EXTRAPOLATION OF CROSS-SECTION DATA TO ZERO ENERGY FOR LONG-RANGE EFFECTIVE POTENTIALS.
Doctoral thesis (revised ed.),
NEW YORK UNIV N Y
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The effective one-body potential representing a particlecompound-system interaction usually has a very complicated short-range behavior, but a relatively simple, and more or less known, long-range tail U which can be nonlocal and energy-dependent. With U present, the usual effective-range-theory ERT expansion for a singlechannel scattering phase shift eta is inapplicable. Recent extensions of ERT include the effects of long-range potentials, but since eta then becomes very energydependent, one would need many terms to obtain the desired accuracy, so the results are of restricted use. We show that one can first solve, numerically, a one-body problem which includes only U, and then use a modified ERT expansion for the difference delta between eta and the phase shift due to U alone. Since the rapid energy dependence due to U is thus extracted out exactly, terms in the expansion which depend upon the short-range potential in the presence of U are more slowly varying in energy they involve a number of adjustable parameters to be determined experimentally, but only a few are usually needed. The procedure thus makes possible the extrapolation of low-energy scattering data down to zero energy, even when effective long-range potentials are present. Author