Clusters in Nuclei, Volume 3

255 Pages·2014·7.68 MB·English

by  A. Deltuva, A. C. Fonseca, R. Lazauskas (auth.), Christian Beck (eds.)

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Editor
Clusters in Nuclei,
Volume 3
Editor
Christian Beck
Dept. de Recherches Subatomiques
Institut Pluridisciplinaire Hubert Curien
Strasbourg, France
ISSN 0075-8450 ISSN 1616-6361 (electronic)
Lecture Notes in Physics
ISBN 978-3-319-01076-2 ISBN 978-3-319-01077-9 (eBook)
DOI 10.1007/978-3-319-01077-9
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The third volume of the Series Lecture Notes
in Physics “Clusters in Nuclei” is dedicated
to the memory of Professor Marten Bren-
ner (1926–2012) as well as to Professor
V.V. Volkov for his 90th anniversary and to
Professor D.M. Brink
Preface
This is the third volume in the series of Lecture Notes in Physics entitled “Clusters in
Nuclei” based on the well known Cluster Conferences that have been running since
decades, on two recent “State Of The Art in Nuclear Cluster Physics” Workshops, as
well as on successfull Theoretical Winter Schools, tradionnally held on the Campus
of the Université de Strasbourg, Strasbourg, France.
A great deal of research work has been accomplished in the field of alpha clus-
tering and in cluster studies of light neutron-rich nuclei. The scope of this Series
of lecture notes is to deepen our knowledge of the field of nuclear cluster physics
which is one of the domains of heavy-ion nuclear physics facing the greatest chal-
lenges and opportunities.
The purpose of this third and last volume of Lecture Notes in Physics “Clusters
in Nuclei”, is to promote the exchange of ideas and discuss new developments in
“Clustering Phenomena in Nuclear Physics and Nuclear Astrophysics” from both
the theoretical and experimental points of views. It is aimed to retain the pedagog-
ical nature of our earlier Theoretical Winter Schools and should provide a helpful
reference for young researchers entering the field and wishing to get a feel of con-
temporary research in a number of areas.
The various aspects of the main topics in this last volume of “Clusters in Nu-
clei” are divided into six chapters, each highlighting new ideas that have emerged
in recent years:
• Faddeev Equation Approach for Three-Cluster Nuclear Reactions
• Electromagnetic Transitions as a Probe of Nuclear Clustering
• “Tomography” of the Cluster Structure of Light Nuclei via Relativistic Dissocia-
tion
• From Light to Hyper-heavy Molecules and Neutron-Star Crusts in a Dynamical
Mean-Field Approach
• Covalent Binding on the Femtometer Scale: Nuclear Molecules
• Clusterization in Ternary Fission
The first chapter entitled Faddeev Equation Approach for Three-Cluster Nuclear
Reactions by Deltuva, Fonseca and Lazauskas shows how well the formalism based
vii
viii Preface
on Faddeev-like equations is capable to describe nuclear three-cluster reactions,
which include elastic, break-up and transfer channels. For the sake of pedagogy,
the formalism is presented in two different techniques based on momentum space
and configuration space representions explained in detail. Comparison with previ-
ous calculations based on approximate methods used in nuclear reaction theory is
discussed.
The second chapter of Jenkins on Electromagnetic Transitions as a Probe of
Nuclear Clustering investigates a number of cases where electromagnetic transitions
can be used to further our understanding of clustering, from heavy-ion radiative
capture to superdeformation in alpha-conjugate nuclei.
“Tomography” of the Cluster Structure of Light Nuclei via Relativistic Dissoci-
ation is deeply discussed in Chap. 3 by Zarubin to demonstrate the capabilities of
relativistic nuclear physics for the development of the physics of nuclear clusters.
Nuclear track emulsion is an effective technique for pilot studies to study the cluster
dissociation of a wide variety of light relativistic nuclei within a common approach.
Analysis of the peripheral interactions of relativistic isotopes of beryllium, boron,
carbon and nitrogen, including radioactive ones, with nuclei of the emulsion com-
position, allows the clustering pattern to be presented for a whole family of light
nuclei.
The Chap. 4 entitled From Light to Hyper-Heavy Molecules in Dynamical Mean-
Field Approach by Simenel describes a microscopic approach for low-energy colli-
sions between atomic nuclei is the time-dependent Hartree-Fock theory, providing
a mean-field dynamics of the system. This approach and some of its extensions are
used to predict the evolution of out-of-equilibrium nuclear systems. The formation
of light molecules and the dynamics of α-clustering are discussed. Di-nuclear sys-
tems formed in transfer, deep-inelastic, and quasi-fission reactions, as well as hyper-
heavy molecules produced in reactions between actinides are also investigated. The
formation and stability of structures in neutron star crusts are finally discussed.
von Oertzen and Milin are trying in Chap. 5 (Covalent Binding on the Femtome-
ter Scale: Nuclear Molecules) to definitively demontrate that Nuclear molecules are
objects having two or more individual clusters as centres with extra nucleons (usu-
ally neutrons) binding them. The clusters have to be strongly bound themselves,
while they get bound into molecules due to the specific properties of the nucleus-
nucleus potentials and exchange of nucleons. A large number of strongly deformed
nuclear states in light nuclei with neutron excess have been experimentally identified
in the last decades, and some of them have been associated with covalent structures,
mainly via their grouping into rotational bands.
Finally, the last chapter Clusterization in Ternary Fission proposed by Kamanin
and Pyatkov treats most of experimental findings of the new kind of ternary decay of
low excited heavy nuclei called “collinear cluster tri-partition” due to the features of
the effect observed namely decay partners fly away almost collinearly and at least
one of them has magic nucleon composition. At the early stage of our work the
process of “true ternary fission” (fission of the nucleus into three fragments of com-
parable masses) was considered to be undiscovered for low excited heavy nuclei.
Preface ix
Manifestations of new decay channel observed in the frame of different experimen-
tal approaches are discussed. Special attention is paid to the connection between
conventional binary fission and ternary fission processes.
Each of the three volumes contains lectures covering a wide range of topics from
nuclear cluster theory to experimental applications that have gained a renewed inter-
est with available Radioactive Ion Beams facilities and modern detection techniques.
We stress 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 coverage of the
field but are written instead in the pedagogical style of graduate lectures and thus
have a reasonable long ‘shelf life’.
The edition of this book could not have been possible without stimulous discus-
sions with Profs. Greiner, Horiuchi, Schuck and Zagrebaev. Our appreciation goes
to all our co-lectures for their valuable contributions. We acknowledge also all the
referees for their comments on the Chapters that are included in this volume. I would
like here to thank, more particularly, Prof. Poenaru for his constant helpful sugges-
tions from the beginning to the end. Special thanks go Dr. Christian Caron and all the
members of his Springer-Verlag team (in particular, Mrs Angela Schulze-Thomin,
Gabriele Hakuba, and Donatas Akmanavicˇius) for their help, fruitful collaboration
and continued support for this ongoing project.
Strasbourg, France Christian Beck
May 2013
Contents
1 Faddeev Equation Approach for Three-Cluster Nuclear Reactions . 1
A. Deltuva, A.C. Fonseca, and R. Lazauskas
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Momentum-Space Description of Three-Particle Scattering . . . . 2
1.2.1 Alt, Grassberger, and Sandhas Equations . . . . . . . . . . 3
1.2.2 Inclusion of the Coulomb Interaction . . . . . . . . . . . . 5
1.2.3 Practical Realization . . . . . . . . . . . . . . . . . . . . . 8
1.3 Configuration Space . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Faddeev-Merkuriev Equations . . . . . . . . . . . . . . . . 11
1.3.2 Complex Scaling . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Application to Three-Body Nuclear Reactions . . . . . . . . . . . 15
1.4.1 Numerical Comparison of AGS and FM Methods . . . . . 16
1.4.2 Comparison with Traditional Nuclear Reaction Approaches 18
1.4.3 Beyond Standard Dynamic Models . . . . . . . . . . . . . 19
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Electromagnetic Transitions as a Probe of Nuclear Clustering . . . . 25
David G. Jenkins
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Gamma-Ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Physics Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 27
8
2.3.1 Molecular Transitions in Be . . . . . . . . . . . . . . . . 27
12
2.3.2 Alpha Clustering in C . . . . . . . . . . . . . . . . . . . 29
2.3.3 E0 Transitions . . . . . . . . . . . . . . . . . . . . . . . . 29
12 12
2.4 C + C Clustering . . . . . . . . . . . . . . . . . . . . . . . . 30
12 12
2.4.1 Searching for Transitions Within C + C Cluster Bands . 30
2.4.2 Connecting Carbon-Carbon Resonances to Low-Lying
States: Heavy-Ion Radiative Capture . . . . . . . . . . . . 31
2.4.3 Total Cross-Section Measurements . . . . . . . . . . . . . 35
2.4.4 Strength Distribution Measurements Using DRAGON . . . 36
xi