intro&review 2008 2
TRANSCRIPT
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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 .
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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 .
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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
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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
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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?
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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).
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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
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