The internal structure of the neutron

 

The average size of a nucleus is about 10 fm (femtometer). Each nucleus is made up of two types of tiny globes, namely nucleons, measuring nearly 2 fm each. These are the protons and neutrons. With the proton we are lucky, because we can determine its inner structure using laboratory equipment. As a starting point for the calculation, we have the value of the magnetic moment. The other thing that is nice about protons (for scientists) is that they can be accelerated in an electric field, which is controlled by the magnetic field, making it relatively easy to handle.

 

   This is not the case with the neutron. Neutron sources are usually radioactive fissile materials. The speed and direction of the radiated particles cannot be influenced from the outside, and their detection is possible only indirectly. The internal components are generally known, but there is currently no elaborate experimental method of detecting anything about the internal structure. However, we know the magnetic moment of the neutron, which is a good basis for calculating its internal structure. It is essential, however, to assume that the interior of the neutron is in many respects identical to that of the proton. This assumption makes it possible to set up our hypothesis about the complete internal structure of the neutron based on the small volume of data available. This is why a summary of the proton was included in the first part of the dissertation. See the full text about the proton here.⁽¹⁾

 

The inner structure of the proton

 

I have already written a study with this title and described the calculation method and the results. However, I was intentionally only approximate in terms of accuracy as it was simpler and easier overview it like this. Here, I repeat the results of the calculation, but with the highest possible level of accuracy:

Proton and quarks 2018

 

 

 

 

 

  

Accuracy and reliability  Unfortunately, higher accuracy does not mean that the referenced calculation is totally reliable and accurate. Simplified hypotheses, unconfirmed regularities and neglections are hiding in the background. Without incorporating these uncertainties, however, one cannot explore the structure of the proton. It is thus necessary to review both the reliable and ambiguous basic data.

 

The three quarks  According to the literature on the subject, there are three valence quarks in the proton, namely: u  u  d. The first step is to determine the sequence in space of these three quarks. The innermost quark is a u quark (the u₁ quark) with an electrical charge of +2/3 units. In the middle there is a d quark with an electrical charge of -1/3 units. In the outside there is also a u quark (the u₃ quark) with an electrical charge of +2/3 units.

 

The spin  The spin of the particles is one of the most definite pieces of basic data. Every subatomic particle has a spin with a value of S₀=52.7285863×10^-36 kgm²/s. Composite particles may have 0 or multiple spins, but this is always due to inhibition or summation. In atomic physics, the spin is symbolized by ½, although using this abstract symbol the true meaning of the spin is somewhat obscured. The spin should actually be called angular momentum or rotational momentum. If we multiply the mass of the rotating particle by its speed and the radius of its circular orbit, then we will get a very accurate value of the s₀ spin. Let us suppose that the valence quarks, which are electrically charged, are moving on circular orbit, and we already know the radius of the orbit as well. In this case, the S₀=mcr formula will allow us to calculate with a high level of accuracy the required m weight of the orbiting quark. The combined mass of the three circling quarks must not exceed the measured mass of the proton, namely m_p=938.27211 MeV. As we saw in the table, we were able to meet this boundary condition without any problems.

 

The charge radii  There is another, well-supported part of the calculation. This is the radius of the inner sphere measured by Islam et al., namely the r = 0.20  0.44  0.87 fm values.⁽²⁾ It is no great leap of imagination to assume that the radius values are actually doubling one after the other. We will see later that we can calculate the outer circular radius  r₃  with high precision. On this basis, we can calculate the internal radii with the aforementioned doubling assumption.

 

The mass increase  Physicists have managed to measure the mass of free quarks, although the results are fairly small values: m_u = 2.01 MeV, m_d = 4.79 MeV. However, there is something that can help us, that is, the well-known effect, that near the speed of light there is a rapid mass increase, which can be calculated using the Lorentz factor: m’/m₀ = (1-v²/c²)^-1/2. It may be interesting to calculate the velocity difference Dv=c-v  through which the quark in question approaches the speed of light thus obtaining the excess mass required for the s₀ spin.

 

The magnetic moments  Let us see how the magnetic moments of the two inner quarks inhibit each other. Compared to the u₁ quark, the orbit radius of the d quark is twice as large, meaning that the area enclosed by the circular current is four times bigger. At the same time, its electrical charge and orbital frequency are only half. As regards magnetic moment, these factors precisely compensate and inhibit each other. Consequently, the calculation is based on the equality of the magnetic moment of the proton and the same for the outer u₃ quark. This condition gives us the r₃ radius of the u₃ quark orbit_. Not incidentally, this result is almost identical to the radius of the outer spherical shell measured. The quark orbits are shown in Figure 1. Figure 1 also shows the rotational directions, i.e. the two inner quarks have a positive rotation direction while the opposite is true for the outer quark. In this way, the sum of the spins results in the expected ½ value.

 

Additional information

 

The magnetic moment  Let us see how the magnetic moments of the two inner quarks inhibit each other. The orbit radius of the d quark is twice as large as that of the u₁ quark, which means that the area enclosed by the circular current is four times bigger. At the same time, the electrical charge and the number of rotations are only half. In terms of magnetic moment, these factors precisely compensate and inhibit each other.

 

The circular currents  Additional calculations also produce some remarkable numeric values. One of these is the unexpectedly high value of the circular currents created by quarks. For example, there is a constant 5,784 amp current flowing on the orbit of the outer quark. It is natural then to think of nucleons are held together by electromagnets, in this case single-turn electric coils. The currents flowing in these coils are extremely strong, and the nucleons are joined into atomic nuclei by the very powerful magnetic attractions formed in this way.

 

The centrifugal forces  An unexpected phenomenon is the excessive value of the centrifugal forces. For the outer quark, this value is 20,365 newtons, but in the inner quarks its strength is even higher.

 

The spherical shells  Although the calculations are based on a two dimensional model and appear to be all right, the quarks actually follow a spherical orbit and are similar in this respect to the atomic shells. Exploring the spherical shells in three dimensions is, of course, not possible, as it is necessary to take into account the 4^th or even more dimensions. Our geometric knowledge currently lacks the necessary means of working with or even understanding these extra dimensions.

 

   After all, the known international calculations about the size of the proton still differ, although they are fairly close to each other. Let us look at some of these calculations:

 

r_p = 0.8418467 [fm]    96.0%              Tony Skyrme, 2010, calculation

r_p = 0.8768 [fm]          100%               CODATA Committee, 2006

r_p = 0.87 [fm]              99.2%              Islam et al., 2009, measurements

r_p = 0.8810410[fm]    100.5%            Tom Tushey, 2017, calculation

 

 

The internal structure of the neutron

 

What we know for certain about neutrons is that they are electrically neutral, and their main mass is also made up of three valence quarks. An additional 20% of mass comes from the so-called sea quark. However, the composition of quarks in the neutron differs from that of the proton, namely: u  d  d. It is generally believed that the size of the proton is the same as that of the neutron. We will see, however, that the neutron is calculated to be 37% larger than the proton. Considering the small number of atomic models known so far, this does not cause any problems because smaller protons fit well beside larger neutrons. This is because the radius of the neutron is 1.2069892 fm. Presumably there also are three shells in the neutron, but they have not been detected or weighed so far. As a result, we have significantly less control data to help us detect the internal structure of the neutron, whereas for the proton we have a fair amount of data available.

 

   If we want a chance to really solve the problem, we have to make two assumptions. Namely, the inner u₁ quark and the middle d₁ quark rotate on the same orbit as they do in the proton. Without these assumptions, I see no hope of revealing the inner structure of the neutron in the coming decades. This location of the two inner quarks makes the question about magnetic moments very easy to answer. As we observed with the proton, the two inner quarks exactly inhibit each other's magnetic moment. As for the calculation, it remains the outer d₃ quark with its magnetic moment that determines the magnetic moment of the neutron:  T_d3=T_n. The magnetic moment of the neutron is a known value: T_n=-9.66236×10^-27 Am².

 

 

   Based on the above, the radii of the two inner quark orbits can be the same as those considered for proton-related calculations. These values are approximately r₁=0.22 fm and r₂=0.44 fm. The electrical charge and the necessary magnetic moment of the d₃ quark are known. Therefore, it is easy to calculate the radius of the circular path, which finally proves to be r₃=1.20698929 fm. (See Figure 2.) However, other data in the table below can be calculated in a similar way to the calculation used for the proton.

 

 

Neutron and Quarks 2018

 

 

 

 

Finally, let us try to answer the unusual question of how a lonely neutron spontaneously transforms into a proton. In the 1930s the renowned physicist Paul A.M. Dirac discovered that the vacuum is filled with virtual electrons and positrons. The charge of the virtual positron is 1 unit (the same as for the real positron), but it has 0 energy and 0 mass. If such a +3/3e charge virtual particle connects to the -1/3e charge of the neutron’s outer d₃ quark, then a +2/3e charge u quark is generated. However, the currently existing r₃ = 1.20 fm radius is too large for the u quark. Therefore, the freshly generated u quark returns to its stable 0.88 fm radius orbit. Meanwhile, the magnetic moment of the particle becomes +14.1×10^-27 Am². The charge of the electron generated during the process comes from its virtual counterpart, i.e. the positron, while its actual material may be taken from the sea quark.

 

   There is a similar, broadly accepted, nucleon transformation in astronomy. Inside the Sun, at huge pressures, despite the repulsive forces, two protons sometimes conglutinate. It is amazing, but at such times one of the protons turns into a neutron. It can be assumed that the first step of the transformation is the “borrowing” of a virtual particle from the vacuum. In this case, the said particle is a virtual electron with -3/3e charge.

 

   Neutron stars also support such surprising, or even extreme, information about the proton. For example, the centrifugal force of the outermost d₃ quark is 10,851 newtons. Based on this and the neutron surface, we can calculate the pressure, and it turns out that the neutron can withstand a pressure of 10³³ pascals. The enormous pressure in neutron stars crushes the atomic electron shell, but it cannot destroy the outer spherical shell of the neutrons.

 

   In light of this, we would expect that based on the unconfirmed assumptions or missing data the results included in the table are rather uncertain or can even take multiple values. If we look at the basic data, their amount also seems to be insufficient: u, d, d quarks,  T_n  m_n  m_u0  m_d0  1/3e  S₀  c. It was surprising to me also that I was able to create only this single version. If no one else can find a new acceptable configuration, then this will make very likely that we have actually identified the inner structure of the neutron. Let us hope that Nature was using this logic as well!

 

15 August 2018

Tom Tushey

independent researcher

tom.tushey@gmail.com

 

 

References:

⁽¹⁾   Infinite Energy ISSUE 132. MARCH/APRIL 2017

⁽²⁾   Islam, M. et  al. December 2009, „Picturing the proton by elastic scattering”
      http://cerncourier.com/cws/article/cern/41014

  

Oldal: The internal structure of the neutron
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