  In this paper we develop a technique for determining interatomic potentials
in materials in the quantum regime from single--shell Extended X-ray Absorption
Spectroscopy (EXAFS) spectra. We introduce a pair distribution function, based
on ordinary quantum time--independent perturbation theory. In the proposed
scheme, the model potential parameters enter the distribution through a
fourth--order Taylor expansion of the potential, and are directly refined in
the fit of the model signal to the experimental spectrum. We discuss in general
the validity of our theoretical framework, namely the quantum regime and
perturbative treatment, and work out a simple tool for monitoring the
sensitivity of our theory in determining lattice anharmonicities based on the
statistical $F$--test. As an example, we apply our formalism to an EXAFS
spectrum at the Ag K--edge of AgI at T=77 K. We determine the Ag--I potential
parameters and find good agreement with previous studies.
