We perform a theoretical study of the response of neutral and ionized
metal clusters to the elastic impact of slow electrons. We center our
attention on Na-40 and Na-41(+) closed-shell clusters. A phase-shift a
nalysis is performed for both systems. The total cross section for the
neutral cluster presents resonances related with the existence of qua
sibound states when studied as a function of incident energy. For the
ionised cluster we show the calculated ratio of the angular distributi
on to the Rutherford differential cross section, near and far from a r
esonance. The existence of resonances as well as the associated energi
es are very sensitive to the mean interaction potential. As a conseque
nce, elastic scattering of slow electrons on clusters could be a usefu
l tool in the study of the electronic structure of clusters.