Abstract
The effect of $\ensuremath{\xi}R$ curvature coupling terms in the equation of motion of a massless scalar field are considered on a cosmic-string background. Realistic two- and four-dimensional models of a string, where the space-time curvature is spread over a region of nonzero size ${r}_{0}$, are constructed. In two and four dimensions, the nonzero $\ensuremath{\xi}$ term modifies the behavior within a region centered about the string, whose radius is proportional to ${r}_{0}$; however, the constant of proportionality may be exponentially large. For the standard idealized string (a conical space-time) which has no intrinsic length scale, the effects of nonzero $\ensuremath{\xi}$ do not appear.
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