Monday, April 23, 2007

De-coherence and the differential topology of nuclear reactions

I have already described the basic ideas of nuclear string model in the previous postings (such as this). Nuclear string model allows a topological description of nuclear decays in terms of closed string diagrams and it is interesting to look what characteristic predictions follow without going to detailed quantitative modelling of stringy collisions possibly using some variant of string models.

In the de-coherence process explaining giant resonances eye-glass type singularities of the closed nuclear string appear and make possible nuclear decays as decays of closed string to closed strings.

  1. At the level of 4He sub-strings the simplest singularities correspond to 4→ 3+1 and 4→ 2+2 eye-glass singularities. The first one corresponds to low energy GR and second to one of higher energy GRs. They can naturally lead to decays in which nucleon or deuteron is emitted in decay process. The singularities 4→ 2+1+1 resp. 4→ 1+1+1+1 correspond to eye-glasses with 3 {\it resp.} four lenses and mean the decay of 4He to deuteron and two nucleons resp. 4 nucleons. The prediction is that the emission of deuteron requires a considerably larger excitation energy than the emission of single nucleon. For GR at level of A=3 nuclei analogous considerations apply. Taking into account the possible tunnelling of the nuclear strings from the nuclear space-time sheet modifies this simple picture.

  2. For GR in the scale of entire nuclei the corresponding singular configurations typically make possible the emission of alpha particle. Considerably smaller collision energies should be able to induce the emission of alpha particles than the emission of nucleons if only stringy excitations matter. The excitation energy needed for the emission of alpha particle is predicted to increase with A since the number n of 4He nuclei increases with A. For instance, for Z=N=2n nuclei n→ n-1 +1 would require the excitation energy (2n-1)Ec=(A/2-1)Ec, Ec≈ .2 MeV. The tunnelling of the alpha particle from the nuclear space-time sheet can modify the situation.

The decay process allows a differential topological description. Quite generally, in the de-coherence process n→ (n-k) +k the color magnetic flux through the closed string must be reduced from n to n-k units through the first closed string and to k units through the second one. The reduction of the color color magnetic fluxes means the reduction of the total color binding energy from n2Ec ((n-k)2+k2 )Ec and the kinetic energy of the colliding nucleons should provide this energy.

Faraday's law, which is essentially a differential topological statement, requires the presence of a time dependent color electric field making possible the reduction of the color magnetic fluxes. The holonomy group of the classical color gauge field GAαβ is always Abelian in TGD framework being proportional to HAJαβ, where HA are color Hamiltonians and Jαβ is the induced Kähler form. Hence it should be possible to treat the situation in terms of the induced Kähler field alone. Obviously, the change of the Kähler (color) electric flux in the reaction corresponds to the change of (color) Kähler (color) magnetic flux. The change of color electric flux occurs naturally in a collision situation involving changing induced gauge fields.

For more details see the chapter Nuclear String Hypothesis of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".

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