The finite lifetime of the bound roton pair is included in the theoretical light scattering cross section to explain the shape of the peak in the observed Raman light scattering cross section in He II. A model Hamiltonian is used to describe interactions between quasiparticles for the helium system. The equation of motion for the bound roton pair state, which is taken to be a collective mode of quasiparticle pairs, is solved. The cross section for light scattering is then derived using Fermi's Golden Rule with the bound roton pair as the final state. Since the bound roton pair can decay into two free phonons, a phenomenological width r is included in the cross section. The peak position and shape of the observed cross section are both fitted using a binding energy of εB = 0.37 K for the bound roton pair.