Optical potential parameters of light nuclear fusion based on precise Coulomb wave functions

TL;DR

This paper uses precise Coulomb wave functions to calculate light nuclear fusion cross sections, calibrates optical potential parameters, and reveals significant differences from previous approximate methods, especially near resonance peaks.

Contribution

It introduces a method based on exact Coulomb wave functions for optical potential calibration, highlighting deviations from prior approximate approaches and analyzing resonance effects.

Findings

Optical potential parameters differ significantly from previous results.

Resonance peaks in fusion reactions are sensitive to Coulomb wave function accuracy.

Small deviations in wave functions can lead to large changes in predicted cross sections.

Abstract

Based on precise Coulomb wave functions (CWFs), we attempt to calculate the fusion cross sections of light nuclei in a complex spherical square-well nuclear potential (i.e., optical potential model). Comparing with experimental benchmark cross section data, we can calibrate optical potential parameters associated with D+D, D+T, D+3He, p+D, p+6Li and p+7Li fusion reactions. Surprisingly, we find that our calculated optical potential parameters are quite different from those of many previous results (e.g., Phys. Rev. C. 61 (2000) 024610, Nucl. Phys. A 986 (2019) 98, etc.), in which approximate Coulomb wave functions (ACWFs) with only retaining the leading terms are exploited for the continuity conditions at the radius of nuclear potential. Furthermore, with the obtained optical potential parameters, we compare the fusion cross sections and astrophysical S-factors with that formulated from ACWFs approach, and also find apparent deviations especially for the fusion reactions with resonance peaks such as D+T and D+3He fusion reactions. We then calculate the phase diagrams of the fusion cross sections with respect to the optical potential parameters and demonstrate several narrow shape resonance belts. It implies that a small deviation of ACWFs from the exact CWFs at nuclear radius might lead to fall off the resonance regimes and therefore causes the big difference on the optical parameters as well as the cross sections.