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The behavior of the shear modulus caused by proliferation of dipoles ofnon-singular screw dislocations with finite-sized core is considered. Therepresentation of two-dimensional Coulomb gas with smoothed-out coupling isused, and the stress-stress correlation function is calculated. A convolutionintegral expressed in terms of the modified Bessel function $K_0$ is derived inorder to obtain the shear modulus in approximation of interacting dipoles.Implications are demonstrated for the shear modulus near the melting transitionwhich are due to the singularityless character of the dislocations.

Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the melting