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
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
2
Neutron-induced Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
3
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
4
Neutron-induced Reactions
n-TOFn-TOFCERNCERN
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
5
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
6
Neutron-induced Reactions
n_TOFn_TOFCERNCERN
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
7
Neutron-induced Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
8
NuclearRadius
Charged Particle Reactions
What is the Gamow Peak?
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
9
Charged Particle Reactions
Electron Screening
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
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
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
12
Charged Particle Reactions
EC = ??
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.
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
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
15
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
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
16
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
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
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.
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
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?)
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
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
23
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