Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Understanding Nuclear Binding Energy with Nucleon Mass Difference via Strong Coupling Constant and Strong Nuclear Gravity

Version 1 : Received: 28 December 2018 / Approved: 29 December 2018 / Online: 29 December 2018 (05:24:57 CET)
Version 2 : Received: 4 January 2019 / Approved: 8 January 2019 / Online: 8 January 2019 (10:57:41 CET)

A peer-reviewed article of this Preprint also exists.

Seshavatharam UVS and Lakshminarayana S. On the role of four gravitational constants in nuclear structure. Mapana Journal of Sciences, 18(1), 21-45 (2019) Seshavatharam UVS and Lakshminarayana S. On the role of four gravitational constants in nuclear structure. Mapana Journal of Sciences, 18(1), 21-45 (2019)

Journal reference: Mapana Journal of Sciences 2019, 18, 2052
DOI: 10.12723/mjs.48.2

## Abstract

With reference to electromagnetic interaction and Abdus Salam’s strong (nuclear) gravity, 1) Square root of ‘reciprocal’ of the strong coupling constant can be considered as the strength of nuclear elementary charge. 2) ‘Reciprocal’ of the strong coupling constant can be considered as the maximum strength of nuclear binding energy. 3) In deuteron, strength of nuclear binding energy is around unity and there exists no strong interaction in between neutron and proton. ${G}_{s}\cong 3.32688×{10}^{28}{\text{}\mathrm{m}}^{3}{\mathrm{kg}}^{-1}{\mathrm{sec}}^{-2}$ being the nuclear gravitational constant, nuclear charge radius can be shown to be, ${R}_{0}\cong \frac{2{G}_{s}{m}_{p}}{{c}^{2}}\cong 1.24\text{}\mathrm{fm}.$ ${e}_{s}\cong \left(\frac{{G}_{s}{m}_{p}^{2}}{\hslash c}\right)e\cong 4.716785×{10}^{-19}\mathrm{C}$ being the nuclear elementary charge, proton magnetic moment can be shown to be, ${\mu }_{p}\cong \frac{{e}_{s}\hslash }{2{m}_{p}}\cong \frac{e{G}_{s}{m}_{p}}{2c}\cong 1.48694×{10}^{-26}\text{}\mathrm{J}{.\mathrm{T}}^{-1}.$ ${\alpha }_{s}\cong {\left(\frac{\hslash c}{{G}_{s}{m}_{p}^{2}}\right)}^{2}\cong 0.1153795$ being the strong coupling constant, strong interaction range can be shown to be proportional to $\mathrm{exp}\left(\frac{1}{{\alpha }_{s}^{2}}\right).$ Interesting points to be noted are: An increase in the value of ${\alpha }_{s}$ helps in decreasing the interaction range indicating a more strongly bound nuclear system. A decrease in the value of ${\alpha }_{s}$ helps in increasing the interaction range indicating a more weakly bound nuclear system. From $Z\cong 30$ onwards, close to stable mass numbers, nuclear binding energy can be addressed with, ${\left(B\right)}_{{A}_{s}}\cong Z×\left\{\left(\frac{1}{{\alpha }_{s}}+1\right)+\sqrt{\sqrt{30×31}}\right\}\left({m}_{n}-{m}_{p}\right){c}^{2}\approx Z×19.66\text{}\mathrm{MeV}.$ With further study, magnitude of the Newtonian gravitational constant can be estimated with nuclear elementary physical constants. One sample relation is, $\left(\frac{{G}_{N}}{{G}_{s}}\right)\cong \frac{1}{2}{\left(\frac{{m}_{e}}{{m}_{p}}\right)}^{10}\left[\sqrt{\frac{{G}_{F}}{\hslash c}}/\left(\frac{\hslash }{{m}_{e}c}\right)\right]$ where ${G}_{N}$ represents the Newtonian gravitational constant and ${G}_{F}$ represents the Fermi’s weak coupling constant. Two interesting coincidences are, ${\left({m}_{p}/{m}_{e}\right)}^{10}\cong \mathrm{exp}\left(1/{\alpha }_{s}^{2}\right)$ and $2{G}_{s}{m}_{e}/{c}^{2}\cong \sqrt{{G}_{F}/\hslash c}.$

## Subject Areas

strong (nuclear) gravity; nuclear elementary charge; strong coupling constant; nuclear charge radius; beta stability line; nuclear binding energy; nucleon mass difference; Fermi’s weak coupling constant; Newtonian gravitational constant; deuteron; interaction range; super heavy elements

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