Trinucleon asymptotic normalization constants including Coulomb effects

Exact theoretical expressions for calculating the trinucleon $S$- and $D$-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Configuration-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the $s$-wave $\mathrm{NN}$ interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the $D$-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ $S$-wave asymptotic norm by less than 1% relative to that of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, that Coulomb effects decrease the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ $D$-wave asymptotic norm by approximately 8% relative to that of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, and that the distorted-wave Born approximation $D$-state parameter, $D_2$, is only 1% smaller in magnitude for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ than for ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ due to compensating Coulomb effects.