  To meet burning needs of high-resolution pressure-induced line-shape
parameters in the UV/visible regions for hot-temperature industrial and
atmospheric applications as well as current and future space missions,
phase-shift theory is examined in its historical context, tested and revisited
using accurate numerical potentials and advanced trajectory models. First, a
general analysis for arbitrary molecular systems is conducted in terms of the
dimensionless parameter $\alpha$ determined by the differences of the
Lennard-Jones parameters in the final and initial electronic absorber's states.
Temperature dependence, use of the power law and influence of Maxwell-Boltzmann
averaging over relative velocities are addressed. Then, interaction-potential
calculations are attempted for some representative molecular pairs (NO-Ar,
NO-N$_2$, OH-Ar and OH-N$_2$) and the isotropic parts are fitted using the 12-6
Lennard-Jones form to get room and high-temperature line-broadening and
line-shift coefficients which are compared to available measurements. It is
shown that the phase-shift theory in its standard rectilinear-trajectory
formulation provides linewidth and shift estimates accurate within 30-40 %.
Attempted improvements using numerical potentials and curved trajectories lead
to closer matches with measurements for some cases but also worsen the
agreement for others. To ensure better theoretical predictions, introduction of
correction terms to the usual phase-shift integral is suggested.
