
Accession Number : AD0613127
Title : EXTRAPOLATION OF CROSSSECTION DATA TO ZERO ENERGY FOR LONGRANGE EFFECTIVE POTENTIALS.
Descriptive Note : Doctoral thesis (revised ed.),
Corporate Author : NEW YORK UNIV N Y
Personal Author(s) : Berger ,R. Oppenheim ; O'Malley ,Thomas F. ; Spruch,Larry
Report Date : 25 SEP 1964
Pagination or Media Count : 8
Abstract : The effective onebody potential representing a particlecompoundsystem interaction usually has a very complicated shortrange behavior, but a relatively simple, and more or less known, longrange tail U which can be nonlocal and energydependent. With U present, the usual effectiverangetheory (ERT) expansion for a singlechannel scattering phase shift eta is inapplicable. Recent extensions of ERT include the effects of longrange 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 onebody 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 shortrange 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 lowenergy scattering data down to zero energy, even when effective longrange potentials are present. (Author)
Descriptors : (*ELASTIC SCATTERING, ELECTRONS), (*POTENTIAL SCATTERING, MATHEMATICAL PREDICTION), (*NUCLEAR CROSS SECTIONS, POTENTIAL SCATTERING), PHASE SHIFT CIRCUITS, ELECTROSTATICS, ATOMIC ENERGY LEVELS, NUMERICAL ANALYSIS
Distribution Statement : APPROVED FOR PUBLIC RELEASE