  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.
