Effect of the Nuclear d — t Resonance on Muon Sticking in μ-Catalyzed Fusion
The generally accepted validity of the sudden approximation for the calculation of the sticking coefficient ω s 0 is questioned. Physically this doubt is motivated by the fact, that due to the 5He3/2+ resonance, the nuclear interaction time (~10−20 s) is nonnegligeable compared to the muon orbiting time (~10−19 s); thus the “propagation” of the muon during the nuclear process can not be excluded.
Calculations are based on a formally exact, coupled two-channel three-body formulation of the fusion process in the dtμ − system [1,2]. After a careful definition of the sticking coefficient within this framework the sudden formula for ω s 0 is derived pointing out the chain of approximations, leading to it. The effect of the nuclear resonance is incorporated in a modified expression for the transition amplitude (and ω s 0 ), in which the simple overlap of the initial and final muon wave functions is replaced by a (free) propagation between them. The characteristic momentum (or inverse range) of this propagation is determined by the difference of the total (three-body) energy of the system and the resonance energy of the heavy-particle subsystem.
Our numerical calculations give an ω s 0 , which is roughly a factor 2 smaller, than the sudden value and is rather sensitive to the nuclear resonance parameters: changing them whithin the experimental errors results in a 10–15% variation of ω s 0 .
KeywordsFusion Reaction Nuclear Resonance Sticking Coefficient Characteristic Momentum Sudden Approximation
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