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We present a calculation of the ground state energy of massive spinor fieldsand massive scalar fields in the background of an inhomogeneous magnetic stringwith potential given by a delta function. The zeta functional regularization isused and the lowest heat kernel coefficients are calculated. The rest of theanalytical calculation adopts the Jost function formalism. In the numericalpart of the work the renormalized vacuum energy as a function of the radius $R$of the string is calculated and plotted for various values of the strength ofthe potential. The sign of the energy is found to change with the radius. Forboth scalar and spinor fields the renormalized energy shows no logarithmicbehaviour in the limit $R\to 0$, as was expected from the vanishing of the heatkernel coefficient $A_2$, which is not zero for other types of profiles.Comment: 30 pages, 10 figure

Vacuum energy in the presence of a magnetic string with a delta function profile