Condensed matter and subthreshold effects

Despite the considerable success of our analysis in epithermal energy scattering above a few eV, low energy processes are complicated by the solid state effects on both $\mu t$ slowing and $d\mu t$ formation.

Our fusion yield dependence on layer thickness is inconsistent with that predicted by the standard Faifman model, or even with our nominal model where the low energy formation rate for is set to 130 $\mu$s^-1. An improved yet still not perfect agreement has been achieved only after inclusion of a small constant term  s^-1 for $d\mu t$ formation. The value of is sensitive to the detail of the $\mu t$ deceleration process, hence it should be taken as a model-dependent phenomenological parameter at this stage.

Regardless of its rate, however, there is an indication that a nonzero value for F=1 formation rates plays an important role in our measurements. The nonresonant $d\mu t$ formation rate is predicted to be very small at low temperature (less than about s^-1), and does not appear to explain our observation regardless of the thermalization model.

Recalling that there is some evidence for subthreshold resonances for F=0, the same might be possible for F=1, although for the latter the resonance energies E_r are expected to be more negative ( meV). However, if one assumed the Breit-Wigner resonance profile as a zeroth approximation (despite the fact that this form is criticized for high densities [160]), the subthreshold formation rate falls off as |E_r|^-5/2 [141], and if one takes into account the experimental evidence for F=0 that s^-1 with meV, it is not completely implausible to have a few $\mu$s^-1 for F=1 at low temperature.

We note that the possibility of a nonzero F=1 rate has not previously been ruled out experimentally either, since in the previous D/T mixture experiments at low temperatures, F=1 rates were usually assumed to be zero in the fit (e.g. Ref. [36]). At any rate, small rates for F=1 would be difficult to measure in the cycling experiments due to fast $\mu t$ spin flip. Thus, our measurements in multilayers may offer a unique sensitivity to the resonance profile at large detuning energy, if theoretical uncertainties due to solid effects can be removed. To our knowledge, there are no realistic calculations of for F=1, and we urge theorists to extend their calculations to F=1.

Calculations for $\mu t$ scattering processes and molecular formation in solid hydrogen are in progress [170]. We eagerly await these new results. Fortunately, the solid state effects did not overwhelm our measurements using very thin layers.