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.

1. 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 Q_W(p)= 1-4sin²(θ_W)Q_{em≈ .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.}
2. 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.

1. The nucleus has non-vanishing W weak charge (weak isospin) for N\ne 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.
2. 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.

1. 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.
2. 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 a_W =(ℏ_eff(ν)/ℏ)(1/2N²α_W)L_ν, where L_ν=ℏ/m(ν) is neutrino Compton length for ℏ and α_W= α/sin²(θ_W).
3. Dark weak bosons are involved and one can argue that the dark weak scale L_w(dark)(ℏ_eff(W)/ℏ)× L_w should not be smaller than the size of neutrino atom characterized by Bohr radius a_W. But what one means with L_w? L_w 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 L_w>a_W, one ends up with problems. For ℏ_eff(ν)=ℏ_eff(W) this would give a_W=(1/22N²g_W²α_w)L_ν ≤ L_W giving m(ν)= m_W= 2N²g_W(e)α_w)m_W. For N= 1 this would give m_ν= 2α_W m_W, which is larger than nucleon mass for α_W≈ α/sin²(θ_W). This does not conform with the fact that neutrino mass is very small.

4. Neutrino mass of .1 eV would correspond to the ordinary Compton length L(ν)≈ 10 \mum which is a typical cell length scale. L_w≈ a_W requires ℏ_eff(W)/ℏ ≈ a_W/L_W≈ 10⁷. The neutrino Bohr radius is about a_W=(sin²(θ_W)/2N²α)L(ν)≈ .32/N² mm. For N=1 corresponding to D and He³. It should be noted that the particle independent gravitational Compton length of Earth is about GM_E/2≈ 5 mm if the gravitational Planck constant satisfies the formula first proposed by Nottale. For larger values of Z, one obtains shorter size scales. For Z= 20 (Ca) one has a_W= 1\mum, the scale of the cell nucleus.
5. A simultaneous W screening and Z⁰ screening are not possible in the general case. Z⁰ screening requires in general more neutrinos than electrons and the surplus neutrinos give a non-vanishing weak isospin coupling to classical W boson fields. This does not occur for hydrogen.
6. Ions would be also ions with respect to Z⁰ charge. This might have some relevance in biology.

In the above arguments I neglected a very important consistency condition. The dark weak scale should not be smaller than the Bohr radius of the dark atom. There are two options corresponding to the screening of the neutron charge by neutrinos and to the screening of the weak Z⁰ charge of protons by dark electrons. It turns out that this condition gives a lower bound for the screened weak Z⁰ charge of neutrons and protons. This allows us to estimate the radius of the volume of condensed matter. For both options this readius is in good approximation about L≈10^-8 meters in both cases and depends on the mass ratio of weak boson and neutrino resp. electron. L depends only weakly on the details of the condensed matter system such as the number of protons or neutrons per atom, and since the living system is mostly water, it is in good approximation determined by water content.

This length scale is fundamental in living matter (thickness of coiled DNA strand, the radius of DNA nucleosome, the thickness of cell membrane). This scale corresponds to p-adic length scale L(151), which corresponds to Gaussian Mersenne prime. There are four miracle p-adic length scales L(151),L(157),L(163), L(167) associated with Gaussian Mersennes and they correspond to biologically important length scales. L(167) corresponds to 2.5 μm. Therefore it seems that the crazy generalization of the atom concept has profound biological implications and means that weak interactions have a central role in quantum biology.

Neutrino atoms would be very large and this means that condensed matter would be analogous to liquid Helium. Neutrino superconductivity and superfluidity are highly suggestive. This would give support for the TGD proposal and classical Z⁰ force could play a central role in condensed matter and in hydrodynamics (see this and this. For instance, hydrodynamical vortices could be interpreted in terms of Z⁰ superfluidity.

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.