PART 2
ELEMENTARY PARTICLE SPATIAL MODELS
of ATOMIC NUCLEI
10. INTRODUCTION TO NUCLEI AND HYDROGEN BURNING
The Elementary Particle Spatial Models (EPSMs) in Part 1 were developed for the proton and neutron. It is natural to test these EPSMs by using them to make the atomic nuclei that the protons and neutrons form. The main purpose of Part 2 is to show that plausible, not definitive, atomic nuclei EPSMs can be developed and hence to provide more credibility to the model developed in Part 1.
An atomic nuclide is an atomic species with a nucleus composed of a specified number of protons and neutrons. The elements are determined by the number of protons; e.g., all carbon atoms have six protons and all oxygen atoms have eight protons. The number of neutrons determines the isotope of that element. Stable carbon can have either six or seven neutrons. Unstable carbon also exists such as carbon-14 where the 14, the mass number, is the total of the protons (6) and neutrons (8). The specific isotope will be abbreviated, as shown in this example for carbon, either as 6C14, as C-14, or as carbon-14.
Nuclei can undergo several types of decays or reactions. Beta decay is the release of either an electron or a positron. Some nuclei can also capture an orbiting electron and this is called electron capture. In alpha decay the nucleus releases a helium-4 nucleus and in fission the nucleus splits into two large pieces. A nucleus can also release or capture a neutron. Man-made reactions and those in the stars include even more reactions. Like alchemy most of these decays and reactions result in a change from one element to another element.
The synthesis of the various atomic nuclei within the stars from hydrogen has been postulated to occur in six processes which are:
1. Conversion of hydrogen to helium by "hydrogen burning"
2. Conversion of helium to carbon, oxygen, etc., by "helium burning"
3. Production of nuclei with 16 ² mass number, A ² 28 by "carbon, oxygen, and neon burning"
4. Production of nuclei with 28 ² A ² 60 by "silicon burning"
5. Production of nuclei with 60 ² A by the "s-, r-, and p-processes"
6. Production of the light nuclei H-2, Li, Be, and B by the "l-process"
HYDROGEN
Hydrogen-1, H-1, 1H1 (99.985%) (spin 1/2 , parity +1)
Hydrogen-1 makes up 99.985% of the hydrogen in nature. The proton has a spin 1/2 and has an even parity (+1). The EPSM for hydrogen nucleus, 1H1, is simply the proton EPSM that was developed in Part 1 of this effort. Figure 2-1 shows two representations of the proton EPSM. The one on the left shows all of the internal bonds within the proton while the one on the right shows only the free dimensionalities marked. The latter presentation will be used throughout Part 2. Both EPSM presentations retain the orientation of the dimensionalities as it was developed in Part 1; however, the orientation will soon change slightly to best suit photographing the structures that come out of EPSM for the nuclei.
Figure 2-1: Hydrogen, 1H1, EPSM or the proton EPSM. The presentation on the right is a simplified version of the one on the left which was developed in Part 1. In the simplified version only the free dimensionalities for the proton are shown.
Hydrogen-2, H-2, 1H2 (0.015%) (spin 1 , parity +1)
Hydrogen-2, or deuteron (D), is the only other stable isotope of hydrogen and the nucleus consists of one proton and one neutron. First, Figure 2-2 shows the neutron EPSM as it was developed in Part 1 and the simplified presentation with only the free dimensionalities of the "electron" and "proton" segments marked. Figure 2-3 shows the hydrogen-2 EPSM. All "connecting" neutrinos have been omitted as they will be throughout most of Part 2 of this effort. The electric charge can be seen to be (4-1)/3 ecu = +1 ecu as expected. The spin is 1; thus, the proton and neutron spins are considered to be parallel or 1/2 + 1/2 = 1.
Figure 2-2: Neutron EPSMs. The presentation on the right is a simplified version of the one developed in Part 1. Only the "proton" and "electron" free dimensionalities are shown for the neutron.
The hydrogen-2 EPSM shown in Figure 2-3 has the dimensionalities in the standard orientation used in Part 1 and up to now in Part 2. A switch to the new presentation is made here for photographic convenience. The new presentation is very similar to the current one except that the top is rotated away from the viewer. In reality only the angle at which the pictures are taken has changed. What is important is that the dimensionalities are still perpendicular to each other and the nucleons still have the same relative positions. Figure 2-4 shows the second presentation which will be used in Part 2 for the hydrogen-2 EPSM. It may appear for this relatively simple nucleus that the change was not worth the effort; however as the structures get larger, the new presentation allows the EPSMs to be photographed easier.
Figure 2-3: Hydrogen-2 EPSM.
Figure 2-4: Hydrogen-2 EPSM shown in revised orientation. The change in orientation is only slight but it does result in more ease in photographing the larger nuclei EPSMs.
Hydrogen-3, H-3, 1H3 (12.3 y : e-) (spin 1/2 , parity +1)
Hydrogen-3, or triton (T), is an unstable isotope of hydrogen and decays with a 12.3 year half-life by beta -1 decay which is an electron that comes from the nucleus. The H-3 nucleus consists of one proton and two neutrons. The two possible H-3 EPSMs are shown in Figure 2-5. The e- decay mode of H-3 indicates that the EPSM on the right in Figure 2-5 is the correct one because the e- particle ("electron" ESU segment) and connecting neutrino (not shown) are available for beta decay.
The beta particles are either electrons or positrons can be represented by the Greek letter, b- , b+ or as e-, e+. The latter will be used here in this internet presentation.
There is a plane of symmetry to the H-3 EPSM which may imply an even parity. H-3 has spin 1/2. Thus, the added neutron spin 1/2 was subtracted from the H-2 spin 1 when the neutron was added to H-2 to form H-3. (Could the H-3 on the left side of Figure 2-5 have spin 3/2?)
Figure 2-5: Two possible hydrogen-3 EPSMs. The EPSM on the right is supported by the fact that hydrogen-3 undergoes beta decay. The electron ESU segment can be easily removed.
HELIUM
Helium-3, He-3, 2He3 (0.000138%) (spin 1/2 , parity +1)
As previously stated, the hydrogen-3 nucleus decays by b- decay. The product of this decay is helium-3. Thus, the He-3 EPSM is configured as shown in Figure 2-6 which is the H-3 EPSM shown on right side of Figure 2-5 without the "dangling" electron ESU segment. There is a plane of symmetry which may imply an even parity. He-3 has spin 1/2 which indicates that the spin 1/2 of the second proton was subtracted from the H-2 spin of 1. A similar thing happened when the spin 1/2 the second neutron was subtracted from H-2 to form H-3.
Figure 2-6: Helium-3 EPSM.
Helium-4, He-4, 2He4 (99.999862%) (spin 0 , parity +1)
The helium-4 nucleus contains two protons and two neutrons. It is also called the alpha(a) particle. Helium-4 accounts for almost all of the nuclei other than hydrogen in the visible universe; and together with hydrogen, they account for more than 99% of the universe's mass. The He-4 nucleus is also particularly stable. The proton-proton and the carbon-nitrogen cycles both lead to a buildup of helium in the sun and other stars. Helium-4 can combine under certain conditions to yield other nuclei including those which are a direct multiple of 2He4 up to 20Ca40. The alpha particle is so stable that some nuclei decay by emitting an alpha particle. Two He-4 EPSMs are possible as shown in Figure 2-7. Both of these EPSMs can be viewed as two hydrogen-2 nuclei combined into one particle.
Figure 2-7: Two possible helium-4 EPSMs. The EPSM on the right has planes of symmetry whereas the EPSM on the left does not.
Helium-4 - Paradigm Lost
Throughout this effort the EPSMs have maintained an spatial orientation for the positive and negative charges. This charge orientation convention has resulted in the helium-4 EPSMs shown in Figure 2-7. However, these He-4 EPSMs with their single free negative 1/3 charge and seven free positive 1/3 charges would seem to be more reactive than the actual He-4 nucleus which is very stable. The charge convention was basic to the model during the development of the elementary particles; however, in the formation of the nucleus from the free elementary particles it is not apparent that the convention needs to be followed.
If the free -1/3 charge of He-4 EPSM on the right hand side of Figure 2-7 is connected to one of the +1/3 charges then various helium-4 EPSMs can be formed that contain a loop as shown in Figures 2-8 and 2-9. Each of these He-4 EPSMs not only eliminates the free -1/3 charge but also adds an addition bond and ring structure to the EPSMs which should increase its stability. A connecting anti-neutrino might not be needed for this "additional bond" to be at least partially effective. The breaking of this additional bond may be needed for He-4 to enter into reactions. Although such "loops" caused by the internal pairing of free dimensionalities may be present in other EPSMs, they will not be considered at this time in any other case.
Figure 2-8: One of the helium-4 EPSMs formed by connecting the -1/3 charge to a +1/3 charge of the same EPSM. The EPSM on the right has the nucleons rotated to form a very compact Helium-4 EPSM. Note: These EPSMs are shown with some of the connecting neutrinos.
Figure 2-9: Another helium-4 EPSM formed by connecting the -1/3 charge to a +1/3 charge. Note: This EPSM is shown with some of the connecting neutrinos.
HYDROGEN BURNING
Hydrogen burning is the process by which a main sequence star, such as our sun, forms helium from hydrogen and emits energy. Two different sets of reactions have been identified:
1. The proton-proton (p-p) chain,
2. The carbon-nitrogen (C-N) chain.
The Proton-Proton Chain:
1. 1H1 + 1H1 + ESU > 1H2 + b+ + n
2. 1H2 + 1H1 > 2He3 + g
3a. 2He3 + 2He3 > 2He4 + (2) 1H1 or,
3b. 2He3 + 1H2 > 2He4 + 1H1
The net result is the conversion of four protons into one helium-4 nucleus, two positrons and two neutrinos and 26.7 MeV of energy. Note, reactions 1 and 2 had to occur twice before reaction 3a, or alternatively, reaction 1 had to occur twice and reaction 2 once before reaction 3b. Also, it should be noted that the text books do not identified an ESU as being involved in the first equation. The use of the ESU in EPSM in the beta + decay has been discussed Part 1. All of the other reactions look straight forward within EPSM except reaction 3a. As it will be seen, it does not appear from the EPSM for He-3 that two He-3 should react. There is no external negative dimensionality on a He-3 EPSM to react with a positive dimensionality on the other He-3. Two processes could allow this reaction within EPSM. First, a spalling or breaking up of one of the He-3 in the collision with the second He-3 resulting in the products of reaction 3a. This process could release a H-1 and form a Li-5 which in turn decays to He-4 and another H-1:
3a'. 2He3 + 2He3 > 3Li5 + 1H1 and,
3Li5 > 2He4 + 1H1
The ESU allows the two He-3 to react much like it allows the two H-1 to react in reaction 1. The H-2 would then cycle back to reaction 2.
First-generation stars must rely upon the p-p chain. However, second-generation and later stars can also use the Carbon-Nitrogen (C-N) cycle which also results in the net conversion of four protons into one helium-4 nucleus, two positrons and two neutrinos and 26.7 MeV of energy. The carbon/nitrogen seed being provided when the stars were forms. The C-N cycle will be returned to later.
THE l-PROCESS
The l-process, or light-process, accounts for the amount of the very light elements; lithium, beryllium, and boron. A gap occurs at these elements within the stars and the element building process continues with Helium Burning. These light elements are now believed to be formed by spallation of interstellar nuclei by cosmic rays. These simple elements are also developed in the p-p process although they mostly decay back to He-4 in further reactions. EPSMs were developed for these elements, but are not shown here at this time.
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