Nuclear fission

Nuclear fission splits an atomic nucleus into two major fragments, usually accompanied by emitted neutrons and gamma rays. It can follow neutron absorption or occur spontaneously in some heavy nuclides. When the products have greater total nuclear binding energy, the decrease in rest energy supplies fragment kinetic energy and radiation.

The fragments are often neutron-rich and undergo subsequent beta decay, producing an evolving inventory of fission products. Some emitted neutrons can cause further nuclear fission, enabling a nuclear chain reaction; others are absorbed without fission or escape.

The discovery combined chemical and physical evidence. Otto Hahn and Fritz Strassmann identified barium among products of neutron-irradiated uranium, rather than merely an adjacent heavy element. Lise Meitner and Otto Robert Frisch interpreted this as division of the atomic nucleus and estimated the large released energy from mass differences. Chemical separation identified the unexpected product: the same procedure could separate a radium isotope from barium, whereas the new radioactive activity followed barium. This chemical comparison did not by itself measure every fragment's motion.^[ref]

Nuclear fission induced before the incident neutron has slowed to thermal energies. It allows otherwise non-thermal-fissile fuel constituents such as uranium-238 to contribute to fission power. A change in their fission fraction need not mean a change in total power.

A nuclide formed in or descended from nuclear fission. The inventory includes unstable species and their decay products and evolves with irradiation and elapsed time.

A nuclear chain reaction is a sequence in which particles released by one nuclear reaction induce further nuclear reactions. In a neutron-driven nuclear fission chain, emitted neutrons can cause new nuclear fission, be absorbed without causing nuclear fission, or leave the material.

In a simple generation model, let $N_g$ be the mean number of chain-carrying neutrons in generation $g$, and let $k_{\mathrm{eff}}$ be their effective reproduction ratio. Then $N_{g+1}=k_{\mathrm{eff}}{N}_g$. For $k_{\mathrm{eff}}<1$ the mean chain dies away; $k_{\mathrm{eff}}=1$ gives a steady mean population; and $k_{\mathrm{eff}}>1$ gives growth in this fixed-coefficient model. Thus a steady chain has reproduction ratio one, while a growing chain is also self-sustaining in the mean. This elementary generation model does not describe every timescale or spatial change.

Whether material is fissile material depends on reaction probabilities, neutron production and losses in a specified setting. A positive nuclear fission Q value establishes that the final products can release energy, but does not by itself establish the neutron balance.

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.

A nuclear reactor sustains and controls a nuclear chain reaction to produce heat or a useful neutron field. Nuclear fission supplies fresh neutrons; absorption and neutron leakage remove them. A steady neutron population requires a balance between production and losses, the condition of nuclear criticality.

The functions of its components are different. Fuel supplies fissioning atomic nuclei; control rods change neutron absorption; coolant transports heat. In a thermal reactor, a neutron moderator reduces neutron energies before subsequent reactions. Slowing neutrons and cooling the fuel are separate physical functions even when the same material performs both.

Chicago Pile-1 demonstrated a controlled self-sustaining chain reaction in 1942 using a uranium–graphite assembly and neutron-absorbing controls. The decisive observation was the neutron population's response to changing absorption, rather than generation of useful electrical power.^[ref] A power reactor adds heat-transfer and conversion equipment; decay heat persists after the chain reaction is stopped.

A boiling water reactor is a nuclear reactor in which water boils inside the reactor vessel and the resulting steam directly drives a turbine. Water serves as both coolant and neutron moderator. Moisture separators and dryers remove entrained liquid before steam reaches the turbine; a condenser and feedwater system return it to the vessel.^[ref]

The heat balance makes its purpose concrete: in a simplified steady model, $\dot{Q}\simeq \dot{m}(h_{\mathrm{steam}}-h_{\mathrm{feedwater}})$, where $\dot{m}$ is the water mass flow and $h$ is specific enthalpy. With an illustrative enthalpy increase of $2MJ/kg$, transporting $2\mathrm{GW}$ of heat requires approximately $1000kg/s$. This is a thermal balance, not the electrical output, because the turbine cycle rejects heat to the condenser.

A boiling water reactor differs from a pressurized water reactor, which keeps its primary coolant liquid and transfers heat to a separate steam-producing circuit. Shutting down the chain reaction does not remove decay heat, so heat removal remains necessary after shutdown.

Chicago Pile-1 was the experimental nuclear reactor that achieved a controlled self-sustaining fission chain reaction on 2 December 1942, in a structure beneath the University of Chicago's Stagg Field stands. The project was led by Enrico Fermi.

Uranium supplied fissile material, graphite moderated neutrons, and neutron-absorbing control rods adjusted the chain reaction. Gradually changing the absorber configuration let the team test approach to criticality. The scientific milestone was controlled neutron multiplication sufficient to sustain the reaction; the pile was an experimental assembly, not a power-producing station.^[ref]

A self-sustaining neutron balance in which production offsets absorption and leakage. In a steady one-group neutron diffusion equation, criticality is a compatibility condition between material parameters and the allowed spatial mode.

Escape of neutrons from a specified region before they participate in further reactions there. A leakage fraction depends on the region's geometry, surrounding materials and energy-dependent transport and absorption, rather than its dimensions alone.

A nuclear reactor on the side of a specified moderation optimum where adding moderator increases neutron multiplication. Removing water then tends to reduce reactor reactivity, under the comparison's other fixed conditions. The optimum and the derivative depend on composition, geometry and operating state.^[ref]

A constituent that absorbs neutrons and thereby reduces their availability for a nuclear fission chain reaction. Effectiveness depends on isotope, neutron spectrum and spatial distribution, not just one thermal cross section.

The reduction of reactor reactivity caused by neutron absorption by xenon-135. In a simplified model its abundance is fed by radioactive iodine decay, while its removal is by radioactive decay and neutron capture. Changes in these pathways can delay its response to a change of neutron flux.

Energy generated in a period divided by rated power times elapsed time. At fixed efficiency, it scales annual thermal energy and fuel consumption.

The ratio of the rate of formation of fissile nuclei to the rate at which the specified fissile inventory is consumed, under stated reaction and accounting conventions. A conversion ratio below one indicates a replacement shortfall in that inventory. It is distinct from neutron multiplication: a reactor's instantaneous neutron balance and its long-term fuel-inventory balance are different questions.

A reduced time-dependent model for a neutron population amplitude coupled to delayed neutron precursor populations. Spatial and spectral shape changes are neglected or represented through prescribed effective coefficients. Such a model illustrates timescale separation without establishing the spatial behaviour or operating limits of an actual reactor.

The effective time associated with successive prompt fission generations in a specified point kinetics model. It is distinct from a macroscopic population growth period, which also depends on reactor reactivity and delayed neutrons.

A timescale-separation approximation that eliminates the rapidly adjusting neutron amplitude in favour of the slower delayed neutron precursor reservoir. It describes behaviour after the short prompt transient and need not resolve the initial adjustment.

The characteristic relation between imposed reactor reactivity and exponential growth or decay rates in a point kinetics model. Several kinetic modes can coexist; the late-time behaviour is determined by the mode with greatest real growth rate that is actually excited.

A dimensionless measure of deviation from critical neutron multiplication. Positive reactivity indicates a supercritical neutron balance; zero gives criticality. The population's actual time evolution also depends on delayed-neutron and feedback dynamics.

The change of reactor reactivity with a specified material temperature, with the other variables held as stated. Several component coefficients need not have the same sign.

The change of reactor reactivity with thermal power along a specified family of states. In a quasistatic process, the chain rule weights each temperature coefficient of reactivity by that component's temperature response to power.

The fuel-temperature derivative of reactor reactivity associated with thermal broadening of nuclear resonances, with the other state variables specified. In ordinary uranium-fueled water reactors it is negative: heating the fuel increases effective resonance capture. Its magnitude depends on spectrum, fuel state and resonance self-shielding, so its sign does not determine how its magnitude changes under a lattice redesign.^[ref]

A movable neutron-absorbing component used to change reactor reactivity. Insertion can make the fission chain reaction subcritical; residual radioactive-decay heat still requires cooling.

A water-cooled and water-moderated nuclear reactor whose primary coolant is pressurized to suppress bulk boiling in the core. Heat is transferred to a secondary circuit through steam generators.