Evolution of the one-quadrupole phonon 2_1hn+_1tn1_1tn,_1tnm_1tns mixed-symmetry state in _1hn1_1hn2_1hn4_1hn,_1hn1_1hn2_1hn6_1hn,_1hn1_1hn2_1hn8_1hn,_1hn1_1hn3_1hn0_1hn,_1hn1_1hn3_1hn2Xe [Elektronische Ressource] / von Laurent Coquard

Coquard

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• Physik

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• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2010
• Nombre de lectures: 17
• Langue: English
• Poids de l'ouvrage: 1 Mo

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EvolutionoftheOne-Quadrupole
+Phonon2 Mixed-Symmetry
1,ms
124,126,128,130,132Statein Xe
ZurErlangungdesGradeseinesDoktors derNaturwissenschaften(Dr. rer. nat.)
genehmigteDissertation vonDipl.-Phys. LaurentCoquard ausSaint-Germainen Laye
(Frankreich)
Juni2010—Darmstadt—D17
Fachbereich Physik
Institut fürKernphysik
Schlossgartenstr. 9
D-64289 Darmstadt+ 124,126,128,130,132Evolution of the One-QuadrupolePhonon2 Mixed-SymmetryState in Xe
1,ms
GenehmigteDissertationvon Dipl.-Phys. LaurentCoquard ausSaint-GermainenLaye(Frankreich)
1. Gutachten: Prof. Dr. N.Pietralla
2. Gutachten: Prof. Dr. T.Kröll
Tagder Einreichung: 09. April 2010
Tagder Prüfung: 10. Mai 2010
Darmstadt— D 17Erklärung zurDissertation
Hiermit versichere ich die vorliegende Dissertation ohne Hilfe Dritter nur mit den angegebenen
Quellen und Hilfsmitteln angefertigt zu haben. Alle Stellen, die aus Quellen entnommen wurden,
sind als solche kenntlich gemacht. Diese Arbeit hat in gleicher oder ähnlicher Form noch keiner
Prüfungsbehörde vorgelegen.
Darmstadt,den24th June 2010
(L. Coquard)
1“If the life is complex it is because there is a real part and an imaginary part.”
(Géraud Devos)
2Abstract
Collective nuclei are characterized by rotational and vibrational states due to a common and therefore “collective” be-
havior of the two constituents of the nucleus: protons and neutrons. The evolution of the collectivity (spontaneous
deformation) is governed by the proton-neutron interaction in the valence shell. Nuclear states that are particularly sen-
sitive to the proton-neutron interaction in the valence shell are the so called mixed symmetry states (MSSs). In this work
+we trace the evolution of the fundamental MSS, i.e the one-quadrupole phonon 2 state, in a transitional region from
1,ms
134 124,126vibrational nuclei ( Xe) toγ-soft nuclei reflecting the O(6)-like structure of the IBM-2 ( Xe). Projectile-Coulomb
excitation of Xe isotopes has been performed at Argonne National Laboratory (ANL) using the Gammasphere array for
the detection ofγ-rays.
124,126First, our data on more than 50 absolute E2 transition rates between off-yrast low-spin states of Xe enable us to
quantitatively test O(6) symmetry in these two nuclei. As a result we find that O(6) symmetry is more strongly broken
in the A= 130 mass region than previously thought. Then, 19 absolute E2 transition strengths have been obtained in
128 π +Xe including the first measurement of the critical B(E2) decays from the second and third J = 0 states. These data
128are compared with the theoretical predictions of the critical point symmetry E(5) and let us conclude that Xe is not an
130E(5) nucleus as previously suggested, leaving Xe as the most likely candidate amongst the xenon isotopes. Finally, the
+ 128,130,132,134one-phonon 2 states or at least a fragment of it have been identified in Xe. This enables us to trace the
1,ms
+evolution of the one-phonon 2 states in the even-even stable xenon isotopic chain from the vibrators near N= 82 to
1,ms
theγ-soft nuclei towards mid-shell.
3Zusammenfassung
Kollektive Kerne können durch Rotations- oder Vibrationsanregungen beschrieben werden, die von dem gemeinsamen
Verhalten der zwei Bestandteile des Kerns, den Protonen und Neutronen, entstehen. Die Entwicklung der Kollektivität,
etwa spontane Kerndeformation, wird durch die Proton-Neutron–Wechselwirkung im Valenzraum beeinflusst. Soge-
nannte gemischt-symmetrische Zustände sind besonders sensitiv auf die pn–Wechselwirkung im Valenzraum. Diese
+Arbeit untersucht die Entwicklung des pn-gemischt-symmetrischen 2 Ein-Quadrupol-Phononzustands im Übergang
1,ms
134von Vibratorstruktur ( Xe) zur Strukturγ-weicher Kerne der O(6)-Symmetrie des Interacting Boson Model (IBM-2)
124,126( Xe). Die zu erforschenden Zustände sind mittels der Methode der Projektil-Coulomb-Anregung am amerikanis-
chen Argonne National Labor(ANL) an Leichtionen-Targets bevölkertworden. Ihreγ-Zerfälle sind mit dem 4π-Halbleiter-
Detektorfeld Gammasphere nachgewiesen.
Die experimentellen Daten mit mehr als 50 absoluten E2 Übergangsraten zwischen off-yrast tief liegenden Zustände in
124,126Xe erlaubten es die O(6) Symmetrie in diesen zwei Kernen quantitativ zu untersuchen. Darüber hinaus liess sich
festellen, dass die O(6) Symmetrie in der A= 130 Mass Region stärker gebrochen ist als es bisher bekannt war. Die 19
128gemessenen absoluten E2 Übergangsraten in Xe inklusive der ersten Messungen von den kritischen B(E2) Zerfällen
π + 128von dem zweiten und dritten J = 0 Zustand, ermöglicht die Schlussfolgerung, dass der Kern Xe nicht an dem kri-
130tischen Punkt E(5) liegt. Xe wird stattdessen als bester Kandidat unter den Xe Isotopen vorgeschlagen. Zudem ist der
+ 128,130,132,1342 Ein-Quadrupol-Phononzustand oder ein Fragment davon in Xe identifiziert worden. Dementsprechend
1,ms
+konnten wir für zum ersten Mal die Entwicklung eines pn-gemischt-symmetrischen 2 Ein-Quadrupol-Phononzustands
1,ms
beim Übergang von Vibratorstruktur zur Strukturγ-weicher Kernen der O(6)-Symmetrie verfolgen.
4Contents
1 Introduction 7
2 Nuclear Deformations 9
2.1 Generalnucleardeformation................................................. 9
2.2 Thevibrationalmodel........ 9
2.3 Therotationalmodel.........10
3 The Interacting Boson Model (IBM) 13
3.1 AssumptionsoftheIBM...............13
3.2 sd-IBM-1.....................................................13
3.2.1 Bosonization.........13
3.2.2 TheLiealgebraU(6) ............14
3.2.3 Hamiltonianandbasisstates .................14
3.2.4 Thethreedynamicalsymmetries:U(5),SU(3),O(6)...15
3.2.5 Electromagnetictransitionoperators.....................17
3.2.6 ConsistentQFormalism(CQF)...................................18
3.3 sd-IBM-2..................................19
3.3.1 F-spin .....................19
3.3.2 HamiltonianoftheIBM-2 .20
3.3.3 Electromagnetictransitionoperators.............21
3.3.4 The Q-phononscheme ...........22
3.3.5 SignaturesforMixed-SymmetryStates ..............................22
3.3.6 GeometricpictureofMixed-SymmetryStates.......23
4 The O(5)-Confined-Beta-Soft model (O(5)-CBS) 25
5 Coulomb excitation theory 29
5.1 Semi-clasicaltheoryofCOULEX...............................................29
5.2 First-ordertime-dependentperturbationtheory ..........30
5.3 Coulombexcitationcrosssections.31
5.4 Coulombexcitationcode:CLX...........32
6 Experiment, Data Analysis 35
6.1 Experiment............................................................35
6.1.1 ATLASfacility.........35
6.1.2 Gammaspherearay.....35
6.2 DataAnalysis......................39
6.2.1 Efficiencycalibration....39
6.2.2 Dopplercorection........................39
6.2.3 Sorting........................................41
6.2.4 Roombackgroundsubtraction.................41
6.2.5 Calculationofcrossections42
6.2.6 Gammaangulardistribution........43
7 Results and Discussion 51
1247.1 Xe................................................................51
1267.2 Xe54
124,1267.3 O(6)-symmetry breaking in theγ-soft nuclei Xe.......59
1287.4 Xe:RobusttestoftheE(5)symmetry.......................67
+
130,1327.5 Xe: Evolution of the one-quadrupole phonon 2 Mixed-SymmetryStateineven-evenXe........75
1,ms
8 Summary and outlook 85
5130A CLX input file: Xe as an example 87
B Error propagation 89
C Angles Germanium Detectors of Gammasphere 91
Bibliography 93
List of publications 99
Acknowlegments 101
Lebenslauf 103
61 Introduction
What is nuclear physics?
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. This branch of
science was born after the discovery of the atomic nucleus by Rutherford in 1911 and investigations from the properties
of the nucleus have continued from Rutherford’s time to the present day. In order to understand the properties of the
nucleus, among which are mass, radius, decay modes, half-lives, reaction modes, cross sections, spin, magnetic dipole
and electric quadrupole moments, excited states, transitions strengths..., experimental as well as theoretical studies have
been carried out for almost one century and we understand an enormous amount. We have models: the shell model and
collective models that provide a framework for our understanding. We have databases where experimental results are
repertoried such as the Evaluated Nuclear Structure Data File in National Nuclear Data Center (NNDC) in Brookhaven,
USA.
In the shell model one fills the shells with nucleons in order of increasing energy, consistent with the requirement of the
Pauli principle, analogous to the filling of electron shells in atoms. Note that the shells exist for both protons and neutrons
individually. The nucleus consists of an inert filled core of closed shells and some number of valence nucleons. Excited
states were found that correspond to the excitation of a nucleon into an orbit of a higher lying shell. Such excitations
are called single-particle excitations and usually lie above 1 MeV. However there exists other types of excitations which
involve more than one single particle. Such excitations are called collective excitations and can be interpreted in the
framework of collective models. Collective excitations can be vibrations or ro