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The Internal structure of protons and neutrons

An average nucleus is about 10 FM (femtometres) in size but is made up of two types of balls, each nearly 2 FM in size. These are called protons and neutrons. We are lucky with the proton because we have been able to measure its internal structure in experimental facilities. We also have the magnetic moment of the proton, T=14.10606630*10-27 Am2. The proton has the pleasant property that it can be accelerated in an electric field and controlled by a magnetic field, so it is relatively easy to handle. This is not the case for the neutron. The neutron source can only be radioactive fissile material and cannot be trapped in its path. The speed and direction of the ejected particles cannot be controlled from the outside, and their detection is very difficult. At present, there is no way to measure their external size, let alone detect their internal structure.

The internal structure of a proton

I have previously written a paper with this title(1), which describes the method of calculation and the results but is intended only to an approximate degree. The reduced precision was intended for simplicity and clarity. I will now repeat the results of the calculation here with the highest precision available:

Proton and quarks 2018   

                    Quarks                                    r                     radius       10-15                     {m}                                    Tp                     10-27                     {Am2} magnetic moment                                    f                     1023                     {Hz}                     frequency                                                         {A}                                                              circular                      current                                                         {fm}                      wavelength                                    m                     mass {MeV}                                    c-v                                    {m/s}                
                    u1                                    0,22026025                                    3,52651658                                    2,17                                    23138                                    1,38                                    447,94052                                    11953                
                    d2                                    0,44052051                                    -3,52651658                                    1,08                                    5784                                    2,77                                    223,97026                                    74714                
                    u3                                    0,88104101                                    14,10606630                                    0,54                                    5784                                    5,54                                    111,98513                                    191306                
                    Amount:                                                                             -                                    14,10606630                                    -                                    -                                    -                                    783,89591                                    -                
                    Proton:                                                                             0,88104101                                    14,10606630                                    -                                    -                                    -                                    938,27211                                    -                
                    Difference:                                                                             -                                    0                                    -                                    -                                    -                                    154,37620                                    -                

Unfortunately, the term "greater accuracy" does not mean that the calculation referred to is reliable and accurate. It hides simplistic hypotheses, unconfirmed regularities, and omissions. However, without applying these uncertainties, it is not possible to get from one to two in the exploration of the structure of the proton. It is, therefore, necessary to review both the reliable and the uncertain handholds.    

   The spin, the so-called purity of the particles, is one of the most reliable handholds of the calculation. All subatomic particles have spin, S0=52.7285863*10-36 kgm2/s. In nuclear physics, the symbolic notation for the spin is 1/2, although the meaning is then obscured. (Composite particles can have 0 or more spin, but in this case, there is always a case of extinction or condensation.) If we multiply the mass of an orbiting subatomic particle by its velocity and the radius of its orbit, we should obtain the exact value of the spin with strict precision. Suppose that electrically charged valence quarks orbit at close to the speed of light, and we know the radius of the orbit too. In this case, we can calculate the mass m of the orbiting quark from the formula S0=mcr with high precision. The total mass of the 3 quarks in the proton cannot exceed the mass of the proton mp=938.27211 MeV. As we will see later, this condition was met without any problems.


   Mass increase Physicists estimate the mass of free quarks to be between 2 and 4 MeV. However, near the speed of light, there is a rapid increase in mass, which can be calculated using the Lorentz factor (m'/m0=(1-v2/c2)-0,5). From the calculated data, we can obtain the velocity difference Δv=c-v with which a given quark approaches the speed of light and gains excess mass. The quark masses at rest are u=2.01 MeV, d=4.79 MeV.(2)    

   Three quarks Now determine the order of the 3 valence quarks orbiting inside the proton. Inside there is a quark u (quark u1) with an electric charge of +2/3 units. In the middle is a d quark with a charge of -1/3 units. Outside is also u quark (a quark called u3), also with an electric charge of +2/3 units.    

    Measurement results There is one well-supported part of the calculation, and that is the radius of the 3 inner spheres measured by Islam et al: r=0.20 0.44 0.87 FM. (3) It doesn't take much imagination to assume that the values of the rays are doubled. If the order of the quarks is u d u, then the magnetic moments of the inner and middle quarks cancel each other out. In this case, only the outer quark gives the magnetic moment of the proton.    

   Magnetic momentum The calculation is then based on the equation of the magnetic moment of the proton and the magnetic moment of the outer quark u3. From this condition, the radius r3 of the orbit of the u3 quark is given. Its value corresponds to the radius of the outer sphere measured in the experiment. The arrangement of orbits and quarks is shown in Figure 1.    

More details 


 The magnetic moment Let's see how the magnetic moment of the two inner quarks cancels each other out. Compared to the u1 quark, the radius of the orbit of the d quark is twice as large, so the area enclosed by the circular current is four times as large. However, its electric charge and orbital number are only half. These factors exactly balance and cancel each other out in terms of the magnetic moment.    

   Spin equilibrium The spin of the proton is known to be 1/2, and this value is released by the inner two quarks orbiting in one direction, while the outer one orbits in the opposite direction. The proton's 1/2 spin is ok. The two inner quarks orbit in the same direction is the orbit, while the outer quarks are orbit in the opposite directions. This in turn gives a spin of 2/2 due to the addition of the spins. The outer quark u3 orbits in the opposite direction, so its spin of 1/2 is subtracted from the previous value. The result of the sums gives the well-known spin value of the proton, 1/2.  


   Circular flows Further calculations yield some more remarkable numerical values. One of these is the unexpectedly large value of the circular currents produced by quarks. For example, the orbit of the outer quark has a continuous current of 5784 amperes. It is then natural to think that nucleons are held together by electromagnetic forces. In the single filament coils, extremely strong currents circulate and the nucleons are bound together by the extremely strong magnetic attractions that are created by the atomic core.    

   Centrifugal forces Another unexpected phenomenon is the excessive value of centrifugal forces. This is 20365 newtons for the outer quark and even higher for the inner quark. Although the calculations are done in a plane and look ok, the quarks cover a spherical orbit, and in this, they resemble the electron shells of an atom. These tracks can only be accessed by using the 4th dimension.    After all, the international calculations of the size of the proton that have been known so far are different, but they are close enough. Let's look at the results of the relevant calculations, which have some uncertainties. Here are a few:    

rp = 0.8418467 {fm}, 96.0%, Tony Skyrme, calculation, 2010  

rp = 0.8768 {fm}, 100%, CODATA Commission, 2006  

rp = 0.87 {fm}, 99.2%, Islam and mts measurement, 2009  

rp = 0.8810410 {fm}, 100.5%, Tom Tushey, calculation, 2017  

The internal structure of the neutron

All that is known for sure about the neutron is that it is electrically neutral, and its main mass is also made up of 3 valence quarks. (This is supplemented by 20% of so-called sea quarks.) However, the composition of the quarks is different from that of the proton, namely u d d. The final result of the calculation will show that the neutron is 37% larger than the proton, the radius of the neutron is 1.2069892 FM. The radius of the neutron is 1.2069892 FM. This does not cause any confusion for the nucleus model, because the smaller protons fit well next to the larger neutrons, Presumably, there are 3 spherical shells inside the neutron too, but these have never been detected and measured. As a consequence, we have significantly fewer control data to reveal the inner structure than we had for the proton.

   To have any chance of solving the problem, we have to make two insecure assumptions. Namely, that the inner u1 quark and the central d1 quark orbit in the same way as they do in the proton. As we will see below, there is a good chance. Without assumptions, I see no hope for exploring the interior of the neutron in the coming decades. The arrangement of the two inner quarks in this way provides a huge relief in terms of magnetic moments. Because in this case they exactly cancel each other out. For the calculation, we are left with the outer quark d3, whose magnetic moment determines the magnetic moment of the neutron: Td3=Tn, while the magnetic moment of the neutron is already known: Tn=-9.66236*10-27 Am2.

   As shown above, the radius of the orbits of the inner two quarks is simply taken from the proton calculation. Their values are approximately r1=0.22 FM, r2=0.44 FM. Knowing the electric charge and the required magnetic moment of the quark d3, it is easy to calculate the radius of the orbit, which finally comes to r3=1.20698929 FM. (See Figure 2) The other data in the table below are calculated in the same way as for the proton.

Neutrons and quarks 2018 

                    Quarks                                    r                     radius 10-15                     {m}                                    Tn                     10-27                     {Am2}  magnetic moment                                    f                     1023                     {Hz}                     frequency                                    I                     {A}  circular current                                                         {fm}                      wavelength                                    m                      mass {MeV}                                    c-v                                    {m/s}                
                    u1                                    0,22026025                                    3,52651658                                    2,17                                    23138                                    1,38                                    447,94052                                    11953                
                    d2                                    0,44052051                                    -3,52651658                                    1,08                                      5784                                    2,77                                    223,97026                                    74714                
                    d3                                    1,20698----                                    -9,66236000                                    0,40                                      4222                                    7,58                                    81,74347                                    561347                
                    Amount:                                                                             -                                    -9,66236000                                    -                                    -                                    -                                    753,65425                                    -                
                    Proton:                                    1,20698----                                    -9,66236000                                    -                                    -                                    -                                    939,56551                                    -                
                    Difference:                                                                             -                                    0                                    -                                    -                                    -                                    185,91126                                    -                

   Finally, we try to answer the unusual question of how an alone neutron spontaneously transforms into a proton. As early as the 1930s, the famous physicist P. A. M. Dirac suggested that a vacuum is filled by virtual electrons and positrons. The charge of a virtual positron is also equal to unity (e), like that of a real positron, but it has 0 energy and 0 mass.

   When such a particle with a charge of +3/3e is added to the -1/3e charge of the d3 quark, u quark with a charge of +2/3e is produced. However, the current orbit of radius r3=1.20 FM is too large for u quark. Therefore, the newly formed u quark might take matter from the neutron sea and then emit energy and particles back to its stable orbit of radius 0.88 FM. During this process, the magnetic moment of the particle takes on a value of +14.1*10-27 Am2.

   A similar nucleon transformation exists and is essentially accepted in astronomy. Inside the Sun, two protons are occasionally squeezed together by high pressure, despite repulsive forces. Shockingly, one of the protons is then converted into a neutron. The first step in the transformation is presumably the pick-up of a virtual particle from the vacuum. In this case, the particle is a virtual electron with a charge of -3/3e, which is the basis of the transformation process. Incidentally, neutron stars also support the surprising and extreme data for the proton. For example, left out of the table, but interesting would be the centrifugal force of the 3 quarks that are being resisted by some unknown vacuum force. This is for the outermost d3 quark Fd3 cantrip = 10851 newtons. If we determine the pressure per 1 m2 from this number, it can withstand ~2*1033 pascals of pressure. The enormous pressure of a neutron star can collapse the electron shell of an atom, but it cannot collapse the outer shell of a neutron quark.

   In hindsight, it was a lucky choice to leave the radius of the two inner quarks unchanged. This meant that only the outer quark had to be transformed and its orbit changed, while the nucleon's interior remained unchanged. The virtual electron left behind in the vacuum also receives matter and energy from the transforming neutron and leaves the site as a complete electron.

   From what has been said, one would expect that the results of the table may be rather uncertain and even ambiguous due to unconfirmed assumptions or missing data. If we look at the initial data, the amount of data seems to be insufficient: u, d, d quarks, Tn mn mu0 md0 1/3e S0 c. However, it was surprising to me that I was able to construct only this single variation. If no one else can come up with another arrangement, likely, we have indeed found the internal structure of the neutron. Let us hope that Nature once followed this logic.


Tom Tushey 

Mechanical engineer 

Hobby physicist 

Scientific writer