### Still about nuclear string hypothesis

The nuclear string model has evolved dramatically during last week or two and allows now to understand both nuclear binding energies of both A>4 nuclei and A≤4 nuclei in terms of three fractal variants of QCD. The model also explains giant resonances and so called pygmy resonances in terms of decoherence of Bose-Einstein condensates of exotic pion like color bosons to sub-condensates. In its simplicity the model is comparable to Bohr model of atom, and I cannot avoid the impression that the tragedy of theoretical nuclear physics was that it was born much before any-one new about the notion of fractality. For these reasons a second posting about these ideas involving some repetition is in order.

** 1. Background**

Nuclear string hypothesis is one of the most dramatic almost-predictions of TGD. The hypothesis in its original form assumes that nucleons inside nucleus organize to closed nuclear strings with neighboring nuclei of the string connected by exotic meson bonds consisting of color magnetic flux tube with quark and anti-quark at its ends. The lengths of flux tubes correspond to the p-adic length scale of electron and therefore the mass scale of the exotic mesons is around 1 MeV in accordance with the general scale of nuclear binding energies. The long lengths of em flux tubes increase the distance between nucleons and reduce Coulomb repulsion.

A fractally scaled up variant of ordinary QCD with respect to p-adic length scale would be in question and the usual wisdom about ordinary pions and other mesons as the origin of nuclear force would be simply wrong in TGD framework as the large mass scale of ordinary pion indeed suggests. The presence of exotic light mesons in nuclei has been proposed also by Chris Illert based on evidence for charge fractionization effects in nuclear decays.

**2. A>4 nuclei as nuclear strings consisting of A< 4 nuclei**

During last weeks a more refined version of nuclear string hypothesis has evolved.

- The first refinement of the hypothesis is that
^{4}He nuclei and A<4 nuclei and possibly also nucleons appear as basic building blocks of nuclear strings instead of nucleons which in turn can be regarded as strings of nucleons. Large number of stable lightest isotopes of form A=4n supports the hypothesis that the number of^{4}He nuclei is maximal. Even the weak decay characteristics might be reduced to those for A<4 nuclei using this hypothesis. - One can understand the behavior of nuclear binding energies surprisingly well from the assumptions that total
*strong*binding energy associated with A≤ 4 building blocks is*additive*for nuclear strings and that the addition of neutrons tends to reduce Coulombic energy per string length by increasing the length of the nuclear string implying increase binding energy and stabilization of the nucleus. - In TGD framework tetra-neutron is interpreted as a variant of alpha particle obtained by replacing two meson-like stringy bonds connecting neighboring nucleons of the nuclear string with their negatively charged variants. For heavier nuclei tetra-neutron is needed as an additional building brick and the local maxima of binding energy E
_{B}per nucleon as function of neutron number are consistent with the presence of tetra-neutrons. The additivity of magic numbers 2, 8, 20, 28, 50, 82, 126 predicted by nuclear string hypothesis is also consistent with experimental facts and new magic numbers are predicted.

** 3. Bose-Einstein condensation of color bonds as a mechanism of nuclear binding**

The attempt to understand the variation of the nuclear binding energy and its maximum for Fe leads to a quantitative model of nuclei lighter than Fe as color bound Bose-Einstein condensates of ^{4}He nuclei or rather, of pion like colored states associated with color flux tubes connecting ^{4}He nuclei.

- The crucial element of the model is that color contribution to the binding energy is proportional to n
^{2}where n is the number of color bonds. Fermi statistics explains the reduction of E_{B}for the nuclei heavier than Fe. Detailed estimate favors harmonic oscillator model over free nucleon model with oscillator strength having interpretation in terms of string tension. - Fractal scaling argument allows to understand
^{4}He and lighter nuclei as strings formed from nucleons with nucleons bound together by color bonds. Three fractally scaled variants of QCD corresponding A>4 nuclei, A=4 nuclei and A<4 nuclei are thus involved. The binding energies of also lighter nuclei are predicted surprisingly accurately by applying simple p-adic scaling to the parameters of model for the electromagnetic and color binding energies in heavier nuclei.

**4. Giant dipole resonance as de-coherence of Bose-Einstein condensate of color bonds**

Giant (dipole) resonances and so called pygmy resonances interpreted in terms of de-coherence of the Bose-Einstein condensates associated with A≤ 4 nuclei and with the nuclear string formed from A≤ 4 nuclei provide a unique test for the model. The key observation is that the splitting of the Bose-Einstein condensate to pieces costs a precisely defined energy due to the n^{2} dependence of the total binding energy.

- For
^{4}He de-coherence the model predicts singlet line at 12.74 MeV and triplet (25.48, 27.30,29.12) MeV at ≈ 27 MeV spanning 4 MeV wide range which is of the same order as the width of the giant dipole resonance for nuclei with full shells. - The de-coherence at the level of nuclear string predicts 1 MeV wide bands 1.4 MeV above the basic lines. Bands decompose to lines with precisely predicted energies. Also these contribute to the width. The predictions are in a surprisingly good agreement with experimental values. The so called pygmy resonance appearing in neutron rich nuclei can be understood as a de-coherence for A=3 nuclei. A doublet (7.520,8.4600) MeV at ≈ 8 MeV is predicted. At least the prediction for the position is correct.

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