Model for asymptotic $D$-state parameters of light nuclei: Application to $^4He$

Abstract

A simple method for calculating the asymptotic $D$ state observables for light nuclei is suggested. The method exploits the dominant clusters of the light nuclei. The method is applied to calculate the $^4He$ asymptotic $D$ to $S$ normalization ratio $ρ^α$ and the closely related $D$ state parameter $D_2^α$. The study predicts a correlation between $D_2^α$ and $B_α$, and between $ρ^α$ and $B_α$, where $B_α$ is the binding energy of $^4He$. The present study yields $ρ^α\simeq -0.14$ and $D_2^α\simeq -0.12$ fm$^2$ consistent with the correct experimental $η^D$ and the binding energies of the deuteron, triton, and the $α$ particle, where $η^d$ is the deuteron $D$ state to $S$ state normalization ratio.