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Resonance Reactions
HW 34
In the 19F(p,) reaction:
• The Q-value is 8.??? MeV.
• The Q-value for the formation of the C.N. is 12.??? MeV.
• For a proton resonance at 668 keV in the lab system, the
corresponding energy level in the C.N. is at 13.??? MeV.
• If for this resonance the observed gamma energy is 6.13 MeV,
what is the corresponding alpha particle energy?
• If for this resonance there has been no gamma emission
observed, what would then be the alpha particle energy?
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
1
Neutron Resonance Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
2
Neutron Activation Analysis
(Z,A) + n  (Z, A+1)
 (-delayed -ray)
(Z+1, A+1)
http://ie.lbl.gov/naa
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
3
Neutron Attenuation
Neutrons
Target
Thickness “x”
dI
  t ndx
I
I  Ioe
 t nx
Similar to -attenuation. Why?
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
4
Neutron Moderation
Show that, after elastic scattering the
ratio between the final neutron energy E\
and its initial energy E is given by:
E \ A2  1  2 A cos CM

E
( A  1) 2
2
\
E 
 A 1
For a head-on collision:    

 E  min  A  1 
After n s-wave collisions:
HW 35
ln E  ln E  n
\
n
2
E
(
A

1
)
A 1


ln
where   ln \   1 
2A
A 1
 E  av
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
5
Neutron Moderation
HW 35 (continued)
How many collisions are needed to thermalize a 2 MeV
neutron if the moderator was:
1H
4He
238U
Discuss the effect of the thermal motion of the moderator
atoms.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
6
Nuclear Fission
Surface effect
Coulomb effect
~200 MeV
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
7
Nuclear Fission
• B.E. per nucleon for 238U (BEU) and 119Pd (BEPd) ?
• 2x119xBEPd – 238xBEU = ??  K.E. of the
fragments   1011 J/g
• Burning coal  105 J/g
• Why not spontaneous?
• Two 119Pd fragments just touching  The Coulomb
barrier is:
(46) 2
V  1.44MeV . fm
 250MeV  214MeV
12.2 fm
• Crude …! What if 79Zn and 159Sm? Large neutron
excess, released neutrons, sharp potential edge…!
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
8
Nuclear Fission
• 238U (t½ = 4.5x109 y) for -decay.
• 238U (t½  1016 y) for fission.
• Heavier nuclei??
• Energy absorption from a neutron (for example) could
form an intermediate state  probably above barrier 
induced fission.
• Height of barrier above g.s. is called activation energy.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
9
Activation Energy (MeV)
Nuclear Fission
Liquid Drop
Shell
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
10
Nuclear Fission
4 3
R
3
=
4
ab 2
3
R  ab
3
2
Volume Term (the same)
a  R (1   )
R
b
1 
Surface Term Bs = - as A⅔ (1  25  2  ...)
Coulomb Term BC = - aC Z(Z-1) / A⅓ (1  15  2  ...)
 13
aC Z (Z  1) A
 aS A 3  fission

1
5
2
2
5
Z
 ~ 47
A
2
Crude: QM and original shape
could be different from spherical.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
11
Nuclear Fission
2
(120)
 48
300
Consistent with activation energy
curve for A = 300.
Extrapolation to 47   10-20 s.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
12
Nuclear Fission
235U
+n

93Rb + 141Cs + 2n
Not unique.
Low-energy
fission
processes.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
13
Nuclear Fission
Z1 + Z2 = 92
Z1  37, Z2  55
A1  95, A2  140
Large neutron excess
Most stable:
Z=45
Z=58

Prompt neutrons within 10-16 s.
Number  depends on nature of
fragments and on incident particle energy.
The average number is characteristic of
the process.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
14
Nuclear Fission
The average
number of
neutrons is
different, but
the
distribution is
Gaussian.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
15
Higher than Sn?
Delayed neutrons
~ 1 delayed neutron
per 100 fissions, but
essential for control
of the reactor.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
16
Nuclear Fission
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
17
Nuclear Fission
1/v
Fast neutrons
should be
moderated.
235U
thermal cross sections
fission  584 b.
scattering  9 b.
radiative capture  97 b.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007
(Saed Dababneh).
Fission Barriers
18
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