Scattering of radial-symmetric spin wave at vortex in two-dimensional easy-plane ferromagnet

In the long-wave approximation (the wave number is much less than the inverse size of the vortex core) the scattering amplitude for the radial-symmetric spin wave (the azimutal number m = O) at vortex is found. The analysis is done by combining analytical and numerical calculation, but the main approximation for the scattering amplitude does not contain the values obtained from the numerical analysis. It is shown that the scattering intensity for the radial-symmetric spin wave turns out to lower than for the translation mode (m = &plusmn1) with the same wave number.