Diagrammatic perturbation theory is used to consider the problem of the coupling of a molecular group libration to the lattice vibrations in solids exhibiting rotational tunneling detected by inelastic neutron scattering. The technique is applied to a molecular group of symmetry C3 in presence of the hindering potential of the solid. The spectral density for transitions between rotational tunneling states in the ground librational level is obtained as a function of temperature. Low temperature results are presented for di erent phonon spectrum parameters. They are used to check the assumption that this coupling is the origin of the peculiar behaviour of the line shifting and broadening as a function of temperature in the INS spectra of such systems.