Diffraction of a plane wave by a hollow sphere with a slot

A solution is obtained to the vector problem of the diffraction of a plane wave incident along the axis of symmetry on an ideally conducting hollow sphere with a slot, in the case of an arbitrary relationship between wavelength and the geometric parameters of the problem. The diffracted field is determined in the form of Fourier series; and rapidly converging systems of linear algebraic equations of the second kind are obtained for the coefficients of these series. The applicability of the reduction method is substantiated. Numerical results for a sphere with a slot are compared with available results for an ideally conducting sphere.