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Journal of Physics & Optics Sciences

Resolution of the Fundamental Equation of the Mathematical Formulation of Nuclear Collision Mechanisms Model

Ettabiy Abderrahmane

Published May 6, 2024• 1 citation
Publisher

Abstract

The fundamental equation of the model titled “mathematical formulation of nuclear collision mechanisms” [1] was solved. The solution is compounded of two steps, the first step consists in calculating the values of the parameters of the mechanism-operator underlying a given nuclear collision and the second step, consists in deducing the open channels for this collision. Knowing that the equation is not classic, its resolution has required the development of an innovative mathematical method that sets on the use of physical constraints of the problem.

DOI
10.47363/jpsos/2024(6)243

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The fundamental equation of the model titled “mathematical formulation of nuclear collision mechanisms” [1] was solved. The solution is compounded of two steps, the first step consists in calculating the values of the parameters of the mechanism-operator underlying a given nuclear collision and the second step, consists in deducing the open channels for this collision. Knowing that the equation is not classic, its resolution has required the development of an innovative mathematical method that sets on the use of physical constraints of the problem.
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Non-relativistic quantum scattering theory informs our broad understanding of nuclear collision processes. However, detailed theoretical insights into the dynamics of fusion, whereby the colliding nuclei form a compound nucleus, remain elusive with conventional approaches. Fundamentally, understanding the complex dissipative processes inherent to compound nucleus formation and when they occur during the collision remains challenging. This, for example, prevents a consistent description of heavy-ion fusion over a wide range of collision energies and hinders searches for new super-heavy elements. To understand these dynamics, we need time-dependent approaches to nuclear collisions. In this thesis, a non-relativistic, time-dependent wave packet theory for potential scattering of charged quantum particles (such as nuclei) has been developed. It formally extends the application of Tannor and Weeks's (1993) formulation of the scattering matrix theory to systems containing the long-range Coulomb potential, by utilising Dollard's (1964) Møller operators. Using the asymptotic localisation of wave packets, analytical theorems have been formulated that allow convenient numerical application of this method. Numerical tests illustrating the theory mark the first rigorous application of this method in nuclear physics. Further insights are gained through a novel analysis of the wave packet time-correlation function (which underlies the theory) to understand how different dynamical processes, such as the formation of long-lived, quasi-bound states, during scattering contribute to the scattering matrix. This provides guidance on using the time-correlation function to obtain fusion observables, along with the associated challenges. Furthermore, this analysis showed that time-correlation functions can be obtained from static calculations, opening numerous new possibilities for studying the dynamics of nuclear reactions, in general, using this approach. This work opens new avenues for studying the dynamics of compound nucleus formation and other dissipative processes in nuclear reactions.
Quantum mechanics (QM) and quantum electrodynamics (QED) are often touted as the most successful theories ever. In this paper, this claim is critically evaluated by a test of internal consistency for the ability to calculate the conjugate observables of the nature of the free electron, ionization energy, elastic electron scattering, and the excited states of the helium atom using the same solution for each of the separate experimental measurements. It is found that in some cases quantum gives good numbers, but the solutions are meaningless numbers since each has no relationship to providing an accurate physical model. Rather, the goal is to mathematically reproduce an experimental or prior theoretical number using adjustable parameters including arbitrary wave functions in computer algorithms with precision that is often much greater (e.g. 8 significant figures greater) than possible based on the propagation of errors in the measured fundamental constants implicit in the physical problem. Given the constraints of adherence to physical laws and internal consistency, an extensive literature search indicates that quantum mechanics has never solved a single physical problem correctly including the hydrogen atom and the next member of the periodic chart, the helium atom. Rather than using postulated unverifiable theories that treat atomic particles as if they were not real, physical laws are now applied to the same problem. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of − e moving in the Coulombic field of the proton and the wave equation as modified after Schrodinger, a classical approach is explored which yields a model which is remarkably accurate and provides insight into physics on the atomic level. The proverbial view deeply seated in the wave-particle duality notion that there is no large-scale physical counterpart to the nature of the electron is shown not to be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantum atomic problems. Specifically, a theory of classical quantum mechanics (CQM) was derived from first principles as reported previously [1-7] that successfully applied physical laws to the solution of atomic problems that has its basis in a breakthrough in the understanding of the stability of the bound electron to radiation. Rather than using the postulated Schrodinger boundary condition: “ 0 Ψ→ as →∞ r ,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound 1 = n -state electron cannot radiate energy. Although it is well known that an accelerated point particle radiates, an extended distribution, modeled as a superposition of accelerating charges, does not have to radiate. A simple invariant physical model arises naturally wherein the predicted results are extremely straightforward and internally consistent requiring minimal math as in the case of the most famous equations of Newton, Maxwell, Einstein, de Broglie, and Planck on which the model is based. No new physics is needed; only the known physical laws based on direct observation are used. The accurate solution of the helium atom is confirmed by the agreement of predicted and observed conjugate parameters using the same unique physical model in all cases.