Neutron Generation Using Ultra-Intense Laser Plasma Interactions
Neutron Interactions (revisited)
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Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 1 Neutron Interactions (revisited) • Chadwick’s discovery. • Neutrons interact with nuclei, not with atoms. (Exceptions). • Recall from basic Nuclear Physics: 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.
description
Neutron Interactions (revisited). Chadwick’s discovery. Neutrons interact with nuclei, not with atoms. (Exceptions). Recall from basic Nuclear Physics: Inelastic scattering ( n,n \ ). Q = -E* Inelastic gammas. Threshold? - PowerPoint PPT Presentation
Transcript of Neutron Interactions (revisited)
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Neutron Interactions (revisited)
• Chadwick’s discovery.• Neutrons interact with nuclei, not with atoms. (Exceptions).
• Recall from basic Nuclear Physics: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 Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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• 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.
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Neutron Scattering (revisited)
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4
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Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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• 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
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Reaction Cross Section (revisited)
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Reaction Cross Section (Simple terms)
XA (Area of what??!!)
Monoenergetic (and unidirectional) 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
NX??
Total microscopic cross section
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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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 microscopic cross section
Total number of nuclei in the
target
AAI
I tt
Effective cross-sectional area of the nucleus.
Study
examples in
Lamarsh
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Reaction Cross Section (Simple terms)
AAI
I tt
The probability for a neutron to hit a nucleus (per unit area of target):
Function of
what?
Typical nucleus (R=6 fm): geometrical R2 1 b.Typical : <b to >106 b.
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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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
Volume of the target
Macroscopic total cross
section.Probability per
unit path length.
tt
XteIXI
1
)( 0
Mean free path
Study
examples in
LamarshTotal
microscopic cross section
Nuclear Reactor Theory, JU, First Semester,2010-2011 (Saed Dababneh).
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Neutron Attenuation
X
X
t
t
eXP
eXP
1)(
)(
ninteractio
ninteractiono
Recall t = N t
Probability per unit path length.
X
I0 I
Probability
mfp for scattering s = 1/s
mfp for absorption a = 1/a
…………. total mfp t = 1/t
XteIXI 0)(
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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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 Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Reaction Cross Section
d,Ia
\
Detector for particle “b”
\\NI
dRd
a
b
“X“ t
arge
t Nuc
lei /
cm2
“a” particles / s
“b” particles / scm2
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Reaction Cross Section
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 Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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n-TOFn-TOFCERNCERN
Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).
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1/v
235U thermal cross sectionsfission 584 b.scattering 9 b.radiative capture 97 b.
Fast neutrons should be moderated.
Fission Barriers
Neutron Cross Section (Different Features)
