HL-5 May 2005Kernfysica: quarks, nucleonen en kernen1 Outline lecture (HL-5) Collective excitations...

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


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


Giant Dipole Resonance, schematic

prolate deformed 150Nd

field inducesoscillations: || symmetry axis symmetry axisE


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


1 particle – 1 hole excitationsshell structure and groups of ph-excitations in doubly magic nucleus

MeVA 3/141


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


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


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


A dependence of giant resonance excitation

E0 80 A-1/3 MeV


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


giant resonances: collective motion of p,n

I=0 I=1

J=0+

J=1-

J=2+


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


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

HL-5 May 2005Kernfysica: quarks, nucleonen en kernen1 Outline lecture (HL-5) Collective excitations...

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