In spontaneous fission, the nucleus will tunnel through the quantum barrier preventing the fissioning to two lighter nuclei. We study nuclear reactions here merely to introduce the processes of nuclear fission and fusion. Please refer to Krane s book for more details.
Induced fission occurs when the nucleus requires some extra energy to lift it over the barrier.
Usually, this occurs with the presence of a neutron. This changes the eg pairing terms in the SEMF and the entire binding energy changes. Once a nucleus is struck, it can undergo fission, with the subsequent emission of both energy and other neutrons. To get to the high cross section region, that neutron may have to thermalise. It does this by scattering off other nuclei particularly the lighter ones.