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    EG21001 Nuclear Physics

    Fission & Fusion

    Allan Gillespie

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    Nuclear Fission

    Steps in the Discovery of Fission:

    We have seen that neutron-capture by a nuclide with atomic number Z, followed by--decay, gives a new nuclide with Z+1. Fermi attempted to produce a transuranicelement, Z = 93, from Uranium (Z=92) by this process. The result was indeed neutron

    capture, butproduct nuclide was -unstable with 4 separate half lives.

    Experiments of Hahn & Strassmann (1939) in Berlin showed that the products were

    isotopes of Ba, La and Ce - i.e. much lighter nuclides.

    Meitner and Frisch gave correct interpretation of experiments - uranium nucleus is

    unstable after neutron capture, and may divide into two nuclei of roughly equal size.Energy released is very large, corresponding to Q of approx 200 MeV. The term

    fission(borrowed from description of cell division in biology) was coined.

    Fission results primarily from competition between nuclear and Coulomb forces inheavy nuclei. It can occurspontaneously as a natural decay process (like decay),

    or it can be inducedby the absorption of a relatively low-energy particle, such as aneutron or photon. Induced fission much more important than spontaneous fission.

    Although any nucleus will fission if we provide enough excitation energy, the

    process is only important in practice forheavy nuclei (thorium and beyond).

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    Key to obtaining large total energy releases from fission - both in nuclear reactors

    and nuclear weapons - is the concept of a chain reaction, where incoming neutronproduces several further neutrons as reaction products, and these in turn induce

    newfission events, and so on ...

    Fission in isotopes of UraniumBoth common isotope (99.3%) 238U and uncommon (0.7%) isotope 235U (plusseveral other nuclides) can be split by n-bombardment -- 235U by slow neutrons but238U only by neutrons with min energy of ~1 MeV. Fission resulting from neutron

    capture is called induced fission, and materials like 235U are called fissile materials.

    In general,

    cross section

    probability of


    [unit: barns (b)]

    = thermal


    Ek = 0.025 eV

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    Some nuclides can also undergo spontaneous fissionwithout initial n-capture, butthis is quite rare.

    When 235U captures a neutron, the resulting nuclide 236U* is formed in a highly

    excited state and splits into 2 fission fragmentsalmost instantaneously, releasingan (enormous) kinetic energy of about 200MeV per nucleus, and on average 2.5


    Strictly speaking, it is 236U* and not 235U that undergoes fission, but it is usual to

    speak ofthe fission of235U.

    Fission is a catastrophic reaction for a nucleus, and consequently there is nounique fission reaction. A typicalreaction channel for235U is:

    235 1 236 * 140 94 1

    92 0 92 54 38 0( ) 2 200+ + + + +U n U Xe Sr n MeV

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    Over 100 different nuclides, representing more than 20 different elements, have

    been found among fission products (leading to a major problem with nuclear waste

    from reactors). Figures show distribution of mass numbers in fission fragments:

    Mass distribution of possible fission fragmentsof235U. Splitting into two fragments of unequalmass is more likely than symmetrical fission.

    Note logarithmic vertical scales.

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    Fission fragments always have too many neutrons to be stable (why?), and

    usually respond by undergoing a series of- decays until finally a stable value of

    N/Z is reached:

    140 140 140 140 14054 55 56 57 58 ( ) ( )Xe Cs Ba La Ce stable four decays

    94 94 9438 39 40 ( ) ( )Sr Y Z stable two decays

    The neutron excess of fission fragments also explains why 2 or 3 free neutrons

    are released during the fission process.

    Fission Chain Reaction

    Since fission triggered by n-bombardment releases neutrons that can triggerfurther fissions, there exists possibility of a chain reaction. This can be made toproceed slowly and in a controlled manner in a nuclear reactor, or explosively in a

    nuclear weapon. Energy release in a nuclear chain reaction is far greater than in

    any chemical reaction. e.g. U burned to uranium dioxide in chemical reaction:

    U + O2 UO2

    Heat of combustion is 4500 J/g. Expressed as energy per atom, this is ~11 eV.

    By contrast, fission liberates about 200 MeV per atom/nucleus, nearly 20 milliontimes as much energy.

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    Schematic of fission process

    Model of nuclear fission

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    Control of Fission in a Nuclear Reactor

    Nuclear reactor = system in which a controlled nuclear chain reaction is used to

    liberate energy. In a nuclear power plant, this energy is used to generate steam,which operates a turbine and turns an electrical generator.

    For a steady non-explosive reaction, each fission should cause one additional

    fission; two will cause an explosion; less than one on average causes reaction to dieout. Since, on average, each 235U fission produces 2.5 neutrons, 40% of the

    neutrons are needed to sustain a chain reaction. The size of the fissile material must

    be large enough so that not too many neutrons stray through its surface and are lost

    to the reaction. There is therefore a critical size to produce a self-sustainingreaction. The critical size forpure 235U is about the size of a grapefruit.

    Dependence on neutron kinetic energy

    n-induced fission is most effective when neutrons are moving slowly they shouldhave a small kinetic energy of the order of 1/40 eV referred to as thermalised or

    thermal (or slow) neutrons, because their k.e. is roughly same as the k.e. of room

    temperature air molecules. Slow-moving n has much greater probability of capture

    (cross section) because it spends more time near nucleus.

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    Slow neutrons -at thermal energies Ek ~ 0.025 eV, v ~ 2000 ms-1

    are much more likely to be captured and cause fission in 235U than

    Fast neutrons - at Ek ~ 1MeV, v ~ 2 x 107 ms-1

    Hence large part of total volume of a (thermal) reactor consists of a moderator(low atomic number material, e.g. carbon or water) which is a non-reactive passive

    material that slows down fission neutrons to thermal velocities by collisions with

    moderator atoms.

    Neutrons are slowed down ballistically by allowing them to collide with other

    nuclei and give up some kinetic energy at each (perfectly elastic) collision. Can

    easily show that most effective moderation occurs when moderator nuclei have

    smallest values of A (i.e. as close to A=1 as possible).

    Nucleus common form No. of collisions

    to thermaliseHydrogen Normal water 19

    Deuterium Heavy water 32

    Carbon Graphite 110

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    A moderator separate from the fuel is required because fast neutrons from

    fissions (energies around 1 MeV) cannotbe slowed down to thermal energies

    within the fissile uranium core itself because the majority 238U componentstrongly absorbs neutrons in the 1 130 eV energy range (fig below).

    capture of neutrons in 238U(cross section is probability of neutron-capture)

    Solution is to allow the fission

    neutrons to enter the separate

    moderator then re-enter the

    fissile core to generate furtherfissions, once slowed down to

    thermal velocities (avoiding the

    resonances in the cross section).



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    First nuclear reactor Enrico Fermi, Chicago, 1942.

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    Instrumentation is required to control a reactor. Rate of reaction is controlled byinserting or withdrawing control rods made of elements (such as boron orcadmium) whose nuclei are good neutron absorbers. These rods can be lowered

    into the pile to make it sub-critical. Also have shut-down rods to rapidly closedown reactor in an emergency (or a borated liquid system to flood the reactor core).

    Not all neutrons are emitted instantaneously. Most are produced without delay

    so-called 'prompt neutrons'. Some of fission products are radioactive n-emitters

    that produce 'delayed neutrons' (with delays ranging from seconds to minutes).

    Removal of control rodsand overheating can be


    Chernobyl, Ukraine, 25 April, 1986

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    The integrated Caesium

    ground-level air

    concentration pattern

    four days after the

    beginning of theChernobyl accident.

    (April 1986)

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    A typical sequence of processes in fission. A 235U nucleus absorbs aneutron and gives rise to fission; two prompt neutrons and one delayed

    neutron are emitted. Following moderation, two neutrons cause new

    fissions and the third is captured by 238U resulting finally in 239Pu.



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    A reaction that is sub-critical for prompt neutrons can be critical from prompt-and-delayed neutrons together (sometimes called delayed-critical). Principle is that byputting reactor together with control rods in place, rods can be carefully withdrawn

    at frequent intervals during construction. By seeing to it that reactor never goescritical for prompt neutrons (that is, prompt critical) it is assumed that reactor will be

    sufficiently sluggish that human responses can prevent reactor running away

    destructively. Basic design of a nuclear power plant is shown below.


    reactor (PWR, USA)

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    Typical fissionpower reactors

    Torness, Scotland

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    inside a nuclear power reactor

    Sizewell A and B

    power stations

    Dungeness B

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    20Indian Point nuclear plant, New York.

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    21Hartlepool, UK

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    Depending on the moderator material chosen, it may be necessary to enrich the235U component in the nuclear fuel above its natural value of 0.7%, typically to 3%or so, by isotope-separation processing. Since enrichment is an essential

    component of nuclear weapons construction, this can lead to a coupling of nuclear

    power programmes and WMDs.

    Nuclear Weapons

    In (very simplified) essence, a nuclear fission weapon like the Hiroshimaatomic bomb brings together several sub-critical masses of highly enriched

    uranium to make a super-critical mass. This requires exotic chemical implosion

    technology to overcome the natural forces of thermal expansion. Such

    considerations at least ensure that a nuclear reactor cannot produce the densityeffects required to initiate a nuclear weapon.

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    Fast Reactors

    No cooling down of neutrons: no moderator

    Fissile reactor core can therefore be smaller

    Core surrounded by 238U (or depleted U)

    Coolant often liquid sodium

    239Pu + 235U



    238U + 1n 239Np 239Pu

    - : 23 min - : 2.3 days

    239Pu in presence of fast neutrons

    produces 2.9 neutrons breeder reactor

    Easy to separate fissile material created (different Z)

    Dounreay nuclearplant

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    radiation (blue)

    from -emission

    in Harwellnuclear reactor

    N l W

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    Small-scale nuclearweapons testing

    atomic cannon test, 1953

    Trinity tests, 1945

    Nuclear Weapons

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    N l F i

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    Nuclear Fusion

    In a nuclearfusion reaction, two or more small light nuclei come together, orfuse, to

    form a larger nucleus. Fusion reactions release energy for the same reasons (ofbinding energy) as fission reactions, but the BE/nucleon curve shows that there is

    potential foreven greater energy releasein fusion, because of the slope of the curveat small A.

    Fusion Reactions in the Sun

    (i) Proton Cycle:Fusion of four H nuclei into a He nucleus is

    believed to be primary energy source in our Sun.

    This reaction is called the proton cycle:

    p + p d + e+ + e where p =11H and d =


    p + d 32He +

    32He +


    42He + p + p , ( called helium burning )

    Sequence results in a total mass-energy conversion of26.7 MeV. This fusion is

    "contained" on the Sun by the enormous gravitational field, and a continuous

    reaction takes place.

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    Fig 1. Temp of Sun is ~ 107 K

    (ii) CNO cycle:Another possible cycle (proposed by Bethe) to convert hydrogen into helium in

    the Sun involving carbon, nitrogen, oxygen and helium. The net effect is:

    4p 42He + 2e+ + 24.7MeV

    Fig. 2: Sequence of events in the carbon cycle

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    A man-made fusion reaction on Earth might utilise one of the reactions below:

    Reaction Energy Released


    D(d,p)T 4.02

    T(p,)4He 19.6

    T(d,n)4He 17.6

    6Li(n,)T 4.96


    4He 22.4


    4He 17.3


    8Be 14.9

    Fusion in Sun and stars is contained by tremendous gravitational field of Sun,and a continuous reaction takes place. By contrast, fusion reaction which takes

    place in an H-bomb is a destructive explosion, since it is not contained.

    At first glance it appears that fusion on Earth is hopeless, not only because we

    must achieve enormous temperatures necessary, but at same time we need tocontain reaction at a temperature many orders of magnitude above that at which

    earth materials vaporise. In fact, to obtain fusion we do not need high

    temperatures as such - what we need are high velocity particles. e.g. any particle

    with k.e. = 0.025 eV has a kinetic temperature of 293K , whereas a particle havingk.e. = 1 keV has a kinetic temperature equivalent of 11.6 million K.

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    Basic physical and technical problems of fusion power lie in developing systemscapable of producing the heat necessary to create a hydrogen plasma (>100 millionK) under controlled conditions, and maintaining that temperature for a period of up

    to several seconds. At these temperatures the fusion reactions are calledthermonuclear reactions.

    Critical quantity in a fusion reactor is productof plasma temperature and number

    density of particles. Nuclei of heavy hydrogen isotopes - deuterium and tritium - areeasiest nuclei to fuse. Resulting products of fusion are helium gas and neutron

    radiation. This process is seen as the most promising, and therefore the

    development ofD/T fusion reactors has become focal point of international efforts.

    Fusion Power

    A. The Tokamak - Magnetic Confinement Fusion

    Most promising route towards a nuclear fusion reactor makes use of a powerfulmagnetic field to confine a hydrogen plasma.

    At the extreme temperatures involved, the D-T gas becomes completely ionised,

    with all the atomic electrons stripped off their atoms, and the resulting plasmaacts like two independent fluids of positive and negative particles.

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    Fusion plasma located within toroidal high-vacuum chamber, and magnetic

    fields of su...