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Bound Electron Screening Corrections to Reactions in Hydrogen Burning Processes

How important would be a precise assessment of the electron screening effect, on determining the bare astrophysical $S$-factor ($S_b(E)$) from experimental data? We compare the $S_b(E)$ obtained using different screening potentials, (1) in the adiabatic limit, (2) without screening corrections, and (3) larger than the adiabatic screening potential in the PP-chain reactions. We employ two kinds of fitting procedures: the first is by the conventional polynomial expression and the second includes explicitly the contribution of the nuclear interaction and based on a statistical model. Comparing bare $S$-factors that are obtained by using different screening potentials, all $S_b(E)$ are found to be in accord within the standard errors for most of reactions investigated, as long as the same fitting procedure is employed. $S_b(E)$ is, practically, insensitive to the magnitude of the screening potential.