Screening Effects on the Tunnelling Probability for Deuterium-Tritium Fusion Using the WKB Approximation

This research examines how environmental screening — the influence of surrounding charged particles — modifies the probability of quantum tunnelling in deuterium–tritium (D–T) fusion reactions. Using the screened Coulomb (Yukawa) potential, the study models how plasma conditions or metallic confinement environments alter the effective potential barrier through which nuclei must tunnel. The work employs the WKB (Wentzel–Kramers–Brillouin) approximation, a semi-classical approach to solving the Schrödinger equation, to quantify tunnelling probabilities across a range of screening strengths and kinetic energies.

By comparing three physical contexts — weakly screened tokamak plasmas, strongly screened stellar plasmas, and lattice-confined metallic environments — the paper demonstrates how screening significantly enhances tunnelling probabilities at sub-keV energies. The screening parameter k0k_0k0​, related to the Debye length in plasmas, reshapes the potential barrier by reducing its height and width, thus allowing fusion to occur at lower incident energies than in an ideal vacuum. However, at higher kinetic energies (above ~2 keV), the influence of screening diminishes as particles possess enough energy to overcome the Coulomb barrier without quantum effects dominating.

The study’s main contribution lies in refining the mathematical connection formulas across classical turning points, where standard WKB methods typically break down. By applying local linearization and Airy-function matching, the author constructs a consistent framework for tunnelling in screened systems. This theoretical insight helps explain why environmental conditions — such as dense plasma or metallic confinement — can dramatically enhance fusion rates, offering potential pathways to more feasible solid-state or low-energy fusion mechanisms. The results underscore the importance of quantum effects and environmental parameters in both astrophysical processes and future sustainable fusion technologies.