The electronic structure of hydrogen-adsorbate-induced states on Gd(0001) was investigated by means of photoelectron spectroscopy with linearly polarized radiation. Clean and well-ordered rare-earth (0001) surfaces exhibit a highly localized surface state near the Fermi edge. After the adsorption of hydrogen the surface state disappeared, and an additional sharp feature at about 4-eV binding energy was observed. For this latter (Formula presented)-like state the ratio of the radial matrix elements as well as the relative phase shifts were determined to be (Formula presented) and (Formula presented) respectively using the possibility to rotate the electric-field vector continuously.