On the surface energy of metals according to the hydrodynamic model with spatial dispersion

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Abstract
For a spatially dispersive plasma (the 'semi-classical infinite-barrier hydrodynamic model with non-local response') the difference sigma corr(Q) between its surface energy and that of the corresponding neutral fluid is determined. Special attention is paid to the behaviour of sigma corr(Q) as the wavenumber cut-off Q recedes to infinity. If Q is strictly independent of system size, then sigma corr( infinity ) is convergent, as pointed out by Horing, Kamen and Gumbs (1985). It is also surprisingly if accidentally close to the measured surface energy of simple metals. If Q is dependent on size in such a way that the total number of normal modes is unchanged when new surfaces are created by cleavage, then sigma corr(Q to infinity ) is divergent, and negative.

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