the present experiments are performed with a he droplet source 
 combined with a pick - up cell containing h2o vapor , an ion 
 source , and a mass spectrometer system to analyze the resulting anions 
 as previously described in detail . the 
 helium droplet beam is formed by expansion of he through a nozzle 
 of 5 m diameter into vacuum at a temperature between 9 and 
 11 k and at a constant pressure of 20 bar . at a distance of 1 cm downstream , 
 the he droplets pass a skimmer before they enter a differentially 
 pumped chamber containing a pick - up cell , an ion source , and a mass 
 analyzer . after passing the pick - up cell , the h2o - doped 
 helium droplets enter the collision region of the ion source , where 
 free electron attachment to the doped droplets takes place . the electron 
 beam is generated by a home - built hemispherical electron monochromator , 
 which provides an electron beam with a full width at half - maximum 
 of about 100 mev . the electron energy scale is calibrated by measuring 
 the well - known resonance in sf6 yielding sf6 close to threshold ( 0 ev ) . ion yields at negative electron energies are 
 caused by the finite resolution of the electron beam . anions formed 
 are mass selected by a quadrupole mass filter and detected by a channel 
 electron multiplier . in general , the number of pick - up events can 
 be changed by adjusting the water pressure in the pick - up cell . all 
 h2o partial pressures mentioned were determined by an ion 
 gauge mounted at the ion source chamber . hence , the exact pressure 
 in the pick - up cell is unknown ; however , the chamber pressure can 
 be considered a qualitative measure of the pressure in the pick - up 
 cell .
for 
 bulk liquid helium the bottom of the conduction band ( v0 ) is above the vacuum level . in this case 
 the 
 surface of the liquid represents an electronic surface barrier for 
 an electron to be injected into the liquid . 
 here we study the electronic 
 conduction band for doped helium droplets of different sizes . utilizing 
 an electron monochromator , the onset of the ( h2o)2 ion yield corresponding to v0 is determined for helium droplets doped with the water 
 dimer . 
 while for larger droplets the onset approaches the well - known 
 bulk value of about 1 ev , the barrier does not continuously decrease 
 with smaller droplet size . 
 a minimum value of v0 = 0.76  0.10 ev is observed , which corresponds to a 
 droplet size of nmin = 1600  900 . 
 for droplet sizes below nmin , 
 a peak at 
 0 ev appears , which is well - known from neat h2o 
 clusters . 
 hence , we interpret nmin as 
 the smallest droplet size in which the electronic band structure is 
 formed in liquid helium droplets .