Nuclear Evidences for Confirming the Physical Existence of 585 GeV Weak Fermion and Galactic Observations of TeV Radiation

1. Introduction

It is generally believed that, electrons and nucleons are fermions and are responsible for the observed spectrum of electromagnetic radiation that propagates in the form of photons. At sub nuclear level, it is well established that, quarks are fermions and play a vital role in generating baryons and mesons. Gluons are believed to be the force carriers between quarks and hadrons. Here we would like to emphasize the point that, whether it is electromagnetic interaction or strong interaction, fermions are supposed to be the ‘field generators’ and photons and gluons are believed to be the ‘force carriers’. It is very clear to say that, ‘field generators’ and ‘force carriers’ both are essential elements in understanding their respective interactions and both can be considered as a representation of ‘head’ and ‘tail’ of a coin. Coin ‘without head’ or ‘without tail’ – is practically an ambiguous physical issue. In this context, with reference to the well believed and well understood ‘weak’ interaction [1,2] – we sincerely appeal that,

1)

There is a scope for understanding weak interaction with its ‘weak field generating fermion’.

2)

There exists a ‘weak field fermion’ corresponding to the currently believed three weak bosons.

In this context, in our recently proposed ‘4G model of final unification’ associated with three large atomic gravitational constants pertaining to the three atomic interactions [3,4,5,6,7,8,9,10,11,12,13,14,15,16], we have proposed the existence of a weak fermion of rest energy 585 GeV. Considering the basic concepts of super symmetry [17,18,19,20,21,22,23], one can think about the possible existence of weak fermion. Here it seems important to mention the historical literature for the introduction of large gravitational constants by Nobel laureates and other scientists. In 1970s to 1990s, for understanding strong interactions, K. Tenakone, J.J.Perng, K.P. Sinha, Usha Raut, C. Sivaram, V. de Sabbata, S. I. Fisenko, M. M. Beilinson, B. G. Umanov, Abdus Salam, J. Strathdee, E. Recami, V. Tonin-Zanchin, Sergey G. Fedosin, O.F. Akinto and Farida Tahir proposed the existence of nuclear gravitational constant having a very large magnitude [24,25,26,27,28,29,30,31,32]. Thus, we have developed our model and quantified the magnitude of the strong nuclear gravitational constant [33,34,35,36,37]. In 2013, for understanding weak interactions, Roberto Onafrio, proposed the existence of weak gravitational constant having a large magnitude [38,39]. E. A. Pashitskii and V. I. Pentegov further extended the subject [40]. Motivated with these large coupling constants, for understanding the electromagnetic interactions, we have proposed the existence of another large gravitational constant [41,42].

Considering our 4G model of Final unification and its 3 assumptions, in our early and recent publications we have developed many relations in nuclear and particle physics. In this paper, we review the key nuclear relations that help in understanding and confirming the physical existence of our proposed 585 GeV electroweak fermion. Proceeding further, we show the possibility of confirming the physical existence of 585 GeV weak fermion with reference to the observed tera electron volt (TeV) photon radiation coming from astrophysical objects.

Starting from section 2 to section 14, directly and indirectly, we are showing different possible nuclear applications and evidences for understanding and confirming the physical existence of 585 GeV weak fermion. In section 15, including the Fermi’s weak coupling constant and Newtonian gravitational constant, we have developed a procedure for estimating and fitting the fundamental physical constants. In section 16, we have outlined the mechanism of understanding and confirming the physical existence of the proposed weak fermion via galactic TeV photons. We have proposed our conclusions in section 17.

2. Three Assumptions, Five Definitions and Many Applications

Our way of approach is completely different from current models of unified physics and it may take some time for its understanding, implementation and review. We would like to emphasize the point that, compared to String theory [43,44,45,46], our approach is very simple, elegant and workable. It may be noted that, even though there is mathematical beauty and good physics towards the unification of gravity and atomic interactions, String theory is not able to estimate and fit the fundamental physical constants. Proceeding further, its predictions are beyond the scope of current engineering and technology. Roger Penrose and other scientists are very unhappy with the multiple and impractical solutions of String theory. In this context, readers are encouraged to visit the URL: https://www.youtube.com/watch?v=q1ubpGylbWs. One important aspect of our approach is to widen the scope and applicability of String theory towards the three atomic interactions with testable predictions and possible experimental designs [47]. Readers are encouraged to work on the data presented in Table 1 and Table 2.

In our 4G model of final unification, there exists 3 assumptions, 5 definitions and many inferences. Considering the proposed assumptions and definitions, we have presented various applications in nuclear physics. We would like to emphasize the point that, with reference to the current knowledge of physics, so far, no physics model has shown such a wide range of applications in a unified approach. It may be noted that, as per the current notion of standard model of particle physics, weak interaction neither involves in forming particle bound states and nor in particle binding energy scheme. An interesting point of our research is that weak interaction plays a vital role in understanding the origins of quantum mechanics, nuclear stability and binding energy. Weakness of our model is: 1) Lack of mathematical approach; 2) Missing links between the proposed relations; Here, we would like to highlight the point that understanding fundamental things in a broad view is not so simple and certainly beyond the scope of human thinking and imagination. We are sure that, with further research and fine tuning, things can be improved in a phased manner, and the four fundamental branches of physics can be understood in a better way.

3. Three Assumptions of 4G Model of Final Unification

Following our 4G model of final unification, we proposed the following assumptions.

1) There exists a characteristic electroweak fermion of rest energy, $M_{wf}{c}^2\cong 584.725 \mathrm{GeV}$. It can be considered as the zygote of all elementary particles.

2) There exists a nuclear elementary charge in such a way that, ${\left({\displaystyle \frac{e}{e_n}}\right)}^2\cong {\alpha }_s\cong 0.1151935$ = Strong coupling constant [48,49] and $e_n\cong 2.946362e$.

3) Each atomic interaction is associated with a characteristic large gravitational coupling constant. Their fitted magnitudes are,

$\begin{array}{l}{G}_e\cong \mathrm{Electromgnetic} \mathrm{gravitational} \mathrm{constant}\cong 2.374335\times {10}^{37}{ \mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}\\ G_n\cong \mathrm{Nuclear} \mathrm{gravitational} \mathrm{constant}\cong 3.329561\times {10}^{28}{ \mathrm{m}}^3{ \mathrm{kg}}^{-1}{\sec }^{-2}\\ G_w\cong \mathrm{Electroweak} \mathrm{gravitational} \mathrm{constant}\cong 2.909745\times {10}^{22}{ \mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}\end{array}$Based on these fits,

Considering the ratio of Planck scale to the nuclear scale, Newtonian gravitational constant [50,51,52,53] can be fitted with, $G_N\cong {\displaystyle \frac{G_w^{21}{G}_e^{10}}{G_n^{30}}}\cong 6.679851\times {10}^{-11}{ \mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}$.

On interpreting or eliminating the large numbers, neutriono rest mass [7,54,55] can be inferred as, $m_{xf}\cong \left({\displaystyle \frac{\sqrt{G_w{G}_N}}{G_n}}\right)M_{wf}\cong \left({\displaystyle \frac{m_e^6}{m_p^5}}\right)$. Thus, $m_{xf}\cong 4.365\times {10}^{-47} \mathrm{kg}\cong 2.45\times {10}^{-11}eV/c^2.$Strong coupling constant [49] can be fitted with, ${\alpha }_s\cong {\displaystyle \frac{G_w^6{G}_e^4}{G_n^{10}}}\cong \mathrm{0.115193455.}$Independent of system of units, Avogadro like large number [56,57,58,59] can be fitted with a relation of the form, ${\displaystyle \frac{\mathrm{Product} \mathrm{of} \mathrm{short} \mathrm{range} \mathrm{gravitational} \mathrm{constants}}{\mathrm{Product} \mathrm{of} \mathrm{long} \mathrm{range} \mathrm{gravitational} \mathrm{constants}}}\cong {\displaystyle \frac{G_n{G}_w}{G_N{G}_e}}\cong {\displaystyle \frac{G_n^{31}}{G_w^{20}{G}_e^{11}}}\cong 6.1088144\times {10}^{23}.$Neutron lifetime [7,60,61,62,63,64] can be fitted with, $t_n\cong {\displaystyle \frac{G_e^2{m}_n^2}{G_w\left(m_n-m_p\right)c^3}}\cong 874.94 \sec .$ It seems that, outside the nucleus, neutron experiences electromagnetic interaction and weak interaction helps neutron to decay into proton, electron and neutrino.

Characteristic atomic radii [7,65,66,67,68,69,70] can be addressed with $R_{atom}\cong A^{1/3}\left({\displaystyle \frac{2\sqrt{G_n{G}_e}{M}_U}{c^2}}\right)\cong A^{1/3}\times 32.86 \mathrm{pm}$ where $A$ represents the mass number and $M_U\cong 931.5 \mathrm{MeV}/c^2$ represents the unified atomic mass unit. Starting from the 3rd period, $R_{atom}\cong \left\{\left[4-\left({\displaystyle \frac{A}{Z}}\right)\right]{\left({\displaystyle \frac{Z_{fp}}{Z}}\right)}^2\right\}\left[A^{1/3}\left({\displaystyle \frac{2\sqrt{G_n{G}_e}{M}_U}{c^2}}\right)\right]$ where $Z$ represents the atomic number and $Z_{fp}$ represents the atomic number of the first element of the period. It needs further study and fine tuning.

Bohr radius of hydrogen atom can be addressed with, $a_0\cong \left({\displaystyle \frac{4\pi {\epsilon }_0{G}_n{m}_p}{e^2{c}^2}}\right)\left(G_e{m}_e^2\right)$. Energy conservation point of view, it can be expressed as, ${\displaystyle \frac{G_e{m}_e^2}{a_0}}\cong {\displaystyle \frac{e^2}{4\pi {\epsilon }_0\left(G_n{m}_p/c^2\right)}}.$ It may be noted that, as per the current models, there is no solid interconnection between nuclear charge radius and Bohr radius.

4. Interaction Ranges Associated with the 3 Atomic Interactions and the Scope for 4G Model of String Theory

By following the above assumptions, it is possible to estimate the three atomic interaction ranges in the following way.

Electroweak interaction range can be expressed as,

$R_w\cong {\displaystyle \frac{2G_w{M}_{wf}}{c^2}}\cong 6.7494\times {10}^{-19}\mathrm{m}$ (1)

Nuclear interaction range can be expressed as,

$R_n\cong {\displaystyle \frac{2G_n{m}_p}{c^2}}\cong 1.2393\times {10}^{-15}\mathrm{m}$ (2)

Electromagnetic interaction range can be expressed as,

$R_e\cong {\displaystyle \frac{2G_e{m}_e}{c^2}}\cong 4.813\times {10}^{-10}\mathrm{m}$ (3)

Here, we would like to highlight the following two points.

1) Proposed weak interaction range, ${\displaystyle \frac{2G_w{M}_{wf}}{c^2}}\cong \sqrt{{\displaystyle \frac{G_F}{\hslash c}}}$ where $G_F$ is the Fermi’s weak coupling constant [1,2,52,53].

2) String theory [43,44,45] can be made practical with reference to the three atomic gravitational constants associated with weak, strong and electromagnetic interaction gravitational constants. See Table 1. and Table 2. for sample string tensions [46] and energies without any coupling constants.

5. Our 5 Definitions Related to Final Unification

In a unified approach, we have defined 5 relations in the following way.

Electron rest mass is defined as,

$m_e\equiv \left({\displaystyle \frac{G_w}{G_n}}\right)M_{wf}$ (4)

Proton rest mass is defined as,

$m_p\equiv \left({\displaystyle \frac{G_n^2}{G_e{G}_w}}\right)M_{wf}$ (5)

Nuclear and electromagnetic charge ratio is defined as

$\left({\displaystyle \frac{e}{e_n}}\right)\equiv {\displaystyle \frac{\hslash c}{G_n{m}_p^2}}$ (6)

Product of Reduced Planck’s constant and speed of light is defined as

$\hslash c\equiv G_w{M}_{wf}^2$ (7)

Ratio of forces related to proton and electron is defined as

${\displaystyle \frac{e_n^2}{4\pi {\epsilon }_0{G}_n{m}_p{m}_e}}\equiv 4{\pi }^2$ (8)

6. Understanding the Reduced Planck’s Constant and Its Integral Nature

Based on relation (7), the well believed quantum constant $\hslash c$ seems to have a deep inner meaning with reference to electroweak interaction. Following relation (7), there is a possibility to understand the integral nature of quantum mechanics with a relation of the form, $n^2\hslash \equiv {\displaystyle \frac{G_w{\left(n{M}_{wf}\right)}^2}{c}} \mathrm{where} n=1,2,3,\mathrm{..}$ Compared to large massive structures, -like living creatures- as elementary particles are having discrete nature, we would like to emphasize the point that, discreteness may be the root cause of quantum behavior at microscopic level. With reference to proton and electron rest masses, it seems possible to have different relations like,

$\begin{array}{l} \hslash \cong \left({\displaystyle \frac{e}{e_n}}\right)\left({\displaystyle \frac{G_n{m}_p^2}{c}}\right)\cong {\displaystyle \frac{G_w{M}_{wf}^2}{c}}\cong {\displaystyle \frac{G_n{M}_{wf}{m}_e}{c}}\\ \cong \left({\displaystyle \frac{G_w{G}_e}{G_n}}\right){\displaystyle \frac{m_p{m}_e}{c}}\cong {\displaystyle \frac{m_e\sqrt{\left(G_n{m}_p\right)\left(G_e{m}_e\right)}}{c}}\end{array}$ (9)

We would like to emphasize the point that, at first, one should understand the origin of the quantum constants. Then only, one may be able to understand the potential consequences of the quantum constants. Integral nature, wave nature, particle nature, position and momentum - all these physical properties seem to be inherently connected with the generation of the quantum constant. Including string theory, current physical models are simply inserting the quantum constant $\hslash$ and trying to understand the consequences. It needs further study with reference to EPR argument and other physical logics [10,71,72,73,74]. We are working in this new direction.

7. Understanding Proton-Electron Mass Ratio

Considering weak, nuclear and electromagnetic interactions,

${\displaystyle \frac{m_p}{m_e}}\cong {\displaystyle \frac{G_n^3}{G_w^2{G}_e}}$ (10)

Strong coupling constant [48,49] can be expressed as,

${\alpha }_s\cong {\left({\displaystyle \frac{e}{e_n}}\right)}^2\cong {\left({\displaystyle \frac{\hslash c}{G_n{m}_p^2}}\right)}^2\cong {\displaystyle \frac{G_e{m}_e^3}{G_n{m}_p^3}}\cong {\displaystyle \frac{G_w^6{G}_e^4}{G_n^{10}}}$ (11)

Hence, proton and electron mass ratio can be expressed as,

$\begin{array}{l}{\displaystyle \frac{m_p}{m_e}}\cong {\displaystyle \frac{e_n^2{G}_e{m}_e^2}{e^2{G}_n{m}_p^2}}\cong \left({\displaystyle \frac{e_n^2}{4\pi {\epsilon }_0{G}_n{m}_p^2}}\right)÷\left({\displaystyle \frac{e^2}{4\pi {\epsilon }_0{G}_e{m}_e^2}}\right)\\ \cong {\left({\displaystyle \frac{e_n^2{G}_e}{e^2{G}_n}}\right)}^{1/3}\cong {\left[\left({\displaystyle \frac{e_n^2}{4\pi {\epsilon }_0{G}_n}}\right)÷\left({\displaystyle \frac{e^2}{4\pi {\epsilon }_0{G}_e}}\right)\right]}^{1/3}\end{array}$ (12)

In terms of specific charge ratios,

$\left({\displaystyle \frac{e}{m_e}}\right)÷\left({\displaystyle \frac{e_n}{m_p}}\right)\cong {\displaystyle \frac{e{m}_p}{e_n{m}_e}}\cong {\displaystyle \frac{\hslash c}{G_n{m}_p{m}_e}}\cong {\displaystyle \frac{G_e{m}_e^2}{\hslash c}}\cong \sqrt{{\displaystyle \frac{R_e}{R_n}}}\cong {\displaystyle \frac{G_w{G}_e}{G_n^2}}\cong {\displaystyle \frac{M_{wf}}{m_p}}$ (13)

$\left({\displaystyle \frac{e_n}{m_p}}\right)÷\left({\displaystyle \frac{e}{m_e}}\right)\cong {\displaystyle \frac{e_n{m}_e}{e{m}_p}}\cong {\displaystyle \frac{G_n{m}_p{m}_e}{\hslash c}}\cong {\displaystyle \frac{\hslash c}{G_e{m}_e^2}}\cong \sqrt{{\displaystyle \frac{R_n}{R_e}}}\cong {\displaystyle \frac{G_n^2}{G_w{G}_e}}\cong {\displaystyle \frac{m_p}{M_{wf}}}\cong 0.001605$ (14)

Here it is very interesting to note that,

${\displaystyle \frac{m_p}{M_{wf}}}\cong \left({\displaystyle \frac{\sqrt{{\left(m_{\pi }{c}^2\right)}^0{\left(m_{\pi }{c}^2\right)}^{\pm }}}{\sqrt{{\left(m_w{c}^2\right)}^{\pm }{\left(m_z{c}^2\right)}^0}}}\right)\cong \left({\displaystyle \frac{\sqrt{134.98\times 139.57} \mathrm{MeV}}{\sqrt{80379.0\times 91187.6} \mathrm{MeV}}}\right)\cong 0.0016032$ (15)

Here ratio of rest mass of proton to the assumed electroweak fermion is equal to the ratio of mean mass of pions to the mean mass of electroweak bosons. Based on this unique and concrete observation, we are very confident to say that strong and weak interactions play a vital role exploring the secrets of nuclear structure.

8. Understanding the Nucleon Magnetic Moments

Characteristic nucleon magnetic moment having a nuclear charge of $e_n$ and electromagnetic charge of $e$ can be expressed as,

$\begin{array}{l}{\mu }_X\cong {\displaystyle \frac{\hslash \sqrt{e_{n}e}}{2m_p}}\cong {\displaystyle \frac{e\hslash }{2\sqrt{m_e{M}_{wf}}}}\cong 8.6696\times {10}^{-27} \mathrm{J}{.\mathrm{Tesla}}^{-1}\\ \mathrm{where} M_{wf}\cong 1.042367\times {10}^{-24} \mathrm{kg}\end{array}$ (16)

Neutron magnetic moment [52,53] can be fitted with,

${\mu }_n\cong \left(1+{\alpha }_s\right){\displaystyle \frac{\hslash \sqrt{e_{n}e}}{2m_p}}\cong \left(1+{\alpha }_s\right){\displaystyle \frac{e\hslash }{2\sqrt{m_e{M}_{wf}}}}\cong 9.6684\times {10}^{-27} \mathrm{J}{.\mathrm{Tesla}}^{-1}$ (17)

Proton magnetic moment [52,53] can be fitted with,

${\mu }_p\cong \left(1.5+{\alpha }_s\right){\displaystyle \frac{\hslash \sqrt{e_{n}e}}{2m_p}}\cong {\displaystyle \frac{e\hslash }{2\sqrt{m_e{M}_{wf}}}}\cong 1.40\times {10}^{-26} \mathrm{J}{.\mathrm{Tesla}}^{-1}$ (18)

Ratio of neutron and proton magnetic moments can be expressed as,

${\displaystyle \frac{{\mu }_n}{{\mu }_p}}\cong {\displaystyle \frac{\left(1.0+{\alpha }_s\right)}{\left(1.5+{\alpha }_s\right)}}\cong 0.69$ (19)

9. Understanding the Fermi’s Weak Coupling Constant

Fermi’s weak coupling constant [1,2,52,53] can be fitted with the following relations.

$\begin{array}{l}{G}_F\cong {\left({\displaystyle \frac{m_e}{m_p}}\right)}^2\hslash c{R}_n^2\cong \hslash c{R}_w^2\\ \cong G_w{M}_{wf}^2{R}_w^2\cong 1.440206\times {10}^{-62} \mathrm{J}{.\mathrm{m}}^3\end{array}$ (20)

It is a very simple relation and demonstrates the confirmation of the physical existence of the proposed 585 GeV weak fermion. Obtained value is matching with the recommended value by 99.7%. It needs further study. In terms of electromagnetic, nuclear and gravitational interactions confined to radius of $R_n\cong {\displaystyle \frac{2G_n{m}_p}{c^2}}\cong 1.2393\times {10}^{-15}\mathrm{m},$ $G_F$can be expressed as,

$G_F\cong \left[{\left(G_e^2{G}_N\right)}^{{\displaystyle \frac{1}{3}}}{m}_p^2\right]{\left({\displaystyle \frac{2G_n{m}_p}{c^2}}\right)}^2$ (21)

10. Understanding Nuclear Stability Associated with Beta Decay

Nuclear stability means, finding stable atomic nuclides having long living time compared to other living atomic nuclides having short living time. By beta decay, mostly short living atomic nuclides emit electrons and positrons transform to stable atomic nuclides. In general, Beta decay process is believed to be associated with weak interaction. In this context, we noticed that, starting from Z=2 to 92,

$\begin{array}{l}{A}_s\cong 2Z+\beta {\left(2Z\right)}^2\cong 2Z+4\beta Z^2\cong 2Z+0.00642Z^2\\ \mathrm{where}, \\ A_s\cong \mathrm{Light} \mathrm{house} \mathrm{like} \mathrm{stable} \mathrm{mass} \mathrm{number}\\ \mathrm{Z}\cong \mathrm{Proton} \mathrm{number}\\ \beta \cong \mathrm{Specific} \mathrm{charge} \mathrm{ratios} \mathrm{of} \mathrm{proton} \mathrm{and} \mathrm{electron}\\ \cong \left({\displaystyle \frac{e_n}{m_p}}\right)÷\left({\displaystyle \frac{e}{m_e}}\right)\cong {\displaystyle \frac{e_n{m}_e}{e{m}_p}}\cong \sqrt{{\displaystyle \frac{R_n}{R_e}}}\cong {\displaystyle \frac{m_p}{M_{wf}}}\cong 0.001605\\ 4\beta \cong 4\times 0.001605\cong 0.00642 \end{array}$ (22)

Here we wish to call $\beta$ as the electroweak coefficient. Thus,

${\displaystyle \frac{A_s-2Z}{4Z^2}}\cong \beta$ (23)

One can find a similar relation in the literature [75]. This relation can be well tested for Z=21 to 92. For example,

$\begin{array}{l}{\displaystyle \frac{45-\left(2\times 21\right)}{4{\left(21\right)}^2}}\cong 0.00170;{\displaystyle \frac{63-\left(2\times 29\right)}{4{\left(29\right)}^2}}\cong 0.00149; \\ {\displaystyle \frac{89-\left(2\times 39\right)}{4{\left(39\right)}^2}}\cong 0.00181;{\displaystyle \frac{109-\left(2\times 47\right)}{4{\left(47\right)}^2}}\cong 0.0017;\\ {\displaystyle \frac{169-\left(2\times 69\right)}{4{\left(69\right)}^2}}\cong 0.00163;{\displaystyle \frac{238-\left(2\times 92\right)}{4{\left(92\right)}^2}}\cong 0.001595; \end{array}$This is one best practical and quantitative application of our proposed electroweak fermion and bosons. Following this relation and based on various semi empirical mass formulae, by knowing any stable mass number, its corresponding proton number can be estimated with,

$Z\cong {\displaystyle \frac{A_s}{1+\sqrt{1+4\beta A_s}}}\cong {\displaystyle \frac{A_s}{1+\sqrt{1+0.00642A_s}}}\cong {\displaystyle \frac{A_s}{2+0.0153A_s^{2/3}}}$ (24)

$\mathrm{where} {\displaystyle \frac{a_c}{2a_{asy}}}\cong {\displaystyle \frac{0.71 \mathrm{MeV}}{2\times 23.21 \mathrm{MeV}}}\cong {\displaystyle \frac{0.6615 \mathrm{MeV}}{2\times 21.6091 \mathrm{MeV}}}\cong 0.0153$With even-odd corrections and further study, super heavy atomic nuclides can be estimated easily. In this context, we have developed the following relation.

$\begin{array}{l}{A}_s\cong \mathrm{RoundOff}\left\{{\left(Z+\left({\displaystyle \frac{e_n}{e}}\right)\right)}^{1.2}-\sqrt{{\displaystyle \frac{e_n}{e}}}\right\}\cong \mathrm{RoundOff}\left\{{\left(Z+2.9464\right)}^{1.2}-1.7165\right\}\\ \mathrm{where} {\left({\displaystyle \frac{e_n}{e}}\right)}^{{\displaystyle \frac{1}{6}}}\cong {\left({\displaystyle \frac{1}{{\alpha }_s}}\right)}^{{\displaystyle \frac{1}{12}}}\cong 1.19733\cong 1.2\end{array}$ (25)

With even odd corrections,

$A_s\cong \left[\mathrm{RoundOff}\left\{{\left(Z+2.9464\right)}^{1.2}-1.7165\right\}+\left[0,1\right]\right]$ (26)

Here,

1) If Z is even and obtained $A_s$ is odd, then, $A_s\cong A_s+1.$2) If Z is even and obtained $A_s$ is even, then, $A_s\cong A_s.$3) If Z is odd and obtained $A_s$ is odd, then, $A_s\cong A_s.$4) If Z is odd and obtained $A_s$ is even, then, $A_s\cong A_s+1.$See Table. 3 presented in the next section for the estimated light house like stable mass numbers and corresponding nuclear binding energy.

11. Understanding Nuclear Binding Energy

In our recent publications pertaining to 4G model of final unification and based on strong and electroweak interactions, we have developed a completely new formula for estimating nuclear binding energy [76,77,78,79,80]. With reference to currently believed Semi Empirical Mass Formula (SEMF), we call our formula as ‘Strong and Electroweak Mass Formula’ (SEWMF). Our formula constitutes 4 simple terms and only one energy coefficient of magnitude 10.1 MeV. First term is a volume term, second term seems to be a representation of free nucleons associated with electroweak interaction, third term is a radial term and fourth one is an asymmetry term about the mean stable mass number. Considering this kind of approach, nuclear structure can be understood in terms of strong and weak interactions in a theoretical approach positively [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. For Z=6 to 118, improved binding energy relation can be expressed as follows. This relation and its corresponding paper is in review.

$BE\cong \left(A-A_{free}-A_{radial}-A_{asym}\right)\left(B_0\cong 10.1 \mathrm{MeV}\right)$ (27)

where $A\times 10.1 \mathrm{MeV}$ represents the volume term

$A_{free}\times 10.1 \mathrm{MeV}$ represents the modified electroweak term

$A_{radial}\times 10.1 \mathrm{MeV}$ represents the radial term

$A_{asym}\times 10.1 \mathrm{MeV}$ represents the modified asymmetry term

$\begin{array}{l}{B}_0\cong -{\displaystyle \frac{e_n^2}{8\pi {\epsilon }_0\left(G_n{m}_p/c^2\right)}}\cong -10.1 \mathrm{MeV}\\ \cong {\displaystyle \frac{1}{2}}\left[\left(2m_u{c}^2+m_d{c}^2\right)+\left(m_u{c}^2+2m_d{c}^2\right)\right]\cong 10.1 \mathrm{MeV}\\ \mathrm{where} \left(m_u,m_d\right) \mathrm{reprsent} \mathrm{Up} \mathrm{and} \mathrm{Down} \mathrm{quark} \mathrm{masses}.\end{array}$$\begin{array}{l}BE\cong \left\{A-\left\{\overline{\left({\displaystyle \frac{1}{2}}\right)+\beta \left[\left(Z^2+N^2+{\left({\displaystyle \frac{Z^2}{N}}\right)}^2\right)-N^2{\left({\displaystyle \frac{N-Z}{N+Z}}\right)}^2\right]}\right\}-A^{1/3}-{\displaystyle \frac{{\left(A_s-A\right)}^2}{A_s}}\right\}10.1 \mathrm{MeV}\\ \mathrm{where},\beta \cong 0.001605\end{array}$ (28)

Extrapolation point of view, there is a considerable error for very low and very high mass numbers of any Z and we are working in all possible ways. Close to the light house like stable mass numbers of Z=6 to 118,

$BE\cong \left\{A_s-\left\{\overline{\left({\displaystyle \frac{1}{2}}\right)+0.001605\left[\left(Z^2+N^2+{\left({\displaystyle \frac{Z^2}{N}}\right)}^2\right)-N^2{\left({\displaystyle \frac{N-Z}{N+Z}}\right)}^2\right]}\right\}-A_s^{{‌}^{1/3}}\right\}10.1 \mathrm{MeV}$ (29A)

We are working on understanding the electroweak term in various possible ways. See the following Table. 3 for the estimated binding energy of Z=6 to 118 with light house like mass numbers estimated from relation (26). For data comparison, we have taken the following advanced binding energy formula presented in reference [78].

$\left.\begin{array}{l}BE\cong \left\{\left[1+\left({\displaystyle \frac{4k_v}{A^2}}\right)\left|T_z\right|\left(\left|T_z\right|+1\right)\right]a_v*A\right\}+\left\{\left[1+\left({\displaystyle \frac{4k_s}{A^2}}\right)\left|T_z\right|\left(\left|T_z\right|+1\right)\right]a_s*A^{{\displaystyle \frac{2}{3}}}\right\}\\ +\left\{a_c*\left({\displaystyle \frac{Z^2}{A^{1/3}}}\right)\right\}+\left\{f_p*{\displaystyle \frac{Z^2}{A}}\right\}+E_p\end{array}\right\}$ (29B)

where, $T_z\cong 3\mathrm{rd} \mathrm{component} \mathrm{of} \mathrm{isospin}={\displaystyle \frac{1}{2}}\left(Z-N\right)$

$\left\{\left.\begin{array}{l}{a}_v=-15.4963 \mathrm{MeV}, a_s=17.7937 \mathrm{MeV}\\ k_v=-1.8232, k_s=-2.2593\\ a_c=0.7093 \mathrm{MeV}, f_p=-1.2739 \mathrm{MeV}\\ d_n=4.6919 \mathrm{MeV}, d_p=4.7230 \mathrm{MeV}\\ d_{np}=-6.4920 \mathrm{MeV}\end{array}\right\}\right.$ and $\left.\left\{\begin{array}{l}\mathrm{for} \left(Z, N \right) \mathrm{Odd}, E_p\cong {\displaystyle \frac{d_n}{N^{1/3}}}+{\displaystyle \frac{d_p}{Z^{1/3}}}+{\displaystyle \frac{d_{np}}{A^{2/3}}}\\ \mathrm{for} \left(\mathrm{Odd} Z, \mathrm{Even} N \right), E_p\cong {\displaystyle \frac{d_p}{Z^{1/3}}}\\ \mathrm{for} \left(\mathrm{Even} Z, \mathrm{Odd} N \right), E_p\cong {\displaystyle \frac{d_n}{N^{1/3}}}\\ \mathrm{for} \left(\mathrm{Even} Z, \mathrm{Even} N \right), E_p\cong 0\end{array}\right.\right\}$In Table 3,

As= Estimated light house like stable mass number

EBE = Estimated binding energy in MeV

EBEPN = Estimated binding energy per nucleon in MeV

RBE= Reference binding energy in MeV

RBEPN = Reference binding energy per nucleon in MeV

Diff.BE= Difference in Reference and Estimated binding energy.

Based on Liquid drop model, close to beta stability line, number of free nucleons associated with nuclear volume and surface area, can be addressed with an approximate relation of the form,

$\begin{array}{l}{A}_{free}\cong {\displaystyle \frac{1}{2}}+\left[0.000634\left({\underset{¯}{\left(A+Z^{2/3}+N^{2/3}\right)}}^2+\left({\displaystyle \frac{2Z}{A}}\right){\left({\displaystyle \frac{Z^2}{N}}\right)}^2\right)\right]\\ \cong {\displaystyle \frac{1}{2}}+\left[0.000634\left({\underset{¯}{\left(\overline{\left(Z+Z^{2/3}\right)}+\overline{\left(N+N^{2/3}\right)}\right)}}^2+\left({\displaystyle \frac{2Z}{A}}\right){\left({\displaystyle \frac{Z^2}{N}}\right)}^2\right)\right]\end{array}$ (30)

where $\beta \left({\displaystyle \frac{m_e}{m_n-m_p}}\right)\cong {\displaystyle \frac{m_p{m}_e}{M_{wf}\left(m_n-m_p\right)}}\cong 0.000634$

12. Understanding the Mean Lifetime of Neutron

Ratio of neutron-proton mass difference to electron rest mass can be expressed as,

$\left.\begin{array}{l}\left({\displaystyle \frac{m_n-m_p}{m_e}}\right)\cong \ln \left(4\pi \right)\cong 2.531024247 \mathrm{and}\\ {\displaystyle \frac{\left(939.5654205-938.27208816\right) \mathrm{MeV}}{0.51099895 \mathrm{MeV}}}\\ \cong {\displaystyle \frac{1.2933324 \mathrm{MeV}}{0.51099895 \mathrm{MeV}}}\cong 2.530988371\end{array}\right\}$ (31)

Relation (31) can be understood with the following relation (32). It may be noted that, ${\displaystyle \frac{e^2{G}_n{m}_p^3}{4\pi {\epsilon }_0{\left(\hslash /2\right)}^2}}\cong {\displaystyle \frac{4e^2{G}_n{m}_p^3}{4\pi {\epsilon }_0{\hslash }^2}}\cong 80.693732 \mathrm{MeV}.$ With a marginal error, it is matching with twice of the potential depth of nucleon (40 MeV) associated with Fermi gas model [81,82] of the nucleus.

$\left.\begin{array}{l}\mathrm{Let},\left({\displaystyle \frac{m_n-m_p}{m_e}}\right)\cong \ln \sqrt{\left({\displaystyle \frac{e^2{G}_n{m}_p^3}{4\pi {\epsilon }_0{\left(\hslash /2\right)}^2}}\right)÷\left(m_e{c}^2\right)}\\ \cong \ln \sqrt{{\displaystyle \frac{4e^2{m}_p}{4\pi {\epsilon }_0\hslash m_{e}c}}\left({\displaystyle \frac{G_n{m}_p^2}{\hslash c}}\right)}\cong \ln \sqrt{{\displaystyle \frac{4e_n^2{m}_p}{4\pi {\epsilon }_0\hslash m_{e}c}}\left({\displaystyle \frac{\hslash c}{G_n{m}_p^2}}\right)}\\ \cong \ln \sqrt{\left({\displaystyle \frac{4e_n^2}{4\pi {\epsilon }_0{G}_n{m}_p{m}_e}}\right)}\cong \ln \sqrt{4\left({\displaystyle \frac{e_n^2}{4\pi {\epsilon }_0{G}_n{m}_p{m}_e}}\right)}\\ \cong \ln \sqrt{4\left(4{\pi }^2\right)}\cong \ln \sqrt{16{\pi }^2}\cong \ln \left(4\pi \right)\end{array}\right\}$ (32)

Considering $\hslash$ in place of $\left(\hslash /2\right)$ , ${\displaystyle \frac{e^2{G}_n{m}_p^3}{4\pi {\epsilon }_0{\hslash }^2}}\cong 20.173433 \mathrm{MeV}.$If ${\displaystyle \frac{e^2{G}_n{m}_p^3}{4\pi {\epsilon }_0{\hslash }^2}}\cong {\displaystyle \frac{e_n^2}{4\pi {\epsilon }_0\left(G_n{m}_p/c^2\right)}}\cong 20.173433 \mathrm{MeV}$ represents a kind of potential energy, its total energy form is, $-{\displaystyle \frac{e^2{G}_n{m}_p^3}{8\pi {\epsilon }_0{\hslash }^2}}\cong -{\displaystyle \frac{e_n^2}{8\pi {\epsilon }_0\left(G_n{m}_p/c^2\right)}}\cong -10.08672 \mathrm{MeV}.$ Based on these coincidences, bottle method of neutron lifetime [60,61,62,63,64] can be expressed as,

$\left.\begin{array}{l}{t}_n\cong \exp \left[{\displaystyle \frac{2\times \mathrm{Nucleon} \mathrm{potential} \mathrm{well}\left(\approx 40 \mathrm{MeV}\right)}{\left(\mathrm{Neutron}, \mathrm{Proton}\right) \mathrm{rest} \mathrm{energy} \mathrm{difference}}}\right]\left({\displaystyle \frac{\hslash }{m_n{c}^2}}\right)\\ \cong \exp \left[{\displaystyle \frac{e^2{G}_n{m}_p^3}{4\pi {\epsilon }_0{\left(\hslash /2\right)}^2\left(m_n-m_n\right)c^2}}\right]\left({\displaystyle \frac{\hslash }{m_n{c}^2}}\right) \\ \cong \exp \left[4\left({\displaystyle \frac{e_n^2}{4\pi {\epsilon }_0\left(G_n{m}_p/c^2\right)}}\right)\left({\displaystyle \frac{1}{\left(m_n-m_n\right)c^2}}\right)\right]\left({\displaystyle \frac{\hslash }{m_n{c}^2}}\right)\\ \mathrm{where} \mathrm{factor} \text{'}4\text{'} \mathrm{needs} \mathrm{a} \mathrm{review} \mathrm{for} \mathrm{its} \mathrm{physical} \mathrm{interpretation}\end{array}\right\}.$ (33)

Thus, it is possible to show that,

$\begin{array}{l}{t}_n\cong \exp \left[\left({\displaystyle \frac{m_e}{m_n-m_p}}\right){\left(\exp \left({\displaystyle \frac{m_n-m_p}{m_e}}\right)\right)}^2\right]\left({\displaystyle \frac{\hslash }{m_n{c}^2}}\right)\cong 871.04 \sec \\ \cong \exp \left[{\displaystyle \frac{16{\pi }^2}{\ln \left(4\pi \right)}}\right]\left({\displaystyle \frac{\hslash }{m_n{c}^2}}\right)\cong 874.174 \sec .\end{array}$ (34)

Now coming back to our nuclear stability and binding energy relations, we noticed that,

$\left(1+{\displaystyle \frac{e_n}{e}}\right)\left({\displaystyle \frac{m_p}{M_{wf}}}\right)\cong 0.0063340\cong {\left({\displaystyle \frac{1}{4\pi }}\right)}^2\cong 0.0063326$ (35)

If one is willing to replace the factor 4 with $\left(1+{\displaystyle \frac{e_n}{e}}\right)\cong 3.9464$ in relation (22), nuclear beta stability relation can be expressed as,

$A_s\cong 2Z+{\left({\displaystyle \frac{Z}{4\pi }}\right)}^2$ (36)

13. Understanding the Root Mean Square Radius of Proton and Nuclear Charge Radii

Root mean square radius of proton [83,84] can be understood with

$\begin{array}{l}{R}_p\cong \left(1+{\displaystyle \frac{e_n}{e}}\right)\left({\displaystyle \frac{\hslash }{m_{p}c}}\right)\cong \left({\displaystyle \frac{\hslash }{m_{p}c}}\right)+\left({\displaystyle \frac{G_n{m}_p}{c^2}}\right)\\ \cong \left(1+{\displaystyle \frac{e}{e_n}}\right)\left({\displaystyle \frac{G_n{m}_p}{c^2}}\right)\cong 8.3\times {10}^{-16} \mathrm{m}\end{array}$ (37)

Considering higher powers of $\left({\displaystyle \frac{e}{e_n}}\right)$,

$R_p\cong \exp \left({\displaystyle \frac{e}{e_n}}\right)\left({\displaystyle \frac{G_n{m}_p}{c^2}}\right)\cong 1.4041\left({\displaystyle \frac{G_n{m}_p}{c^2}}\right)$ (38)

Thus, $R_p\cong \left(1.3394 \mathrm{to} 1.4041\right)\left({\displaystyle \frac{G_n{m}_p}{c^2}}\right)\cong \left(8.3 \mathrm{to} 8.7\right)\times {10}^{-16} \mathrm{m}$ (39)

For medium and heavy atomic nuclides, nuclear charge radii [85,86,87] can be expressed as,

$\begin{array}{l}{R}_{\left(Z,N\right)}\cong \left[Z^{1/3}+{\left(\sqrt{ZN}\right)}^{1/3}\right]\left({\displaystyle \frac{G_n{m}_p}{c^2}}\right)\\ \cong \left[Z^{1/3}+{\left(\sqrt{ZN}\right)}^{1/3}\right]\times 0.6197\times {10}^{-15} \mathrm{m}\end{array}$ (40)

Estimated data can be compared with the data available at https://www-nds.iaea.org/radii/ and http://zgwlc.xml-journal.net/fileZGWLC//journal/article/file/6bed4d71-97cc-4f48-9f0f-20af839757da.txt. See Table. 4 (attached at the end of the paper). Estimated data has been compared with the data presented in reference [86], https://www-nds.iaea.org/radii/.

Thus, by knowing the nuclear charge radii, nuclear gravitational constant [24,25,26,27,28,29,30,31,32,33,34,35,36,37] can be estimated as,

$G_n\cong {\left[Z^{1/3}+{\left(\sqrt{ZN}\right)}^{1/3}\right]}^{-1}\left({\displaystyle \frac{c^2{R}_{\left(Z,N\right)}}{m_p}}\right)$ (41)

This relation can be thoroughly investigated and modified for a better understanding and accuracy for the whole range of atomic nuclides.

14. Understanding Various Quantum Constants

Believing in these simple and workable relations, Planck’s constant and corresponding magnetic flux quantum [5,52,53] can be expressed as follows.

$h\cong \sqrt{\left({\displaystyle \frac{e_n^2}{4\pi {\epsilon }_{0}c}}\right)\left({\displaystyle \frac{G_e{m}_e^2}{c}}\right)}$ (42)

$\left({\displaystyle \frac{h}{e}}\right)\cong \left({\displaystyle \frac{e_n}{e}}\right)\sqrt{{\displaystyle \frac{G_e{m}_e^2}{4\pi {\epsilon }_0{c}^2}}}\cong \left({\displaystyle \frac{e_n}{e}}\right)\sqrt{{\displaystyle \frac{{\mu }_0}{4\pi }}\left(G_e{m}_e^2\right)}$ (43)

With reference to experimental magnetic flux quantum $\left({\displaystyle \frac{h}{2e}}\right)$, factor $\left({\displaystyle \frac{1}{2}}\right)$ is missing in this relation. It can be understood as follows.

Total magnetic flux generated for one electron can be,

${\Phi }_{Total}\cong \left({\displaystyle \frac{e_n}{e}}\right)\sqrt{\left({\displaystyle \frac{{\mu }_0}{4\pi }}\right)G_e{m}_e^2}\cong {\displaystyle \frac{h}{e}}$ (44)

For a simple two-pole system, quantum of magnetic flux per pole can be,

${\Phi }_{per/pole}\cong {\displaystyle \frac{{\Phi }_{Total}}{2}}\cong {\displaystyle \frac{1}{2}}\left({\displaystyle \frac{e_n}{e}}\right)\sqrt{\left({\displaystyle \frac{{\mu }_0}{4\pi }}\right)G_e{m}_e^2}\cong {\displaystyle \frac{h}{2e}}$ (45)

Following this logic, quantum of resistance can be expressed as,

${\displaystyle \frac{h}{e^2}}\cong \left({\displaystyle \frac{e_n}{e}}\right)\left({\displaystyle \frac{m_e}{e}}\right)\sqrt{{\displaystyle \frac{G_e}{4\pi {\epsilon }_0{c}^2}}}$ (46)

We are working in this direction.

15. Discussion on Estimating the Newtonian Gravitational Constant, the Proposed Weak Gravitational Constant and the Charge Ratio

In a unified approach, Newtonian gravitational constant can be estimated with many relations. Based on atomic interferometry, its experimental value seems to vary in a wide range of (6.672 to 6.693) x 10^-11 cubic meters per kilogram second squared [88,89,90]. Based on relation (21),

$\begin{array}{l}{G}_N\cong {\displaystyle \frac{G_F^3{c}^{12}}{64G_e^2{G}_n^6{m}_p^{12}}}\cong {\displaystyle \frac{G_F^3}{G_e^2{m}_p^6}}{\left({\displaystyle \frac{2G_n{m}_p}{c^2}}\right)}^{-6}\cong {\displaystyle \frac{G_F^3}{G_e^2{m}_p^6{R}_0^6}}\\ \mathrm{where} R_0\cong {\displaystyle \frac{2G_n{m}_p}{c^2}}\cong 1.2393\times {10}^{-15} \mathrm{m}\end{array}$ (47)

If the recommended value [52,53] of $G_F\cong 1.435851032\times {10}^{-62} \mathrm{J}{.\mathrm{m}}^3,$ estimated value of $G_N\cong 6.61938\times {10}^{-11}{ \mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}.$Considering relation (20), obtained value of $G_F\cong 1.440206\times {10}^{-62} \mathrm{J}{.\mathrm{m}}^3$ and estimated value of $G_N\cong 6.679794\times {10}^{-11}{ \mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}.$With reference to the recommended value [52,53] of $G_N\cong 6.6743\times {10}^{-11}{ \mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}$and based on our proposed relations (20), (21) and (47), values of $G_F$and $G_N$ are closely fitting with each other. This kind of approach can be recommended for further research.

Here it may be noted that, based on the relations (8) and (11)

$G_e\cong {\left({\displaystyle \frac{m_p}{2\pi m_e}}\right)}^2{\displaystyle \frac{e^2}{4\pi {\epsilon }_0{m}_e^2}}$ (48)

Thus, with reference to the known nuclear and atomic physical constants and their accuracy,

$G_N\cong {\left({\displaystyle \frac{m_e}{m_p}}\right)}^8{\left({\displaystyle \frac{4\pi {\epsilon }_0}{e^2}}\right)}^2{\displaystyle \frac{16{\pi }^4{G}_F^3}{m_p^2{R}_0^6}}\cong {\left({\displaystyle \frac{m_e}{m_p}}\right)}^{10}\left[{\left({\displaystyle \frac{4\pi {\epsilon }_0}{e^2}}\right)}^2{\displaystyle \frac{16{\pi }^4{G}_F^3}{m_e^2{R}_0^6}}\right]$ (49)

Interesting observation is that,

$\begin{array}{l}{G}_w\cong {\left({\displaystyle \frac{4\pi {\epsilon }_0}{e^2}}\right)}^2{\displaystyle \frac{16{\pi }^4{G}_F^3}{m_e^2{R}_0^6}}\\ \cong \mathrm{Proposed} \mathrm{Weak} \mathrm{gravitational} \mathrm{constant}\end{array}$ (50)

Thus, ${\displaystyle \frac{G_N}{G_w}}\cong {\left({\displaystyle \frac{m_e}{m_p}}\right)}^{10} \left(\mathrm{or}\right){\displaystyle \frac{G_w}{G_N}}\cong {\left({\displaystyle \frac{m_p}{m_e}}\right)}^{10}$ (51)

Based on relations (6), (10), (11), (20) and (21),

${\displaystyle \frac{\hslash c}{G_n{m}_p^2}}\cong {\displaystyle \frac{e}{e_n}}\cong {\displaystyle \frac{G_w^3{G}_e^2}{G_n^5}}\cong {\left({\displaystyle \frac{G_n^{15}{G}_N}{G_w^{12}{G}_e^4}}\right)}^{{\displaystyle \frac{1}{3}}}$ (52)

Unification point of view, relations (21), (50), (51) and (52) need a thorough study.

Based on relations (7), (20), (21), (42), (43), (48) and (51), quantitatively,

${\displaystyle \frac{e_n}{e}}\cong {\displaystyle \frac{4{\pi }^2{m}_e}{\alpha m_p}}\cong {\displaystyle \frac{m_p^2}{M_{wf}{m}_e}}$ (53)

Proceeding further, Strong coupling constant can be expressed as,

${\alpha }_s\cong {\left({\displaystyle \frac{e}{e_n}}\right)}^2\cong {\displaystyle \frac{M_{wf}^2{m}_e^2}{m_p^4}}$ (54)

Thus, in a unified data fitting approach,

1) Step-1: After a systematic study and understanding of nuclear charge radii, from relation (41), $\left(G_n\right) \mathrm{and} \left(G_n{m}_p/c^2\right),\left(2G_n{m}_p/c^2\right)$ can be estimated.

2) Step-2: From relation (6), $\left({\displaystyle \frac{e_n}{e}}\right)$ can be estimated.

3) Step-3: From relation (11), $\left({\alpha }_s\right)$ can be estimated.

4) Step-4: From relation (53), $\left(M_{wf}\right)$ can be estimated.

5) Step-5: From relation (7), $\left(G_w\right)$ can be estimated.

6) Step-6: From relation (52), $\left(G_e\right) \mathrm{and} (G_N)$ can be estimated.

7) Step-7: From relation (20) or (21), $\left(G_F\right)$ be estimated.

8) Step-8: With further study, all obtained values can be verified for their estimated accuracy with reference to relations like (8), (9), (10), (37 to 39) and (42 to 51).

9) Step-9: A cyclic review on Step-1 to Step-8

10) Step-10: To standardize the obtained numerical values, eliminating unwanted relations, exploring new relations, developing a cohesive and workable physical model.

See Table 4. (attached at the end of the paper), for the estimated data based on the reference nuclear charge radii [86]. In this attempt, we consider elementary charge, permittivity of free space, proton and electron rest masses and reduced Plank’s constat as inputs. All the estimated values are in SI units. It may be noted that, in a verifiable approach, we consider the fundamental ratio $\left({\displaystyle \frac{h}{\hslash }}\right)\cong 2\pi$ as a cross-check value. In the first row of Table 4, we have presented the average values of the estimated physical constants corresponding to 890 nuclear charge radii. For the time being, it can be considered as a case study.

16. Tera Electron Volt Photon Radiation Coming from Galaxies

In the near future, by increasing the operating capacity of particle accelerators it seems possible to confirm the existence of 585 GeV. It can be understood by observing Tera electron volt (TeV) photons coming by annihilation of 585 GeV fermions within the core of the particle accelerator or surroundings of astrophysical objects. At the vicinity of compact stars or exploding stars, TeV radiation can be understood with three theoretical methods [91,92,93,94,95]. As we are beginners of astrophysics domain, we appeal the science community to see the possibility of considering the proposed 585 GeV weak fermion with a charge of $\left(\pm e\right)$ in place of electron and proton. As it is assumed that, 585 GeV weak fermion is the mother of all elementary particles, at very high energies, it can be assumed as relatively stable for the possible occurrence of the following accelerating mechanisms.

Method-1: Generation and Annihilation of 585 GeV Weak Fermions

a) 585 GeV fermions are generated by the decay of high energy elementary particles available within the core of the hot astrophysical objects.

b) 585 GeV weak fermions emit high energy radiation via annihilation mechanism.

Method-2: Annihilation of Accelerated 585 GeV Weak Fermions

a) 585 GeV fermions are forced to accelerate by the surrounding shock waves.

b) Accelerated 585 GeV weak fermions emit high energy photons via synchrotron mechanism or annihilation.

Method-3: Accelerated 585 GeV Weak Fermions Sharing Energy to Low TeV Photons

a) 585 GeV fermions are forced to accelerate by the surrounding shock waves.

b) By following Inverse Compton Effect (ICE), low TeV photons gain energy from high energy 585 GeV weak fermions resulting in much higher TeV photons.

17. Conclusion

Even though our approach is lagging in mathematical approach and links are missing in developing a perfect model, compared to string theory, following our approach, there is a possibility of understanding and fitting the fundamental constants and there is a scope for developing unified physical concepts in a better way. In a microscopic approach, considering relations (1) to (54), it seems possible to understand and confirm the physical existence of the proposed 585 GeV weak fermion directly and indirectly. We would like to emphasize the point that the “ratio of mean mass of pions to the mean mass of weak bosons” is accurately matching with the “ratio of mass of proton to the proposed weak fermion”. It can be considered as a strong support and evidence for confirming the physical existence of the proposed weak fermion. In a macroscopic approach, by considering TeV photons coming from astrophysical objects, there is a scope and possibility for confirming the physical existence of 585 GeV weak fermion. It needs further study.

Data availability statement: The data that support the findings of this study are openly available.