Study of the dynamics of cascade processes of muonic atoms by multi group method

Studies on exotic atoms are important in different ways. They are important for strong interaction with nucleus and the theory of QCD in low energies. They are also important in muon catalyzed fusion (μCF). Their properties can be revealed by studies on cascade of muonic atoms. In this paper, unlike the others, we do not consider the kinetic energy of muonic atoms, constant (the kinetic energy of muonic atoms can vary due to cascade processes). We have used multi group method. The energy dependence of the rates of collisional cascade processes can take into account by this method. In addition, the energy spectra of muonic atoms in the ground state are calculated. For this purpose we divided the energy spectrum to 10 groups, and then use the rate of external Auger effect, Coulomb de-excitation, muon transfer and elastic scattering to solve the dynamics of cascade processes in each group. These equations are coupled linear differential equations. To solve them we use the Runge-Kutta method in the fourth order. One of the conclusions of this paper is that, this energy spectrum is not Maxwellian distribution. Finally our results are compared with the results of the Monte-Carlo simulation.