nuclear and radiation physics, bau, 1 st semester, 2006-2007 (saed dababneh). 1 neutron-induced...
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
1
22 nXHCCHbY IIIn
Neutron-induced Reactions
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
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
2
Neutron-induced Reactions
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
3
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
4
Neutron-induced Reactions
n-TOFn-TOFCERNCERN
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
5
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
6
Neutron-induced Reactions
n_TOFn_TOFCERNCERN
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
7
Neutron-induced Reactions
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
8
NuclearRadius
Charged Particle Reactions
What is the Gamow Peak?
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
9
Charged Particle Reactions
Electron Screening
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
10
Charged Particle Reactions
e2 = 1.44x10-12 keV.mTunneling probability:
In numerical units:
For -ray emission:
2eP v
eZZ
221
)(
)(29.312 21 keVE
uZZ
CM
Sommerfeld parameterGamow factor
12)( LLL EE
31)( EEDipole
Multipolarity
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
11
Charged Particle Reactions
EE
1)( 2
2)( eE
)(1
)( 2 ESeE
E
Nuclear (or astrophysical) S-factor
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
12
Charged Particle Reactions
EC = ??
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
13
Resonance Reactions
E tCN particle emission E E > spacing between virtual states continuum. (Lower part larger spacing isolated resonances).D bound states -emission E isolated states.
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
14
Resonance Reactions
Entrance Channel
a + XExit
Channelb + 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 30HW 30
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Resonance Reactions
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
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
16
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
17
Resonance Reactions
bbplL
lb 222
1max, )12( lbb lll
)()(
7.656)(2
keVEub
CM HW 31HW 31
)1()12)(12(
122max aX
XaaX JJ
J
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
18
Resonance Reactions
22
2 )()(
o
fresponse
Damped OscillatorDamped Oscillator
eigenfrequency
Dampingfactor
Oscillator strength
22
2 )()()(
R
ba
EEE
0
1
t
ot
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
19
Resonance Reactions
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 32 HW 32 When does R take its maximum value?
ba
Usually a >> b.
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
20
Resonance Reactions
Ja + JX + l = J(-1)l (Ja) (JX) = (J)
(-1)l = (J) Natural parity.
ExitChannel
b + Y
Compound Nucleus C*
ExcitedState
ExJ
Entrance Channel
a + X
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
21
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
Resonance Reactions
Charged particleradiative capture (a,)(What about neutrons?)
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
22
Resonance Reactions14N(p,)
• Q = ??• EC = ??• ER = 2.0 MeV
Formation via s-wave protons, J = ½, p = 0.1 MeV, dipole radiation E = 9.3 MeV, = 1 eV.Show that = 0.33 eV.
• If same resonance but at ER = 10 keVp = ?? E = ?? = ??Show that = 3.3x10-23 eV.
HW 33HW 33
Huge challenge to experimentalists
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Resonance J Estimated Energy (keV) (eV)
566 2+ 1.93- 0.154+ 0.01
470 0+ 0.6 1- 0.2
Experimental upper limit < 1.7 eV
-transfer reactionsAngular distribution
18O(, )22Ne