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A method for determination of optimum muon cycling coefficient and energy gain in the HT mixture with very low tritium concentration is proposed. The kinetics of the mu-atomic and mu-molecular processes preceding the pt reaction in the ptµ molecule is described. The time variations of γ quanta and conversion muons and the other particles formation in nuclear fusion reactions in ptµ molecules are studied. Our calculations show that, the optimum value of muon cycling coefficient at Ct=0.01 is equal to 106. In this paper our obtained results from theoretical calculations and experimental results are compared with together and we can receive that the obtained results are in good agreement with measured values. the rate of muon transfer from pµ atom to triton, the rate of transition between hyperfine levels of tµ atoms, the rate of formation of the ptµ molecule, the rate of nuclear synthesis in it and muon sticking) to interpret correctly the results of experiments in the triple mixture of hydrogen isotopes H-D-T and to describe the kinetics of all processes occurring in the mixture. From the theoretical point of view, the experiments investigating µCF processes in hydrogen -tritium mixture will allow one to test an algorithm describing a three-body system of particles interacting according to coulomb rule. It is necessary to emphasize the importance of the µCF study in HT mixture in order to obtain the information about characteristics of pt-reaction at ultra law energy range (≈KeV). The investigation of the reaction between light nuclei at ultra law energies (≈KeV) is very important for verification of fundamental symmetries in string interactions (3)-(5) the contribution of muon exchange currents and to solve some astrophysical problems. At present, there are few experiments that investigate characteristics of µCF in a H-T mixture. Only one was performed with a HT mixture and the references with triple mixture H-D-T. In this paper the authors survey the major areas of research: Section I describes the details of the kinetics of the µCF in HT mixture, while Sec. II describes the nonlinear point dynamics equations in HT mixture. Sec.III discusses on the numerical solution of these equations versus time in muon life time range. Sec.IV describes the optimum cycling coefficient and energy gain. The final section presents an overview of what is known, and outline some directions for future research.

Studies on the Kinetics of Muon Catalyzed Fusion in the HT Mixture with Very Low Tritium Concentration