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Stable extrapolation of scattering amplitudes using unitarity
ANNALS
OF PHYSICS:
74, 603-604 (1972)
Abstracts
of Papers
to Appear
in Future
Issues
Stable Extrapolation of Scattering Amplitudes Using Unitarity. F. J. YNDURAIN. CERN, Geneva. Unitarity in all three channels for the TN system is used to show that a) one can, given the first LrrN partial waves and the 7dv total cross-sections, extrapolate to find the RN -+ 71~ waves, the whole amplitude, and the ?rN waves, in the unphysical regions; and this within absolute error bands, and b) from either of those quantities, we construct Pad& approximants which are then shown to converge to the cuts (4pa < t 5 2M2) again here within an explicit error band. It is shown that the method is stable under perturbations, giving also the explicit form in which such perturbations propagate. The analysis is carried first for amplitudes with positivity, and then extended to any amplitude. This paper is the first of a series, and only the theory is presented. Modification of Hauser-Feshbach Calculations by Direct-Reaction Channel Coupling. MITSUJI KAWAI. Department of Physics, SUNY at Stony Brook, Stony Brook, New York 11790, A. K. KERMAN. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, AND K. W. McVou. Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544 and Department of Physics, Indiana University, Bloomington, Indiana 47401. If open channels are strongly coupled by direct reactions, the traditional Hauser-Feshbach method of calculating fluctuation cross sections is invalid, because of non-statistical correlations which the direct channel-coupling induces between resonance partial widths in different channels. The fluctuation cross sections can still be computed from the optical S-matrix elements, however, and the formulae necessary for doing so are obtained here with the aid of an “optical background” representation of the full S-matrix. The resulting compound-elastic cross section is increased over the Hauser-Feshbach expression by a factor of 2(r > D) or 3(r < D) in the large-N limit, and compound-reaction cross sections are increased by roughly a factor of (N + 1)/N, where N is the number of directly-coupled open channels. A Study of the Neutron Plus W System Using the Unified Reaction Formalism, I. Elastic Scattering. TED T. LEUNG. Aerospace Research Laboratories, Wright-Patterson AFB, Dayton, Ohio and RICHARD D. KOSHEL, Ohio University, Athens, Ohio. In this paper a consistent application of Feshbach’s unified reaction formalism is applied to the neutron plus 12C system. A collective model is used for the isC system. Calculations of the differential cross sections, polarization, and level structure are presented. Scattering From Non-overlapping Potentials. I - General Formulation. DAN AGASSI. Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot AND AVRAHAM GAL. Racah Institute of Physics, The Hebrew University of Jerusalem. The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low-energy and high energy are considered. Applications to high energy scattering of elementary particles on nuclei are briefly discussed. 603 Copyright All rights
0 1972 by Academic Press, Inc. of reproduction in any form reserved.
OF PHYSICS:
74, 603-604 (1972)
Abstracts
of Papers
to Appear
in Future
Issues
Stable Extrapolation of Scattering Amplitudes Using Unitarity. F. J. YNDURAIN. CERN, Geneva. Unitarity in all three channels for the TN system is used to show that a) one can, given the first LrrN partial waves and the 7dv total cross-sections, extrapolate to find the RN -+ 71~ waves, the whole amplitude, and the ?rN waves, in the unphysical regions; and this within absolute error bands, and b) from either of those quantities, we construct Pad& approximants which are then shown to converge to the cuts (4pa < t 5 2M2) again here within an explicit error band. It is shown that the method is stable under perturbations, giving also the explicit form in which such perturbations propagate. The analysis is carried first for amplitudes with positivity, and then extended to any amplitude. This paper is the first of a series, and only the theory is presented. Modification of Hauser-Feshbach Calculations by Direct-Reaction Channel Coupling. MITSUJI KAWAI. Department of Physics, SUNY at Stony Brook, Stony Brook, New York 11790, A. K. KERMAN. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, AND K. W. McVou. Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544 and Department of Physics, Indiana University, Bloomington, Indiana 47401. If open channels are strongly coupled by direct reactions, the traditional Hauser-Feshbach method of calculating fluctuation cross sections is invalid, because of non-statistical correlations which the direct channel-coupling induces between resonance partial widths in different channels. The fluctuation cross sections can still be computed from the optical S-matrix elements, however, and the formulae necessary for doing so are obtained here with the aid of an “optical background” representation of the full S-matrix. The resulting compound-elastic cross section is increased over the Hauser-Feshbach expression by a factor of 2(r > D) or 3(r < D) in the large-N limit, and compound-reaction cross sections are increased by roughly a factor of (N + 1)/N, where N is the number of directly-coupled open channels. A Study of the Neutron Plus W System Using the Unified Reaction Formalism, I. Elastic Scattering. TED T. LEUNG. Aerospace Research Laboratories, Wright-Patterson AFB, Dayton, Ohio and RICHARD D. KOSHEL, Ohio University, Athens, Ohio. In this paper a consistent application of Feshbach’s unified reaction formalism is applied to the neutron plus 12C system. A collective model is used for the isC system. Calculations of the differential cross sections, polarization, and level structure are presented. Scattering From Non-overlapping Potentials. I - General Formulation. DAN AGASSI. Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot AND AVRAHAM GAL. Racah Institute of Physics, The Hebrew University of Jerusalem. The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low-energy and high energy are considered. Applications to high energy scattering of elementary particles on nuclei are briefly discussed. 603 Copyright All rights
0 1972 by Academic Press, Inc. of reproduction in any form reserved.