It's true particles can be noted to scatter. And in fact we see this when we look at the bubble chamber traces. Or the tracks left behind.
We note that some of them succumb to the path of least resistance...this is a straight line. These traces can be very long. We notice that some of them do not, and occupy circular or spiral "fizzle outs". We expect to have a situation where a smaller particle broken down from the first one will make the straight paths longer and longer until we see them pass through the Earth...it is more likely they will be destroyed in the fire or the increase in density to where poles of magnetic particles are forced into patterns and create a secondary force of nature called magnatism. Apart from its' presence with mass and density.
In other words, not only does the Earth have a gravitational field around it, it also has a magnetic field around it.
Based on what type of material it is, this magnatism may act to increase the overall gravitational force exerted on that material.
Say a large ball magnet were placed on the surface of the Earth...would it experience more of a pull to the ground only because it was heavy? No. Because it was heavy and highly magnetic too, being attracted to the huge ball magnet in the center of the Earth.
Since nutrons are highly magnetic and very small in mass but traveling at great speeds it is likely they will bond with the core magnet and stay put. But some have theorized they continue to go through the core magnet and keep on going, we don't know this for sure.