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HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 1
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
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 2
photon-induced n emission in Nd
spherical
deformedNd(,n) cross section dominatedby broad resonanceNd(,p) …?
sources:a) in-flight positron annihilationb) bremsstrahlung from intense
electron beam
Eresonance 2 Eshell
“Giant resonance”GR single-particle
coherent process
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 3
Giant Dipole Resonance, schematic
prolate deformed 150Nd
field inducesoscillations: || symmetry axis symmetry axisE
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 4
particle-hole excitation
Fermi level
J
doubly magic nucleus (Fermi level between two shells):elementary excitations:
example 16O1d3/22s1/21d5/2
1p1/21p3/2
possible particle-hole
states with J =1-
2/32/1
2/12/1
2/32/3
2/12/3
2/52/3
11
1
21
1
11
1
21
1
11
1
dp
sp
dp
sp
dp
almost degenerate states: strong mixing by p-h interaction
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 5
1 particle – 1 hole excitationsshell structure and groups of ph-excitations in doubly magic nucleus
MeVA 3/141
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 6
particle – hole interactions
exchange term direct term
scattering annihilation/creation
i
N
iiph
jjjj
phV
ph
jjhhppmm
jjph
excitation
cJMjjcJM
JMjjJMjj
aaJMmjmjJMjjsHFg
hp
hp
hp
hp
ph
1
1
'1'1
1
0;1 . .
12
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 7
schematic model of collective excitation
1
...
and 1
1
0
10
1100
011
N
i ij
N
iij
ji
iii
jjijj
i
N
iiii
N
ii
iiiphjji
EEV
cVcEE
cVcEEc
cVEcVHVHHE
HENiJMjjhp
}V0
N poles at unperturbed EiN-1 solutions E=E’i:
/
E
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 8
collective state2 states generated by coherent superposition:
NV
1
0
0
1
0
EEEE
V
C
N
i iC
small variation of EiE0
EC = E0 + NV0 2E0
exp.
energy shift #N of (almost) degeneratesingle-particle states
0
0
and
const.
EEi
cEE
Vc
i
j
Cj
iC
Ci
constructive sum of amplitudes: coherent surface vibration 0
2
100
02
110
1
1
naanaapaapaaTJjj
naanaapaapaaTJjj
hphphphp
hphphphp
jjjjjjjjph
jjjjjjjjph
;
;
1 low-lying collective (isospin T=0) state
p,n opposite phaserepulsive Vij
p,n in phaseattractive Vij
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 9
A dependence of giant resonance excitation
E0 80 A-1/3 MeV
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 10
collective excitations in the shell model p-n oscillations in phase: I=0, energy shifted downwardsp-n oscillations opposite phase: I=1, energy shifted upwards
G. Quadrupole R. (high)
G. Quadrupole R. (low)
low lying Quadrupole vibration
low lying Octupole vibration
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 11
giant resonances: collective motion of p,n
I=0 I=1
J=0+
J=1-
J=2+
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 12
extended modelsShortcomings 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 stateor by annihilation of virtual p-h state in g.s.
Improvement: BCS g.s. with pair configurations
0ph
hp
hp jjjj
jj aac
0phhphp
hp
hp jjjjjjjj
jj aayaax
0
kk aa
jp jh j´p j´h
HL-5 May 2005 Kernfysica: quarks, nucleonen en kernen 13
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
•I=1 state shifted up•I=0 state shifted down
•features of Giant Resonances: E0, E1, E2•ground state correlations: RPA