Nuclear Reactions

HUS

Nuclear ReactionsNuclear Reactions

MScMSc. . NguyNguynn VnVn QunQun

Department of Nuclear Physics

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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


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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


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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


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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.


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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


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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


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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).


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Public domain image from wikipedia


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Power plant often discharge their circulating water directly back to the ocean. Strict environmental

prottectitionregullatitions

Temperature increases by 5-10 Farenheits

Image by MIT


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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


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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


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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)


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Macroscopic to microscopic worldMacroscopic to microscopic world

Cutaway of PWR pressure vessel and Cutaway of PWR pressure vessel and internalsinternals

Fission chain reaction


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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


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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.


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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)


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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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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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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


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ExothermicExothermic

Source: http://www.mpoweruk.com

Fission of Uranium 235


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EndothermicEndothermic


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RadiativeRadiative capture (capture (BBtt bbcc xx))


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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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Neutron absorption (Neutron absorption (HHpp thth neutron)neutron)


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Beta (minus) decay (Phn r -)


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Positron emission (Positron emission (PhnPhn rr +)+)


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Capture of electron (Capture of electron (BBtt electron)electron)


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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


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Type of decayType of decay


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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.


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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


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Decay chain (Decay chain (ChuChuii phnphn rr))

A B + C D + E

tAA

AeNtN )0()(

)()()(

tNtNdt

tdNBBAA

B

))(0()( ttAAB

AB

BA eeNtN


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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


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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


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Thorium series (Thorium series (ChuChuii phnphn rr ccaa ThoriThori))

Source: http://www.pubs.usgs.gov


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Neptunium series (Neptunium series (ChuChuii phnphn rr ccaa NeptuniNeptuni))

Source: http://www.wikimedia.org


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Uranium series (Uranium series (ChuChuii phnphn rr ccaa UraniUrani))

Source: http://www.pubs.usgs.gov


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Actinium series (Actinium series (ChuChuii phnphn rr ccaa ActiniActini))

Source: http://www.metadata.berkeley.edu


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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


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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%)


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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)


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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


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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


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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


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Liquid drop model (Liquid drop model (MMuu gigitt))

Source: http://large.stanford.edu


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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


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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


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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


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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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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.


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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.


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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


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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.


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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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Nuclear Reactions