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This paper constructs the interaction potential of the SH(X2?) radical by using the coupled-cluster singles-doubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, oe, oekhe, ae and Be values are of 3.7767eV, 0.13424 nm, 2699.846 cm[?]1, 47.7055cm[?]1, 0.2639cm[?]1 and 9.4414cm[?]1, respectively, which are in excellent agreement with those obtained from the measurements. A total of 19 vibrational states has been found when J = 0 by solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH(X2?) potential energy curve. Over the impact energy range from l.0 × 10[?]11 to 1.0 × 10[?]4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the l = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions. [ABSTRACT FROM AUTHOR]