Abstract
The line shape of the plasmon resonance in a cold, small sodium cluster (Na8) is calculated taking into account its coupling to the quantal quadrupole fluctuations of the cluster shape. This coupling is found to give rise to a small damping factor (Γ/ħω1∼0.03, where ħω1 denotes the energy centroid and Γ the full width at half maximum of the resonance), and to an asymmetric line shape with Gaussian behaviour in the wings.
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The full leading order term is bilinear in the dipole amplitude and linear in the quadrupole amplitude and thus the expression in (1) neglects terms depending on ((c † 1 c † 1 +c 1 c 1)2 (c † 2 +c 2))0. These terms generate couplings to states lying ≈2ħω1 away from the resonance line and are consequently quite irrelevant for the line shape issues discussed in the present note
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The zero point amplitude (α(0) 2≈0.02) implied by the parameters (16) is much smaller than the deformation necessary to produce crossings between single-particle orbits in different shells (α(0) 2≪N −1/3). Consequently, it is appropriate to calculate the potential energy as sum of single-particle energies, neglecting the true surface energy which plays a role for deformations implying a large number of level crossings
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On leave of absence from University of Coimbra, Portugal
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Pacheco, J.M., Broglia, R.A. & Mottelson, B.R. The intrinsic line width of the plasmon resonances in metal microclusters at very low temperatures: quantal surface fluctuations. Z Phys D - Atoms, Molecules and Clusters 21, 289–292 (1991). https://doi.org/10.1007/BF01426388
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DOI: https://doi.org/10.1007/BF01426388