Results of nuclear resonance fluorescence experiments on117 Sn are reported. More than 50 γ transitions with Eγ < 4 MeV were detected indicating a strong fragmentation of the electromagnetic excitation strength. For the first time microscopic calculations making use of a complete configuration space for low-lying states are performed in heavy odd-mass spherical nuclei. The theoretical predictions are in good agreement with the data. It is concluded that although the E1 transitions are the strongest ones also M 1 and E2 decays contribute substantially to the observed spectra. During the last years the study of the properties of multi-phonon excitations in atomic nuclei has been one of the key topics in nuclear structure research. The main motivation for these studies is to gain insight into the applicability of a picture of harmonic excitations to a finite strongly interacting fermion system, like an atomic nucleus. At present, systematic experimental information on the properties of low-lying two-phonon states [1-3] as well as on two-phonon giant resonances [4,5] in even-even spherical nuclei is available.The 1 − component of a two-phonon quintuplet built up of collective quadrupole and octupole phonons, [2, is a very good candidate for the investigation of anharmonic properties of low-lying excited states. This state is practically a pure two-phonon state with very weak admixtures of other configurations [3]. In addition, a tool which is very selective to its excitation, namely nuclear resonance fluorescence (NRF), is available. The main conclusion from systematic studies [2,3,[6][7][8] [11] have been reported. From very general arguments one expects rather weak changes in the properties of collective vibrations when they are coupled to an odd quasiparticle. However, even the first NRF experiments indicate a rather strong fragmentation of the excitation strength. To minimize the number of possible excited levels it is imperative to consider this coupling of collective vibrations to an odd quasiparticle in a nucleus with ground state spin 1/2.In the present letter we report on NRF experiments on 117 Sn (J π g.s. = 1/2 + ) in which 59 transitions with E γ < 4.05 MeV have been observed. It is clear that a detailed theoretical analysis which provides information on the structure of the excited states, is necessary to explain the results of this experiment. For this reason a full microscopic calculation of the properties of multi-phonon states in heavy odd-mass spherical nuclei has been performed for the first time.Experimental results have been obtained at the bremsstrahlung NRF-facility at the 4.3 MV Dynamitron accelerator of the Stuttgart University [1]. The electron energy was 4