Table Of ContentLecture Notes in Physics
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.J .M Arias M.I. 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
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© Springer-Verlag Berlin Heidelberg 5991
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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.
