Neutron enigma and Einstein's second coefficient: may the smaller lifetime of ultra-cold neutrons be explained by the induced decay (similar to fission process and lasers)?
Modern physics is quickly developing the unified theory of wave-particle mathematical formalism. While the exact equations, which would describe in one limit the particle (pure mass, Newton-Einstein mechanic) and in another limit the pure wave (Maxwell equation) are far from completion, the preliminary use of such concept may allow to explain some modern phenomena and predict new.
The idea is: any matter is neither particle nor wave but both. It means that it has two intrinsic parts: matter and wave, considered for some approximation as a sum. The closest modern approach would be consider De-Broglie wave as material and consider any particle as consisted of two parts: usual particle (inertial mass) and De-Broglie wave. In this case the photon must have a finite (despite enormously small) mass and any moving particle has the added energy associated with dragging De-Broglie wave. Photon is almost pure De-Broglie wave and stopped classical particle (neutron) is almost pure particle. However, even the highest energy gamma-quantum has some finite mass inside and even ultra-cold neutron has some energy associated with De-Broglie wave - the matter and wave are inseparable in principle.
In this case the idea of reciprocity of physical phenomena may appear: each phenomena for particles has the similar phenomena for waves and vice versa. Photon - almost pure wave - has Einstein's first and second coefficients associated with him. Any particle like neutron must have reciprocal coefficients associated with De-Broglie part of particle. First coefficient A is responsible for spontaneous decay of excited atom and the corresponding coefficient is simply spontaneous decay of neutron. Einstein's second coefficient is responsible for induced decay of excited atom (lasers) and the corresponding second coefficient for neutron would be the induced decay of excited nucleus (another neutron).
It is interesting that such idea is already applied to fission process, where the energy dependence of the cross-section of fission induced by neutron has in excellent agreement with squared De-Broglie wavelength (at least at lower energies and without consideration of resonances). From the wave-particle unification point of view the fission process is laser like process but for nuclei. It may be even possible that in fission the created neutrons have exactly the same De-Broglie wave as the initial neutron, but since in neutrons contrary to photons the De-Broglie part of matter is small, the neutrons as a whole are not looking exactly coherent as created photons in laser. The matter part of neutrons is obviously not synchronized and de-coherent. And the cross-section of both processes is governed by the similar equations:
Ramsauer model for fission: σ(E)~π(R+λ)²~ λ² for small energies

Einstein's second coefficient:

σ₂₁=A₂₁*g(λ)*(λ²)/(8π*n²)

In both cases the cross-section is proportional to λ²
For the case of neutron enigma it means that the effect of deviation of lifetime for neutrons would be even more pronounced in the case of ultra-ultra cold neutrons and it will also strongly depend upon the concentration of neutrons (very much like for efficient nuclear explosion the critical mass is necessary or critical density).
Hopefully the future experiments concerning the neutron enigma will involve more and more slow neutrons and this predicted effect will be observed.
Einstein's second coefficient was derived using perturbation theory by Dirak (P.A.M. Dirac, Proc.Roy.Soc., A114, 243, 1927 "The quantum theory of the Emission and Absorption of Radiation")
Most probably exactly the same formalism may lead to the derivation of the cross-section in the case of fission process and for neutron enigma, assuming the De-Broglie wave is considered instead of photons as in the article.
That does  not mean that the De-Broglie wave may be treated separately as a similar to photons (see the beginning of the blog). The idea is that particle is a sum of De-Broglie wave and particle is a very rough approximation. The real mathematical description of such matter-wave object is absent now. However, even the simplistic treatment of the particle as a sum of matter and wave may help to establish the reciprocal phenomena for both particles and waves (like the idea of existence of Einstein's second coefficient for the particles).