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The Substructures of Nuclei and Their Interactions

Two previous studies (1 and 2) presented the case that the neutrons and protons of a nucleus combine into alpha particles and nucleon pairs whenever possible. The potential energy lost upon the formation of these substructures contributes to the binding energies of nuclei.

A nuclide is then composed of alpha particles, possibly a neutron-proton pair (called a deuteron), neutron-neutron pairs or proton-proton pairs and possibly a singleton neutron or proton. There cannot be more than one deuteron because two would constitute an alpha particle. Likewise if there is at least one neutron-neutron pair there cannot be any proton-proton pairs because two such pairs would constitute an alpha particle. Furthermore if there is a singleton neutron there cannot be a singleton proton because that combination would constitute a deuteron.

The binding energies of nuclides are composed of one part from the formation of substructures such as alpha particles and another part, called structural binding energy which is due to the arrangement of the substructures within the nuclei. After the number of the constituents (alpha particles, deuteron and other nucleonic pairs and any singleton nucleons) the structural binding energies were computed by deducting 28.3 MeV for each alpha particle, 2.2 Mev for a deuteron, 2.2 Mev for each proton pair and 2.7 MeV for each neutron pair. The figures for the neutron and proton pairs came from a previous study. Then the numbers of interactions for the six types of substructures were computed. If the number of alpha particles is #a then the number of interactions of alpha particles is #a(#a-1)/2 and likewise for the numbers of the interactions of the #nn neutron pairs and #pp proton pairs. There can be no interactions of deuterons but the number of interactions of alpha particles with the deuteron is #a#d and likewise for the other nucleon pairs, #a#nn and #a#pp. The number of singleton neutron, zero or one, is denoted as *n and likewise for any singleton proton, *p.

The regressions of the structural binding energies on the number of interactions of the various types were carried out for each different alpha particle shell. No constant term was included in the regression equations. The results are given below.

Alpha Shell #pp*p #nn*n #pp#pp #nn#nn #d#pp #d#nn #a*p #a*n #a#pp #a#nn #a#d #aa
42 and up 0 0.26832 0 2.10787 0 -1.28067 0 0.18173 0 -0.76336 0.96757 0.59088 0.976
26 to 41 0 0.49373 0 0.60723 0 0.48507 0 0.54453 0 0.16534 0.37888 0.26922 0.956
15 ot 25 -13.38034 -0.70701 -29.95966 -1.4068 12.60038 1.62803 1.60606 1.0632 1.91887 1.0541 -1.42425 0.4228 0.975
8 to 14 -2.11002 -0.45355 0.63001 -1.27367 2.53342 2.26266 0.63053 1.25076 0.222 1.39756 -0.29379 1.00912 0.981
4 to 7 -1.9455 -1.31854 -3.06967 -2.63923 2.74687 2.77028 0.8176 1.63292 0.82367 2.36404 -0.09669 1.7035 0.993
2 to 3 -0.51177 -0.13183 -5.14972 -2.26194 2.94251 2.39813 -0.47445 0.28227 0.26041 2.19268 2.98188 3.30185 0.993
1 -0.46627 0.11953 -2.39847 -2.1791 3.8052 3.51574 -1.8388 -1.04965 -3.01211 -0.13875 5.84895 0 0.965
0 -3.09806 0.65964 -13.97955 -7.58725 3.29349 1.77652 0 0 0 0 0 0 0.925

In the table if a coefficient is shown as 0 it means that there was no variation in the number of interactions of that variable for that shell.

(To be continued.)


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