  Nuclear astrophysics simulations aiming to study the origin of the elements
in stars require a multitude of nuclear physics input. Both systematic model
dependent and statistically correlated uncertainties need to be considered. An
application where realistic uncertainty assessments are especially important is
the intermediate neutron capture process or i process: a neutron capture regime
with neutron densities intermediate between the slow and rapid processes.
Accordingly, the main network flux proceeds on the neutron-rich unstable
isotopes up to 4-5 species off the valley of stability. The i process has been
clearly identified to be active in post-AGB stars during the Very Late Thermal
Pulse H-ingestion event, and a recent work infers about its important role in
early generations of stars. Here we demonstrate the effect of propagating
systematic nuclear uncertainties from different theoretical models to final
abundances for a region around the 2$^\mathrm{nd}$ peak at $A-Z=80$ for
elemental ratio predictions involving Ba, La and Eu in i-process conditions.
These elements are used to distinguish different n-capture contributions
observed in low-metallicity stars. For the simple 1-zone model adopted here,
predictions vary as much as a factor of 22 in on possible observational plane
([La/Eu] vs. [Ba/La]). To consider statistically correlated uncertainties, we
similarly perform a full nuclear physics uncertainty study within a given
Hauser-Feshbach model and demonstrate the role of correlations on the final
stellar abundance uncertainties. We show that in i-process conditions the main
result of neglecting correlations is to underestimate the impact of nuclear
uncertainties on the final nucleosynthesis yields by as much as two orders of
magnitude. (continued in document)
