The abrupt discontinuity of the background in the semi-infinite jellium results in a decaying oscillatory (Bardeen) spatial response of the electron gas. Related phenomena are the Friedel oscillations around an impurity in a metal, and the Ruderman-Kittel coupling between two localized magnetic moments embedded in a sea of conduction electrons. We have found that the ¹⁰⁹Ag (I= 1/2 ) NMR linewidth in nanometre-sized supported (and therefore isolated) silver particles shows a size effect that may be due to Bardeen-Friedel oscillations. The linewidth is also temperature dependent, in a way that cannot easily be explained as an effect of paramagnetic impurities; we suggest that thermal vibrations, known to have comparatively large amplitudes in small particles, wash out the abruptness in the background-charge discontinuity, and thus diminish the amplitude of the oscillations.