Revisiting the Gamow Factor of Reactions on Light Nuclei

TL;DR

This paper revises the Gamow factor for light nuclei reactions by accounting for nuclear potential dependence, revealing higher penetration probabilities near the Coulomb barrier and impacting experimental cross-section measurements.

Contribution

It introduces a corrected model for penetration probabilities that considers nuclear potential depth, improving upon the conventional Gamow factor for light nuclei.

Findings

Penetration probabilities are higher than traditional estimates near the Coulomb barrier.

The modified Gamow factor affects the determination of the Gamow peak energy.

Implications for electron screening effects are discussed.

Abstract

This study provides an improved understanding of the penetration probabilities (PPs) in nuclear reactions of light nuclei by correcting the assumptions used in the conventional Gamow factor. The Gamow factor effectively describes the PP in nuclear reactions based on two assumptions: low particle energy than the Coulomb barrier and neglecting the dependence of nuclear interaction potential. However, we find that the assumptions are not valid for light nuclei. As a result of a calculation that excludes the assumptions, we obtain the PP that depends on the nuclear interaction potential depth for the light nuclei. For the potential depth fitted by the experimental fusion cross-section, we present that PPs of light nuclei (D+D, D+T, D+$^3$He, p+D, p+$^6$Li, and p+$^7$Li) become higher than the conventional one near the Coulomb barrier. We also discuss the implications of the modified PP, such as changes in the Gamow peak energy, which determine the measurement of the energy range of the nuclear cross-section in experiments, and the electron screening effect.