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Nuclear Fission elementary principles. BNEN 2012-2013 Intro William D’haeseleer. Mass defect & Binding energy. Δ E = Δ m c 2. Nuclear Fission. Heavy elements may tend to split/fission But need activation energy to surmount potential barrier Absorption of n sufficient in

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Nuclear fission elementary principles

Nuclear Fission elementary principles

BNEN 2012-2013 Intro

William D’haeseleer

Nuclear fission
Nuclear Fission

  • Heavy elements may tend to split/fission

  • But need activation energy to surmount potential barrier

  • Absorption of n sufficient in

    233U 235U 239Pu … fissile nuclei

  • Fission energy released ~ 200 MeV

  • Energetic fission fragments

  • 2 à 3 prompt neutrons released upon fission

Nuclear Fission + products

Ref: Duderstadt & Hamilton

Practical fission fuels
Practical Fission Fuels


Ref: Lamarsh NRT







BNEN NRT 2009-2010

William D’haeseleer

Practical fission fuels1
Practical Fission Fuels

From these, only appears in nature (0.71%)

The other fissile isotopes must be “bred”

out of Th-232 (for U-233)

out of U-238 (for Pu-239)

Practical fission fuels2
Practical Fission Fuels

Fertile nuclei

Nuclei that are not easily “fissile” (see further)

but that produce fissile isotopes

after absorption of a neutron

Practical fission fuels3
Practical Fission Fuels

* Thorium-uranium

β (22 min)

β (27 d)

- not much used so far

- but large reserves of Th-232

- new interest because of ADS (cf. Rubbia)

Fissile by slow (thermal) neutron

Practical fission fuels4
Practical Fission Fuels

* Uranium-Plutonium

β (23 min)

β (2.3 d)

- up till now mostly used for weapons

- is implicitly present in U-reactors

- now also used as MOX fuels

- the basic scheme for “breeder reactors”

Fissile by slow (thermal) neutron

Practical fission fuels5
Practical Fission Fuels

Fissionable nuclei

Th-232 and U-238 fissionable with threshold energy

U-233, U-235 & Pu 239 easily fissionable = “fissile”

-- see Table 3.1 --

Practical fission fuels6
Practical Fission Fuels


Eth=1.4 MeV






BNEN NRT 2009-2010

William D’haeseleer

Fission chain reaction
Fission Chain Reaction

Chain reaction

235 U

Fission chain reaction1
Fission Chain Reaction

  • k= multiplication factor

  • k= (# neutrons in generation i) /

    (# neutrons in generation i-1)

  • k= 1  critical reactor

  • k>1  supercritical

  • k<1 subcritical

Critical mass
Critical mass

  • Critical mass is amount of mass of fissile material, such that

    Neutron gain due to fission


    Neutron losses due to leakage & absorption

  • Critical mass

    = minimal mass for stationary fission regime

Probability for fission
Probability for fission

Logarithmic scale !

Comparison fission cross section U-235 and U-238 [Ref Krane]

BNEN NRT 2009-2010

William D’haeseleer

Cross section of fissionable nuclei
Cross Section of Fissionable Nuclei

  • Thermal cross section

    Important for “fissile” nuclei, is the so-called

    thermal cross section

    -- See Table 3.2 --

Cross section of fissionable nuclei2
Cross Section of Fissionable Nuclei

  • Absorption without fission

    σγ for these nuclei ~ other nuclei

     behaves like 1/v for small v

    at low En, inelastic scattering non existing

     only competition between -fission

    -radiative capture

Cross section of fissionable nuclei4
Cross Section of Fissionable Nuclei

α > 1 more chance for radiative capture


α < 1 more chance for fission

Cross section of fissionable nuclei6
Cross Section of Fissionable Nuclei

Then with

Relative probability fission =

Relative probability rad. capture =

Thermal reactors
Thermal reactors

  • Belgian fission reactors are “thermal reactors”

  • Neutrons, born with <E>=2MeV to be slowed down to ~ 0.025 eV

  • By means of moderator:

    • Light material: hydrogen, deuterium, water


Fission products fragments4
Fission products / fragments

Fission products generally radioactive

Dominantly neutron rich

Mostly β- decay

The products of fission neutrons
The products of fission: neutrons

→ Besides fission also absorption



See table 3.2

η=number of n ejected per n absorbed in the “fuel”

The products of fission neutrons2
The products of fission: neutrons

η(E) for

U-233, U-235, Pu-239 & Pu-241

BNEN NRT 2009-2010

William D’haeseleer

Ref: Duderstadt & Hamilton

The products of fission neutrons3
The products of fission: neutrons

To be compared with curve for α(cfr before)

Ref: Duderstadt & Hamilton

The products of fission neutrons4
The products of fission: neutrons

η usually also defined for mixture U-235 and U-238


  • Natural U consist of 99.3% 238U & 0.7% 235U

  • NU alone cannot sustain chain reaction

  • NU in heavy water moderator D2O can be critical (CANDU reactors)

  • Light water (H2O) moderated reactors need enrichment of fissile isotope 235U

  • Typically in thermal reactors 3-5% 235U enrichment

  • For bombs need > 90% enrichment

Production of transurans
Production of transurans


of 235U content

and Pu isotopes

in typical LWR

Reactor power burn up
Reactor power & burn up

● Fission Rate

= # fissions per second

given: a reactor producing P MW

fission rate

Reactor power burn up1
Reactor power & burn up

● Burn up

= amount of mass fissioned per unit time

 Burn up = fission rate * mass of 1 atom

Burn up =

for A = 235 ; ER = 200 MeV … Burn Up = 1P gram/day

! For a reactor of 1 MW, 1 gram/day U-235 will be fissioned !

Reactor power burn up2
Reactor power & burn up

Hence, burn up

But fuel consumption is larger

→ because of radiative capture

Amount of fuel fissioned

Reactor power burn up3
Reactor power & burn up

consumption rate

Energy “production” per fissioned amount of fuel:


- assume pure U-235, and assume that all U-235 is fissioned;

- then: energy “production” 1MWD/g = 106 MWD/tonne

- but also radiative capture only 8 x 105 MWD/tonne

- but also U-238 in “fuel”  in practice ~ 20 to 30 x 10³ MWD/tonne

(however, recently more)

~ 50 to 60 x 103 MWD/tonne

Actinide buildup ref clefs cea nr 53
Actinide Buildup [Ref: CLEFS CEA Nr 53]

Total U 955 746 941 026 923 339

Total Pu 9 737 11 338 13 000

Composition of spent fuel
Composition of spent fuel

  • Typical for LWR:

Fission products ref clefs cea nr 53
Fission Products [Ref: CLEFS CEA Nr 53]

TOTAL 33,6 46,1 61,4

Fission products ref clefs cea nr 531
Fission Products [Ref: CLEFS CEA Nr 53]

Category UOX 33 GWa/tUi UOX 45 GWa/tUi UOX 60 GWa/tUi

Enr 3.5% Enr: 3.7% Enr: 4,5%

Amount kg/tUi Amount kg/tUi Amount kg/tUi

Uranium 955.746 941.026 923.339

Plutonium 9.737 11.338 13.0

FP 33.6 46.1 61.4

TOTAL 999.083 998.464 997.739

Remainder converted to energy via E=∆m c2

Delayed neutrons
Delayed neutrons

  • Recall 2 à 3 prompt neutrons, released after ~10-14 sec

  • Thermalized after ~1 μsec

  • Absorption after ~200 μs ~ 10-4 s

  • Difficult to control

  • Nature has foreseen solution! Delayed Neutrons

  • Recall β decay from some fission products

Neutron emission after decay
Neutron emission after β decay

After β decay, if energy excited state daughter larger than “virtual energy” (binding energy weakest bound neutron) in neighbor:

Thenn emissionrather thanγ emission

Called “delayed neutrons”

Delayed neutrons1
Delayed neutrons

  • Small amount of delayed neutrons suffices (fraction ~0.0065) to allow appropriate control of reactor

  • Easy to deal with perturbations