Semiclassical Wormholes with a Smooth Throat

We propose a procedure for calculating heat kernel coefficients and use it to derive the expression for any heat kernel coefficient $B_i$ for an arbitrary profile of the throat. We give an explicit form of these coefficients up to $B_3$. We study domains of possible existence of wormholes for different values of the throat length-to-radius ratio and a nonminimal coupling constant.