HUS
Nuclear ReactionsNuclear Reactions
MScMSc. . NguyNguynn VnVn QunQun
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Learning ObjectivesLearning Objectives
History Recap (Tm lc lch s)1
Understand the different length scales of nuclear physics (Nmc cc thang n v trong vt l ht nhn). 2
Know the nomenclature for isotopes and nuclear reactions (Bitcc thut ng v cc ng v v phn ng ht nhn). 3
Know the different types of neutron nuclear collisions and theirrelationship to each other (Bit cc kiu tng tc ca neutron vmi quan h gia chng).
4
Basic principles of nuclear reactor (Cc nguyn l c bn ca lphn ng).5
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Learning ObjectivesLearning Objectives
Neutron sources (Ngun neutron)6
Basic principles of nuclear reaction (Cc nguyn l c bn caphn ng ht nhn).7
Binding energy curve (ng cong nng lng lin kt). 8
Liquid drop model (M hnh mu git cht lng).9
Fission reaction (Phn ng phn hch).10
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Learning ObjectivesLearning Objectives
Ordinary differential equation review (Nhc li v phng trnh vi phn thng).11
Radioactive decay (Phn r phng x).12
Decay chain (Chui phn r phng x). 13
Chart of nuclide (ng phn b cc ht nhn).14
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
History recapHistory recap
1789 1932 1938 1951
Uranium was discovered in 1789 by Martin Klaproth, a German chemist, and named after the planet Uranus.
James Chadwick discovered the neutron.
Nuclear fission discovered by the German chemists Otto Hahn.
Experimental Breeder Reactor I (EBD I) is the world's first electricity-generating nuclear power plant.
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Why nuclear?Why nuclear?
The same value (cng mt gi tr)The same value (cng mt gi tr)
Generation energy(Nng lng sinh ra)
1,780 tonscoal
17,000 m3
gas
3.5 barrels oil
0.7 g Uranium
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Why nuclear?Why nuclear?
15%
44%16%
15%
10%
Barrier to constructing nuclear power plant in US
What is the biggest?
2008 survey of energy professionals
Political Resistance
Nuclear waste disposal issues
Cost of NPP constructionFear of nuclearaccident
Others
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Basic principles of nuclear reactorBasic principles of nuclear reactor
Simple device (Thit b n gin)
Fission fuel realeases energy in the core (Nhin liuphn hch gii phng nng lng trong li).
Heat is transported away by a coolant which couples the heat source to a rankine steam cycle (Nhit c truyn ibng mt b lm mt gm c 2 ngun nhit theo chu trnh hirankine).
Very similar to a coal plant, with the exception of the combustion process (Rt ging vi nh my s dng than, khc qu trnh t chy nhin liu).
Main complication arises from the spent fuel, a mix of over 300 fission products (Rc ri chnh xut hin l do nhin liu chy, y l hn hp bao gm hn 300 snphm phn hch).
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Basic principles of nuclear reactorBasic principles of nuclear reactor
Public domain image from wikipedia
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Basic principles of nuclear reactorBasic principles of nuclear reactor
Power plant often discharge their circulating water directly back to the ocean. Strict environmental
prottectitionregullatitions
Temperature increases by 5-10 Farenheits
Image by MIT
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Basic principles of nuclear reactorBasic principles of nuclear reactor
CoolingTower
ElectricGeneratorMain
Turbine
MainCondenser
CirculatingWater Pump
If far from a water source, cooling towers are used to transfer the heat to air.
Water vapor is visible at the contact of the warm wet air insidethe tower with the cool dry air outside
Image by MIT
Department of Nuclear Physics
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Nguyen Van Quan
Reactor concepts (Reactor concepts (CCcc khkhii ninimm ccaa ll phphnn ngng))
1
Fuel (Fuel (NhinNhin liliuu))- Uranium (Urani)- Plutonium (plutoni)- Thorium (Thori)
2
Coolant (Coolant (ChChtt llmmmmtt))
- Light water (nc nh)- Heavy water (nc nng)- Sodium (Na)- Molten salt (mui nngchy)- Helium(He)- CO2- Lead-Bismuth (Pb-Bi)-
3
Moderator (Moderator (ChChttllmm chchmm))
- Light water (nc nh)- Heavy water (nc nng)- Graphite (than ch)- Be
Department of Nuclear Physics
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Nguyen Van Quan
Neutrons in a reactor (Neutron Neutrons in a reactor (Neutron trongtrong ll phphnn ngng))
Fuel Rods (Cc thanh nhin liu)
Contr
ol R
od
(T
ha
nh
i
ukh
in)
Reacto
r V
ess
el W
all
(Th
nh
thn
gl
)
Shie
ld W
all
(Th
nh
t
ng
che
chn)
Mod
era
tor
(wate
r)
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Macroscopic to microscopic worldMacroscopic to microscopic world
Cutaway of PWR pressure vessel and Cutaway of PWR pressure vessel and internalsinternals
Fission chain reaction
Department of Nuclear Physics
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Nguyen Van Quan
NomenclatureNomenclature--Isotopes (Isotopes (ThuThutt ngng--ngng vv))
Z is the atomic number(Z l s th t nguyn t)
A is atomic mass(A l khi lng nguyn t)
XAZN=A-Z is number
of neutrons(N l s neutron)
Nuclei with the same Zand different A are called
isotopes (Cc ht nhn ccng Z v khc A c gi
l cc ng v)
U23592 U23892
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Nuclear stability (Nuclear stability (TTnhnh bbnn ccaa hhtt nhnnhn))
As Z increases, the long range Coulomb repulsion between protons is balanced by the presence of additional neutrons to provide additional short-range attractive nuclear forces
Z tng, lc y Coulomb gia cc proton l cn bngbi s hin din ca neutron to nn lc ht ht nhn khong cch ngn.
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Distribution of stable nuclides (Distribution of stable nuclides (PhnPhn bb cccc hhtt nhnnhn bbnn))
4OddOddEven
50EvenOddOdd
266
53OddEvenOdd
159EvenEvenEven
#NuclidesNZA
Odd (l) v Even (chn)
Department of Nuclear Physics
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Nguyen Van Quan
Nuclear Collision reactionsNuclear Collision reactions
U U
a+b c+d a(b, c)d
10 n
23592
23692
UnU 2369223592 ,
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Nguyen Van Quan
Fundamental laws (Fundamental laws (CCcc nhnh lulutt cc bbnn))
Conservation Conservation lawslaws
AA
CC
BBDD
Nucleons (S nucleon)Total A remains the same
Energy (Nng lng)Energy, including rest mass, is conserved
Charge (in tch)Total Z remains the same
Momentum (Xung lng)
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Nguyen Van Quan
Q Q -- value (value (GiGi trtr Q)Q)
2)( cMMMMTTQ DcBAif
Exothermic reaction produces energy.
Endothermic reaction requires energy
Q>0 exothermic Phn ng ta nhit
Q
Department of Nuclear Physics
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Nguyen Van Quan
ExothermicExothermic
Source: http://www.mpoweruk.com
Fission of Uranium 235
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Nguyen Van Quan
EndothermicEndothermic
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Nguyen Van Quan
RadiativeRadiative capture (capture (BBtt bbcc xx))
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Nguyen Van Quan
Neutron Scattering (Neutron Scattering (TTnn xx neutron)neutron)
Elastic scattering (Tn x n hi) Inelastic scattering (tn x khng n hi)
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Nguyen Van Quan
Neutron absorption (Neutron absorption (HHpp thth neutron)neutron)
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Nguyen Van Quan
Beta (minus) decay (Phn r -)
Department of Nuclear Physics
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Nguyen Van Quan
Positron emission (Positron emission (PhnPhn rr +)+)
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Nguyen Van Quan
Capture of electron (Capture of electron (BBtt electron)electron)
Department of Nuclear Physics
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Nguyen Van Quan
Gamma Decay (Gamma Decay (PhnPhn rr gamma)gamma)
Source: http://hyperphysics.phy-astr.gsu.edu
Emission gamma
Pht ra tia gamma.
Occurs when nucleus transitions from a higher to lower energy state
Xy ra khi ht nhn dch chuyn ttrng thi nng lng cao xungtrng thi c nng lng thp hn.
Energy of photon?
Equal to the change in energy of nuclear state
Nuclear structure?
Does not change
Department of Nuclear Physics
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Nguyen Van Quan
Type of decayType of decay
Department of Nuclear Physics
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Nguyen Van Quan
Binding Energy (Binding Energy (NngNng llngng linlin kktt))
Binding EnergyA = ZMp + NMn MX
The weights of these constituent masses exceeds the weight of the nucleus if we add the masses of Z protons and N neutrons that make up a nucleus. The difference is the mass defect which is positive for all nuclides. Multiplying by c2 yields the binding energy of the nucleus.
When the nucleus is formed, the loss in mass is due to the conversion of mass to binding energy. It is defined as the energy that is supplied to a nucleus to completely separate its nucleons.
A measure of nuclear stability is obtained when the binding energy is normalized to the number of nucleons.
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Binding Energy Curve (Binding Energy Curve (ngng cong cong nngnng llngng linlin kktt))
Source: http://www.schoolphysics.co.uk
Exothermic reactions result in reaction products with higher binding energy.
Cc phn ng ta nhitsinh ra cc sn phmphn hch c nnglng lin kt cao hn.
Two options
Fission of heavy nuclides
Fusion of light nuclides
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Decay chain (Decay chain (ChuChuii phnphn rr))
A B + C D + E
tAA
AeNtN )0()(
)()()(
tNtNdt
tdNBBAA
B
))(0()( ttAAB
AB
BA eeNtN
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Decay chain (Decay chain (ChuChuii phnphn rr))
Norm
aliz
ed a
ctivity
AA (t)/AA (0)
AB (t)/AA (0)
0.75
0.50
0.25
Norm
aliz
ed a
ctiv
ity
0.75
0.50
0.25
Norm
aliz
ed a
ctiv
ity
0.75
0.50
0.25
1.00
1.00 1.00
0 1 2 3 4t
B = A/5 B = A
B = 5A
0 1 2 3 4t
0 1 2 3 4t
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Decay chains (Decay chains (ChuChuii phnphn rr))
Definition of Decay Chain:
The radioactive decay of different discrete radioactive decay products as a chained series of transformations.
nh ngha chui phn r: L mt chui cc bin iphn r phng x ca cc sn phm phn r gin onkhc nhau.
Decay chains
Thorium series or 4n
Neptunium series or 4n+1
Uranium or Radium series 4n+2
Actinium series or 4n+3
Department of Nuclear Physics
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Nguyen Van Quan
Thorium series (Thorium series (ChuChuii phnphn rr ccaa ThoriThori))
Source: http://www.pubs.usgs.gov
Department of Nuclear Physics
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Nguyen Van Quan
Neptunium series (Neptunium series (ChuChuii phnphn rr ccaa NeptuniNeptuni))
Source: http://www.wikimedia.org
Department of Nuclear Physics
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Nguyen Van Quan
Uranium series (Uranium series (ChuChuii phnphn rr ccaa UraniUrani))
Source: http://www.pubs.usgs.gov
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Actinium series (Actinium series (ChuChuii phnphn rr ccaa ActiniActini))
Source: http://www.metadata.berkeley.edu
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Neutron Sources (Neutron Sources (NguNgunn neutron)neutron)
Spontaneous Fission
T phn hch
Alpha Neutron Source
Ngun alpha neutron
Photoneutrons
Cc quang neutron
Accelerated charged particles
Gia tc cc ht tch in
Fission
Phn hch
Fusion
Nhit hch
Department of Nuclear Physics
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Nguyen Van Quan
Spontaneous FissionSpontaneous Fission
Spontaneous fission (SF) is a form of radioactive decay characteristic for very heavy isotopes. In practice, only energetically feasible for atomic masses above 230 amu. It is theoretically possible for any atomic nucleus with mass >= 100 amu.
Radioisotopes for which spontaneous fission is a no negligible decay mode may be used as neutron sources notably Cf-252 (half-life 2.645 years, SF branch ratio 3.09%)
Department of Nuclear Physics
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Nguyen Van Quan
Spontaneous FissionSpontaneous FissionSource: Applied Radiation and Isotopes, Volume 70, Issue 8, August 2012, Pages 14571463
The simulated 252Cf neutron spectrum (Watt fission distribution, blue), the measured data scaledto match the simulated spectrum (black), and the scaling function (orange)
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Alpha Neutron SourceAlpha Neutron Source
Neutron energy spectra for 252Cf and 241AmBe isotopic neutron source.
Source: Nuclear Instruments and Methods in Physics Research Section A: Volume 577, Issue 3, 11 July 2007, Pages 756761
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
PhotoneutronsPhotoneutrons Spectrum (Spectrum (PhPh quangquang neutron)neutron)
Source: Robert C. Runkle at al, NIM A
Photoneutron emission spectra for various target materials demonstrating the high-energy photofission signature region using a 12-MeV endpoint bremsstrahlung source
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Fission (Fission (PhnPhn hhchch))
198-207~207
3-12-(n, gamma)
-~12Neutrinos
77Gamma (FP)
55Prompt neutrons
77.5Prompt gammas
88Beta (FP)
168168Fission products
Energy recuperatedEnergy releasedPhn hch ca 235U bi
neutron nhit
Department of Nuclear Physics
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Nguyen Van Quan
Liquid drop model (Liquid drop model (MMuu gigitt))
Source: http://large.stanford.edu
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Liquid drop model (Liquid drop model (MMuu gigitt))
In nuclear fission, the short nuclear bonds of the nucleons keeps the nucleus together. Initially, thepotential energy of the nucleus is equal to the binding energy of the nucleons (no kinetic energy). To deform the nucleus, energy must be provided in an effort to increase the average distance between the nucleons, thus increasing the potential energy of the nucleus. However, the strong nuclear forces are very short. Thus when the separation starts, the repulsive forces diminish and the potential energy diminishes as well. There is thus a threshold energy required (about 6 MeV) for fission.
Quantum mechanics also explains how spontaneous fission can happen, but with very-low probability, through a tunnellingeffect without any energy input
Department of Nuclear Physics
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Nguyen Van Quan
Critical Energy (Critical Energy (nngnng llngng ttii hhnn))
Critical Energies Compared to Binding Energy of Last NeutronSo snh nng lng ti hn vi nng lng lin kt ca neutron ngoi cng
+1.0 MeV7.0 MeV6.0 MeV233U
+0.3 MeV6.8 MeV6.5 MeV235U
+1.6 MeV6.6 MeV5.0 MeV239Pu
-1.5 MeV5.5 MeV7.0 MeV238U
-2.1 MeV5.4 MeV7.5 MeV232Th
BEn EcritBinding energy of the
last neutron BEn
Critical Energy
Ecrit
Target Nucleus
Department of Nuclear Physics
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Nguyen Van Quan
Fission cross section of fissionable nucleiFission cross section of fissionable nuclei
Source: Robert C. Runkle at al, NIM A
Comparison of neutron-induced (dotted lines) and photon-induced (solid lines) fission cross-sections as a function of particle energy for various isotopes
Department of Nuclear Physics
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Nguyen Van Quan
Fertile materialsFertile materials
Materials that can undergo transmutation to become fissile materials.
L nhng vt liu c th tri qua qu trnh bin i tr thnh vt liuc th phn hch.
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Nguyen Van Quan
Fission ProductsFission Products
Materials that can undergo transmutation to become fissile materials.
L nhng vt liu c th tri qua qu trnh bin i tr thnh vt liuc th phn hch.
Department of Nuclear Physics
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Nguyen Van Quan
Stability of fission productsStability of fission products
Neutron rich fission products beta decay towards stability.
Cc sn phm phn hch u giu neutron s phn r beta chuyn
thnh cc ht nhn bn.
Department of Nuclear Physics
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Nguyen Van Quan
Neutron multiplication (Neutron multiplication (HH ss nhnnhn neutron)neutron)
k = multiplication factor = Number of neutrons in one generation
Number of neutrons in preceding generation
Critical, k=1
Sub-critical, k1
N(t)
N(0)
k>1
k=1
k
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Prompt neutron (Neutron Prompt neutron (Neutron ttcc ththii))
(E) = 0.453e1.036 E sinh 2.29E
(E )(E )dEdE is average number of fission neutrons emitted with energy in E to E+dEper fission neutron.
(E )(E )dEdE l s neutron phnhch trung bnh pht ratrong khong nng lng tE ti E+dE trn mtneutron phn hch.
Department of Nuclear Physics
HUSHUS
Nguyen Van Quan
Delayed neutron (Neutron Delayed neutron (Neutron trtr))
Less than 1% of neutrons from fission are considered delayed. Delayed neutrons appear long after the fission event through the decay of certain fission products, also called neutron precursors. These delayed neutrons are essential to the control of nuclear reactors since they appear many orders of magnitude later than the prompt neutrons.
87Br 55s
87Kr
87Kr*
87Rb
87Sr
Neutron 86Kr + Neutron
Emission
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