An ab initio configuration interaction (CI) study including spin-orbit coupling is carried out for the ground and low-lying excited states of the HI molecule by employing a relativistic effective core potential for the iodine atom. The computed spectroscopic constants for the X (1)Sigma(+) ground and b (3)Pi(Omega) Rydberg states are in good agreement with available experimental data, as are the vertical excitation energies for the repulsive a (3)Pi(1), a (3)Pi(0)(+), and A (1)Pi(1) states of the A band. The a (3)Pi(0)(+) state is found to possess a shallow minimum of 600 cm(-1) depth outside the Franck- Condon region, at approximate to 5.1 a(0). The electric-dipole moments have also been calculated for transitions from the ground to the A band states. Contrary to what is usually assumed, the a (3)Pi(1), A (1)Pi(1)<-- X0(+) transition moments are found to depend strongly on internuclear distance. Employing the computed potential energy and transition moment data, partial and total absorption spectra for the A band are calculated and the I* quantum yields, Phi(I)*(nu), are determined as a function of excitation energy. The maximal Phi(I)*(nu) values are calculated to be 0.55-0.59 and lie at 39 000-40 000 cm(-1), which agrees well with experimental results. The influence of the t (3)Sigma(1)(+) state and of the nonadiabatic effects on the Phi(I)*(nu) values is found to be negligible in the essential part of the A band. Finally, it is shown that significantly higher I* quantum yield values (up to 0.8-0.9) may be achieved when vibrationally hot HI molecules are excited in the appropriate spectral range.