Outline lecture (HL-5)

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Outline lecture (HL-5)

• Collective excitations of nuclei
• photo-excitation of GDR
• particle-hole excitations
• particle-hole interactions
• schematic model for coherent p-h excitations
• features of Giant Resonances
• ground state correlations RPA
• Literature PR 18

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photon-induced n emission in Nd
Nd(?,n) cross section dominated by broad
resonance Nd(?,p) ? ? sources a) in-flight
positron annihilation b) bremsstrahlung from
intense electron beam Eresonance ? 2
?Eshell Giant resonance ?GR ? ?
?single-particle coherent process
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Giant Dipole Resonance, schematic
prolate deformed 150Nd
field induces oscillations
symmetry axis ? symmetry axis
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particle-hole excitation
doubly magic nucleus (Fermi level between two
shells) elementary excitations
example 16O 1d3/2 2s1/2 1d5/2 1p1/2 1p3/2
possible particle-hole states with J? 1-
Fermi level
J
almost degenerate states strong mixing by p-h
interaction
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1 particle 1 hole excitations
shell structure and groups of ph-excitations in
doubly magic nucleus
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particle hole interactions
scattering annihilation/creation
exchange term direct term
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schematic model of collective excitation

V0?
N poles at unperturbed Ei N-1 solutions EEi
/?
E
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collective state
2 states generated by coherent superposition
p,n opposite phase repulsive Vij
p,n in phase attractive Vij
small variation of Ei?E0 EC E0 N?V0 ? 2E0

exp.
energy shift ? N of (almost) degenerate single-p
article states
constructive sum of amplitudes coherent surface
vibration
1 low-lying collective (isospin T0) state
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A dependence of giant resonance excitation
E0 ? 80 A-1/3 MeV
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collective excitations in the shell model
p-n oscillations in phase ?I0, energy
shifted downwards p-n oscillations opposite
phase ?I1, energy shifted upwards
G. Quadrupole R. (high) G. Quadrupole R. (low)
low lying Octupole vibration
low lying Quadrupole vibration
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giant resonances collective motion of p,n
?I0 ?I1
J?0
J?1-
J?2
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extended models
Shortcomings of present Ansatz with excited
state g.s. is single-particle product
state, correlations only in excited
states, neglect residual interaction in g.s.
Improvement (Random Phase
Approximation) excited state virtual 2p-2h
states in g.s., soft Fermi surface, e.g. photon
interaction by excitation of p-h state or by
annihilation of virtual p-h state in
g.s. Improvement BCS g.s. with pair
configurations
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Summary lecture (HL-5)

• Collective excitations of nuclei
• photo-excitation of GDR coherent process
• particle-hole excitations almost degenerate
• particle-hole interactions mixing
• schematic model for coherent p-h excitations
• I1 state shifted up
• I0 state shifted down
• features of Giant Resonances E0, E1, E2
• ground state correlations RPA