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

We compute the ground state energy of a massive scalar field in the background 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 related scattering problem, the renormalization is performed with the help of the heat kernel expansion. The energy is found to be negative for attractive and for repulsive backgrounds as well.