNA and leads to consistent increase in the mutation rate.
But there is absolutely no reason to believe the mechanism is direct stress of DNA, the biology is vastly more complicated. One can get germ-line mutation by exposing flowers to heat, by placing them next to a flame (Darwin noticed this and reports it in the Origin). One can also get mutations by various stress mechanisms in different ways that are not affecting the DNA in a cleaving sort of way.
The notion that mutations are primitive undirected random events belongs to the prehistory of biology, before 2001, and predates the recognition that there is a big brain of RNA in the eukaryotic cell, directing everything that is going on. I am not sure how many biologists believe this, but it was proposed by John Mattick in 2001, and as far as I am concerned, it is certainly correct.
The RNA brain is as important to the cell as your brain is important to you.
It directs alternative splicing, gene shutting on/off (by sending out micro-RNA's), transcription and translation, and it also just does thinking, by computing with gigabytes of data.
Given this (although it is possibly still a minority view), the only correct mechanism to attribute germ-line mutations to is to active RNA editing of the DNA in germ-line, both in response to complicated RNA messaging, and in response to heavy gigabyte-sized (or, in an egg, terabyte sized) internal RNA computation, and through the direction of crossing-over. The RNA is sensitive to radiation in both getting cleaved and getting bent, but it is also temperature sensitive, and generally as fungible as you would expect of RAM. The DNA is kept stable and is corrected, and is as immutable (except for direct editing) as you would expect of ROM.
The result of the RNA editing is major modifications in non-coding regions, and these control everything we think of as complicated biology, including embryogenesis, neurogenesis, neuron activity, everything sophisticated. The proteins are as complicated as muscle and bone, doing mechanical and chemical things, but no significant computation. The mutations in genes are mostly meaningless random-drift spot-mutations that are neutral as far as selection is concerned (protien coding genes have not been the major determinant of evolution at least since we diverged from something slightly more complex than a worm).
Given this point of view, the background of ionizing radiation is no more significant for mutation generation than the thermal background of random motion--- it is one more source of error that the computational mechanism of RNA evolves to correct. If you have a high radiation environment, organisms will adapt to it by adding more error correction (there are such organisms around), and if you have a low radiation environment, you will still mutate at the same rate, since the mutations are introduced from inside, they are not external to the system.
The above is what I believe, but I haven't been following the literature to see how mainstream this view has become in the last few years. I am sure it is more mainstream now than in 2003, when it was considered lunatic crazy.