To Validate the Role of Electromagnetic and Strong Gravitational Constants via the Strong Elementary Charge

Within the atomic medium, in analogy with gravity and Schwarzschild interaction, atomic phenomena can be understood with large values of gravitational constants. It may be noted that, larger the magnitude of gravitational constant, smaller is the magnitude of the operating force. The key points to be noted are: 1) There exists a strong elementary charge and squared ratio of electromagnetic and strong interaction charges is equal to the strong coupling constant. 2) There exists a gravitational constant associated with strong interaction, Gs= 3.329561213x10 m kgsec 3) There exists a gravitational constant associated with electromagnetic interaction, Ge= 2.374335685 x10 m kgsec ; As the magnitude of operating force is far less than the magnitude of (c/G), protons and electrons cannot be considered as black holes. With further research and analysis, massive origin of protons and electrons can be understood. In this paper, by quantifying the strong interaction elementary charge, an attempt is made to validate the role of the proposed electromagnetic and strong interaction gravitational constants.


Introduction
In order to unify cosmology, quantum mechanics and the four observed fundamental cosmological interactions, a 'unified force' is required. In this connection ( ) 4 c G can be considered as the classical force or astrophysical force limit. For a detailed description on this characteristic limiting force, readers are strongly encouraged to see the historical paper by G.W.Gibbons [1]. Similarly, ( ) 5 c G can be considered as the classical power limit. If it is true that c and G are fundamental physical constants, then ( ) 4 c G and ( ) 5 c G can also be considered as fundamental compound physical constants. These classical limits are more powerful than the Uncertainty limit. These two characteristic limits are for future experimental verification with nuclear weapons, particle accelerators, nuclear reactors and rocket propulsion units etc. Moreover, these two characteristic limits can be understood with future astrophysical and cosmological interpretations, observations and inferences. In contrast to the current notion of black hole physics, the Schwarzschild radius of a black hole [2,3] can be understood with the characteristic astrophysical Proceeding further, it may be noted that, from gravity point of view, so far no model succeeded in understanding the link between strongly interacting massive fermions and massive celestial objects. The authors would like to stress the Universal Journal of Physics and Application 9(5): 216-225, 2015 217 fact, strongly interacting massive fermions are only playing a major role in the formation of observable luminous and non-luminous massive celestial objects that follow gravitational interaction. By interconnecting the strong coupling constant and gravitational constant via the Schwarzschild interaction, in this paper, qualitatively and quantitatively the authors reviewed the basics of strong nuclear interaction along with electron-proton interaction. The authors humbly and sincerely agree that, even though the proposed results are interesting and important at fundamental, they require deep mathematical and theoretical back up to proceed further. Considering the failure of current theoretical models in view -the authors request the science community to recommend the content of this paper for further research and development.
In the recently published papers and references therein [4,5,6,7], by introducing two different gravitational constants (one for the electromagnetic interaction and another for the strong interaction), the authors developed many characteristic unified relations. In this paper, by quantifying the strong interaction elementary charge, an attempt is made to validate the role of the proposed electromagnetic and strong interaction gravitational constants. With further research and analysis, status of their authentic physical existence can be understood.

Understanding the Role of ( )
If no force (or force of zero magnitude) acts on the mass content M of the assumed massive body, its radius becomes infinity. With reference to the average magnitude of 4 4 0, 2 This proposal is very simple and seems to be different from existing concepts and may be a unified form of Newton's law of gravity, the special theory of relativity and the general theory of relativity.

To Derive the Planck Mass
So far no theoretical model has proposed a derivation for the Planck mass. To derive the Planck mass the following two conditions can be considered.
Assume a gravitational force of attraction between two particles of mass ( ) P M separated by a minimum distance (r min ) to be, With reference to wave mechanics, let min 2 . .
Here, P λ represents the wavelength associated with the Planck mass. With these two assumed conditions, the Planck mass can be obtained as follows.

Understanding the Strength of Any Interaction
From the above relations it is reasonable to say that, 1) If it is true that c and G are fundamental physical constants, then ( ) If X is very small,

Three Basic Assumptions of Final Unification
The following three assumptions can be considered in a final unification program [8,9].
Assumption-1: The gravitational constant associated with the electromagnetic interaction , With these three assumptions, the key features of nuclear and atomic structure can be understood. With reference to the Schwarzschild interaction, for electromagnetic interaction, Here the authors would like to stress the fact that, as the magnitude of operating force is far less than the magnitude of ( ) 4 c G , protons and electrons cannot be considered as black holes. Within the nuclear medium, in analogy with gravity and Schwarzschild interaction, nuclear phenomena can be understood with large value of gravitational constant. With further research and analysis, massive origin of protons and electrons can be understood.

Important Results
A) Strong coupling constant: It can be understood as follows.
L) Planck's constant: It can be understood as follows. The very interesting point to be noted here is that, Proton's magnetic moment is associated with its strong elementary charge. Neutron's magnetic moment seems to be the difference of magnetic moment associated with strong interaction and magnetic moment associated with electromagnetic interaction. Considering relations (7)

Proton-neutron Beta Stability Line
Inside an atomic nucleus, 'beta decay' is a type of radioactive decay in which a proton is transformed into a neutron, or vice versa. This process allows the atom to move closer to the optimal proton-neutron ratio. The important point here is that most naturally occurring isotopes on Earth are beta stable. Beta-decay stable isobars are the set of nuclides which cannot undergo beta decay. A subset of these nuclides are also stable with regards to double beta decay as they have the lowest energy of all nuclides with the same mass number. This set of nuclides is also known as the 'line of beta stability'. The line of beta stability can be defined mathematically by finding the nuclide with the greatest binding energy for a given mass number and can be estimated by the classical semi-empirical mass formula.
The naturally occurring stable mass number connected with the proton number can be expressed as follows [10].  and semi-magic numbers can be fitted [4,5]. One very interesting observation is that,

To Fit and Understand the Nuclear Binding Energy
Step-1: To Find the Characteristic Binding Energy Potential Individual self potential energy of the strongly interacting proton can be fitted as follows.
( ) For the semi-empirical mass formula, starting from Z=30, at the stable mass numbers it is possible to show that, the ratio of binding energy and proton number is close to 19.7 MeV and is independent of the stable mass number. See the last column of table-1.
Starting from Z=30 to Z=100, average value of binding energy/proton number for 71 isotopes is 19.7 MeV. Here the authors would like to call this as "nuclear binding energy potential". This energy unit can be fitted as follows.
In the following sub sections, to fit the nuclear binding the authors consider a value of 19.7 MeV that is very close to 20.17 MeV.
Step-2: To Find the Binding Energy at Stable Mass Number of ≥ Z 30 For Z=30 onwards, at the stable mass number, nuclear binding energy can be approximately fitted with the following relation. Step Step   In the following table-1 and figure-1, the authors tried to compare the estimated binding energy with data obtained from the semi empirical mass formula (SEMF). In the figures, "Green color" thin curve indicates the binding energy estimated with SEMF and "red color" bold curve indicates the estimated binding energy. In a macroscopic approach, starting from 20 MeV to 2000 MeV one cannot find much difference in both of the curves. Relations (24) to (29) need in depth study at fundamental level.  In the following table-2 and figure-2, the authors tried to compare the estimated binding energy of isotopes of Z=60 with data obtained from the semi empirical mass formula (SEMF). In the figure-2, "Green color" curve indicates the binding energy estimated with SEMF and "red color" dashed curve indicates the estimated binding energy.