A model of the phenomenon of "cold thermonuclear fusion" (CTF) and a scheme for its experimental verification are proposed. The CTF model assumes that when a palladium matrix with deuterium adsorbed into it is heated, a nuclear deuterium desorption channel occurs.

It follows from theorems [1,2] that a narrow-band N-level energy spectrum ε_n with attenuation widths γ_n due to a single decay channel is rearranged when the level widths intersect in the zone, with the formation of one super radiant level (SRL) E with a width of γ_E ≃ Nγ_n. 

CTF involves the occurrence of high-energy nuclear reactions under normal conditions, with energies of at least 1 MeV. Is it possible? We think so. 

To understand the realism of CTF, let us consider a physical process in which great energy is present at the real and virtual levels.

It is known that during first-order phase transitions a large amount of energy is released, but this energy is volumetric - usually it is not localized in space and not synchronized in time.

While searching for the desired phase transition, we found a high-energy and surface-localized process - gas desorption from the metal matrix.

The electron levels of the absorbed gas hybridize with the electrons of the metal matrix, forming a narrow energy band with them.

When heated, a positively charged ion first flies out of the sample, to which a band electron is attached after some time. The electron recombination time is determined by the widths of the levels with a single desorption decay channel.

If we apply the FK model [3] to gas desorption, then this process is described by structural phase transitions with a ladder dependence of the gas concentration inside the sample on temperature, with abrupt changes in pressure at the steps of the ladder. Pressure restrains the escape of gas ions, being the main reason that limits the rate of its outflow and creates an internal stress field.

Superradiant levels (SRLs) do not form in crystals under normal conditions, but when heated, gas ions escaping from the crystal matrix become part of an open quantum mechanical system. As a result - SRLs  appear.

From [1,2] it follows that the widths of the (SRLs) desorption channel of decay are not limited in any way and in microcrystals can reach several MeV.

We consider the following CTF model realistic: - a matrix of a metal that adsorbs hydrogen well, for example Pd, saturated with deuterium when heated, pushes out the deuterium nucleus. A superradiant electron E^- should join it, but there is a faster, nuclear desorption channel - the virtual collapse of one of the internal deuterium nuclei into two virtual neutrons with the further formation of two tritium nuclei, or tritium and a neutron:

                                                                                                            (1)

where E^- is an electron at a superradiant level; ,  - virtual neutron and neutrino, thus we have:

                                          ;                                                                      (2)

or:

                                                                                                              (3)

Microscopic Pd crystals in this process play the role of an electron accelerator, catalyzing the nuclear process. Under nonequilibrium conditions, the neutron channel of the CTF (3) can kinematically prevail over the tritium channel (2), which we have repeatedly observed.