13. CARBON BURNING, SILICON BURNING AND MAGIC

As the helium is burned, the star's core becomes a mixture of carbon and oxygen. If a star is large enough the core temperature will rise sufficiently to start the carbon burning process, e.g.:

_{6}C^{12} + _{6}C^{12 } > _{ 10}Ne^{20 }_{ }+_{
2}He^{4}

_{6}C^{12} + _{6}C^{12 } > _{ 11}Na^{23 }_{ }+_{
1}H^{1}

Taking the C-12 EPSM as (1He,1SiL) would lead to Ne-20 EPSM as being (1He,2SiL), as stated above. Sodium-23 has spin 3/2, even parity, and is stable. A candidate for Na-23 EPSM would be (1H-2,1He-5,2SiL) where the He-5 EPSM is shown on the right side of Figure 2-16.

Silicon burning begins by splitting of a silicon nuclei and the pieces interacting with nuclei in the core to produce new nuclei up to and just above iron. The following are some examples of (alpha, gamma) reactions along with the simplest EPSM initial candidates:

_{14}Si^{28} + _{2}He^{4 } > _{ 16}Si^{32 }(1SiL,2PiL) + g

_{16}S^{32} + _{2}He^{4 } > _{ 18}Ar^{32 }(1He,1SiL,2PiL) + g

_{18}Ar^{32} + _{2}He^{4 } > _{ 20}Ca^{40 }(2SiL,2PiL) + g

_{20}Ca^{40} + _{2}He^{4 } > _{ 22}Ti^{44 }(1SiL,3PiL) + g

_{22}Ti^{44} + _{2}He^{4 } > _{ 24}Cr^{48 }(1He,1SiL,3PiL) + g

_{24}Cr^{48} + _{2}He^{4 } > _{ 26}Fe^{52 }(2SiL,3PiL) + g

_{26}Fe^{52} + _{2}He^{4 } > _{ 28}Ni^{32 }(1He,1SiL,3PiL) + g

Various other reactions such as (proton, gamma), (proton, neutron), (alpha, proton), (alpha, neutron), and various other combinations of proton, gamma, alpha, and neutron reactions results in an equilibrium with Si-28. Apparently, this proceeds in equilibrium for a while until another contraction of the core occurs at which time some of the silicon nuclei break down into a's and react with other nuclei to form a Fe-Ni core.

THE s-, r-, and p- PROCESSES

A critical point is being approached in this initial effort to model the atomic nuclei. "Helium Burning" is about to end. Helium burning of calcium-40 produces titanium-44; however, titanium-44 is not stable and it decays to calcium-44. Also, calcium-44 can be made into titanium-48, the most abundant titanium, by helium burning. That is suppose to be the end of helium burning even though it looks inviting to keep adding helium to obtain many of the higher elements. In fact, if you continue the helium burning chain from calcium-44 you obtain the most abundant isotopes of titanium, chromium, iron and zinc along with the second most abundant isotope of nickel. The same trend continues with zinc after additional neutrons are provided by germanium and selenium similar to the way neutrons were added going from calcium-40 to calcium-44.

When helium burning stops the star must heat up before new reactions are available. This next set of reactions form the elements up through iron, cobalt and nickel. In fact these elements are the heaviest that can be formed in a main stream star such as our sun.

The nuclei above the peak at Fe-Ni are formed through a process of neutron capture and b+ decays. This is a very complicated process involving a multitude of neutron absorption times versus decay times. The process is defined as a s-process if the time between successive neutron captures is much greater than the b+ decay time (likely to decay before capturing another neutron). And, correspondingly the process is defined as an r-process if the nuclei is more likely to capture another neutron before decaying. The p-process result in some isotopes that are rich in protons by reactions including (p, n) reactions. The very heaviest nuclei can be made only with the conditions of a super nova.

Up to now the number of nucleons in each isotope were few and Helium Burning products provided calibration points in the process. In addition, Part 2 was started not so much to give the definitive configurations of the nuclei within EPSM but more to show that meaningful nuclei EPSMs could be developed from the proton and neutron EPSMs that came out of Part 1.

The nuclei above calcium with an even number of protons usually have 4 to 10 stable isotopes. If there is an unstable isotope in the group, it is an isotope with an odd number of neutrons. The nuclei with an even number of protons and an even number of neutrons have spin 0 and even parity. If the model continues to use only one helium-4 at most, Si Layers along with neutron loading, and Pi Layers then EPSMs can be readily developed for the nuclei at least as far up as lead which is the heaviest stable nucleus with an even number of proton. Lead has 82 protons and the heaviest lead (Pb-208) has 126 neutrons. Thus, 44 (i.e., 126 - 82) of the neutrons are associated with neutron loading of Si Layers under the current model. This corresponds to eleven Si Layers with four added neutrons each for a total of 44 protons and 88 neutrons. There are 38 protons and 38 neutrons remaining after the minimum number of Si Layers are accounted for. The greatest number of Pi Layers available out of 38 protons and 38 neutron is six. What is left is one helium-4 with two protons and two neutrons. Thus, a lead-208 EPSM is (1He,11[SiL+4n],6PiL). There are 18 layers in lead using this model which limits the largest layer to twelve nucleons. All of the EPSMs for the nuclei between calcium and lead with an even number of protons can be developed using the same method.

The nuclei with an odd number of protons are quite different. There is usually either one stable isotope with an odd number of neutrons or two stable isotopes both with an odd number of neutrons. In the latter case the two stable isotopes are separated by an unstable isotope with an even number of neutrons. In the cases with a single stable isotope there is a relatively stable isotope, but still unstable, in the place where the second stable isotope might be located. The spin of these stable nuclei is usually a large fractional spin. Within EPSM, as it presently exists, this has meant several smaller layers with at least one with a fractional spin.

THE MAGIC IS FOUND

When the stable isotopes are examined it is found that there are selected proton and/or neutron numbers which have more than the usual number of stable nuclei. These have been called the "magic numbers". The magic numbers are 2, 8, 20, 28, 50, 82, and 126. These numbers are suppose to represent closed nucleon shells similar to the closed electron shells in atoms. The elements with a magic number of protons are helium (2 protons), oxygen (8 protons), calcium (20 protons), nickel (28 protons), tin (50 protons), and lead (82 protons). Some nuclei have double magic number, i.e., both the number of protons and the number of neutrons are magic numbers. The nuclei with double magic numbers , not all of which are stable, are:

He-4 (2 protons and 2 neutrons)

O-16 (8 protons and 8 neutrons)

Ca-40 (20 protons and 20 neutrons)

Ca-48 (20 protons and 28 neutrons)

Ni-56 (28 protons and 28 neutrons)

Sn-132 (50 protons and 82 neutrons)

Pb-208 (82 protons and 126 neutrons)

Helium has 2 protons and the extra stability of He-4 was discussed earlier. He-3, the other stable nucleus with 2 protons, is the decay product of H-3. The following are possible EPSMs for other stable nuclei with magic numbers of proton (with even neutrons):

O-16 (2SiL), O-18 (1SiL,1[SiL+2n])

Ca-40 (2Sil,2PiL), Ca-42 (1SiL,1[Sil+2n],2PiL), Ca-44 (1SiL,1[Sil+4n],2PiL),

Ca-44 (1[SiL+2n],[Sil+4n],2PiL), Ca-48 (2[Sil+4n],2PiL)

Ni-58 (1He,1SiL,1[SiL+2n],3PiL), Ni-60 (1He,1SiL,1[SiL+4n],3PiL),

Ni-62 (1He,1[SiL+2n],1[SiL+4n],3PiL), Ni-64 (1He,2[SiL+4n],3PiL)

Sn-112 (1He,3SiL,3[SiL+4n],4PiL, Sn-114 (1He,2SiL,1[SiL+2n],3[SiL+4n],4PiL),

Sn-116 (1He,2SiL,4[SiL+4n],4PiL), Sn-118 (1He,1SiL,1[SiL+2n],4[SiL+4n],4PiL),

Sn-120 (1He,1SiL,5[SiL+4n],4PiL), Sn-122 (1He,1[SiL+2n],5[SiL+4n],4PiL),

Sn-124 (1He,6[SiL+4n],4PiL),

Pb-20 (1He,1[SiL+2n],10[SiL+4n],6PiL), Pb-208 (1He,11[SiL+4n],6PiL)

Thus, it appears that even with the simple assumption of using no more than a one helium-4, Si Layers along with neutron loading, and Pi Layers then EPSMs can be developed that can account for nuclei with a magic number of protons with spin 0 and even parity.

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