Each piece is a nucleus on to itself. The neutron is able to enter the nucleus because of its neutral charge. An electron or proton would be repelled by the outer electrons or the nucleus. Fission can also take place when synthetic nuclei are produced. Sometimes synthetic nuclei will split apart without a nuetron crashing into it.
Fusion is the bringing together of two or more nuclei, to form one larger nucleus.
However it is often the bringing together of two nuclei that are not stable. For fusion to take place there must be extremely high temperatures and pressure. However it will give off very high amounts off energy. Fission and fusion can both be used to create energy. However both will give off some radiation.