  The $\bar PANDA$ experiment at FAIR (Facility for Antiproton and Ion
Research) in Darmstadt (Germany) is designed for $\bar p p$ annihilation
studies and it will investigate fundamental questions of hadron and nuclear
physics in interactions of antiprotons with nucleons and nuclei. Gluonic
excitations and the physics of hadrons with strange and charm quarks will be
accessible with unprecedented accuracy, thereby allowing high precision tests
of the strong interactions. In particular, the $D_{s0}^*(2317)^+$ and
$D_{s1}(2460)^+$ are still of high interest 11 years after their discovery,
because they can not be simply understood in term of potential models. The
available statistics and resolution of the past experiments did not allow to
clarify their nature. Recently LHCb at CERN has made progresses in this
respect, but still not at the level of precision required in order to clarify
the puzzle of the $cs$-spectrum. $\bar PANDA$ will be able to achieve a factor
20 higher mass resolution than attained at the B-factories, which is expected
to be decisive on these and second-order open questions. The technique to
evaluate the width from the excitation function of the cross section of the
$D_s$ mesons will be presented, and ongoing simulations performed with
$PandaRoot$ will be shown.
