Understanding Nuclear Binding Energy with Nucleon Mass Difference via Strong Coupling Constant and Strong Nuclear Gravity
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 ≅ 3.32688 × 10 28 m 3 kg - 1 sec - 2 being the nuclear gravitational constant, nuclear charge radius can be shown to be, R 0 ≅ 2 G s m p c 2 ≅ 1.24 fm . e s ≅ ( G s m p 2 ℏ c ) e ≅ 4.716785 × 10 − 19 C being the nuclear elementary charge, proton magnetic moment can be shown to be, μ p ≅ e s ℏ 2 m p ≅ e G s m p 2 c ≅ 1.48694 × 10 − 26 J . T - 1 . α s ≅ ( ℏ c G s m p 2 ) 2 ≅ 0.1153795 being the strong coupling constant, strong interaction range can be shown to be proportional to exp ( 1 α s 2 ) . Interesting points to be noted are: An increase in the value of α s helps in decreasing the interaction range indicating a more strongly bound nuclear system. A decrease in the value of α s helps in increasing the interaction range indicating a more weakly bound nuclear system. From Z ≅ 30 onwards, close to stable mass numbers, nuclear binding energy can be addressed with, ( B ) A s ≅ Z × { ( 1 α s + 1 ) + 30 × 31 } ( m n − m p ) c 2 ≈ Z × 19.66 MeV . With further study, magnitude of the Newtonian gravitational constant can be estimated with nuclear elementary physical constants. One sample relation is, ( G N G s ) ≅ 1 2 ( m e m p ) 10 [ G F ℏ c / ( ℏ m e c ) ] where G N represents the Newtonian gravitational constant and G F represents the Fermi’s weak coupling constant. Two interesting coincidences are, ( m p / m e ) 10 ≅ exp ( 1 / α s 2 ) and 2 G s m e / c 2 ≅ G F / ℏ c .