The capture of a neutron can split a nucleus - but only for
certain isotopes like U-235 and Pu-239.
Two naturally occurring isotopes undergo spontaneous fission,
meaning the nucleus splits without neutron capture. These are 235U
and 238U. A few other isotopes undergo spontaneous fission, but
these are produced by an earlier neutron capture. Spontaneous
fission is the result of quantum tunnelling, which is rather
difficult to explain. There are related links below.