Time independent description of thet(d, n)? fusion reaction in the presence of a muon

Abstract

We describe the (en#)-(dt#) continuum above and below the d+(t#)xs threshold using the R-matrix formalism. The continuum is explicitly constructed in an adiabatic approximation, and the asymptotic phase shifts and amplitudes in all channels are obtained. The energy eigenstates are used to compute the fusion reaction cross section for in-flight d+ (t/~) fusion, and fusion reaction rates involving transitions from the d + (t#) 1 s continuum to be below threshold continuum states. PACS: 24.90; 25.30 Conventional muon catalyzed fusion processesMuon catalyzed d-t fusion is the first application of particle physics towards energy production. The muon (/~), a 106 MeV massive fermion with a half-life of 2.2 ~ts, is combined with the hydrogen isotopes deuterium (d) and tritium (t) to form muonic molecular ions. In such molecules the isotopes are separated by less than 500 fm and undergo a nuclear fusion reaction, liberating the muon and several MeV of energy. The liberated muon is then free to catalyze the next fusion. For a detailed description of the catalytic cycle, see [1].The complex quantum dynamics leading to d-t fusion has received much attention in recent years. The path from a free muon to the point of being liberated by the fusion reaction is conventionally believed to proceed via several intermediate steps. Apart from the processes of thermalization of fast muons, the Auger capture of the muon by a hydrogen nucleus, the radiative cascade of the muon down from the high orbit in which it is captured, and the transfer of the muon to the heavier hydrogen isotope, the resonant formation of the (dtl~) (11) state, of the order of 108-109 s-1. The formation rate is still not precisely known as it is critically sensitive to the value of the resonance energy. For a recent review, see [2], and recent conference proceedings [3].The present theoretical understanding of the (dt#) system, however, appears to be incomplete, as two important experimental observations have up to now defied a satisfactory theoretical explanation. The first is the anomalous low temperature molecular formation rate of (dr#) in D 2 molecules as apposed to that in DT molecules [4]. Down to 100 ~ the formation rate of (dtp) in D2 molecules tends towards a constant value of about 4 x 108 s-1, whereas in DT molecules the formation rate tends to zero, as predicted in the resonance model. The second observation is that the experimental sticking fraction co, (i.e. the probability of the muon sticking to the alpha particle after fusion, having allowed for muon regeneration) is measured to be 0.45% [5], whereas theoretical calculations have predicted a sticking fraction in excess of 0.54% or more [6]. Both of the processes are intimately tied to the molecular formation and fusion processes, and these discrepancies between theory and experiment encourage us to believe that the conventional picture of the dt fusion catalytic cycle dominated by the formation of the (dt#)(la) state is incorrect or at least incomplete.In this work, we examine for the first t...