Transition rates via Bethe ansatz for the spin-

We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional $s=\frac{1}{2}$ Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions $z_1,\ldots,z_r$ of the Bethe ansatz equations, the size of the determinants is of order $r\times r$. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field