Nuclear fission

A sequence in which particles released by one nuclear reaction induce further reactions. In a neutron-driven fission chain, neutron capture, leakage and non-fission absorption compete with neutron production. A sustained chain requires an effective reproduction factor of one; whether material is fissile material cannot be determined from a single positive fission Q value.

Material convertible into a fissile material by neutron capture followed by nuclear transformations. A central example is uranium-238 capturing a neutron and undergoing two beta-minus decays to plutonium-239. Fertile does not mean that thermal-neutron capture immediately causes fission.

Material capable of sustaining a nuclear chain reaction with slow neutrons in a suitable configuration. Fissility involves capture and fission probabilities, neutron production and losses, rather than positive fission Q value alone. Uranium-235 and plutonium-239 are common examples; fissile is more specific than fissionable by sufficiently energetic neutrons.

In a simple compound-nucleus picture, compare the neutron-capture excitation energy to the fission barrier of the capture product. If its neutron separation energy already exceeds the barrier, slow-neutron capture can lead to prompt fission without a positive kinetic-energy threshold. If it lies below, finite neutron kinetic energy is needed for appreciable over-barrier fission; sub-barrier tunnelling and detailed resonance widths soften a literal sharp-threshold picture.

The yield of fragments as a function of fragment mass number or mass fraction. Low-excitation actinide nuclear fission commonly gives two peaks, corresponding to complementary lighter and heavier fragments. Smooth liquid-drop fission energy by itself does not predict this yield: nuclear-shell structure and the dynamics of the descent toward scission matter. Increasing excitation can weaken shell effects and change the distribution. A two-peaked illustrative curve is therefore not a universal measured spectrum.

Nuclear fission without an incoming particle supplying the activation energy. A metastable atomic nucleus can tunnel through a fission barrier along collective deformation coordinates. The rate depends exponentially on a barrier action involving its height, width and collective inertia, so positive liquid-drop fission energy alone does not imply an observable rate.

The increase in a nucleus's collective deformation potential energy between a local minimum and a saddle on a path toward separated fragments. A positive final-state Q value does not remove this intermediate barrier. A nucleus can cross it after sufficient excitation energy, or undergo quantum tunnelling. The relevant barrier for neutron-induced fission belongs to the compound nucleus formed after capture, not automatically to the target before capture.

For two spherical fragments with the same proton fraction as the parent, let $(A_1,Z_1)=y(A,Z)$ and $(A_2,Z_2)=(1-y)(A,Z)$. In the semi-empirical mass formula without nuclear pairing, nucleon rest energies, the volume term and the nuclear symmetry energy cancel in the parent-minus-fragment mass difference. The remaining Q value is the displayed competition between increased surface energy and reduced nuclear Coulomb energy. Its symmetric value is positive whenThis is an energy-release condition, not the disappearance of a fission barrier or a prediction of a short mean lifetime.

Ignore nuclear pairing and use the continuous proportional-fragment model of liquid-drop fission energy. Put $S=a_S{A}^{2/3}$, $x=a_C{Z}^2/(a_{S}A)$ and $t=y^{1/3}+(1-y{)}^{1/3}$. As $y$ runs from zero to $1/2$, $t$ rises from $1$ to $2^{2/3}$. The identity $u^3+v^3=1$ with $u=y^{1/3}$ and $v=(1-y{)}^{1/3}$ givesThe derivative changes sign at most once, from negative to positive. Thus the global maximum on the closed continuous interval occurs at either the no-split endpoint $Q=0$ or the symmetric split. If positive fission energy is available, the symmetric value is the global maximum. This qualification matters: symmetry alone makes $y=1/2$ stationary but does not make it a maximum for all parameters. In fact, $Q^{\prime \prime }(1/2)<0$ requires $Z^2/A>(2/5)a_S/a_C$; below that value the symmetric split is a local minimum. Real discrete fragments and nuclear-shell corrections are outside this continuous smooth model.