We report on observations and analysis of the C 2 Swan band v = 0 sequence in the optical spectrum of Comet Hale-Bopp. One set of observational data was obtained when this comet was at a large heliocentric distance (3.03 AU). This unusual distance provided the opportunity to enhance our knowledge of the intercombination transitions in C 2 . These transitions are forbidden for electric dipole radiation, but they exist due to higher order multipole radiation. Although the transition probabilities are several orders of magnitude smaller than allowed electronic transitions, the intercombination bands play a key role in the fluorescence process of the C 2 radical. This role is to provide a cooling path for rotational and vibrational populations seen in the visible spectrum. Because their exact transition probability is not yet completely clear, better quantitative knowledge of these transitions can help constrain C 2 quantities in comets. To analyze the data, an equilibrium fluorescence model with 5652 different vibrational levels was created. This model included the triplet and singlet systems of C 2 involved in the fluorescence process. Theoretical spectra corresponding to different values of the electronic transition moments for the a 3 u -X 1 + g and c 3 + u -X 1 + g transitions were computed. These spectra were then compared to the observational data. A good fit is obtained for transition moments of 5 Γ 10 -6 β€ |D a-X | 2 = |D c-X | 2 β€ 10 -5 atomic units (a.u.), for spectra obtained far from the nucleus where the fluorescent equilibrium is reached.