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Within the trace-logarithm formalism for the effective action we investigate the vacuum interaction of cosmic strings and the influence of string's width on this effect. For the massless real scalar field we compute the Casimir contribution into the total vacuum energy. The dimensional-regularization technique is used. It is shown that the regularized Casimir term contains neither the UV divergences, nor the divergences related with the nonintegrability of the renormalized vacuum mean of the energy-momentum tensor. In the case of two infinitely-thin strings, the limit coincides with the known result. The effect related with the finite width becomes significant on the distances of several core diameters.
Grats et al. (Wed,) studied this question.