Deformed Nuclei

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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Lecture 9
Deformed Nuclei
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Single proton outside closed shell
Q is negative (zero for core and negative for
single proton)
e.g. 19F Calc. -0.036 Meas. -0.12
Single proton missing from closed shell
  e.g. 27Al (28Si p) Calc 0.036 Meas 0.14
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Predictions for Q for neutrons
For a single neutron outside a closed core,
expect Q0, since neutron has no charge.
NOT TRUE the neutron attracts the protons and
makes a ridge
So Q is ve for a single neutron just as for a
single proton!
e.g. 17O (16O n) calc 0.038 meas. 0.026
Conversely a neutron hole leads to ve Q
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Shell-model Quadrupole moments
At best we can account for sign, and approximate
size for nuclei near closed shells..not really
encouraging
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Electric Quadrupole moments
Shell model can account for Q if N or Z near
within /-1 of magic numbers
The further away from magic numbers the worse the
agreement
Some nuclei have extreme deformations and we need
another model
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The shell Model so far
How good is it???
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The shell Model so far
How good is it???
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The shell Model so far
How good is it???
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The shell Model so far
How good is it???
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The shell Model so far
How good is it???
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The shell Model so far
How good is it???
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Modifying the Nuclear Shell Model
19F
Predicted ground-state I? ?
Observed ground-state I? ½ !!
19F is not spherical Assumed SM Potential was
spherically symmetric Deformed nuclei have
axially symmetric mass distribution ? Axially
symmetric average potential
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? ---a measure of deformation
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Nilsson and the deformed Shell Model
Assumed SM potential spherically symmetric
? nucleon in same potential regardless of
orientation
For deformed nucleus this is not true!
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Oblate Q ve, ? -ve
Prolate Q ve, ? ve
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Shell-model levels for spherical nucleus
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Shell-model levels for deformed nucleus
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Shell-model levels for deformed nucleus
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IGS 5/2
Measured ½!!
19F Z9, N10
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IGS 5/2
Measured ½!!
19Ne Z10, N9
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24Mg Z12, N12 IGS 0
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23Na Z11, N12
IGS 5/2
Measured IGS 3/2
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The Collective model
Can we account for nuclear properties modelling
the nucleus as a whole?.collectively
We did this with the Semi-empirical mass
formulapredicted binding energies
We will consider
Rotations of deformed nuclei
Oscillations of spherical nuclei
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Rotational states in deformed nuclei
We will examine these nuclei with large ve
deformations
We will restrict our discussion to nuclei with N
and Z even (i.e. Nuclei with GS I? 0
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Rotational states in deformed nuclei

• Spin and parity of states
• 0, 2, 4, 6, 8, ..

2 Spacing of excited states Geometrically
increasing
Why??
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Rotational states in deformed nuclei
Consider rotation about axes other than symmetry
axis
Classically Rotational AM L ??
I even only, because of parity of GS
I 0, 2, 4, 6, etc
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Rotational states in deformed nuclei
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Rotational states in deformed nuclei
The theoretical ratio of En/E2
Is greater than the measured ratio (data points)
Reason Nucleus is not a rigid body. At higher E,
(higher ?), it stretches.
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Levels for the nucleus 130Sn
A spherical nucleus!
GS I? 0 as expected
Can we explain the level structure
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