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

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 ${}^{4}He$ asymptotic $D$ to $S$ normalization ratio ${\rho }^{\alpha }$ and the closely related $D$ state parameter $D_2^{\alpha }$. The study predicts a correlation between $D_2^{\alpha }$ and $B_{\alpha }$, and between ${\rho }^{\alpha }$ and $B_{\alpha }$, where $B_{\alpha }$ is the binding energy of ${}^{4}He$. The present study yields ${\rho }^{\alpha }\simeq -0.14$ and $D_2^{\alpha }\simeq -0.12$ fm${}^2$ consistent with the correct experimental ${\eta }^D$ and the binding energies of the deuteron, triton, and the $\alpha$ particle, where ${\eta }^d$ is the deuteron $D$ state to $S$ state normalization ratio.

Comments: 20 pages, text and one postscript figure included