Trinucleon asymptotic normalization constants: Comparison of 3He and 3H.

Abstract

Calculations of the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are extended to include all two-body partial waves up to j\ensuremath{\le}4 (34 three-body channels). Wave functions were generated with configuration-space, Faddeev-type equations for Hamiltonians based upon the two-body forces of Reid and the Argonne group, plus the Tucson-Melbourne and Brazilian model three-body forces. Comparison with previously published results is made. Results for ${C}_{S}$, ${C}_{D}$, \ensuremath{\eta}, and ${D}_{2}$ are interpolated as a function of binding to extract best estimates for $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$. In agreement with our earlier (jl=1) calculations, we find that Coulomb effects increase the S-wave asymptotic normalization of $^{3}\mathrm{He}$ by less than 1% over that of $^{3}\mathrm{H}$ and that Coulomb effects decrease the D-wave asymptotic normalization of $^{3}\mathrm{He}$ relative to that of $^{3}\mathrm{H}$ by about 6%. The distorted-wave Born approximation D-wave parameter ${D}_{2}^{C}$ for $^{3}\mathrm{He}$ is almost identical to ${D}_{2}$ for $^{3}\mathrm{H}$. Finally, we predict the ratio of the the D-wave to S-wave asymptotic normalization constants to be \ensuremath{\eta}${(}^{3}$H)\ensuremath{\simeq}0.046 and ${\ensuremath{\eta}}^{C}$${(}^{3}$He)\ensuremath{\simeq}0.043. .AE