Relations between the Quantum Eigenvalue m and Transition Rates of Charged Particles Held in Gravitational Eigenstates in Nonrelativistic Regions of Deep Gravitational Wells

This paper continues an ongoing investigation into the theoretical behavior of charged particles held in gravitational eigenstates in nonrelativistic regions of deep gravitational wells. Previous theoretical studies have shown that gravitational eigenstates in deep gravitational wells can exhibit extremely small interaction cross-sections and lifetimes which exceed the age of the universe as a result of the composition of the eigenspectrum of their wave functions. Particles in gravitational eigenstates could provide an explanation for the source of dark matter without the need to resort to exotic particles or exotic physics. However, the development of the theory of gravitational eigenstates is challenging due to the extreme scale of quantum eigenvalues involved. Recent research has sought empirical trends for state-to-state transition rates and lifetimes of gravitational eigenstates to extrapolate computationally practical calculations to galactic scales. In earlier studies, support was found for decreasing interaction cross-sections with increasing quantum eigenvalues n and l, however, the initial quantum eigenvalue m was set to zero, and only the Delta m = 0 decay channel was calculated [1]. This paper explores how different values of m and Delta m affect state-to-state transition rates and state lifetimes. It is demonstrated that the sum of all possible Delta m decay channels is constant for all m. It was found that the Delta m = 0 decay channel represents the greatest state-to-state transition rate when m = 0. This paper shows that a maximum constraint on state-to-state transition rate for m = 0 can be achieved through only evaluating the Delta m = 0 decay channel.