Causality and the threshold anomaly of the nucleus-nucleus potential |
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| Affiliation: | 1. KEK Theory Center, Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan;2. J-PARC Branch, KEK Theory Center, IPNS, KEK, 203-1 Shirakata, Tokai, Ibaraki 319-1106, Japan;3. General Education, Faculty of Engineering, Osaka Institute of Technology, Osaka 535-8585, Japan;4. Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japan;1. Department of Physics, Sciences Faculty, Golestan University, P. O. Box 49138-15759, Gorgan, Iran;2. Department of Physics, Sciences Faculty, Hakim Sabzevari University, P. O. Box 397, Sabzevar, Khorasan Razavi, Iran;1. Dipartamento di Fisica e Astronomia, Universitá di Catania, via S. Sofia 64, I-95123 Catania, Italy;2. INFN, Laboratori Nazionali del Sud, via S. Sofia 62, 1-95123 Catania, Italy;3. Instituto de Estructura de la Materia, CSIC, Serrano 113 bis, E-28006 Madrid, Spain;4. Departamento de FAMN, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain;5. Departamento de Física Aplicada, Universidad de Huelva, Campus de El Carmen, E-21071 Huelva, Spain;6. Centro Nacional de Aceleradores, Universidad de Sevilla, Junta de Andalucía-CSIC, 41092 Sevilla, Spain;7. INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy;8. Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, Mexico City 01000, Mexico;9. INFN, Sezione di Catania, via S. Sofia 64, 1-95125 Catania, Italy;10. Department of Physics, Chalmers University of Technology, S-41296 Göteborg, Sweden;11. Physics Department, Lund University, Box 118, SE-221 00, Lund, Sweden;12. School of Physics and Astronomy, University of Edinburgh, JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom of Great Britain and Northern Ireland;13. Grupo de Física Nuclear & IPARCOS, Facultad de Ciencias Físicas, CEI Moncloa, 28040 Madrid, Spain;14. ISOLDE, EP Department, CERN, CH-1211 Geneva-23, Switzerland;15. LIP - Laboratory for Instrumentation and Experimental Particle Physics, Lisbon, Portugal;p. Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus, Denmark;q. Centro de Estudios Avanzados en Física, Matemáticas y Computación (CEAFMC), Department of Integrated Sciences, University of Huelva, 21071 Huelva, Spain;r. Ruđer Bošković Institute, Bijenička cesta, 54, HR-10000 Zagreb, Croatia;1. Institut d''Astronomie et d''Astrophysique, Université Libre de Bruxelles, CP-226, 1050 Brussels, Belgium;2. CEA, DAM, DIF, F-91297 Arpajon, France |
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| Abstract: | According to the causality principle, a scattered wave cannot be emitted before the arrival of the incident wave. This principle implies the existence of a dispersion relation between the real and the imaginary parts of the optical potential. We discuss the difference between the dispersion relations which hold for nucleus-nucleus scattering on the one hand and for nucleon-nucleus scattering on the other hand. In the case of nucleus-nucleus scattering, the dispersion relation predicts that the modulus of the real part of the optical potential has a bell-shaped maximum, as a function of energy, when the imaginary part approaches zero, i.e. for energies near the top of the Coulomb barrier. The shape of this apparent anomaly is investigated in the framework of several models. It is shown that there exists an algebraic model which is at the same time simple and sufficiently accurate in the sense that the difference between its outcome and that of more realistic models is smaller than the uncertainties introduced by the assumptions which have to be made. Various systems are discussed, in particular 16O + 280Pb and α + 40Ca. Several implications of the anomaly are pointed out, including its effect on the sub-barrier fusion of two heavy ions. |
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