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We present a calculation of the ground state energy of massive spinor fields and massive scalar fields in the background of an inhomogeneous magnetic string with potential given by a delta function. The zeta functional regularization is used and the lowest heat kernel coefficients are calculated. The rest of the analytical calculation adopts the Jost function formalism. In the numerical part of the work the renormalized vacuum energy as a function of the radius R of the string is calculated anddoi:10.1103/physrevd.62.085024 fatcat:fuyih2cjdfdfbprbh3k7gmqdpe