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 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ asymptotic D to S normalization ratio ${\mathrm{\rho }}^{\mathrm{\alpha }}$ and the closely related D-state parameter ${\mathit{D}}_2^{\mathrm{\alpha }}$. The study predicts a correlation between ${\mathit{D}}_2^{\mathrm{\alpha }}$ and ${\mathit{B}}_{\mathrm{\alpha }}$, and between ${\mathrm{\rho }}^{\mathrm{\alpha }}$ and ${\mathit{B}}_{\mathrm{\alpha }}$, where ${\mathit{B}}_{\mathrm{\alpha }}$ is the binding energy of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The present study yields ${\mathrm{\rho }}^{\mathrm{\alpha }}$≃-0.14 and ${\mathit{D}}_2^{\mathrm{\alpha }}$≃-0.12 ${\mathrm{fm}}^2$ consistent with the correct experimental ${\mathrm{\eta }}^{\mathit{d}}$ and the binding energies of the deuteron, triton, and the α particle, where ${\mathrm{\eta }}^{\mathit{d}}$ is the deuteron D-state to S-state normalization ratio.

• Received 26 October 1993

DOI:https://doi.org/10.1103/PhysRevC.50.822