Extrapolation of Cross-Section Data to Zero Energy for Long-Range Effective Potentials
- 15 February 1965
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 137 (4A), A1068-A1075
- https://doi.org/10.1103/physrev.137.a1068
Abstract
The effective one-body potential representing a particle-compound-system interaction usually has a very complicated short-range behavior, but a relatively simple, and more or less known, long-range tail which can be nonlocal and energy-dependent. With present, the usual effective-range-theory (ERT) expansion for a single-channel scattering phase shift is inapplicable. Recent extensions of ERT include the effect of long-range potentials, but since then becomes very energy-dependent, 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 , and then use a modified ERT expansion for the difference between and the phase shift due to alone. Since the rapid energy dependence due to is thus extracted out (exactly), terms in the expansion which depend upon the short-range potential in the presence of 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.
Keywords
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