Shape-Independent Expansion for the ${}^3{S}_1{-}^3{D}_1$ Mixing Parameter

Abstract

A low-energy shape-independent expansion is suggested for the function $[tan(2{ϵ}_{BB})/(2k^2)]$, where ${ϵ}_{BB}$ is the Blatt-Biedenharn mixing parameter for the ${}^3{S}_1-$ ${}^3{D}_1$ channel. This expansion allows an evaluation of the mixing parameter ${ϵ}_{BB}$ from a knowledge of the deuteron asymptotic $D$ to $S$ ratio, pion mass and other low-energy observables, such as the scattering lengths, deuteron binding etc., of the nucleon-nucleon system. We demonstrate that the correct long range behavior of the tensor potential is essential for a realistic reproduction of ${ϵ}_{BB}$.

Comments: 7 pages, text and two postscript figures included