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Multipole response of metal spheres to q-dependent excitation operators
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We have obtained the once and thrice energy-weighted moments of the random-phase-approximation (RPA) response to q-dependent excitation operators of type
j
L
(qr)
Y
L
0
for metal spheres described within a spherical jellium model. These two moments, in conjunction with the Thomas-Fermi estimation of the RPA inverse energy-weighted moment, are used to study the response of these systems as a function of q. For small values of q, we recover the surface-mode systematics, whereas for large q’s the response is mainly determined by electron-hole excitations. For intermediate q values, bulk oscillations are found and their connection with the hydrodynamical-model predictions is established. In the limit of a big sphere, we have obtained an improved bulk-plasmon pole approximation for the dispersion relation which includes in a very easy way exchange and correlation effects. We have found that these corrections are not negligible. The moments of the response corresponding to a plane wave
e
i
q
⋅
r
are also discussed. Numerical applications to the case of Na spheres whose ground-state structure is described by models of different complexity (constant electronic density, Thomas-Fermi or Kohn-Sham) are presented.
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SERRA, Llorenç, et al. Multipole response of metal spheres to q-dependent excitation operators. Physical Review B. 1990. Vol. 41, num. 6, pags. 3434-3446. ISSN 0163-1829. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/9763