SIZE-DEPENDENT IONIZATION-ENERGY OF A METALLIC CLUSTER - RESOLUTION OF THE CLASSICAL IMAGE-POTENTIAL PARADOX

The ionization energy for a metallic cluster of radius R is I(R) = W alphae2/R + O(R-2), where W is the work function. Two different class ical values for alpha have been derived: 1/2 from the spherical-capaci tor approach, and 3/8 from the image-potential approach. We present a ''classical jellium'' or Wigner-crystal model in which alpha = 1/2 and W = 9/10e2/r(s). In the image-potential approach to the ''perfect-con ductor'' model, we discover an additional work 1/8e2/R, resolving the contradication in favour of alpha = 1/2. The experimental deviation fr om alpha = 1/2 is a quantum effect.