  Context. Pulsational pair-instabilitye supernovae (PPISNe) and pair
instability supernovae (PISNe) are the result of a thermonuclear runaway in the
presence of a background electron-positron pair plasma. As such, their
evolution and resultant black hole (BH) masses could possibly be affected by
screening corrections due to the electron pair plasma.
  Aims. Sensitivity of PISNe and PPISNe to relativistic weak screening has been
explored.
  Methods. In this paper a weak screening model that includes effects from
relativistic pair production has been developed and applied at temperatures
approaching and exceeding the thresh old for pair production. This screening
model replaces "classical" screening commonly used in astrophysics.
Modifications to the weak screening electron Debye length are incorporated in a
computationally tractable analytic form with.
  Results. In PPISNe the BH masses were found to increase somewhat at high
temperatures, though this increase is small. The BH collapse is also found to
occur at earlier times, and the pulsational morphology also changes. In
addition to the resultant BH mass, the sensitivity to the screening model of
the pulsational period, the pulse structure, the PPISN-to-PISN transition, and
the shift in the BH mass gap has been analyzed. The dependence of the
composition of the ejected mass was also examined.
