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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen1 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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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen2 photon-induced n emission in Nd spherical deformed Nd( ,n) cross section dominated by broad resonance Nd( ,p) …? sources: a) in-flight positron annihilation b) bremsstrahlung from intense electron beam E resonance 2 E shell “Giant resonance” GR single-particle coherent process

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen3 Giant Dipole Resonance, schematic prolate deformed 150 Nd field induces oscillations: || symmetry axis symmetry axis

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen4 particle-hole excitation Fermi level J doubly magic nucleus (Fermi level between two shells): elementary excitations: example 16 O 1d3/2 2s1/2 1d5/2 1p1/2 1p3/2 possible particle-hole states with J =1 - almost degenerate states: strong mixing by p-h interaction

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen5 1 particle – 1 hole excitations shell structure and groups of ph-excitations in doubly magic nucleus

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen6 particle – hole interactions exchange term direct term scattering annihilation/creation

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen7 schematic model of collective excitation } V 0 N poles at unperturbed E i N-1 solutions E=E’ i : / E

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen8 collective state 2 states generated by coherent superposition: small variation of E i E 0 E C = E 0 + N V 0 2E 0 exp. energy shift #N of (almost) degenerate single-particle states constructive sum of amplitudes: coherent surface vibration 1 low-lying collective (isospin T=0) state p,n opposite phase repulsive V ij p,n in phase attractive V ij

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen9 A dependence of giant resonance excitation E0 80 A -1/3 MeV

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen10 collective excitations in the shell model p-n oscillations in phase: I=0, energy shifted downwards p-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

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen11 giant resonances: collective motion of p,n I=0 I=1 J =0 + J =1 - J =2 +

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen12 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 j p j h j´ p j´ h

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HL-5 May 2005Kernfysica: quarks, nucleonen en kernen13 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

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