The nucleon-pair shell model (NPSM) with broken symmetry basis is studied. The results demonstrate the validity of NPSM with symmetry broken basis, which leads to a significant reduction in the dimensionality of the multi-pair configuration space. We have observed that the axial-deformed basis provides a satisfactory description of the low-lying spectrum, even without the need for the projection procedure. In the case of the triaxial-deformed basis, we have investigated the variation after angular momentum projection, indicating the potential for NPSM to find exact solutions in the half-closed system.

The atomic nucleus contains protons and neutrons surrounded by a structured electron cloud. Some combinations of protons and neutrons induce the nucleus to behave like a microscopic magnet, possessing a unique magnitude and orientation known as the nuclear magnetic moment (µ). When the numbers of protons and neutrons are both even then µ=0, but otherwise each nu-clide’s nuclear magnetic moment is unique. A second unique nuclear physical property relates to the nucleon binding energy (BE), which can be thought of as the energy between protons and neu-trons bound within the nucleus. The sequence of stable nuclides increases one nucleon at a time through 36Ar. The binding energy associated with the addition of each successive nucleon (∆BE) through this progression is unique. The hypothesis here is that the unique non-zero magnetic mo-ment and ∆ binding energy of each nuclide derive from its respective microscopic nuclear struc-ture, analogous to the way that the atomic physical properties of an element ultimately derive from its unique electron orbital structure. By extension, the identification of nuclear periodic pat-terns might eventually inform a theory of nuclear structure. The light, stable nuclides through 36Ar were arranged in ascending order according to atomic mass, and their nuclear magnetic mo-ments and binding energies were evaluated for periodic patterns. Fixed-period lengths from 4 through 18 nuclides per period were considered. These fixed periods, each of equal length, were stacked one upon the other and analyzed for vertical trends. The best evidence of periodicity in both µ and ∆BE converges precisely at the fixed 12-nuclide period. Implications for nuclear structure are discussed.

The mass of the nucleons is calculated from first principles by defining the quark as a non-gravitational particle, subject to Dirac’s equation with non-canonical gamma matrices. Unlike the canonical electron-type, this Dirac particle has two real dipole moments, which allows a structural modelling of hadrons. It is shown how such modelling reveals striking correspondences and differences between dually related particles and properties like electrons and quarks, photons and gluons, pions and nucleons, spin and isospin and protons and neutrons. It is a stepping stone to the actual calculation, which competes in precision with lattice QCD. The appendix contains a Lorentz covariance proof of hadrons composed by such particular Dirac-type quarks.

Following the concept of strong interaction, theoretically, fusion of proton seems to increase the binding energy of final atom by 8.8 MeV. Due to Coulombic repulsion, asymmetry effect, pairing effect and other nuclear effects, final atom is forced to choose a little bit of binding energy less than 8.8 MeV and thus it is able to release left over binding energy in the form of internal kinetic energy or external thermal energy. Thus, in cold fusion, heat release to occur, binding energy difference of final atom and base atom seems to be less than 8.8 MeV. Qualitatively, energy released during cold fusion seems to be approximately equal to 8.8 MeV minus the difference of binding energy of final and base atoms. Based on this idea, under normal conditions, for the case of ₂He⁴, fusion of four protons can liberate (35.2-28.3)=6.9 MeV and it is 3.5 times less than the current estimates. Point to be understood is that, lesser the binding energy of final atom, higher the liberated thermal energy and vice versa. With a suitable catalyst and sufficient hydrogen under suitable pressure, if reactor’s temperature is maintained at (1000 to 1500) ⁰C, there seems a lot of scope for a chain reaction of cold fusion in which light isotopes transform to their next stage with increased proton number or mass number and liberate safe and clean heat energy continuously. By arranging 4 to 6 reactors and charging them periodically in tandem, required thermal energy can be produced continuously. In this new direction, by carefully selecting the base isotope and its corresponding catalyst, experiments can be conducted and ground reality of cold fusion can be understood at various temperature and pressure conditions.

We propose that quarks and gluon flux tubes emerge from networks of standing vacuum waves. Each unbound nucleon, in its ground state, may be electromagnetically modeled as massless quantized charge on two pairs of orbiting arcs. Each charge arc is associated with a superposition of radially-oriented vacuum fundamental harmonics. These quantum superpositions of radial waves are coupled to nucleon mass-energy. The charge arcs orbit on the two surfaces of a spindle torus with polar charge-exclusion zones. These ground-state models of unbound nucleons may be interpreted as pairs of virtual Möbius bands. The optimal triangular Möbius band may explain proton uniqueness. These unbound proton and neutron models are shown to be precisely connected via a parameter dependent on neutron mass and the sum of the up and down bare quark masses. Due to this precise connection, and the relatively high experimental precision of proton magnetic moment, neutron magnetic moment is calculated about two orders of magnitude more precisely than the most accurate experiments to date. This quantum network-based approach to modeling unbound low-energy nucleons calculates several other measurable parameters.

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. $G_s\cong 3.32688\times {10}^{28}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}$ being the nuclear gravitational constant, nuclear charge radius can be shown to be, $R_0\cong \frac{2G_s{m}_p}{c^2}\cong 1.24\mathrm{fm}.$ $e_s\cong \left(\frac{G_s{m}_p^2}{\hslash c}\right)e\cong 4.716785\times {10}^{-19}\mathrm{C}$ being the nuclear elementary charge, proton magnetic moment can be shown to be, ${\mu }_p\cong \frac{e_s\hslash }{2m_p}\cong \frac{e{G}_s{m}_p}{2c}\cong 1.48694\times {10}^{-26}\mathrm{J}{.\mathrm{T}}^{-1}.$ ${\alpha }_s\cong {\left(\frac{\hslash c}{G_s{m}_p^2}\right)}^2\cong 0.1153795$ being the strong coupling constant, strong interaction range can be shown to be proportional to $\exp \left(\frac{1}{{\alpha }_s^2}\right).$ 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, ${\left(B\right)}_{A_s}\cong Z\times \left\{\left(\frac{1}{{\alpha }_s}+1\right)+\sqrt{\sqrt{30\times 31}}\right\}\left(m_n-m_p\right)c^2\approx Z\times 19.66\mathrm{MeV}.$ 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, ${\left(m_p/m_e\right)}^{10}\cong \exp \left(1/{\alpha }_s^2\right)$ and $2G_s{m}_e/c^2\cong \sqrt{G_F/\hslash c}.$