Summary of the model of dark nucleosynthesis

The books of Steven Krivit (see Hacking the atom, Fusion fiasco, and Lost history ) have been of enormous help in polishing the details of the model of dark nucleosynthesis explaining the mysterious aspects of what has been called cold fusion or LENR (Low energy nuclear reactions). Here

Summary of the model of dark nucleosynthesis model

Recall the basic ideas behind dark nucleosynthesis.

1. Dark nuclei are produced as dark proton sequences at magnetic flux tubes with distance between dark protons with h_eff/h= 2¹¹ (approximately proton/electron mass ratio) very near to electron Compton length. This makes possible formation of at least light elements when dark nuclei transform to ordinary ones and liberate almost entire nuclear binding energy.
   
   
2. Also more complex nuclei can form as nuclei of nuclei from ordinary nuclei and sequences of dark protons are at magnetic flux tubes. In particular, the basic rule (A,Z)→ (A+1,Z+1) of Widom-Larsen model is satisfied although dark beta decays would break this rule.
   

   In this case the transformation to ordinary nuclei produces heavier nuclei, even those heavier than Fe. This mechanism could make possible the production of heavy nuclei outside stellar interiors. Also dark beta decays can be considered. They would be fast: the idea is that the Compton length of weak bosons is scaled up and within the region of size scale of Compton length weak interactions have essentially the same strength as electromagnetic interactions so that weak decays are fast and led to dark isotopes stable against weak interactions.
   
   

3. The transformation of dark nuclei to ordinary nuclei liberates almost all nuclear binding energy. This energy could induce the fission of the daughter nucleus and emission of neurons causing the decay of ordinary nuclei, at least those heavier than Fe.
   
   
4. Also the dark weak process e^-+p→ n+ν liberating energy of order electron mass could kick out neutron from dark nucleus. This process would be TGD counterpart for the corresponding process in WL but having very different physical interpretation. This mechanism could explain production of neutrons which is by about 8 orders slower than in cold fusion model.
   
   
5. The magnetic flux tubes containing dark nuclei form a positively charged system attracted by negatively charged surfaces. The cathode is where the electrons usually flow to. The electrons can generate negative surface charge, which attracts the flux tubes so that flux tubes end up to the cathode surface and dark ions can enter to the surface. Also ordinary nuclei from the cathode could enter temporarily to the flux tube so that more complex dark nuclei consisting of dark protons and nuclei are formed. Dark nuclei can also leak out of the system if the flux tube ends to some negatively charged surface other than cathode.
   
   

The findings described in the the books of Krivit, in particular the production of neutrons and tritium, allow to sharpen the view about dark nucleosynthesis.

1. The simplest view about dark nucleosynthesis is as a formation of dark proton sequences in which some dark protons transform by beta decay (emission of positron) to neutrons. The objection is that this decay is kinematically forbidden if the masses of dark proton and neutron are same as those of ordinary proton and neutron (n-p mass difference is 1.3 MeV). Only dark proton sequences would be stable.
   

   Situation changes if also n-p mass difference scales by factor 2^-11. The spectra of dark and ordinary nuclei would be essentially identical. For scaled down n-p mass difference, neutrons would be produced most naturally in the process e^-+p→ n+ν for dark nuclei proceeding via dark weak interactions. The dark neutron would receive a large recoil energy about m_e≈ .5 MeV and dark nucleus would decay. The electrons inducing the neutron emission could come from the negatively charged surface of cathode after the flux tube has attached to it. The rate for e^-+p→ n+ν is very law for ordinary weak Planck constant. The ratio n/T ∼ 10^-8 allows to deduce information about h_eff/h: a good guess is that dark weak process is in question.
   
   

2. Tritium and other isotopes would be produced as several magnetic flux tubes connect to a negatively charged hot spot of cathode. A reasonable assumption is that the ordinary binding energy gives rise to an excited state of the ordinary nucleus. This can induce the fission of the final state nucleus and also neutrons can be produced. Also scaled down variants of pions can be emitted, in particular the pion with mass of 17 MeV (see this)
   
   
3. The ordinary nuclear binding energy minus the n-p mass difference 1.3 MeV multiplied by the number of neutrons would be released in the transformation of dark nuclei to ordinary ones. The table below gives the total binding energies and liberated energies for some lightest stable nuclei.
   
   

   
   

   The ordinary nuclear binding energies E_B for light nuclei and the energies Δ E liberated in dark → ordinary transition.

   Element	4He	3H	T	D
   EB/MeV	28.28	7.72	8.48	2.57
   Δ E/MeV	25.70	6.41	5.8	1.27

   
   
   

   Gamma rays are not wanted in the final state. For instance, for the transformation of dark ⁴He to ordinary one, the liberated energy would be about 25.7 MeV. If the final state nucleus is in excited state unstable against fission, the binding energy can go to the kinetic energy of the final state and not gamma ray pairs are observed. If two 17 MeV pions π₁₁₃ are emitted the other one or both must be on mass shell and decay weakly. The decay of off-mass π₁₁₃ could however proceed via dark weak interactions and be fast so that the rate for this process could be considerably faster than for the emission of two gamma rays.
   
   

The relationship of dark nucleosynthesis to ordinary nucleosynthesis

One can raise interesting questions about the relation of dark nucleosynthesis to ordinary nucleosynthesis.

1. The temperature at solar core is about 1.5× 10⁷ K corresponding to energy about 2.25 keV. This temperature is obtained by scaling factor 2^-11 from 5 MeV which is binding energy scale for ordinary nuclei. That this temperature corresponds to the binding energy scale of dark nuclei might not be an accident.
   

   That the temperature in the stellar core is of the same order of magnitude as dark nuclear binding energy is a highly intriguing finding and encourages to ask whether dark nuclear fusion could be the key step in the production of ordinary nuclei.
   

   Could dark nucleosynthesis in this sense occur also pre-stellar evolution and thus proceed differently from the usual p-p-cycle involving fusion processes? The resulting ordinary nuclei would undergo only ordinary nuclear reactions and decouple from the dark dynamics. This does not exclude the possibility that the resulting ordinary nuclei form nuclei of nuclei with dark protons: this seems to occur also in nuclear transmutations.
   
   

2. There would be two competing effects. The higher the temperature, the less stable dark nuclei and the longer the dark nuclear strings. At lower temperatures dark nuclei are more stable but transform to ordinary nuclei decoupling from the dark dynamics. The liberated nuclear binding energy however raises the temperature and makes dark nuclei less stable so that the production of ordinary nuclei in this manner would slow down.
   

   At what stage ordinary nuclear reactions begin to dominate over dark nucleosynthesis? The conservative and plausible looking view is that p-p cycle is indeed at work in stellar cores and has replaced dark nucleosynthesis when dark nuclei became thermally unstable.
   

   The standard view is that solar temperature makes possible tunnelling through Coulomb wall and thus ordinary nuclear reactions. The temperature is few keVs and surprisingly small as compared to the height of Coulomb wall E_c∼ Z₁Z₂e²/L, L the size of the nucleus. There are good reasons to believe that this picture is correct. The co-incidence of the two temperatures would make possible the transition from dark nucleosynthesis to ordinary nucleosynthesis.
   
   

3. What about dark nuclear reactions? Could they occur as reconnections of long magnetic flux tubes? For ordinary nuclei reconnections of short flux tubes would take place (recall the view about nuclei as two-sheeted structures). For ordinary nuclear the reactions at energies so low that the phase transition to dark phase (somewhat analogous to the de-confinement phase transition in QCD) is not energetically possible, the reactions would occur in nuclear scale.
   
   
4. An interesting question is whether dark nucleosynthesis could provide a new manner to achieve ordinary nuclear fusion in laboratory. The system would heat itself to the temperatures required by ordinary nuclear fusion as it would do also during the pre-stellar evolution and when nuclear reactor is formed spontaneously (see Oklo reactor.
   
   

This is only rough overall view and it would be unrealistic to regard it as final one: one can indeed imagine variations. But even its recent rough form it seems to be able explain all the weird looking aspects of CF/LENR/dark nucleosynthesis. To pick up one particular interesting question: how significantly dark nucleosynthesis could contribute to the generation of elements heavier than Fe (and also lighter elements)? It is assumed that the heavier elements are generated in so called r-process involving creation of neutrons fusing with nuclei. One option is that r-process accompanies supernova explosions but SN1987A did not provide support for this hypothesis: the characteristic em radiation accompanying r-process was not detected. Quite recently the observation of gravitational waves from the fusion of two neutron stars generated also visible radiation, so called kilonova (see this), and the radiation accompanying r-process was reported. Therefore this kind of collisions generate at least part of the heavier elements.

See the article Cold fusion again or the chapter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy" with the same title. See also the article Cold fusion, low energy nuclear reactions, or dark nuclear synthesis?.

For a summary of earlier postings see Latest progress in TGD.

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