About neutrino atoms
The notion of Platonization of physics provides precise geometric correlates for atomic and nuclear energy shells. Platonization leads to a strong support for the existence of dark variants of weak and other interactions with scaled up ranges. This idea is central in TGD inspired biology, condensed matter physics and hydrodynamics. One could do without this assumption but this hypothesis provides a solution to a well-established tritium beta decay anomaly.
Consider now a model for neutrino atoms.
- One must distinguish between two weak charges:namely the weak charges associated with W boson exchanges and Z0 exchanges. Protons and neutrons have opposite W charges identifiable as weak isospins. They also have non-vanishing Z0 charges due to the mixing of the neutral SU(2) boson with U(1) boson caused by the electroweak symmetry breaking. Z0 weak charge is given for protons as QW(p)= 1-4sin2(θW)Qem≈ .041 and for electrons as QW(e)=-QW(p)≈ -0.41. For neutrons resp. neutrinos having no em charge, the weak charge is -1 resp. +1.
- If the weak charges of the nucleons couple independently to the classical Z0 gauge field, also nuclei with weak charge have a weak charge to which the contribution of protons is rather small. Nuclear screening of the weak Z0 charge is not possible whereas the isospins can sum up to zero so that the W boson weak charge of a Z=N nucleus vanishes. For the Z0 screening to occur, neutrino atoms are necessary. In this case, electrons automatically screen the protonic nuclear charge and neutrinos the neutron charge so that the e-ν atoms have the same structure as nuclei.
Consider W screening first.
- The nucleus has non-vanishing W weak charge (weak isospin) for Nne Z so that screening of weak isospin inside the nucleus is not possible. Most nuclei have several isotopes so that this condition is satisfied for most isotopes. The most interesting nuclei are long-lived and stable nuclei.
- The study of the table of nuclides appearing in a very old text book published 1963 gives some idea about the situation. Typically the most abundant stable nuclei have N=Z. Only He3 is stable and has a neutron deficit. There can be stable isotopes with neutron surplus of 1 unit for nuclei lighter than O and heavier than H3 (, which has two surplus neutrons and is stable). Stable nuclei heavier than N can have a surplus varying from 1 to 2 and O is the first nucleus having 3 stable isotopes. For Ca the number of stable isotopes is 4.
There are also stable nuclei with a maximal abundance with N>Z. 3Li7, 11Na23, 15P31, 17Cl36 ,19K39, 26Fe55 are biologically interesting. Consider next the Z0 weak screening.
- Nuclei themselves cannot carry out Z0 screening but for neutral atoms the protons and electrons have opposite Z0 charges so that the screening of proton Z0 charge could occur automatically for neutral atoms. N neutrinos are needed to screen the neutron Z0 charge of neutrons and for the presence of surplus neutrons requires N>Z neutrinos.
- If the size scale is longer than the size of the atom, the atom + nucleus can be approximated as a point-like weak Z0 charge equal to -N. Nonrelativistic model for neutrino atom assuming massive neutrino would predict that its Bohr radius is given by aW =(ℏeff(ν)/ℏ)(1/2N2αW)Lν, where Lν=ℏ/m(ν) is neutrino Compton length for ℏ and αW= α/sin2(θW).
- Dark weak bosons are involved and one can argue that the dark weak scale Lw(dark)(ℏeff(W)/ℏ)× Lw should not be smaller than the size of neutrino atom characterized by Bohr radius aW. But what one means with Lw? Lw is the scale below which the Z0 boson is effectively massless and one can argue that onside this scale is infinite with the flux tubes, just as for photons. In longer scales dark weak bosons have a scaled up weak scale.
If one requires Lw>aW, one ends up with problems. For ℏeff(ν)=ℏeff(W) this would give aW=(1/22N2gW2αw)Lν ≤ LW giving m(ν)= mW= 2N2gW(e)αw)mW. For N= 1 this would give mν= 2αW mW, which is larger than nucleon mass for αW≈ α/sin2(θW). This does not conform with the fact that neutrino mass is very small.
See the article About Platonization of Nuclear String Model and of Model of Atoms or the chapter with the same title.
For a summary of earlier postings see Latest progress in TGD.
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.
Source: http://matpitka.blogspot.com/2023/09/about-neutrino-atoms.html
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