Shell model. Notes: 1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei. 2. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate. - PowerPoint PPT Presentation
Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 (Saed Dababneh). 1 Shell model Notes: 1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei. 2. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate. 3. Simple versions of the shell model do not take into account pairing forces, the effects of which are to make two like-nucleons combine to give zero orbital angular momentum. The pairing force increases with l. 4. Shell model does not treat distortion effects (deformed nuclei) due to the attraction between one or more outer nucleons and the closed-shell core.
Transcript
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell modelNotes: 1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei. 2. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate. 3. Simple versions of the shell model do not take into account pairing forces, the effects of which are to make two like-nucleons combine to give zero orbital angular momentum. The pairing force increases with l.4. Shell model does not treat distortion effects (deformed nuclei) due to the attraction between one or more outer nucleons and the closed-shell core.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell modelFermi Gas
EF n2/3
Range ?
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
Transition probability?
Nuclear reactions?
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
Ground state: (near closed shells)
1. Angular momentum of odd-A nuclei is determined by the angular momentum of the last nucleon that is odd. 2. Even-even nuclei have zero ground-state spin, because the net angular momentum associated with even N and even Z is zero, and even parity. 3. In odd-odd nuclei the last neutron couples to the last proton with their intrinsic spins in parallel orientation.
Provided that the ordering is known….!!
A < 150190 < A < 220
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
Near valley of
stability
No spin-orbit
coupling
Harmonic oscillator
Near drip line
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
• 17 p, 21 n.• p in 1d3/2 l s = +• n in 1f7/2 l s = -• Rule 3 sp sn lp ln
• ½ + ½ + 3 – 2 = 2
total = -
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
Excited states:
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Extreme independent particle model!!! Does the core really remain inert?
Shell model
1d5/2
2s1/2
1d3/2
1p1/2
?
l pairing
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
• Extreme independent particle model only 23rd neutron.• More complete shell model all three “valence” nucleons.
HW 21HW 21
Discuss the energy levels of nuclei with odd number of nucleons in the 1f7/2 shell.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
)1(2
)1()1()1(
)1(2
)1()1()1(
jj
sslljjg
jj
sslljjgg lsj
Dipole Magnetic Moment
Nj jg HW 22HW 22 Show that
and examine Eqs. 5.9 in Krane. In addition, work out problem 5.8 in Krane Conclusion?Proton: gs(free) = 5.5856912 ? gl = 1 ?Neutron: gs(free) = -3.8260837 ? gl = 0 ?What about + and -?
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
Electric Quadrupole MomentRefined QM
12
121
)1(2
12 322
053
j
nAr
j
jQ
<r2> for a uniformly charged sphere
jn 21 Number of protons in
a subshell
ExtremesSingle particle: n = 1 - ive QSingle hole: n = 2j +ive Q
Examine Table 5.1 and Fig.5.10 in
Krane
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Shell model
ValidityA < 150
190 < A < 220
Nuclide Q (b)2H (D) +0.00288
17O -0.0257859Co +0.4063Cu -0.209133Cs -0.003
161Dy +2.4176Lu +8.0
209Bi -0.37
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective model• Large quadrupole moments nucleus as a collective body (Liquid drop model).• Interactions between outer nucleons and closed shells cause permanent deformation.• Single-particle state calculated in a non-spherical potential complicated.• Spacing between energy levels depends on size of distortion.• Doubly magic 1st excited state away from GS.• Near closure single-particle states.• Further away from closure collective motion of the core excited states.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective model
• A net nuclear potential due to filled core shells exists.
• Collective model combines both liquid drop model and shell model.
• Two major types of collective motion:Vibrations: Surface oscillations.Rotations: Rotation of a deformed shape.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective modelSymmetry
axis
)1(22
2
1
22
IIl
E
l
E
gg
g
g 2
Symmetry only even IGS (even-even) 0+
)2/(20)4(
23.152/4.91)2/(6)2(
0)0(
2
22
g
gg
E
keVkeVE
E
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective model
HW 23HW 23 compare measured energies of the states of the ground state rotational band to the calculations.Rigid body or liquid drop? Intermediate Short range and saturation of nuclear force.
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
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Collective model
Spin parity Emeasured
(keV)E/E(2+) I(I + 1)/6
12+
10+ 1518.00 16.61 18.33
8+
6+ 7.00
4+ 299.44 3.28 3.33
2+ 91.4 1.0 1.0
0+ 0
164Er
Higher angular momentum centrifugal stretching higher moment of inertia lower energy than expected.
HW 23 HW 23 (continued)(continued)
Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).
