This work deals with the study of an erupting prominence embedded in the core of a CME and focuses on the derivation of the prominence plasma filling factor. We explore two methods to measure the prominence plasma filling factor that are based on the combination of visible-light and ultraviolet spectroscopic observations. Theoretical relationships for resonant scattering and collisional excitation are used to evaluate the intensity of the H I Lyman-{alpha} and Lyman-{beta} lines, in two prominence points where simultaneous and cospatial LASCO-C2 and UVCS data were available. Thermodynamic and geometrical parameters assumed for the calculation are provided by both observations and the results of a detailed 1D non-LTE radiative-transfer model of the prominence, developed in our previous work (Heinzel 2016). The filling factor is derived from the comparison between the calculated and the measured intensities of the two lines. The results are then checked against the non-LTE model in order to verify the reliability of the methods. The resulting filling factors are consistent with the model in both the prominence points when the separation of the radiative and collisional components of the total intensity, required to estimate the filling factor, is performed using both the line intensities. An exploration of the parameter space shows that the results are weakly sensitive to the plasma velocity, but they depends more strongly on the assumed kinetic temperatures. The combination of visible-light and ultraviolet Lyman-{alpha} and Lyman-{beta} data can be used to approximately estimate the geometrical filling factor in erupting prominences, but the proposed techniques are reliable only for emission that is optically thin in the lines considered, condition that is not in general representative of prominence plasma.
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