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We compute the ground state energy of a massive scalar field in thebackground of a cylindrical shell whose potential is given by a delta function.The zero point energy is expressed in terms of the Jost function of the relatedscattering problem, the renormalization is performed with the help of the heatkernel expansion. The energy is found to be negative for attractive and forrepulsive backgrounds as well.Comment: 17 pages, 5 figure

Vacuum energy of a massive scalar field in the presence of a semi-transparent cylinder