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Neutron Attenuation (revisited)

0

t t

mf for scatterin = 1/

teIXI=

0)(

unit path

length.mfp for absorption a= 1/a

.

X

total mfp t= 1/t

Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

1XteXP

e

=

=

1)(ninteractio

ninteractionoProbability

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Neutron Flux and Reaction Rate

Recall Ft= n v tN=ItSimultaneous beams, different intensities, same energysame energy.

t

=t A

+B

+C

+ =t

nA

+ nB

+ nC

+ v

In a reactorreactor, if neutrons are moving in all directionsall directions=

A B C

Ft=

tnv

neutron flux = nvNot talking

about a beam

Reaction RateR F = = =nvNNuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

2

same energysame energy

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Neutron Flux and Reaction Rate

erent energ eserent energ esDensity of neutrons with energy betweenEandE+dE

Reaction rate for those monoenergetic neutronsdR = E n E dE v E

= )( dEEnn

== )()()( dEEEndEE

0 00

==00

)()()()()( dEEEdEEEnER ttt

Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

3= 0 )()( dEEERii

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Neutron Flux and Reaction Rate

n genera , neutron ux epen s on:

Neutron energy, E., .

Neutron angular direction, . Time .

Various kinds of neutron fluxes (depending on the

degree of detail needed).Time-dependent and time-independent angular

neutron flux.

,,,

Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

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Neutron Moderation HW 6HW 6 (continued)(continued)

epro uce t e p ot.

Discuss the effect of the

n .

moderator atoms.

MostMost

probableprobable

energies?energies?

Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

7

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Neutron Moderation HW 6HW 6 (continued)(continued)

Neutron scattering by light nuclei

then the average energy loss

EE )1(2

1\ +=

EEEE )1(21\ ==

an e average rac ona energy oss

)1(2

1 =E

How many collisions are needed to thermalize a 2 MeV

neutron if the moderator was:1H 2H 4He graphite 238U ?

What is special about 1H?

y we cons ere e ast c scatter ng When does inelastic scattering become important?

8Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

Coulomb effectSurface effect

~200 MeV

9Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

B.E. per nucleon for238U(BEU) and119Pd(BEPd) ?

2x119xBE 238xBE = ?? K.E. of the

fragments 1011J/g Burning coal 105J/g

Why not spontaneous?

Two119

Pdfragments just touching

MeVMeVfmMeVV 214250)46(

.44.1

2

>=

Crude ! What if79Zn and 159Sm? Large neutron

excess, released neutrons, sharp potential edge,

m.

spherical U!10Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

Liquid Drop

y(Me

V)

Shell

on

Ener

Activat

12Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

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Nuclear Fission

34R += )1(Ra23 abR =

24 ab

=

+= 1Rb

Surface Term Bs = - as A ...)1(

2

5

2 ++

ou om erm C = - aC - ...5 +

32

31

21 1 AaZZa > fission

2Z

Crude: QM and original shape

A could be different from spherical.

13Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

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Nuclear Fission

1202

300 =Consistent with activation energy

curve forA = 300.

Extrapolation to 47 10-20 s.

14Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

235U+ n

93Rb + 141Cs + 2n

.

ow-energy

fission

processes.

15Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

Z1 + Z2 = 92

1 , 2 A1 95, A2 140Large neutron excess

Most stable:

Z=45 Z=58

Prompt neutronsPrompt neutrons within 10-16 s.

on incident neutron energy.

The avera e number is characteristic of the

process.16Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

The averagenumber of

neutrons is

different, but

the

distribution isGaussian.

17Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Why only left

mass

arabola?

Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

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Hi her than S ?

Delayed neutronsDelayed neutrons

~ 1 delayed neutronper 100 fissions, but

essen a or con ro

of the reactor.

In

general,

decay

Waste.

Poison.

high

energy.

19Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

20Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

1/vas neu rons

should bemoderated.

235U thermal cross sections

fission 584 b. 9 b.

radiative capture 97 b.

Fission Barriers 21Nuclear Reactors, BAU, 1st Semester, 2008-2009Saed Dababneh .

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Nuclear Fission

Q for235

U+ n 236

Uis 6.54478 MeV. Table 13.1 in Krane: Activation energyEA for236U 6.2 MeV

-

neutrons.

Q for238U+ n 239Uis 4.??? MeV.

E for239U 6.6 MeV MeV neutrons are needed. Pairing term: = ??? (Fig. 13.11 in Krane). What about 232Pa and 231Pa? (odd Z).

22

-

cross sections than even-N nuclei (Table 13.1 in Krane).Nuclear Reactors, BAU, 1st Semester, 2008-2009

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Nuclear Fission

Why not use it?Why not use it?

f,Th 584 2.7x10-6 700 0.019 b

Nuclear Reactors, BAU, 1st Semester, 2008-2009

Saed Dababneh .

23