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To the H and 'He ground states, we apply the coupled-rearrangement-channel variational method with Gaussian-basis functions which has successfully been used in precise calculations of muonic molecular ions, Coulomb-interacting three-body systems. The trinucleon wave function is decomposed into angular-momentum-projected three-body channels as done in the Faddeev equations method, but the interaction is fully incorporated with no partial-wave decomposition. The radial part of the channel amplitudes is expanded with a sufficient number of Gaussian-tail basis functions of the Jacobi coordinates. The Gaussian ranges are taken to be geometrical progressions which run from very short ranges through large enough ones. This ab initio variational approach is found to describe accurately both the short-range correlations and the asymptotic behavior. The Argonne V&4 potential is used as an example of realistic two-nucleon interactions; for He, the Coulomb potential is included nonperturbatively.The calculation reproduces precisely the results of the Faddeev calculations for 'H and 'He for binding energy, probabilities of the S, S', P, and D states, and the Sand D-wave asymptotic normalization constants. Convergence of the present results is seen at a much smaller number of the three-body channels than in the Faddeev calculations.This is because the interaction is truncated in the angular momentum space in the Faddeev calculations but the full interaction is taken in the present method.

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