A phonon is a vibration in a crystal. A sound, if you wish; that is also true. It is defined in classical mechanics and in quantum mechanics.
This paper does not have a punchline, as the reviewer said. This is probably true, though it does have several specific outputs:
1) The first is that the current science have not created a sufficiently correct model of phonons in metal. The authors began that work.
2) The authors spell out a specific behavior of metals that is pretty complex to explain. The authors acknowledge that this behavior was known before, but not widely known.
3) The authors say that their model differs from the model that is in prevailing use today.
If I were to take the scientific significance of this paper down to the level of a woodworker, they are saying that when you put a specific varnish onto a specific wood in just the right way, the wood may shine slightly differently from what you'd expect. It's a good thing to know, but it's a highly specialized bit of information, and it is of use only to highly skilled woodworkers. For everyone else it's just a bunch of strange words.
The reason why phonons are important is that they are postulated to be the absorption path for gamma rays or other high energy products of fusion. So, these guys are looking into the right way to model it. For larger systems, the Bosch model works, and for smaller systems (like LENR), the Born-Oppenheimer model works better. In the paper, they went through the math for why that is the case.
The Extended Lochon Theory proposes that Phonons are important in the IniTIATion of Cold Fusion, not just the absorption of its products.
Extended Lochon Theory
http://en.wikiversity.org/wiki/Cold_fusion/Theory
Model proposed by KP Sinha and Andrew Meulenberg. Postulates that fusion can occur between hydrogen or deuterium within solid state lattice systems that contain linear defects. Linear defects are degraded surface phenomena caused by heavy loading processes where mobile protons/deuterons are then able to congregate. These interstitial surface anomalies are sometimes referred to as a sub-lattice in ELT and have recently been correlated with Storms’ Nano-crack NAE by Meulenberg himself at ICCF-18.[1]
Longitudinal phonon modes originating from these localized interstitial arrays (Linear NAE plus Ions) A) facilitate the creation of lochons (local charged boson electron pairs) and B) polarize ion pairs within the defects. Lochons will merge with H or D to form H- and D- ions respectively. They also provide strong screening effects between H+/H- and D+/D- nuclei. Lochon assisted screening in conjunction with subsequent deepening of the coulomb potential-well facilitates the initiation of low-level, tunneling-assisted fusion processes.
Absence of radiation is accounted for by two mechanisms. Firstly, gradual dissipation and exchange of thermal energy occurs between ion chains and the lattice before H+H-/D+D- fusion takes place. Secondly, H+H-/D+D- that are deeply bound with lochons do not occupy an excited state above the fragmentation level which prevents gamma transitions after fusion.[2][3]