collective model
DESCRIPTION
Collective model. Vibrational States. Average shape. Instantaneous shape. Collective model. Symmetry. Instantaneous coordinate. Spherical harmonics. r 0 A 1/3. Amplitude. http://wwwnsg.nuclear.lu.se/basics/excitations.asp?runAnimation=beta10. = 1 dipole. = 2 quadrupole. = 3 - PowerPoint PPT PresentationTRANSCRIPT
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
1
Collective modelAverageshape
Instantaneousshape
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
2
Collective model
φ),(θ Y(t)αRR(t) λμλ
λ
λ μλμavr
μ- λ,λμ
Instantaneouscoordinate
Symmetry
Amplitude Sphericalharmonics
r0A1/3
= 0monopole
= 1dipole
= 2quadrupole
= 3octupole
.
http://wwwnsg.nuclear.lu.se/basics/excitations.asp?runAnimation=beta10
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
3
Collective model
YαR
YαYαYα R
),(YαRR(t)
1010avr
1- 1,1- 1,10101111avr
1μ
1
1 μ1μavr
Both monopole and dipole excitations require high energy.
R(t) = Ravr +00 Y00
= 0monopole
= 1dipole
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
4
Collective model
= 2quadrupole
• Quantization of quadrupole vibration is called a quadrupole phonon. • A phonon carries two units of angular momentum.• This mode is dominant. For most even-even nuclei, a low lying state with Jπ=2+ exists.
2020avr
2- 2,2- 2,2,-12,-1202021212222avr
2μ
2
2 μ2μavr
YαR
YαYαYαYαYα R
),(YαRR(t)
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective model
-2 -1 0 1 2
-2 -4 -3 -2 -1 0
-1 -3 -2 -1 0 +1
0 -2 -1 0 +1 +2
1 -1 0 +1 +2 +3
2 0 +1 +2 +3 +4
l = 4 = +4, +3, +2, +1, 0, -1, -2, -3, -4l = 2 = +2, +1, 0, -1, -2l = 0 = 0
Triplet0+, 2+, 4+
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective model
Two-phonon triplet at twice the energy of the single phonon state.
HW 24HW 24Krane 5.10
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Nuclear Reactions
X(a,b)Y• First in 1919 by Rutherford:
4He + 14N 17O + 1H14N(,p)17O
• Incident particle may: change direction, lose energy, completely be absorbed by the target……• Target may: transmute, recoil……• b = Capture reaction.• If B.E. permits fission (comparable masses).• Different exit channels a + X Y1 + b1
Y2 + b2
Y3 + b3 …….
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Nuclear Reactions• Recoil nucleus Y could be unstable or emission.
• One should think about: Reaction dynamics and conservation laws i.e. conditions necessary for the reaction to be energetically possible. Reaction mechanism and theories which explain the reaction. Reaction cross section i.e. rate or probability.
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
9
Nuclear ReactionsConservation Laws• Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??) …….
apa X
pY
pb
Y
bQTTcmcm iffi 22
+ve Q-value exoergic reaction. -ve Q-value endoergic reaction.
aYb TQTT +ve Q-value reaction possible if Ta 0. -ve Q-value reaction not possible if Ta 0. (Is Ta > |Q| sufficient?).
Conservation of momentum ……
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
10
Nuclear Reactions• Conservation of momentum.• We usually do not detect Y.Show that:
• The threshold energy (for Ta): (the condition occurs for = 0º).
• +ve Q-value reaction possible if Ta 0.• Coulomb barriers…….!!!• -ve Q-value reaction possible if Ta > TTh.
bY
aaYYbYabaabab mm
TmmQmmmTmmTmmT
])()[(coscos 2
HW 25HW 25
abY
bYTh mmm
mmQT
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
11
Nuclear Reactions
• The double valued situation occurs between TTh and the upper limit Ta
\.
• Double-valued in a forward cone.
aY
Ya mm
mQT
\
aba
aaYYbY
Tmm
TmmQmmm ])()[(cos max
2
HW 25HW 25 (continued)(continued)
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
12
Nuclear Reactions
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
13
Nuclear Reactions
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
14
Nuclear Reactions
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Nuclear Reactions
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
16
Nuclear Reactions
• If the reaction reaches excited states of Y
58Ni(,p)61Cu
Highest proton energy
exbexYaXex EQcmEcmcmcmQ 02222 )(
less proton energy
even less ….
See Figures 11.4 in Krane
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Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
17
Nuclear Reactions
Neutron scattering• Inelastic Q = -Eex (=-E*).• Elastic Q = 0.
HW 26HW 26Discuss the elastic and inelastic scattering of neutrons using the relations you derived in HW 25.