Phaseshifts, total elastic cross sections and resonances in Ar-Ar scattering

We have performed systematic quantal calculations of Ar-Ar elastic scattering events using accurate pair potentials. Specifically, we have calculated a large number of partial wave phaseshifts, total cross sections and resonance energies over a range of energies covering most of the glory region. The cross sections from two accurate potentials are compared over one glory oscillation and over a region including several shape resonances. The resonance energies obtained from these two potentials also are compared. We discuss the inappropriateness of using Levinson's theorem to define the absolute scale of the phaseshifts for realistic atomic potentials. As an alternative, we define an 'absolute phase-shift' that explicitly accounts for the difference in phase between the true wavefunction and its free particle counterpart. Using this absolute phaseshift, we show that the conventional relationship between the zero energy phaseshift and the number of bound states is preserved for potentials with cores too hard to satisfy the conditions for Levinson's theorem. It also is shown that this absolute phaseshift can be a powerful tool for determining the number of very narrow shape resonances.