Response of the Nuclear System to External Forces: Proceedings of the V La Rábida International Summer School on Nuclear Physics Held at La Rábida, Huelva, Spain 19 June – 1 July 1994 PDF
Preview Response of the Nuclear System to External Forces: Proceedings of the V La Rábida International Summer School on Nuclear Physics Held at La Rábida, Huelva, Spain 19 June – 1 July 1994
Lecture Notes in Physics Board Editorial .H Japan Araki, Kyoto, .E Paris, France Br~zin, .J Ehlers, Garching, Germany .U France Frisch, Nice, .K Hepp, Ztirich, Switzerland .L .R Cambridge, Jaffe, ,AM ASU .R Kippenhahn, G6ttingen, Germany .A .H Heidelberg, WeidenmfiUer, Germany .J Miinchen, Wess, Germany .J Zittartz, ,n16K Germany Editor Managing .W Beiglb6ck Assisted by Mrs. Sabine Landgraf c/o Editorial Physics Springer-Verlag, Department II Tiergartenstrasse ,71 12196-D Heidelberg, Germany The Editorial Policy for Proceedings The series Lecture Notes in Physics reports new developments in physical research and teaching - quickly, informally, and at a high level. The proceedings to be considered for publication in this series should be limited to only a few areas of research, and these should be closely related to each other. The contributions should be of a high standard and should avoid lengthy redraftings of papers already published or about to be published elsewhere. 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Gallardo .M Lozano ).sdE( Response of the Nuclear System to External Forces Proceedings of the V aL adibi~R International Nuclear on School Summer scisyhP at Held aL ,adibi~R niapS ,avleuH June- July 1 91 1994 ~ Springer Editors Jos~ Miguel Arias Maria Isabel Gallardo Manuel Lozano Departamento FAMN, Facultad de Fisica Universidad de Sevilla, Aptdo lo65 o8o14-E SeviUa, Spain 3-540-59007-2 ISBN Springer-Verlag Berlin Heidelberg New York CIP data applied for This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustra- tions, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication orp arts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission ufsoer must always be obtained from Springer-Verlag.Violations are liable for prosecution under the German Copyright .waL © Springer-Verlag Berlin Heidelberg 5991 Printed in Germany Typesetting: Camera-ready by the editors SPIN: 1o1271o5 55/3142-54321o - Printed on acid-free paper Preface The V La R~bida International Summer School, whose proceedings are con- tained in this book, was entitled "Response of the Nuclear System to External Forces". Subjects at the forefront of nuclear research, bordering other areas of many- particle physics, such as electron scattering at different energy scales, new physic- s with radioactive beams, multifragmentation, relativistic nuclear physics, high spin nuclear problems, chaos, the role of the continuum in nuclear physics, or recent calculations with the shell model were presented to a dynamic group of young nuclear physicists. The meeting provided the audience with an opportuni- ty to discuss and assess their feelings about the main future lines of development of nuclear physics. We would like to express here our deep gratitude to all the professors who kindly accepted our invitation to lecture at this summer school. Without their friendly and continuous collaboration the school and this book would have been impossible. They made an important effort in presenting their talks in a ped- agogical way not only at the school but also in their written version presented in this book. Their accesibility and disponibility during the school facilitated informal discussions with students in the rest hours in extra "beach" and "bar" sessions. Special thanks are given to the students. They, together with the lec- turers, contributed to give the school an excellent, from the academic point of view, and a warm, from the personal relationship side, atmosphere. From the less "poetic", but very important, financial point of view, this school would not have been possible without substancial support from several Spanish organizations. First, the School was held at the Universidad Internacional de Andalucia, Sede Iberoamericana de Santa Maria de La R~bida. We are really indebted to the heads of this University, Prof. J. Marchena and Prof. E. GarzSn, for their economical help as well as for their cooperation in organizative aspects of the school. Our gratitude goes to them and the whole staff of this Univer- sity. Second, the national Spanish government, through the Direcci6n General de Investigaci6n Cientifiea y T~cnica (DGICyT), and the regional government, through the Consejeria de EducaciSn y Cieneia de la Junta de Andalucia, gave the school financial support. We would like to acknowledge them for their atten- tion even in these economicaly bad times. Special thanks are given to the Dean of the Physics Faculty of the University of Sevilla, Prof. Antonio C6rdoba, for his kind help when it was needed. Finally we would like to thank the Univer- sity of Sevilla, through its Vieerrectorado de ExtensiSn Universitaria, and the IV bank Caja de Ahorros y Monte de Piedad de Huelva y Sevilla, for their financial assistance. This edition of the school, as all the previous ones, was benefited by the enthusiastic cooperation of our collaborators from the Departamento de F/sica At6mica, Molecular y Nuclear of the University of SeviUa before, during and after the school. Our gratitude to the administrative personal of our Department Jos~ Diaz, Chari Gonz£1ez and Charo Cadierno for their continuous assistance in the organization of the School. Sevilla, Spain J.M. Arias October 1994 M.I. Gallardo M. Lozano Contents • Electron Scattering .................................................. 1 J.D. Walecka • Elementary Nuclear Excitations Studied with Electromagnetic and Hadronic Probes ............................................... 13 A. Richter • Probing Nucleon and Nuclear Structure with High-Energy Electrons ........................................................... 61 B. Frois • Relativistic Theory of the Structure of Finite Nuclei ................ 95 P. Ring • Semiclassical Description of the Relativistic Nuclear Mean Field Theory ...................................................... 115 X. ViSas • Photonuclear Reactions ........................................... 131 E. Oset • Notes on Scaling and Critical Behaviour in Nuclear Fragmentation .................................................... 153 X. Campi and H. Krivirte • The Continuum in Nuclei ......................................... 181 R.J. Liotta • Spherical Shell Model, a Renewed View ............................ 195 A. Pores High Spins and Exotic Shapes ..................................... 211 • S. ~berg • Heavy Ion Scattering Problems; Regular and Chaotic Regimes ..... 231 C.H. Dasso, M. Gallardo and M. Saraceno IIIV • Deterministic Chaos in Heavy-Ion Reactions ....................... 251 M. Baldo, E.G. Lanza and A. Rapisarda • Nuclear Level Repulsion; Order vs. Chaos and Conserved Quantum Numbers ................................................ 263 J.D. Garrett, J.R. German and J.M. Espino • Nuclear Physics and Nuclear Astrophysics with Radioactive Nuclear Beams .................................................... 273 J. Vervier • List of Participants ................................................ 289 Electron Scattering John Dirk Walecka College of William and Mary Williamsburg, Virginia, 23187 CEBAF Newport News, Virginia, 23606 These lectures are divided into two parts. First, I will give an elementary introduc- tion to electron scattering. This material is based on lectures I gave last summer at the 6th Annual Summer School in Nuclear Physics Research held at North Carolina State University in Raleigh, North Carolina. I have written up the first part for the proceedings of this school. Then I will give an overview of the present status of elec- tron scattering, including a description of CEBAF. The second part is based on two talks I gave recently at conferences. Since the material in the second part appears in the published literature in Refs. [1, 2], I will simply refer students to that published material. 1 Electromagnetic Interactions Non-Relativistic Scattering of a Charged Lepton - Born Approzimation. Suppose one scatters a non-relativistic lepton of charge peZ with z = ±1 from the nucleus. The interaction takes place through the Coulomb potential : 1_ (1) 4r J x[ x'| The scattering amplitude is given in first Born Approximation by fB.A.(k', k)- _4zch 22p/e_iq.xv(z)d3z (2) Here p is the reduced mass, hk is the inital momentum, hk' is the final momen- tum, and hq with q = k' - k is the three-momentum transfer whose magnitude is given for elastic scattering by q2 = 2k2(1 _ cosS) = 4k2sin28/2. For a spherically symmetric nuclear charge density pN(z), the Fourier transform of 2 J.D. Walecka the potential in Eq. (1) yields 1 1 e-iq'x ix - x, l pN(X')daxdaz' = ~-~F(q 2) (3) Here F(q )2 is the nuclear "form factor". Now use e2/hc -- 41ra where a 1/137.0 is the fine-structure constant. The differential cross section then follows from the square of the modulus of the scattering amplitude as do- _ 4~ 2 ~4 dn h 4 (hca)2.t IF(q2)12 (hca) 2 = 16 i- -e/21F(q )1 = drof~ehtu.~l~ If(q2) 21 (4) Here E0 = h2k2/2g is the incident energy and trRutherfor d is the familiar cross section for scattering from a point charge. Experimental measurement of this cross section evidently determines the Fourier transform of the nuclear charge density 2 y3d)y(N.Yq'-ef f(q 2) = f sin qy qy PN(Y) d3y Note that F(0) =-- Z, the total nuclear charge. Nuclear Physics. Suppose now that one extends the analysis to deal with the internal quantum dynamics of the nuclear target. The nuclear charge density then becomes an operator in the nuclear Hflbert space PN (x) ~ PN (X) ; Nuclear Density Operator (6) In first quantization, for example, with a collection of structureless nucleons, the nuclear density operator takes the form z j=l The analysis of the scattering amplitude in Eq. (3) indicates that one now requires the nuclear transition matrix elements of the operator = /e-iq'Y~NCy)d3y (8) IUse fe-iq'X(e-~/x)d3x = 47r/(q ~ + ;)2A now let A ~ .0 2 One actually measures the square of the modulus of the form factor, but since it si real here and F(O) = Z, one can track through the zeros and determine both the sign and magnitude.
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