This note gives the complete theory of Ni(64) p interaction inside and outside the Ni(64) nucleus, modelled as a charged sphere as is customary in nuclear physics. Without the m force there is no explanation for LENR in the old physics. However with the m force, the reaction can be explained straightforwardly. The m force also plays a key role in the nuclear strong force theory that binds neutrons and protons inside a nucleus. It is shown that only 3.13 ten power minus 6 % of the Ni(64) transmutes to Cu(63), with the loss of a proton. This explains why only traces of copper are found. This mass loss translates into the visible frequency as observed. If all the Ni(64) transmuted to Cu(63) the radiation emitted would be in the very harmful hard gamma ray region and no nickel would be left. It would all have changed to copper. This is not observed, no gamma rays are emitted in a low frequency nuclear reaction, otherwise LENR devices would not have been granted safety certificates and patents.in many countries on LENR taken out by governments and corporations. To get a LENR reaction going needs a lot of skill and experience, but by matching the net m force to forces in nuclear theory, such as Yukawa, Woods Saxon, Reid and more recent models, an idea can be obtained of which parameters to vary to optimize the reaction. The patents give a lot of detail of how the LENR devices work.

## Note 432(2)

February 20, 2019## UFT 431,3, preliminary version

February 20, 2019This is a very good summary by GJE, the attractive force between neutron and proton in m theory is the attractive m force inferred in UFT417 from Euler Lagrenge analysis and from Hamilton analysis in UFT427. The two classical dynamics systems gave the same m force. This m force can become infinite at the resonance condition, even if a proton near a nucleus such as Ni(64) is not moving. The experimenter designs the conditions under which the force becomes infinite by using the techniques described here by GJE. After Chadwick discovered the neutron, theories were proposed by Dirac, Heisenberg and Fermi to explain how a nucleus could be made up of neutrons and protons. Fermi suggested an exchange force, and Yukawa inferred that the exchanged particle was the meson, or pion, with finite mass. The m theory explains the production of the pion by identifying the m force with the Yukawa force. The m force can explain any exchange particle by identifying it with forces derived from other potentials, such as the Reid potential. However the m force is the most fundamental force because it is a property of space itself. The difference between the Cockcroft Walton experiment and low energy nuclear fusion is the relativistic momentum of the proton. Without resonance the proton has to have a very high relativistic momentum to overcome the Coulomb barrier. With resonance this is not needed and low energy nuclear reaction takes place. In LENR no gamma rays are emitted by observation and many Government and corporate patents and safety certificates. In the atom smashing experiments gamma rays are emitted. For example the collision of a very high energy electron and positron produces two photons at gamma ray frequency and particle annihilation takes place (see UFT247 and UFT248). In low energy nuclear reactions there are no gamma rays because the incoming proton may be static, and the nickel nucleus may be static. In other words nickel powder immersed in hydrogen gas. The binding energy in LENR is released in the form of heat and very intense visible and ultra violet radiation emitted by nickel vapour. In the standard model the force between neutrons and protons is a residual force of an even stronger force that binds quarks together. The big problem with the standard model is that quarks have never been observed in the free state. Only hadrons are observed. The nuclear strong force between protons and neutrons is different from the QCD strong force between quarks. The attractive nuclear strong force between neutrons and protons decreases rapidly with distance and the Coulomb repulsion between protons decreases less rapidly. So heavy nuclei are unstable, notably radium and uranium 235. The Ni(64) isotope is overloaded with neutrons, it is the isotope with the highest number of neutrons. The extra proton makes it unstable, and it transmutes into copper 63, mega electron volts of energy and other particles. It is worth developing the m force with various dm(r)/ dr and m(r). The m force inside the nucleus might become positive at short distances and at resonance the nucleus disintegrates. If the m force is negative at resonance the nucleus becomes very tightly bound.

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## UFT 431,3, preliminary version

February 19, 2019Thanks again! The well known Schroedinger quantization of the Yukawa potential in m space should result in extra structure in analogy with the procedure that led to the Lamb shift in previous work. I will look at this next.

## UFT 431,3, preliminary version

February 19, 2019This is full of interest and an important and clear numerical and graphical demonstration of how low energy nuclear reactions can take place without having to accelerate protons with a Cockroft / Walton generator using 750,000 volts, or a heavy hadron collider. This section has all kinds of important results, and makes a first attempt at understanding how the space parameters m(r) and dm(r) / dr can be related to physical quantities such as surface thickness of the nucleus in a model potential such as the 1954 Woods Saxon potential also used in UFT226 ff. I have only one comment, In Eq. (22) it should be m(r) in the numerator and not m(r) power half. See for example Eq. (11) of UFT417, where the force is F sub 1 = – mMG / r1 squared + ……., where r1 = r / m(r) power half. Horst also succeeds in solving the differential equation at r = R for m(r) and dm(r) / dr of the Woods Saxon potential. Similarly there will be m(r) and dm(r) / dr parameters for any potential used for nuclear physics, notably the Yukawa potential, Reid potential and so on. Some numerical work along these lines has already been done for UFT432, Note (1).

This is the preliminary version of section 3 of UFT 331. I found some

force resonances for special functions m(r). I will add a section on the

solution of the nuclear wave equation. This will give hints how to

compute the mass spectrum of elementary particles.

Horst

## The m theory of all nuclear forces and LENR reactions

February 19, 2019Many thanks, agreed with the typo’s. The graphics of the Yukawa force look very interesting, it is a scaled Coulomb force, and is also used used in the theory of finite photon mass. The photon with mass is a massive boson, and the pion is also a massive boson. To answer the point about partial f / partial r1, I suggest running Eq. (18) through the computer and it should give Eq. (17) using partial f /partial r1 = partial f /partial r partial r / partial r1 where f is a function of r1. Eq. (17) shows that the Yukawa force becomes infinite at the resonance point 2m(r) = r dm(r) / dr. In low energy nuclear reactions the Yukawa force attracts the proton to the Nickel 64 atom, and the Coulomb barrier is overcome at the resonance condition. Inside the nucleus the Yukawa force can become very large at the resonance point. Eq. (17) is a differential equation for dm(r) / dr and m(r) of the Yukawa potential. The Yukawa force becomes very large as r approaches zero. So the pion can be thought of as being the result of a particular space defined by dm(r) / dr and m(r) of the Yukawa potential The force due to the Reid potential (25) also gives rise to its own dm(r) / dr and m(r). So one can begin to think of a strong force made up of these space parameters. The present day quarks can be replaced by space parameters dm(r) / dr and m(r).

he m Theory of all nuclear forces and LENR reactionsTo: Myron Evans <myronevans123>

I evaluated the note by computer. The Yukawa force, derived from the Yukawa potential, is shown in section 1 of the protocol. It contains several terms, but the graph shows that it is very similar to the negative of the Coulomb force, while we have to take in mind that the Coulomb force is not valid within the nucleus. I used g=mu=1 for the plot and otherwise atomic units, so the Coulomb potential energy is in Hartrees.

Horst

Am 18.02.2019 um 11:58 schrieb Myron Evans:

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## The Coulomb Barrier in m Space

February 18, 2019This should be the potential Z sub 1 Z sub 2 m(r) power half / (4 pi epsilon sub 0 r) in frame (r, phi).

## The m theory of all nuclear forces and LENR reactions

February 18, 2019The theory is exemplified with the Yukawa potential between the proton and neutron which inferred the existence of the meson, an exchange particle of quantum field theory later renamed the pion after its discovery in 1947. The Yukawa force (or any model of nuclear force) may be expressed as Eq. (23) or Eq. (24), so the pion is understood in terms of the most general spherically symmetric space (m space) so are all elementary particles. It follows that the quark gluon model can also be so understood and hopefully greatly simplified. There are many empirical models of the nuclear potential and the Reid potential is given as an example.

## Plans for UFT432

February 18, 2019These are to apply m theory to the nuclear force, which is the force that exists between protons and neutrons in a nucleus. It is powerfully attractive at about one femtometre (fm), but rapidly decreases to zero at about 2.5 fm. At less than 0.7 fm it becomes positive and determines the size of a nucleus. It is described by potentials which are used in the Schroedinger equation. All these potentials can be described in terms of the m(r) of the m theory, for example Yukawa, Woods Saxon (1954), Reid (1968), Paris, ArgoneAV18, CD-Bonn and Nijmegen potentials. By 1935, it was known that the nuclear force is mediated by mesons, which were discovered experimentally in the forties. The first quantum theory of the nucleus was developed by Heisenberg and Dirac, shortly after the discovery of the neutron by Chadwick in the Rutherford group in 1932. At the same time in the same group, Cockroft and Walton split the lithium atom. In the sixties and seventies the nuclear force became to be regarded as a residual effect of the strong force binding quarks with gluons to form the nucleons (protons and neutrons). The quarks are held together with colour charge, analogous to electric charge, but much stronger. It is known from immediately preceding papers that the quantum m theory introduces detail into the Dirac equation such as the Lamb shift, and also explains vacuum polarization, the anomalous g factor of the electron and the Casimir force all in terms of one coherent m theory, part of the well known Einstein Cartan Evans (ECE) unified field theory, the first successful unified field theory and accepted by millions around the world. In UFT431, low energy nuclear reactions were explained using the m force, and its ability to resonate. The theory can therefore proceed exactly along the lines of UFT417 and UFT427, but with the Coulomb potential of those papers replaced by the nuclear potentials. Relativistic quantum m theory will then inject more detail into nuclear structure than hitherto known. It may be possible to make the quark gluon theory obsolete and replace it with m theory. That would be a much needed simplification because it would get rid of quantum chromodynamics with all its artificial contrivances such as renormalization, regularization, asymptotic freedom and so on. Both Dirac and Feynman rejected renormalization, so do many others. Chadwick was the son of a weaver and a domestic servant, and became a C. H., a Knight and recipient of the Copley Medal for his discovery of the neutron, and Fellow of Gonville and Caius College Cambridge. He won a scholarship to go to a grammar school, but his parents could not afford even the residual costs, so he went to another Grammar School. He walked four miles to University every day, and four miles back, living at home. Dirac was the son of an immigrant from St. Maurice, Switzerland.