nuclear and radiation physics, bau, second semester, 2009-2010 (saed dababneh). 1 nuclear reactions...
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Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Reactions
Categorization of Nuclear Reactions• According to: bombarding particle, bombarding energy, target, reaction product, reaction mechanism.• Bombarding particle:
Charged particle reactions. [ (p,n) (p,) (,) heavy ion reactions ]. Neutron reactions. [ (n,) (n,p) ….. ]. Photonuclear reactions. [ (,n) (,p) … ]. Electron induced reactions………….
• Bombarding energy: Thermal. Epithermal. Slow. Fast. Low energy charged particles. High energy charged particles.
Neutrons.?
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Reactions• Targets:
Light nuclei (A < 40). Medium weight nuclei (40 < A < 150). Heavy nuclei (A > 150).
• Reaction products: Scattering. Elastic 14N(p,p)14N
Inelastic 14N(p,p/)14N* Radiative capture. Fission and fusion. Spallation. …..
• Reaction mechanism: Direct reactions. Compound nucleus reactions.
• More in what follows ….• What is a transfer reaction….?????
Stripping
Pickup
Reson
ant
Non-resonant
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Reaction Cross Section(s) (Introduction)
• Probability.• Projectile a will more probably hit target X if area is larger.• Classically: = (Ra + RX)2. Classical = ??? (in b) 1H + 1H, 1H + 238U, 238U + 238U • Quantum mechanically: = 2.
• Coulomb and centrifugal barriers energy dependence of .• 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
HW 33HW 33
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Reaction Cross Section(s) (Introduction)
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 and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Reaction Cross Section(s) (Introduction)
Many different quantities are called “cross section”.Krane Table 11.1
NI
r
d
d
drdR
a
b
4
),(4),(
Angular distribution
“Differential” cross section(,) or ( )or “cross section” …!!
Units … !
d
dddd
d
d
ddd
0
2
0
sin
sin
ddE
d
b
2Doubly differential
Energy state in “Y”
dE
d
t for all “b” particles.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Coulomb Scattering
b
d
rmin
vovmin
• Elastic or inelastic.• Elastic Rutherford scattering.• At any distance:V = 0
Ta = ½mvo2
l = mvob
0
4
1 2
a
o
T
d
zZeV
r
zZemvmv
oo
22
212
21
4
1
No dependence on
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Coulomb Scattering
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Coulomb Scattering
bdbnxdf
bnxf
2)(
)( 2
n target nuclei / cm3 x target thickness (thin).nx target nuclei / cm2
b < b > db d
b
HW 34HW 34Show thatand hence 2
cot2
db
24
222
sin
1
4
1
4
)(
ao T
zZe
d
d
Rutherford cross section
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Coulomb ScatteringStudy Fig. 11.10 (a,b,c,d) in Krane
HW 35HW 35Show that the fraction of incident alpha particles scattered at backward angles from a 2 m gold foil is 7.48x10-5.
See also Fig. 11.11 in Krane.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Coulomb Scattering
• Elastic Rutherford scattering.• Inelastic Coulomb excitation.
See the corresponding alpha spectrum of Fig. 11.12 in Krane.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Coulomb Scattering
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
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Nuclear Scattering• 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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ARR
p
h
o
R