  The optical response of quasi-one-dimensional systems is often dominated by
tightly bound excitons, that significantly influence their basic electronic
properties. Despite their importance for device performance, accurately
predicting their excitonic effects typically requires computationally demanding
many-body approaches. Here, we present a simplified model to describe the
static macroscopic dielectric function, which depends only on the width of the
quasi-one-dimensional system and its polarizability per unit length. We show
that at certain interaction distances, the screened Coulomb potential is
greater than its bare counterpart, which results from the enhanced repulsive
electron-electron interactions. As a test case, we study fourteen different
nanoribbons, twelve of them armchair graphene nanoribbons of different
families. Initially, we devised a simplified equation to estimate the exciton
binding energy and extension that provides results comparable to those from the
full Bethe-Salpeter equation, albeit for a specific nanoribbon family. Then, we
used our proposed screening potential to solve the 1D Wannier-Mott equation,
which turn out to be broad approach, that is able to predict binding energies
that match quite well the ones obtained with the Bethe-Salpeter equation,
irrespective of the nanoribbon family.
