### Some tests of nuclear string hypothesis

Nuclear string hypothesis is one of the most dramatic almost-predictions of TGD. The hypothesis 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.

Nuclear string hypothesis leads to rather detailed predictions and allows to understand the behavior of nuclear binding energies surprisingly well from the assumptions that total strong binding energy 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. Perhaps even also weak decay characteristics could be understood in a simple manner by assuming that the stable nuclei lighter than Ca contain maximum number of alpha particles plus minimum number of lighter isotopes. Large number of stable lightest isotopes of form A=4n supports this hypothesis.

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 (see this). 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 and there is evidence for them.

**Note added**: 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 color flux tubes defining meson-like structures connecting them. 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 analogous states formed from nucleons and binding energies are predicted quite satisfactorily. Giant dipole resonance interpreted as a de-coherence of the Bose-Einstein condensate to pieces provides a unique test for the model and precise predictions for binding energies follow.

I am grateful for Elio Conte for discussions which stimulated a more detailed consideration of nuclear string model.

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

P.S. You **must** read this.

## 5 Comments:

04 02 07

"What one can definitely say that each particle is characterized by a collection of p-adic primes and one of them characterizes the mass scale of the particle whereas other characterize its interactions."(Taken from your chapter TGD and Nuclear Physics).Yes Matti:

Now that is a very interesting perspective that seems to make sense. From the traditional quantum mechanics view, each of these numbers that label an elementary particle could be seen as a degree of freedom contained in its wavefunction. To extend the notion of an extension to irrationals, let me say that since one prime labels the interactions of a particle, could the roots of this prime correspond to a more detailed explanation of the type of interaction? So for example, lets say that prime B labels spin interaction.

Will an irrational root of B label spin in the x, y or z direction?

In other words, does the irrational decomposition of the primes that label elementary particles give us more information as to the nature of the interaction?Elegant ideas Matti.

Thanks.

Dear Mahndisa,

I start by answering to a question

Are small p-adic primes important. You did not make it but it popped up in your comment in Kea's blog.Partons regarded as lightlike 3-surfaces assignable to particle as wormhole throats or lightlike boundary components are characterized by p-adic primes, typically rather large, M_127=2^127-1 in case of electron.

I have not been able to decide whether small primes should be relevant for physics in our scales. The interpretation of p-adic length scale hypothesis in the form

p=about 2^k, k a relatively small prime not larger than few hundred for largest cosmological length scales,is that there is small p(=k) p-adicity in CP_2 length scale. Very large values of Planck constants would zoom this length scale to macroscopic length scale and there would be small p p-adicity even in macroscopic length scales. This might relate to the appearance of small primes in periodicities of biological systems.

Then to the questions that you actually made.

So for example, lets say that prime B labels spin interaction. Will an irrational root of B label spin in the x, y or z direction?The most general interpretation is that p-adic primes characterize only the topologies of p-adic counterparts of these 3-surfaces and effective topologies of real 3-surfaces as well as p-adic length scale characterizing coupling constants. Hence I would not assign "roots of primes" to spin or any quantum number.

To extend the notion of an extension to irrationals, let me say that since one prime labels the interactions of a particle, could the roots of this prime correspond to a more detailed explanation of the type of interaction?I take the liberty to replace "roots of prime" with algebraic extensions of rationals in your question. Since rational primes decompose to products of primes of algebraic extensions, I have temptation to answer "yes".

Galois groups associated with extensions could act as subgroups of rotation group so that there would be a connection but at much less concrete level. For instance, the cyclic group C_n and D_2n (reflection added to C_2n) are subgroups of rotation group appear as groups associated with Jones inclusion. They have also interpretation as Galois groups in TGD framework so that Galois groups would act as rotations. More I dare not say!

The construction of S-matrix (speculation, speculation, speculation,....) leads tro the view that partonic 3-surfaces decompose into regions X^2_k such that each of them carries one number theoretic braid whose n_k strands correspond to zeros of polynomial of order n_k. Galois group for the corresponding extension of rational would act as symmetry group for X^2_k regarded as a subsystem of parton. One might say that braids inside parton define decomposition of parton to sub-constituents.

In other words, does the irrational decomposition of the primes that label elementary particles give us more information as to the nature of the interaction?There would be a hierarchy of physical states characterized by increasing dimension of algebraic extensions associated with these braids in accordance with the general vision about evolution of physical complexity as evolution of number theoretical complexity. For the simplest states one would have just single n=1-braid: maybe this applies to simplest elementary particles such as electron.

TGD clearly predicts lots and lots of new and exotic physics. The difference as compared to M-theory is that standard model symmetries emerge as preferred number theoretic symmetries. This gives a firm grasp to experimental world allowing even to say something non-trivial about nuclear physics.

Matti

04 05 07

Thanks for your explanation Matti:) Well, I like looking at small primes and how they fit into an adic description of the universe, maybe slightly differing vision than you but still compatible. I particularly enjoyed the connexion of 5-adicity to arrangement of nucleotides in DNA. As to using large primes to characterize surfaces, that makes sense too:)

04 05 07

Oh and thanks for clarifying the taking roots versus algebraic extensions. I appreciate that.

Small primes could quite well fit

in the picture even in macroscopic length scales and the hexagon in Saturn might relate to this. All is just about finding experimental evidence.

5-adicity of DNA would be of course one example of small-p p-adicity, which I forgot to mention although I almost became mad when fighting with the computer model.

I have been working with nuclear string model extensively. The model is childishly simple but extremely powerful and might do to the nuclear physics same as Bohr model for atomic physics. Yesterday evening I realized that the model predicts, and perhaps even correctly as first check suggests, giant dipole resonance energies if GDR is identified as decoherence of Bose-Einstein condensate into pieces.

This would provide VERY powerful support for the model involving p-adically scaled variants of QCD among other things! Also that graviton corresponds to same M_127 length scale as colored strings connecting ^4He nuclei in TGD Universe so that a lot is in game! There is a file only about this in my website at http://www.helsinki.fi/~matpitka/articles/nuclstring.pdf .

Matti

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