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/nuclearradiation Advanced Statistical Mechanics 761. General subjects to be covered.
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Nuclear Reactors
Nuclear Reactors, BAU, First Semester, 20072008
(Saed Dababneh).
General subjects to be covered
Nuclear Reactors, BAU, 1st Semester, 20072008
(Saed Dababneh).
Review Test 05%
Midterm Exam 20%
Projects, quizzes and HWs 25%
Final Exam 50%
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
b
pb
gs
a
pa
X
+ve Qvalue exoergic reaction.
ve Qvalue endoergic reaction.
pY
Y
Stationary X ??
+ve Qvalue reaction possible if Ta 0.
ve Qvalue reaction not possible if Ta 0. (Is Ta > Q sufficient?).
Conservation of momentum ……
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
HW 1
double valued !?
solve for Q
Q < 0
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
HW 1(continued)
Q < 0
Discuss the elasticand inelastic scatteringof neutronsusing these relations.
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
What about neutron induced reactions?
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
What about neutron induced reactions?
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
What about neutron induced reactions?
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reaction Energetics (revisited)
58Ni(,p)61Cu
even less ….
less proton energy
Highest proton energy
See Figures 11.4 in Krane
What about neutron induced reactions?
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Neutron Interactions (revisited)
Nonelastic
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Neutron Scattering (revisited)
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Reaction Cross Section (revisited)
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Reaction Cross Section (Simple terms)
A (Area of the beam!!)
v
X
Position of a neutron 1 s before arriving at target
Target with N atoms.cm3 or NAX atoms.
Monoenergetic neutrons of speed v (cm.s1) and density n (cm3)
Volume = vA
containing nvA neutrons that hit the “whole” target in 1 s.
Beam Intensity InvA/A = nv (cm2s1)
Number of neutrons interacting with target per second
I, A, X and N
= t I N A X
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Reaction Cross Section (Simple terms)
Study examples in Lamarsh
Total cross section
Total number of nuclei in the target
Effective crosssectional area of the nucleus.
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
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
Study examples in Lamarsh
Total cross section
Volume of the target
Macroscopic total cross section.
Probability per unit path length.
Attenuation not moderation !
Mean free path
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Reaction Cross Section (Simple terms)
Homogeneous Mixture
Molecule xmyn Nx=mN, Ny=nN
given that events at x and y are independent.
Study examples in Lamarsh
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Reaction Cross Section (revisited)
Look for b
Detector for particle “b”
d
Ia
“b” particles / s
,
cm2
“X“ target Nuclei / cm2
“a” particles / s
Typical nucleus (R=6 fm): geometrical R2 1 b.
Typical : <b to >106 b.
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Reaction Cross Section (revisited)
Many different quantities are called
“cross section”.
Krane Table 11.1
Angular distribution
Units … !
“Differential” cross section
(,) or ( )
or “cross section” …!!
Doubly differential
t for all “b” particles.
Energy state in “Y”
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Different Features (revisited)
1/v
Fast neutrons should be moderated.
235U thermal cross sections
fission 584 b.
scattering 9 b.
radiative capture 97 b.
Fission Barriers
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Neutron Induced Reactions (revisited)
X(n,b)Y
b(Q+En)
n(En)
Probability to penetrate the potential barrier
Po(Ethermal) = 1
P>o(Ethermal) = 0
For thermal neutrons
Q >> En
b(Q) constant
Nonresonant
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Neutron Induced Reactions (revisited)
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Statistical Factor (revisited)
HW 3
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Resonance Reactions (revisited)
J
Ex
a + X Y + b Q > 0
b + Y X + a Q < 0
Excited
State
Entrance Channel
a + X
Exit
Channel
b + Y
Inverse Reaction
Compound Nucleus C*
Identical
particles
Statistical
Factor ()
QM
HW 4
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Resonance Reactions (revisited)
Projectile
Projectile
Target
Target
Qvalue
Qvalue
Q + ER = Er
E = E + Q  Eex
Direct Capture
(all energies)
Resonant Capture
(selected energies with large Xsection)
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Resonance Reactions (revisited)
Damped Oscillator
Oscillator strength
Damping
factor
eigenfrequency
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Resonance Reactions (revisited)
BreitWigner formula
Reaction
Elastic scattering
Usually a>> b.
HW 5When does R take its maximum value?
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Resonance Reactions (revisited)
Exit
Channel
b + Y
Ja + JX + l = J
(1)l(Ja) (JX) = (J)
(1)l = (J) Natural parity.
J
Ex
Excited
State
Entrance Channel
a + X
Compound Nucleus C*
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Resonance Reactions (revisited)
What is the “Resonance Strength” …?
What is its significance?
In what units is it measured?
Charged particle
radiative capture (a,)
(What about neutrons?)
Cross section
EC
a
Energy
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Neutron Resonance Reactions (revisited)
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).
Neutron Activation Analysis (revisited)
(Z,A) + n (Z, A+1)

(delayed ray)
(Z+1, A+1)
http://ie.lbl.gov/naa !
Project 1
Nuclear Reactors, BAU, 1st Semester, 20072008 (Saed Dababneh).