The Euroschool Lectures on Physics with Exotic Beams, Vol. III

314 Pages·2009·13.418 MB·English

by  T. Otsuka (auth.), J.S. Al-Khalili, E. Roeckl (eds.)

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J.S. Al-Khalili
E. Roeckl (Eds.)
The Euroschool Lectures
on Physics with Exotic
Beams, Vol. III
123
J.S.Al-Khalili E.Roeckl
UniversityofSurrey Gesellschaftfor
Dept.Physics SchwerionenforschungmbH
Guildford,Surrey (GSI)
UnitedKingdomGU25XH Planckstr.1
[email protected] 64291Darmstadt
Germany
[email protected]
Al-Khalili, J.S., Roeckl, E. (Eds.), The Euroschool Lectures on Physics with Exotic
Beams,Vol.III,Lect.NotesPhys.764(Springer,BerlinHeidelberg2009),DOI10.1007/
978-3-540-85839-3
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Preface
This is the third and final volume in a series of Lecture Notes based on the
highlysuccessfulEuroSummerSchoolonExoticBeamsthathasbeenrunning
yearly since 1993 (apart from 1999) and is planned to continue to do so. It
is the aim of the series to provide an introduction to Radioactive Ion Beam
(RIB) physics at the level of graduate students and young postdocs starting
outinthefield.Eachvolumecontainslecturescoveringarangeoftopicsfrom
nuclear theory to experiment to applications.
Our understanding of atomic nuclei has undergone a major re-orientation
over the past two decades and seen the emergence of an exciting field of
research: the study of ‘exotic’ nuclei. The availability of energetic beams of
short-lived nuclei, referred to as ‘radioactive ion beams’ (RIBs), has opened
the way to the study of the structure and dynamics of thousands of nuclear
species never before observed in the laboratory. This field has now become
one of the most important and fast-moving in physics worldwide. And it is
fair to say that Europe leads the way with a number of large international
projects starting up in the next few years, such as the FAIR facility at GSI
in Germany. From a broader perspective, one must also highlight just how
widely RIB physics impacts on other areas, from energyand the environment
to medicine and materials science. There is little doubt that RIB physics has
transformed not only nuclear physics itself but many other areas of science
and technology too, and will continue to do so in the years to come.
While the field of RIB physics is linked mainly to the study of nuclear
structure under extreme conditions of isospin, mass, spin and temperature,
it also addresses problems in nuclear astrophysics, solid-state physics and the
study of fundamental interactions. Furthermore, important applications and
spin-offs also originate from this basic research. The development of new pro-
duction, acceleration and ion storing techniques and the construction of new
detectors adapted to work in the special environment of energetic radioactive
beams is also an important part of the science. And, due to the fact that one
is not limited anymore to the proton/neutron ratio of stable-isotope beams,
virtually the whole chart of the nuclei opens up for research, so theoretical
models can be tested and verified all the way up to the limits of nuclear
existence: the proton and neutron ‘drip lines’.
VI Preface
The beams of rare and ‘exotic’ nuclei being produced are via two comple-
mentary techniques: in-flight separation and post-acceleration of low-energy
radioactive beams. Both methods have been developed in a number of Eu-
ropean Large Scale Facilities such as ISOLDE (CERN, Switzerland), GANIL
(Caen, France), GSI (Darmstadt, Germany), the Accelerator Laboratory of
theUniversityofJyva¨skyla¨(Finland),INFNLaboratoriNazionalidiLegnaro
(Italy) and the Cyclotron Research Centre (Louvain-la-Neuve, Belgium). In-
deed, so important is the continued running and success of the School that
a number of these European facilities have committed to providing financial
support over the coming years.
While the field of RIB physics is linked mainly to the study of nuclear
structure under extreme conditions of isospin, mass, spin and temperature,
it also addresses problems in nuclear astrophysics, solid-state physics and the
study of fundamental interactions. Furthermore, important applications and
spin-offs also originate from this basic research. The development of new pro-
duction, acceleration and ion storing techniques and the construction of new
detectors adapted to work in the special environment of energetic radioactive
beams is also an important part of the science. And, due to the fact that one
is not limited anymore to the proton/neutron ratio of stable beams, virtually
the whole chart of the nuclei opens up for research, so theoretical models can
be tested and verified all the way up to the limits of nuclear existence: the
proton and neutron ‘drip lines’.
Volumes I and II of this series have proved to be highly successful
and popular with many researchers reaching for it for information or pro-
viding it for their PhD students as an introduction to a particular topic.
They are now even available to download from the Euro School Website
(http://www.euroschoolonexoticbeams.be/eb/pages/lecture notes).Westress
that the contributions in these volumes are not review articles and so are not
meant to contain all the latest results or to provide an exhaustive cover-
age of the field but are written instead in the pedagogical style of graduate
lectures and thus have a reasonably long ‘shelf life’. As with the first two
volumes, thecontributions herearebyleadingscientistsinthefieldwhohave
lectured at the School. They were chosen by the editors to provide a range
of topics within the field and will have updated their material delivered at
the School (sometimes several years ago) to incorporate recent advances and
results.
Finally,wewishtothankthelectureswhohavecontributedtothisvolume
fortheirhardworkanddiligence,andindeedfortheirpatience,atatimewhen
everyone finds it difficult to find the time to lay out their subject in such a
careful, thorough and readable style. We also wish to thank Dr. Chris Caron
and his colleagues at Springer-Verlag for their help, fruitful collaboration and
continued support on this project.
Guildford, UK, J. Al-Khalili
Darmstadt, Germany E. Roeckl
Contents
Shell Structure of Exotic Nuclei
T. Otsuka....................................................... 1
1 Basics of Shell Model ......................................... 1
2 Construction of an Effective Interaction and an Example in the pf
Shell........................................................ 16
3 The N =20 Problem: Does the Gap Change?.................... 18
4 Summary.................................................... 20
References ...................................................... 20
Testing the Structure of Exotic Nuclei via Coulomb
Excitation of Radioactive Ion Beams at Intermediate Energies
T. Glasmacher .................................................. 27
1 Introduction ................................................. 27
2 Experimental Considerations................................... 31
3 Extraction of Transition Matrix Elements from Cross Sections ..... 41
4 Recent Experimental Results .................................. 43
5 Accuracy of the Technique..................................... 48
6 Outlook and Summary........................................ 50
References ...................................................... 50
Test of Isospin Symmetry Along the N=Z Line
S.M. Lenzi, M.A. Bentley ......................................... 57
1 Introduction ................................................. 57
2 Background ................................................. 59
3 Experimental and Theoretical Tools ............................ 67
4 Description of Excitation Energy Differences..................... 73
5 Isobaric Multiplets in the f Shell.............................. 84
7
2
6 Isobaric Multiplets in the sd and fp Shells....................... 92
7 Conclusions and Outlook ...................................... 95
References ...................................................... 97
VIII Contents
Beta Decay of Exotic Nuclei
B. Rubio and W. Gelletly ......................................... 99
1 Introduction ................................................. 99
2 Beta Decay and Nuclear Structure..............................103
3 Experimental Considerations...................................114
4 Some Illustrative Examples ....................................122
5 Future Measurements .........................................147
References ......................................................148
One- and Two-Proton Radioactivity
B. Blank........................................................153
1 Introduction .................................................153
2 One-Proton Radioactivity .....................................155
3 Two-Proton Radioactivity .....................................174
4 Other Exotic Decay Channels..................................190
5 Conclusions..................................................192
References ......................................................193
Superheavy Elements
S. Hofmann .....................................................203
1 Introduction .................................................203
2 Experimental Techniques......................................205
3 Experimental Results .........................................213
4 Nuclear Structure and Decay Properties.........................232
5 Nuclear Reactions ............................................238
6 Summary and Outlook........................................246
References ......................................................248
Experimental Tools for Nuclear Astrophysics
C. Angulo.......................................................253
1 Understanding the Universe ...................................253
2 Relevant Quantities at Stellar Energies..........................256
3 Stellar Cycles and Some Key Reactions .........................260
4 Experimental Techniques in Nuclear Astrophysics ................262
5 Future Challenges and Conclusions .............................279
References ......................................................279
Index..........................................................283
Color Plate Section............................................289
Shell Structure of Exotic Nuclei
T. Otsuka1,2,3,4
1 Department of Physics, University of Tokyo, Hongo, Tokyo, 113-0033, Japan
2 Center for Nuclear Study, University of Tokyo, Hongo, Tokyo, 113-0033, Japan
3 RIKEN, Hirosawa, Wako-shi, Saitama
4 National Superconducting Cyclotron Laboratory, Michigan State University,
East Lansing, MI, USA
Abstract A basic introduction to the nuclear shell model is presented, without
goingtoanydetailsofmany-bodytheories.First,weexplainhowmagicnumbersand
shellstructuresappearfromfundamentalpropertiesofnucleisuchastheshort-range
attractive interaction and density saturation. Some concepts needed to understand
the shell model are explained from scratch. After a general introduction we focus
onatopicofparticularcurrentinterest,theevolutionofshellstructure,anddiscuss
the importance of the tensor force.
1 Basics of Shell Model
Nuclear theory has been developed in order to construct many-body systems
from basic ingredients such as nucleons and nuclear forces (nucleon–nucleon
interactions). The nuclear shell model has been an important part of nuclear
theory, and should make crucial input to this end. We begin by asking three
basic questions:
(i) What is the shell model?
(ii) Why is it useful?
(iii) How do we perform calculations?
1.1 What is the Shell Model?
We begin with some very basic points about nuclear shell structure and the
shell model. Figure 1 shows somewhat schematically the nucleon–nucleon
potential as a function of the distance between the two nucleons, for the
spin-singlet (two interacting nucleons coupled to total spin S=0) and L=0
(L, relative orbital angular momentum of the two nucleons) state. This state
musthaveisospinT=1becauseoftheantisymmetriccouplingofthenucleons.
This is one of the most important states for the nucleon–nucleon potential,
as the potential contains a strongly attractive part. Note that the nucleon–
nucleon potential depends generally on S, L, and J with J(cid:2) = L(cid:2) +S(cid:2). We
Otsuka,T.:ShellStructureofExoticNuclei.Lect.NotesPhys.764,1–25(2009)
DOI10.1007/978-3-540-85839-31 (cid:2)c Springer-VerlagBerlinHeidelberg2009
2 T. Otsuka
Schematic picture of nucleon-
Potential
nucleon (NN) potential
hard core 1 fm
distance between
nucleons
0.5 fm
–100 MeV
Fig. 1. Schematic illustration of the nucleon–nucleon potential
find, in Fig. 1, a hard-core repulsion inside a distance of 0.5fm, while it is
strongly attractive around 1fm. These two features are found also in other
important states, e.g., of spin-triplet and even L states with T=0. The po-
tentials for such states are the origin of the proton–neutron binding in the
deuteron.
From these two features, a hard repulsive core and a strong attraction
around 1fm, we can easily expect that the nuclear potential is such that the
balance between the attractive part around 1fm and the inner repulsive part
conspirestogivearatherconstantdistance(∼1fm)betweennucleons,which
are strongly bound together. The saturation of the density is thus realized at
the same time. Although the actual mechanism contains more sophisticated
dynamics – for instance, the density dependence of the potential – we will
not go into such details. As the nucleon density should be rather constant,
the surface can be defined clearly, despite the fact that the nucleus is such a
complex quantum system with complicated interaction.
The nucleon–nucleon interaction is very complicated, but can produce a
simple mean potential. Figure 2 depicts this situation. A nucleon (open circle
in Fig. 2) well inside the nucleus feels the nucleon–nucleon interaction from
the surrounding nucleons within reach (or range) of the interaction, which is
about1fm.ThespherewithinthisrangeisshowninthedashedlineinFig.2.
As the density of the nucleon is constant inside the nucleus, the mean effect
fromsurroundingnucleonsshouldbealmostconstant,andthemeanpotential
should be almost flat.
Figure3indicatestheeffectfromsurroundingnucleonsforanucleonatthe
surface (shown again by an open circle). Otherwise the legend of the figure is
thesameasFig.2.Thenumberofthesurroundingnucleonsbecomessmaller,
as this nucleon (open circle) moves out, resulting in less binding. Thus, the
mean potential becomes shallower quickly at the surface.
Figure 4 displays schematically what the mean potential looks like. The
single-particlemotioninsidethispotentialcanbesolved.Thisisjustaneigen-
value problem with the eigenstates corresponding to various orbital motions,