Nuclear Oscilations

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Lecture 10
Nuclear Oscilations
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Excited states in 18O
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Excited states in 18O
What are the possible couplings of j for these 2
neutrons?
For GS they coupled to 0
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j
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The 1st excited of 130Sn??
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The 1st excited of 130Sn??
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The 1st excited of 130Sn??
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The 1st excited of 130Sn??
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The 1st excited of 130Sn??
Each term has an energy of gt2 MeV The 2 state
is 1.2 MeV
The lowering occurs by collective
effects Collisions?
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The 1st excited of 130Sn??
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The collective model.Nuclear oscillation
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Excited states for even-even Nuclei
One unit of quadrupole oscillation
phonon
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I4 I2 I0
1 1 1 1 1 1 1 1
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1 1 1 1 1

1
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Low-lying levels for some even-even Spherical
Nuclei
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Isospin
A convenient way to identify whether a nucleon is
a proton or a neutron.
Could use colour
We assign a quantum number t to the nucleon. In
direct analogy to the assigned intrinsic-spin
quantum number s.
neutron
proton
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Isospin for 2-nucleon system

S0
S1
T1
T0
Only one projection Only one quantum state
the deuteron!
Only one projection Only one quantum state

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Nucleon isospin
 Isospin QN for nucleon t ½
Projections tz ½ tz - ½ (proton)
(neutron)
Isospin part of nucleon wavefunction ?t, tz
gt ?pgt ?½, -½gt ?ngt ?½, ½gt
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Vector sum
For a given T, there are (2T1) projections Tz
The isospin part of the nuclear wavefunction is
specified as ?T, Tz gt
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Isospin charge independence of Nuclear Force
Tz1
Tz0
Tz-1
A 14 Z 6 0, 1, or 2 N 6 0, 1, or 2
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Isotopic AnaloguesMirror nuclei
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Isospin triplet A14
Correct energy for different N and Z of nuclei.
Mass of neutron is 0.78 MeV greater than mass of
proton
N8 Z6
N7 Z7
N6 Z8
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Isospin triplet A14
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Well what about these states in mass 14 which
line up.
They all have the same isospin quantum number T
(1 in this case).
How do we find the value of T? We take the
configuration of the A nucleons, and make the
most neutron-rich configuration that is
consistent with the Pauli principle.
The T of this configuration is T ?t for all
14 nucleons Note this is a vector sum, so the
value is T 1
(we could also say that T is the value of Tz for
this most-neutron-rich configuration)
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Isospin determining T for states
T1
Tz1
Tz0
Tz-1
T is the value of Tz for this most-neutron-rich
configuration)
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Isospin triplet A14
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Isospin charge independence of Nuclear Force
T1
Tz1
Tz0
Tz-1
A 14 Z 6 0, 1, or 2 N 6 0, 1, or 2
T0
TZ0
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Isospin triplet A14
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If T1, it must have 3 projections Tz 1, 0, -1.
Tz 1 means a nucleus with 2 nett neutrons
14C Tz 0 means ZN 14N Tz -1 means 2 nett
protons 14O
What is the T of the GS of 14N? GS has S1 . ie p
and n are parallel. There is no way to change a p
to an n without violating Pauli principle.
So TZ T 0
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