Phase-Shift and Potential-Model Analysis of Experimental Information

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First I would like to make a few remarks about potentials and then go on to phase shift analyses and how some of the popular potentials compare to them. Figure 1 shows the sort of progress that has been made in recent years. The 1962 1S0 Hamada-Johnston potential descended to tremendous depths at around 0.5F, just outside an infinitely positive core. Now we have2 much more sensible hard and soft core potentials and they are much easier to use in computer calculations since they do not require such small radial increments for a tabular specification. Finite-core alternatives3, 4 are shown in Figure 2: all three of these give almost identical phase shifts up to 300 MeV, but beyond that their predicted phases diverge. Finally, in Figure 3 we see some momentum-dependent alternatives5. Each of the p2-dependent potentials gives identical phase shifts for all energies, identical also to those from the 0.4F hard-core potential shown. The phases for the O.IF hard (“soft”) core and finite core potentials again diverge from these and from each other above about 300 MeV. That’s all I have to say about recent developments in phenomenological potentials. Now let us turn our attention to phase shifts and see how well the potentials do.