﻿ The Statistical Explanation of the Incremental Binding Energies of Nuclides Due to the Formation of Proton-Protonon Spin Pairs
San José State University

applet-magic.com
Thayer Watkins
Silicon Valley,
& the Gateway
to the Rockies
USA

The Statistical Explanation of the
Incremental Binding Energies of
Nuclides Due to the Formation of
Proton-Proton Spin Pairs

## Background

Nuclei are held together largely by the spin pairing of the nucleons (protons and neutrons) Such spin pairins are exclusive; meaning one neutron can pair with a proton and with one other neutron and no more. The same applies for protons.

There are other nonexclusivee interactions between nucleons but each each such interaction is an order of magnitude smaller than that of a spin pairing.

Therefore It is worthwhile to estimate the increments in binding energy due to the formation of spin pairs and explain their variation in terms of the makeup of the nuclei.

The binding energy due to the formation of a spin pair can be computed as the difference in the incremental binding energy at one point and the average of the value at the two adjacent points, as shown below. This procedure is not valid near where the incremental binding energy makes a big drop.

Regression Results
ConstantRegression
Coefficient
t Ratio
C00
Proton Shells
Shell
Number
Regression
Coefficient
t Ratio
10
21.441617.6
3-0.064221.1
4-3.70736.5
50
60.257866.0
70
Neutron Shells
Shell
Number
Regression
Coefficient
t-ratio
23.3417376.3
30
40
50
60
70
80
Other Variables
(p-n)-0.0118384.4
p-0.005415-6.0

The Excel regression does not compute a coefficient for a variable if it finds something wrong with the dataset with respect to that variable, but it does not reveal the nature of the problem.

The coefficient of determination (R²) for the above regression equation is reported by Excel as 0.956. This is misleading; a mistake that comes from comparing the variation for the regression equation with the variation about a constant of zero. Since the regression equation without a constant term was not of much value the regression was redone allowing for a variable constant term. However the results are not significantly different in terms of the paucity of estimated regression cefficients.,

The comparison of the incremental binding energies for neutrons and for protons indicates that at least for some elements there is no difference between the results for neutrons and protons