*Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like*describing the anomaly is here.

^{140}Pr and^{142}Pm Ions
* We report on time-modulated two-body weak decays observed in the orbital electron capture of hydrogen-like ^{140}Pr^{59+} and ^{142}Pm^{60+} ions coasting in an ion storage ring. Using non-destructive single ion, time-resolved Schottky mass spectrometry we found that the expected exponential decay is modulated in time with a modulation period of about 7 seconds for both systems. Tentatively this observation is attributed to the coherent superposition of finite mass eigenstates of the electron neutrinos from the weak decay into a two-body final state.*

This brings in mind the nuclear decay rate anomalies which I discussed earlier in the posting Tritium beta decay anomaly and variations in the rates of radioactive processes. These variations in decay rates are in the scale of year and decay rate variation correlates with the distance from Sun. Also solar flares seem to induced decay rate variations.

The TGD based explanation relies on nuclear string model in which nuclei are connected by color flux tubes having exotic variant quark and antiquark at their ends (TGD predicts fractal hierarchy of QCD like physics). These flux tubes can be also charged: the possible charges +,-1,0. This means a rich spectrum of exotic states and a lot of new low energy nuclear physics. The energy scale corresponds to Coulomb interaction energy α_{em}m, where m is mass scale of exotic quark. This means energy scale of 10 keV for MeV mass scale. The well-known poorly understood X-ray bursts from Sun during solar flares in the wavelength range 1-8 A correspond to energies in the range 1.6-12.4 keV -3 octaves in good approximation- might relate to this new nuclear physics and in turn might excite nuclei from the ground state to these excited states and the small mixture of exotic nuclei with slightly different nuclear decay rates could cause the effective variation of the decay rate.

The question is whether there could be a flux of X rays in time scale of 7 seconds causing the rate fluctuation by the same mechanism also in GSI experiment. For instance, could this flux relate to synchrotron readiation. Maybe not. In any case, the prediction is what might be called X ray nuclear physics and artificial X ray irradiation of nuclei would be an easy manner to kill or prove the hypothesis.

One can imagine also another possibility.

- The first guess is that the transitions between ordinary and exotic states of the ion are induced by the emission of exotic W boson between nucleon and exotic quark so that the charge of the color bond is changed. In standard model the objection would be that classical W fields do not make sense in the length scale in question. The basic prediction deriving from induced field concept (classical ew gauge fields correspond to the projection of CP
_{2}spinor curvature to the space-time surface) is however the existence of classical long range gauge fields- both ew and color. Classical W field can induce charge entanglement in all length scales and one of the control mechanisms of TGD inspired quantum biology relies on remote control of charge densities in this manner. - In the approximation that one has two-state system, this interaction can be modelled by using as interaction Hamiltonian hermitian non-diagonal matrix V, which can be written as Vσ
_{x}, where σ_{x}is Pauli sigma matrix. If this process occurs coherently in time scales longer than hbar/V, an oscillation with frequency ω= V/hbar results. Since weak interactions are in question, 7 second modulation period for rate might make sense.

The hypothesis can be tested quantitatively.

- The weak interaction Coulomb potential energy is of form
V(r)/hbar= α

_{W}exp(-m_{W}r)/r,where r is the distance between proton center of mass and the end of color flux tube and therefore of order proton Compton length r

_{p}so that one can writer= x× r

_{p}.where x should be of order unity but below it.

- The frequency ω = 2π/τ= V/hbar must correspond to 14 seconds, the oscillation period which is twice the modulation period of the reaction rate. By taking W boson Compton time as time unit this condition can be written as
α

_{w}exp(-y)/y = t_{W}/τ ,y= xr

_{p}/r_{W}= xm_{W}/m_{p}∼ 80× x , α_{w}= α_{em}/sin^{2}θ_{W}. - This gives the condition
exp(-y)/y = (t

_{p}/τ)×sin^{2}θ_{W}/(80×α)allowing anyone possessing MATLAB and skills given by first year course in calculus to solve y since the left hand side is known. Feeding in proton Compton length 1.321×10

^{-15}m and sin^{2}θ_{W}=.23 one obtains that the distance between flux tube end and proton cm is x=.6446 times proton Compton length, which compares favorably with the guess x∼1 smaller than 1. One must however notice that the oscillation period is exponentially sensitive to the value of x. For instance, if the charge entanglement were between nucleons, x>1 would hold true and the time scale would be enormous. Hence the simple model requires new physics and predicts correctly the period of the oscillation under very reasonable assumptions. - One could criticize this by saying that the masses of two states differ by amount which is of order 10 keV or so. This does not however affect the argument since the mass corresponds to the diagonal non-interaction part of the Hamiltonian contributing only rapidly oscillating phases whereas interaction potential induces oscillating mixing as is easy to see in interaction picture.
- If one believes in the hierarchy of Planck constants and p-adically scaled variants of weak interaction physics, charge entanglement would be possible in much longer length scales and the time scale of it raises the question whether qubits could be realized usin proton and neutron in quantum computation purposes. I have also proposed that charge entanglement could serve as a mechanism of biocontrol allowing to induce charge density gradients from distance in turn acting as switches inducing biological functions.

So: it happened again! Again I have given good reason for my learned critics to argue that TGD explains everything so that I am a crackpot and so on. Well... after a first feeling of deep shame I dare to defend myself. In the case of standard model explanatory power has not been regarded as an argument against the theory but my case is of course different since I do not have any academic position since my fate is to live in Finland (still no seminar, colloqium, popular journal article, or public comment about CDF anomaly by any academic theoretical physicist in Finland!). And if my name were Feynman, this little argument would be an instant classic.

In fact it occurred to me that my critics (usually those brave "Anonymous" of blogs- last time in Resonaance- whose contributions as a rule contain zero bits of information) could go through the argument and publicly demonstrate what he believes to be the fatal error. Maybe we could even make a bet. If the critic does not find error he pays 1000 euros. If he finds the error, I pay it. In this case Anonymous should however reveal his name. Some third party revealing also his name would serve as a judge!

For background see chapters TGD and Nuclear Physics (periodic nuclear rate variations in the scale of year) and Nuclear String Hypothesis (GSI anomaly) of "p-Adic length scale Hypothesis and Dark Matter Hierarchy".

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