A microscopic cluster model study of $^3$He+$p$ scatterings

TL;DR

This study compares two microscopic cluster models to analyze $^3$He+$p$ scattering, highlighting the impact of tensor forces and $D$-wave components on phase shifts, with implications for nuclear interaction modeling.

Contribution

It introduces and compares Model T and Model C, demonstrating how tensor forces and $D$-waves influence scattering phase shifts in $^3$He+$p$ interactions.

Findings

Model T shows significant $d$ + 2$p$ influence on $P$-wave resonances.

Model C's $d$ + 2$p$ effect is suppressed, indicating renormalization.

Tensor force effects are crucial for accurate phase shift predictions.

Abstract

We calculate $^3$He+$p$ scattering phase shifts in two different microscopic cluster models, Model T and Model C, in order to show the effects of tensor force as well as $D$-wave components in the cluster wave function. Model T employs a realistic nucleon-nucleon potential and includes the $D$-wave, whereas Model C employs an effective potential in which the tensor-force effect is considered to be renormalized into the central force and includes only the $S$-wave for the cluster intrinsic motion. The $S$- and $P$-wave elastic scattering phase shifts are obtained in the \{$^3$He+$p$\}+\{$d$ + 2$p$\} coupled-channels calculation. In Model T, the $d$ + 2$p$ channel plays a significant role in producing the $P$-wave resonant phase shifts but hardly affects the $S$-wave non-resonant phase shifts. In Model C, however, the effect of the $d$ + 2$p$ channel is suppressed in both of the $S$- and $P$-wave phase shifts, suggesting that it is renormalized mostly as the $^3$He(1/2$^+$)+$p$ channel in the resonance region.