Studies on the kinetics of muon catalyzed fusion in the HT mixture with very low tritium concentration

The idea of muon catalyzed fusion (μCF )was first suggested by C.Frank in 1947 ,[1] when he tried to explain tracks from cosmic rays in photoemulusions exposed at high altitudes .Although his explanations was not correct (the tracks were in reality positive muons from pion decays at rest). The experimental discovery of μCF was achieved at the end of 1956 in Berkeley by L.W.Alvarez team looking at bubble chamber pictures[2]. A muon (μ) is a leptonic elementary particle and has a finite lifetime of 2.2 μs .Since the mass of a muon 207 times larger than an electron, the size of an exotic atom/molecule containing the negative muon is much smaller than an electronic atom/molecule .When the negative muon binds to hydrogenic nuclei (poroton,p,deuteron,d,or triton,t) like H2+, a nuclear fusion reactions occurs in the muonic molecular ion, for example (dtμ)+→ 4He + n + μ- (1) The muon does not take part in the nuclear reaction directly but only catalyzes the reaction. This process the muon catalyzed fusion. The pt reaction is one pf the least known of all processes of μCF in the mixture of hydrogen isotopes. It is very important to gain information on reaction characteristics of all muonic processes in HT mixture(e.g., 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 ,and the rate of nuclear synthesis in it) 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 [6 - 9] and to solve some astrophysical problems [10 - 12].At present ,there are few experiments [13 - 17] that investigate characteristics of μCF in a H-T mixture. Only one [13] was performed with a HT mixture and the references [14 - 17] 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. Our calculations show that ,the optimum value of muon cycling coefficient at Ct = 0.01 (tritium concentration) is equal to 106.The experiments with the HT mixture at the meson facility PSI (Switzerland) are planned to be optimized to gain the precise information about the desired ?μCF .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. References: 1. F.C.Frank, Nature 160,525(1947). 2. L.W.Alvarez, H.Branda, F.S.Craford et al., Phys.Rev.105, 1125 (1957). 3.S.P.Merkuriev,et al.,Proc.Int.Con.on the Theory and Few Body and Quark-Hadronic Systems ,Dubna,D4-87-692,6(1987). 4. J.L.Friar, Proc.Int. Con.on the Theory and Few Body and Quark-Hadronic Systems, Dubna, D4-87-692, 70(1987). 5. H.Paetzgen, Schieck,Few Body Systems,5,171(1988). 6. C.Bargholz, Nucl.Phys.A,474,1(1987). 7. J.L.Fariar,Phys.Lett.B,251,11(1990). 8. J.Torre, B.Goulard, Phy.Rev.C.28, 529(1983). 9. A.C.Phillips, Nucl.Phys.A 184,337(1972). 10. C.Rolfs, Proc.Int.School of Phys.'Enrico Fermi', Course C.3, Monastero, 23 June -3 July 1387.p.417. 11. J.N.bachcall, M.H.Pinsonneault, Rev.Mod.Phys.64, 885(1992). 12.M.Arnould,M.Forestini,Nuclear Astrophysics,Proc.of the Rhird Int.Summer School ,La Rabida, Huelve,Spain,Research Reportsin Physics(Springer -Verlag,1988),p.48. 13. F.J.Hartmann et al.,Muon Catal.Fusion 2,53(1988) . 14. P.Baumann et al., Muon Catal.Fusion 5, 87(1990); F.J.Hartmann et al., Hyp.Int.82,259(1993)., 15-F.Mulhauser et al.Pysc.Rev A 53, 3069(1996). 16- F.Mulhauser et al, Hyp.Int.119,35(1999). 17-V.R.Bom et al., Hypfine Interact.118, 103(1999)