The basic criterion for the transition to dark matter phase having by definition large value of hbar is that the condition α Q1Q2≈1 for appropriate gauge interactions expressing the fact that the perturbation series does not converge. The increase of hbar makes perturbation series converging since the value of α is reduced but leaves lowest order classical predictions invariant.
This criterion can be applied to color force and inspires the hypothesis that valence quarks inside nucleons correspond to large hbar phase whereas sea quark space-time sheets correspond to the ordinary value of hbar. This hypothesis is combined with the earlier model of strong nuclear force based on the assumption that long color bonds with p-adically scaled down quarks with mass of order MeV at their ends are responsible for the nuclear strong force.
The basic assumptions are following.
- Valence quarks correspond to large hbar phase with p-adic length scale L(keff=129)= L(107)/v0≈ 211L(107)≈ 5× 10-12 m whereas sea quarks correspond to ordinary hbar and define the standard size of nucleons.
- Color bonds with length of order L(127)≈ ≈ 2.5× 10-12 m and having quarks with ordinary hbar and p-adically scaled down masses mq(dark)≈ v0mq at their ends define kind of rubber bands connecting nucleons. The p-adic length scale of exotic quarks differs by a factor 2 from that of dark valence quarks so that the length scales in question can couple naturally. This large length scale as also other p-adic length scales correspond to the size of the topologically quantized field body associated with system, be it quark, nucleon, or nucleus.
The wave functions of the nucleons fix the boundary values of the wave functionals of the color magnetic flux tubes idealizable as strings. In the terminology of M-theory nucleons correspond to small branes and color magnetic flux tubes to strings connecting them.
This picture allows to understand the general features of strong interactions.
- Quantum classical correspondence and the assumption that the relevant space-time surfaces have 2-dimensional CP2 projection implies Abelianization. Strong isospin group can be identified as the SU(2) subgroup of color group acting as isotropies of space-time surfaces, and the U(1) holonomy of color gauge potential defines a preferred direction of strong isospin. Exotic color isospin corresponds to strong isospin. The correlation of exotic color with weak isospin of the nucleon is strongly suggested by quantum classical correspondence.
- Both color singlet spin 0 pion type bonds and colored spin 1 bonds are allowed and the color magnetic spin-spin interaction between the exotic quark and anti-quark is negative in this case. p-p and n-n bonds correspond to oppositely colored spin 1 bonds and p-n bonds to colorless spin 0 bonds for which the binding energy is 3 times higher. The presence of colored bonds forces the presence of neutralizing dark gluon condensate favoring states with N-P>0.
- Shell model based on harmonic oscillator potential follows naturally from this picture in which the magnetic flux tubes connecting nucleons take the role of springs. Spin-orbit interaction can be understood in terms of the color force in the same way as it is understood in atomic physics.
- The binding energies per nucleon for A=< 4 nuclei can be understood if they form closed string like structures, nuclear strings, so that only two color bonds per nucleon are possible. This could be understood if dark valence quarks and exotic quarks possessing much smaller mass behave as if they were identical fermions. p-Adic mass calculations support this assumption. Also the average behavior of binding energy for heavier nuclei is predicted correctly.
- For nuclei with P=N all color bonds can be pion type bonds and they have thus maximal color magnetic spin-spin interaction energy. The increase of color Coulombic binding energy between colored exotic quark pairs and dark gluons however favors N>P and explains also the formation of neutron halo outside k=111 space-time sheet.
- Spin-orbit interaction provides the standard explanation for magic numbers. If the maximum of the binding energy per nucleon is taken as a criterion for magic, also Z=N=4,6,12 are magic. The alternative TGD based explanation for magic numbers Z=N=4,6,8,12,20 would be in terms of regular Platonic solids. Experimentally also other magic numbers such as N=14,16,30,32 are known for neutrons. The linking of nuclear strings provides a possible mechanism producing new magic nuclei from lighter magic nuclei and could explain these magic numbers and provide an alternative explanation for higher shell model magic numbers 28,50,82,126.
The view about nucleus as a collection of linked nuclear strings suggests a stringy description of nuclear reactions. Microscopically the nuclear reactions would correspond to re-distribution of exotic quarks between the nucleons in reacting nuclei.
The TGD based explanation of neutron halo has been already mentioned. The recently observed tetra-neutron states are difficult to understand in the standard nuclear physics framework since Fermi statistics does not allow this kind of state. The identification of tetra-neutron as an alpha particle containing two negatively charged color bonds allows to circumvent the problem. A large variety of exotic nuclei containing charged color bonds is predicted.
For more details see the completely revised chapter TGD and Nuclear Physics.