  In this study, by attempting to eliminate the disadvantageous complexity of
the existing particle generators, we present a discrete probabilistic scheme
adapted for the discrete energy spectra in the GEANT4 simulations. In our
multi-binned approach, we initially compute the discrete probabilities for each
energy bin, the number of which is flexible depending on the computational
goal, and we solely satisfy the imperative condition that requires the sum of
the discrete probabilities to be the unity. Regarding the implementation in
GEANT4, we construct a one-dimensional probability grid that consists of
sub-cells equaling the number of the energy bin, and each cell represents the
discrete probability of each energy bin by fulfilling the unity condition.
Through uniformly generating random numbers between 0 and 1, we assign the
discrete energy in accordance with the associated generated random number that
corresponds to a specific cell in the probability grid. This probabilistic
methodology does not only permits us to discretize the continuous energy
spectra based on the Monte Carlo generators, but it also gives a unique access
to utilize the experimental energy spectra measured at the distinct particle
flux values. Ergo, we initially perform our simulations by discretizing the
muon energy spectrum acquired via the CRY generator over the energy interval
between 0 and 8 GeV along with the measurements from the BESS spectrometer and
we determine the average scattering angle, the root-mean-square of the
scattering angle, and the number of the muon absorption by using a series of
slabs consisting of aluminum, copper, iron, lead, and uranium. Eventually, we
express a computational strategy in the GEANT4 simulations that grants us the
ability to verify as well as to modify the energy spectrum depending on the
nature of the information source in addition to the exceptional tracking speed.
