Abstract
In this work we re-examine a model of the nucleons that involve the weak interaction which was once considered by Heisenberg; that is a neutron may have the structure of a dwarf hydrogen-like atom. We formulate a quantum dynamics for the Heisenberg model of the neutron associated with interaction that involves the beta decay in terms of a mixed Coulomb-Yukawa potential and the More General Exponential Screened Coulomb Potential (MGESCP), which has been studied and applied to various fields of physics. We show that all the components that form the MGESCP potential can be derived from a general system of linear first order partial differential equations similar to Dirac relativistic equation in quantum mechanics. There are many interesting features that emerge from the MGESCP potential, such as the MGESCP potential can be reduced to the potential that has been proposed to describe the interaction between the quarks for strong force in particle physics, and the energy spectrum of the bound states of the dwarf hydrogen-like atom is continuous with respect to distance. This result leads to an unexpected implication that a proton and an electron may also interact strongly at short distances. We also show that the Yukawa potential when restrained can generate and determine the mathematical structures of fundamental particles associated with the strong and weak fields.
Highlights
The physical process of beta decay should be described by many different dynamics rather than a single one, only if we can formulate the whole physical process under a mathematical formulation that can give rise to each state by some form of limit associated with mathematical parameters that are used to describe the whole system
In this work we have still been able to discuss in terms of Schrödinger wave mechanics a quantum dynamics of the neutron as a dwarf hydrogen-like atom using a more complete potential which has been studied and applied to various fields of physics, the so-called the More General Exponential Screened Coulomb Potential (MGESCP)
We have shown that the MGESCP potential can be derived from a Dirac-like system of equations which can be reduced from a general system of linear first-order partial differential equations
Summary
There are prominent features that emerge from using the MGESCP potential to describe a neutron as a dwarf hydrogen-like atom, such as the energy spectrum of the bound states is continuous with respect to distance, and, as discussed, the Yukawa potential can be restrained to generate and determine mathematical structures of physical objects that may be identified with the quantum mediators associated with the weak and strong interactions. It is reasonable to suggest that functional potentials in physics may have physical mechanisms to generate mediators of associated physical fields, and these mechanisms can be formulated in terms of differentiable manifolds and their corresponding direct sums of prime manifolds as discussed in our works on the possibility to formulate physics in terms of differential geometry and topology [9]
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