axil. One of the greatest proponents of coherence being the cause of LENR was the late Giuliano Preparata. However he never demonstrated that the PdD lattice actually was coherent. If it had been there would be major anomalies in its specific heat etc.,
Preparata was honest enough to realize that not even coherence was enough to enhance fusion rates. He additionally required so called potential wells, 80-100 eV deep, to force naked deuterons close together. But any such wells would also attract positive helium nuclei even more strongly. As helium does not bind to palladium we can be sure the wells do not exist.
Coherence, by definition, is an ordered state. Thermodynamics requires that the spontaneous creation of ordered states requires the simultaneous release of heat. Conversely heating will tend to destroy coherence. But experimentally we observe a positive correlation of anomalous power with temperature, exactly the opposite of what coherence predicts. I think the coherent class of LENR explanations doesn't hold up to scrutiny.
Invoking coherence is just one way of overcoming the Coulomb barrier. Other ways include muon catalyzed fusion, deep Dirac levels, Storm's electron screening etc. The important point to note is that the Coulomb barrier is not eliminated completely. There must still be QM tunneling. That being the case we expect the p-d->3He reaction to dominate (almost) regardless of hydrogen isotope ratios (due to the low reduced mass). We don't see the expected 3He so we know that LENR does NOT result from the mutual approach of hydrogen nuclei.