﻿ The Binding Energies of Nuclei as Determined by their Substructures and the Interactions Among their Nucleons
San José State University

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Thayer Watkins
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U.S.A.

The Binding Energies of Nuclei as
Determined by their Substructures and
the Interactions Among their Nucleons

Although nuclei are composed of neutrons and protons these nucleons are further organized into structures; neutron spin pairs, proton spin pairs, and neutron-proton spin pairs. In addition to these there are linkages of neutrons and protons of the form -n-p-p-n-, or equivalently, -p-n-n-p- that induce binding energy effects similar to alpha particles. These linkages are called alpha modules in the following analysis. In addition to alpha modules and the three types of spin pairs a nucleus may contain singleton neutrons or protons. These latter are not substructures and their formation do not contribute to the binding energy of the nucleus they are in.

Binding energy is also determined by the interactions of the various substructures but the analysis below presumes that the interactions of the substructures reduces down to interactions among neutrons and protons.

The notation which is used is

• #a = number of alpha modules
• #nn = number of neutron-neutron spin pairs outside of alpha modules
• #pp = number of proton-proton spin pairs outside of alpha modules
• #np = number of neutron-proton spin pairs outside of alpha modules
• N = total number of neutrons in nucleus
• P = total number of protons in nucleus

The number of interactions of neutrons with each other is N(N-1)/2 and likewise for proton interactions. The number of separate interactions of neutrons with protons NP. The binding energy BE is then assumed to be a linear homogeneous function of the numbers of substructures and the numbers of interactions.

The regression equation based upon the above is

#### BE = 39.01#a + 13.64#nn + 1.80#pp + 6.58#np −0.188(N(N-1)/2) −0.486(P(P-1)/2) + 0.273NP t-ratios [510.0]   [76.8]   [3.2]   [14.2]   [-36.9]   [-41.2]   [35.8] R² = 0.99989

If the strong force charge of a proton is taken to be 1.0 and that of a neutron denoted as q, where q may be a negative number, then the regression coefficients should be related to q; i.e.,

#### CNP/CP(P-1)/2 = q/1 = q CN(N-1)/2/CNP = q²/q = q CN(N-1)/2/CP(P-1)/2 = q²/1 = q²

When the regression coefficients are applied the results are:

#### CNP/CP(P-1)/2 = −0.6883 CN(N-1)/2/CNP = −0.5618 CN(N-1)/2/CP(P-1)/2 = (−0.6218)²

These results indicate

• that definitely the strong force charge of a neutron is opposite in sign to that of a proton
• that definitely the strong force charge of a neutron is smaller in magnitude than that of a proton
• that very likely the value of q is −2/3