TABLE OF CONTENTS The experiments measuring IP are performed with the clusters at finite temperatures. Temperature leads to vibrations of the atoms, that is, to fluctuations of the cluster shape, and also to electronic entropy effects. The influence of the temperature on IP has been studied theoretically by Yannouleas and Landman [42] using a shell-correction method (see Section 4.3) corrected for finite temperature effects. The method incorporates several key ingredients: (1) static deformations of the cluster with respect to the spherical shape, (2) dynamic shape fluctuations due to temperature, and (3) electronic entropy. In this case the ionization potential is calculated as
| (5.10) |  |
where F( T, N, q = +1) and F( T, N, q = 0) represent the free energies of the ionized and neutral cluster at temperature T and the symbol ? ?indicates that the free energies are averaged over the shape fluctuations
| (5.11) |  |
The parameters ? and ? specify the triaxial shape of the droplet. These are also used in nuclear physics, where they are called Hill-Wheeler parameters [43]. Equation (5.11) indicates that the cluster explores the free energy surface F( T, N, q; ?, ?) obtained by the finite temperature shell correction method with a probability
| (5.12) |  |
where the denominator is the partition function.
Yannouleas and Landman have compared the experimental ionization potentials of potassium clusters [27, 44] to calculations performed at
