Fusion Cross Section of $\rm T(d,n)^{4}He$ and $\rm ^{3}He(d,p)^{4}He$ Reactions by Four Parameters Formula

TL;DR

This paper presents a simplified model using a complex square well potential to calculate fusion cross sections of light nuclei, achieving excellent agreement with experimental data for key reactions.

Contribution

It introduces a minimalistic four-parameter formula based on complex potential theory to accurately predict fusion cross sections of light nuclei.

Findings

Results closely match experimental data for T(d,n)4He and 3He(d,p)4He reactions.

The simplified model effectively captures essential physics despite ignoring detailed nuclear interactions.

Excellent agreement demonstrates the model's potential for practical fusion cross section calculations.

Abstract

Fusion cross sections of light nuclei are calculated by a complex potential and taking into account of conservation of angular momentum and parity. The nuclear potential is assumed to be as simple as a spherical complex square well with a rigid core. Then, the nuclear phase shift is extracted from continuity condition of inverse of the logarithmic derivative of the wave functions as a complex quantity. The quantum tunneling probability and cross section are obtained via real and complex components of nuclear phase shift. The obtained results for the two most important light nuclei reactions, $\rm T(d,n)^{4}He$, $\rm ^{3}He(d,p)^{4}He$ are compared with other theoretical formulas and experimental data. Despite that the theory is simplified as much as possible and the complexities and details of nuclear interactions has been ignored, excellent agreements with experimental data are achieved.