Upload
afram
View
31
Download
4
Tags:
Embed Size (px)
DESCRIPTION
501503747 Nuclear Reactors. Nuclear Physics at BAU http://nuclear.bau.edu.jo/ This course http://nuclear.bau.edu.jo/Reactors Prerequisites Nuclear and Radiation Physics 742 http://nuclear.bau.edu.jo/nuclear-radiation Advanced Statistical Mechanics 761 - PowerPoint PPT Presentation
Citation preview
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
1
Nuclear Physics at BAU Nuclear Physics at BAU http://nuclear.bau.edu.jo/
This courseThis coursehttp://nuclear.bau.edu.jo/Reactors
PrerequisitesPrerequisites• Nuclear and Radiation Physics 742
http://nuclear.bau.edu.jo/nuclear-radiation • Advanced Statistical Mechanics 761
http://nuclear.bau.edu.jo/Statistical
501503747 Nuclear Reactors
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
2
Grading
Review Test 05%Mid-term Exam 20%Projects, quizzes and HWs 25%Final Exam 50%
• Homeworks are due after one week unless otherwise announced.• Remarks or questions marked in red without being announced as homeworks should be also seriously considered!• Some tasks can (or should) be sent by email:
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
3
Review Test
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
4
Projects
Radiation Protection and Shielding (Due December 6th). Nuclear fuel cycles with emphasis on front ends (Due November 29th).
• Work as a team. Divide and organize the job among you.• Try to explore local applicability. • Presentation: Will be scheduled later.
Other small projects will be announced in class.
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
5
Nuclear Reaction Energetics (revisited)
Conservation Laws• Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??) …….
apa X
pY
pb
Y
bQTTcmcm iffi 22
+ve Q-value exoergic reaction. -ve Q-value endoergic reaction.
aYb TQTT +ve Q-value reaction possible if Ta 0. -ve Q-value reaction not possible if Ta 0. (Is Ta > |Q| sufficient?).
Conservation of momentum ……
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
6
• Conservation of momentum.• We usually do not detect Y.Show that:
• The threshold energy (for Ta): (the condition occurs for = 0º).
• +ve Q-value reaction possible if Ta 0.• Coulomb barriers…….!!!• Neutrons vs. charged particles.• -ve Q-value reaction possible if Ta > TTh.
bY
aaYYbYabaabab mm
TmmQmmmTmmTmmT
])()[(coscos 2
HW 1HW 1
abY
bYTh mmm
mmQT
Nuclear Reaction Energetics (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
7
Nuclear Reaction Energetics (revisited)
• The double valued situation occurs between TTh and the upper limit Ta
\.
• Double-valued in a forward cone.
aY
Ya mm
mQT
\
aba
aaYYbY
Tmm
TmmQmmm ])()[(cos max
2
HW 1HW 1 (continued)(continued)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
8
• Discuss thoroughly the 7Li(p,n) reaction.• During the discussion emphasize on the case when the incident proton beam is 30 keV above the threshold.• Use your computing skills.
Nuclear Reaction Energetics (revisited)
HW 1HW 1 (continued)(continued)
• Discuss the elasticelastic and inelastic inelastic
scatteringscattering of neutronsneutrons using these relations.
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
9
Nuclear Reaction Energetics (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
10
Nuclear Reaction Energetics (revisited)
What about
neutron induced
reactions?
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
11
Nuclear Reaction Energetics (revisited)
What about
neutron induced
reactions?
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
12
Nuclear Reaction Energetics (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
13
Nuclear Reaction Energetics (revisited)
• If the reaction reaches excited states of Y
58Ni(,p)61Cu
Highest proton energy
exbexYaXex EQcmEcmcmcmQ 02222 )(
less proton energy
even less ….
See Figures 11.4 in Krane
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
14
Nuclear Reaction Energetics (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
15
Neutron Interactions (revisited)
• Chadwick’s discovery.• Neutrons interact with nuclei, not with atoms. (Exceptions).
• Recall from Nuclear Physics 742:o Inelastic scattering (n,n\). Q = -E* Inelastic gammas.
Threshold?o Elastic scattering (n,n). Q = ?? (Potential and CN).
Neutron moderation?o Radiative capture (n,). Q = ?? Capture gammas.o (n,), (n,p). Q = ?? Absorption Reactions.o (n,2n), (n,3n) Q = ?? Energetic neutrons on heavy water can easily eject the loosely bound neutron.o Fission. (n,f).
HW 2HW 2 Examples of such exo- and endo-thermic reactions with Q calculations.
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
16
• Elastic or inelastic.• Analogous to diffraction.• Alternating maxima and minima.• First maximum at
• Minimum not at zero (sharp edge of the nucleus??)• Clear for neutrons.• Protons? High energy, large angles. Why?• Inelastic Excited states, energy, X-section and spin-parity.
31
ARR
p
h
o
R
Neutron Scattering (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
17
• Probability.• Projectile a will more probably hit target X if area is larger.• Classically: = (Ra + RX)2. Classical = ??? (in b) n + 1H, n + 238U, 238U + 238U • Quantum mechanically: = 2.
• Coulomb and centrifugal barriers energy dependence of . What about neutrons?What about neutrons?• Nature of force: Strong: 15N(p,)12C ~ 0.5 b at Ep = 2 MeV. Electromagnetic: 3He(,)7Be ~ 10-6 b at E = 2 MeV. Weak: p(p,e+)D ~ 10-20 b at Ep = 2 MeV.• Experimental challenges to measure low X-sections..
CMaXaXaaX
Xa
EEmm
mm
22
Reaction Cross Section (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
18
Reaction Cross Section (Simple terms)
XA (Area of what??!!)
Monoenergetic neutrons of speed v
(cm.s-1) and density n (cm-3)
Target with N atoms.cm-3 or NAX atoms.
Position of a neutron 1 s
before arriving at target
|v|
Volume = vAcontaining nvA neutrons that hit the
“whole!!” target in 1 s.Beam Intensity I nvA/A = nv (cm-2s-1)
Number of neutrons interacting with target per second I, A, X and N= t I N A X
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
19
Reaction Cross Section (Simple terms)
Number of neutrons interacting with target per second= t I N A X
Number of interactions with a single nucleus per second = t I Interpretation and units of .
nvA = IA neutrons strike the target per second, of these
tI neutrons interact with any single nucleus. Thus,
measures the probability for a neutron to hit a nucleus (per unit area of target).
Total cross section Total number of
nuclei in the target
AAI
I tt
Effective cross-sectional area of the nucleus.
Study
examples in
Lamarsh
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
20
Reaction Cross Section (Simple terms)
Number of neutrons interacting with target per second= t I N A X
Number of interactions per cm3 per second (Collision Density) Ft = t I N = I t
t = N t
Total cross section Volume of the
target
Macroscopic total cross
section.Probability per
unit path length.
tt
XteIXI
1
)( 0
Mean free path
Study
examples in
Lamarsh
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
21
Reaction Cross Section (Simple terms)
Homogeneous Mixture
Molecule xmyn Nx=mN, Ny=nN
given that events at x and y are independent.
yyxxyx NN
yx nm
Study
examples in
Lamarsh
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
22
Reaction Cross Section (revisited)
d,Ia
\
Detector for particle “b”
\\ NI
dRd
a
b
“X“ t
arge
t Nuc
lei /
cm2
“a” particles / s
“b” particles / scm2
Typical nucleus (R=6 fm): geometrical R2 1 b.Typical : <b to >106 b.
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
23
Reaction Cross Section (revisited)
Many different quantities are called “cross section”.Krane Table 11.1
\\4
),(4
),(
NI
r
d
d
drdR
a
b
Angular distribution
“Differential” cross section(,) or ( )or “cross section” …!!
Units … !
d
dddd
d
d
ddd
0
2
0
sin
sin
dEd
d 2Doubly differential
dE
d
t for all “b” particles.
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
24
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
25
n-TOFn-TOFCERNCERN
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
26
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
27
1/v
235U thermal cross sectionsfission 584 b.scattering 9 b.radiative capture 97 b.
Fast neutrons should be moderated.
Fission Barriers
Different Features (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
28
Neutron Induced Reactions (revisited)
22 nXHCCHbY IIIn X(n,b)Y
n(En)b(Q+En)
For thermal neutronsQ >> En
b(Q) constant
2
11
vE
)( nln EPvn
Probability to penetrate the potential barrier
Po(Ethermal) = 1P>o(Ethermal) = 0
vEnn
1)( Non-resonant
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
29
Neutron Induced Reactions (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
30
bbplL
lb 222
1max, )12( lbb lll
)()(
7.656)(2
keVEub
CM HW 3HW 3
)1()12)(12(
122max aX
XaaX JJ
J
Statistical Factor (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
31
Resonance Reactions (revisited)
Entrance Channela + X
ExitChannelb + YCompound
Nucleus C*
ExcitedState
ExJ
a + X Y + b Q > 0b + Y X + a Q < 0
Inverse Reaction
22 )1()12)(12(
12XaHCCHbY
JJ
JIIIaX
XaaXaX
QM StatisticalFactor ()
Identicalparticles
• Nature of force(s).• Time-reversal invariance.
22 )1()12)(12(
12YbHCCHXa
JJ
JIIIbY
YbbYbY
??bY
aX
HW 4HW 4
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
32
Projectile
TargetQ-value
Projectile
Q-valueTarget
Direct Capture(all energies)
Resonant Capture(selected energies with large X-section)
E = E + Q - Eex
2XaHY
Q + ER = Er
22XaHEEHE CNrrf
ba
Resonance Reactions (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
33
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
34
Resonance Reactions (revisited)
22
2 )()(
o
fresponse
Damped OscillatorDamped Oscillator
eigenfrequency
Dampingfactor
Oscillator strength
22
2 )()()(
R
ba
EEE
0
1
t
ot
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
35
Resonance Reactions (revisited)
22
2
2
)()()1(
)12)(12(
12)(
R
baaX
XaaX EEJJ
JE
Breit-Wigner formulaBreit-Wigner formula
• All quantities in CM system• Only for isolated resonances.
a
b
e
R
aae
baR
Reaction
Elastic scattering
HW 5HW 5 When does R take its maximum value?
ba
Usually a >> b.
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
36
Resonance Reactions (revisited)
Ja + JX + l = J(-1)l (Ja) (JX) = (J)
(-1)l = (J) Natural parity.
ExitChannelb + Y
Compound Nucleus C*
ExcitedState
ExJ
Entrance Channela + X
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
37
Resonance Reactions (revisited)
Cro
ss s
ecti
on
EC a Energy
What is the “Resonance Strength” …?What is its significance?In what units is it measured?
ba
aXXa JJ
J)1(
)12)(12(
12
Charged particleradiative capture (a,)(What about neutrons?)(What about neutrons?)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
38
Neutron Resonance Reactions (revisited)
Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).
39
Neutron Activation Analysis (revisited)
(Z,A) + n (Z, A+1)-
(Z+1, A+1)
(-delayed -ray)
Project 1Project 1
NAA and UNAA and U