Atomic
and molecular resonances play an important role in many
physical processes, hence developing theoretical tools to properly
calculate these states is required. Recently, we introduced a method
for calculating the electronic resonance complex energies from stabilization
graphs via analytical continuation, specifically, using the Padé
approximant. This method was
shown to be efficient, for example, in interpreting the results of
cold molecular collisions. However, we observed that the complex energies
obtained by Padé depend on the selected set of input points
from the stabilization graph. In addition, unphysical solutions (noise)
may appear and need to be eliminated. Therefore, applying the method
to systems in which the resonance values are unavailable is difficult.
The excited Li–He* Feshbach states, for which autoionization
was recently observed, present such a challenge. Herein, we introduce
a statistical approach to single out the resonance energy from the
false solutions by identifying it as a cluster of Padé solutions.
This clusterization technique was applied to study several electronic
resonance states, for which we obtained excellent agreement with available
data (exact or other theoretical solutions and an experimental result).
Following this, the technique successfully identified the most likely
Li–He* Feshbach resonance energy. Moreover, we concluded that
large input sets generate much noise while restricting the number
of points facilitates clusterization, which makes this approach more
attractive, since input points are obtained from computationally demanding
electronic-structure calculations. Overall, the use of analytical
continuation via Padé, along with the statistical technique
presented herein, offers an efficient approach to calculate resonances.