## Oscillations in Finite Quantum SystemsThis book surveys the physics of small clusters of particles undergoing oscillations and vibrations. These oscillations occur in nuclear physics and the physics and chemistry of atomic clusters. First, the authors survey experimental information on collective vibrations in atoms, metal clusters and nuclei, then they develop theoretical tools to understand these findings. Finally, they discuss important vibrational modes observed in the different systems and mechanisms for the damping of vibrational modes and the effects of excitation energy on the modes. |

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### Contents

Introduction | 1 |

Basic concepts | 33 |

Theoretical tools | 46 |

RPA | 63 |

Dipole oscillations | 81 |

Surface modes | 99 |

Compressional modes | 127 |

Line broadening and the decay of oscillations | 148 |

Thermal effects | 171 |

Mean field theory | 187 |

Numerical RPA | 203 |

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### Common terms and phrases

angular approximation associated assume atomic average calculated Chap charge classical clusters collective compression consider corresponding coupling cross section damping decay defined deformation dependence derived described detail determine dipole discussed displacement field distribution drop effects electron energy equation estimate evaluate example excitation excitation energy expectation expressed external factor Fermi field final finite force formula frequency giant dipole given gives ground important independent integral interaction limit liquid mass matrix element mean measured mechanics metal mode momentum motion neutrons nuclear nucleus observed obtain operator oscillation particle particle-hole peak perturbation photon physics potential produces projectile quadrupole quantum quantum mechanics region relation resonance response result scaling scattering separable shape shell shown in Fig shows simple single single-particle spectrum spherical strength sum rule surface theory transition density vibration wave function width