Refined constraints on chameleon theories are calculated for
atom-interferometry experiments, using a numerical approach consisting in
solving for a four-region model the static and spherically symmetric
Klein-Gordon equation for the chameleon field. By modeling not only the test
mass and the vacuum chamber but also its walls and the exterior environment,
the method allows to probe new effects on the scalar field profile and the
induced acceleration of atoms. In the case of a weakly perturbing test mass,
the effect of the wall is to enhance the field profile and to lower the
acceleration inside the chamber by up to one order of magnitude. In the
thin-shell regime, significant deviations from the analytical estimations are
found, even when measurements are realized in the immediate vicinity of the
test mass. Close to the vacuum chamber wall, the acceleration becomes negative
and potentially measurable. This prediction could be used to discriminate
between fifth-force effects and systematic experimental uncertainties, by doing
the experiment at several key positions inside the vacuum chamber. The
influence of the wall thickness and density is also studied. For the chameleon
potential $V(\phi) = \Lambda^{4+\alpha} / \phi^\alpha$ and a coupling function
$A(\phi) = \exp(\phi /M)$, one finds $M \gtrsim 7 \times 10^{16}$ GeV,
independently of the power-law index. For $V(\phi) = \Lambda^4 (1+ \Lambda/
\phi)$ one finds $M \gtrsim 4 \times 10^{16}$ GeV. Future experiments able to
measure an acceleration $a \sim 10^{-11} \mathrm{m/s^2}$ would probe the
chameleon parameter space up to the Planck scale. Our method can easily be
extended to constrain other models with a screening mechanism, such as
symmetron, dilaton and f(R) theories.