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Dipole Excitations Below the Neutron Separation Threshold in Neutron-Rich Tin Isotopes

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Dipole Excitations Below the Neutron Separation Threshold in Neutron-Rich Tin Isotopes Dipole excitations below the neutron separation threshold in neutron-rich Tin isotopes. Zanetti, Lorenzo (2020) DOI (TUprints): https://doi.org/10.25534/tuprints-00013483 Lizenz: CC-BY-SA 4.0 International - Creative Commons, Attribution Share-alike Publikationstyp: Ph.D. Thesis Fachbereich: 05 Department of Physics Quelle des Originals: https://tuprints.ulb.tu-darmstadt.de/13483 Kernreaktionen GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH Physik Dipole excitations below the neutron separation threshold in neutron-rich Tin isotopes. Vom Fachbereich Physik der Technischen Universit¨atDarmstadt zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von M. Sc. Lorenzo Zanetti aus Mailand Darmstadt 2019 D17 Dipole excitations below the neutron separation threshold in neutron-rich Tin isotopes. Referent: Prof. Dr. Thomas Aumann Korreferent: Prof. Dr. Joachim Enders Tag der Einreichung: 19.11.2019 Tag der m¨undlichen Pr¨ufung: 11.12.2019 Zanetti, Lorenzo: Dipole excitations below the neutron separation threshold in neutron-rich Tin isotopes. Darmstadt, Technische Universit¨atDarmstadt, Year thesis published in TUprints: 2020 Date of the viva voce: 11.12.2019 Published under CC BY-SA 4.0 Interantional https://creativecommons.org/licenes/ To the 2+ state of Tin-132 Abstract Among the many ways to describe and predict the behaviour of a nucleus, we find the nuclear equation of state (EoS). This expression aims to account for the properties of nuclear matter from common run-off-the-mill nuclei, such as those found in nature, to neutron stars and nuclei far from stability synthesized in laboratories. Around the density nuclear matter would assume if it were infinite and constituted in equal parts by neutrons and protons, the nuclear equation of state can be expanded in a Taylor series: the first terms of this series define the behaviour of the equation of state. Of particular interest is the second order term, known as the symmetry energy. Because it is not experimentally accessible, though, a direct measurement cannot be performed and other observables have to be individuated. One of these observables is the dipole polarizability, indicated with αD of the nucleus; this quantity correlates with the thickness of the neutron skin that forms around nuclei with a marked excess of neutrons and, thus, has the potential to put a constraint on the first order coefficient of symmetry energy's Taylor series expansion around the saturation density. This term is known as the \slope" and indicated with the letter L. The dipole polarizability can be obtained by integrating the strength of the nuclear response on all energies; this integral, though, is weighted by the energy: the response at lower energies plays, proportionally, a bigger role than that at higher ones. The aim of this work is to obtain a strength distribution for a neutron-rich isotope of Tin, 132Sn, and thus measure the dipole polarizability. To accomplish this, the data acquired at the GSI facility by the R3B collaboration, in Darm- stadt, have been used and a novel method for profiling the strength of the dipole response of a nucleus from a noisy spectrum has been demonstrated to be promising and, furthermore, it is expected to be portable to other isotopes and experiments where a gamma array detector is used. Zusammenfassung Unter den zahlreichen M¨oglichkeiten, das Verhalten eines Atomkerns zu beschreiben und vorherzusagen, befindet sich die nukleare Zustandsgleichung (EoS). Die EoS zielt darauf ab, die Eigenschaften von Kernmaterie zu erkl¨aren,welche von gew¨ohnlichen Kernen, wie sie in der Natur vorkom- men, bis zu Neutronensternen und Kernen, welche in Laboratorien synthetisiert werden und weit von der Stabilit¨atentfernt sind, reichen. Wenn bei einer bestimmten Dichte der Kernmaterie angenommen wird, dass sie unendlich w¨are und zu gleichen Teilen aus Neutronen und Protonen besteht, dann kann die nukleare Zustands- gleichung in einer Taylor-Reihe erweitert werden: Die ersten Terme dieser Reihe definieren das Verhalten der Zustandsgleichung. Von besonderem Interesse ist der Term zweiter Stufe, der als Symmetrieenergie bekannt ist. Da dieser Term jedoch nicht experimentell zug¨anglich ist, kann keine direkte Messung durchgef¨uhrtwerden und andere Observablen m¨ussenindividualisiert werden. Eine dieser Observablen ist die Dipolpolarisierbarkeit des Kerns, angegeben mit αD. Diese Gr¨oßekorreliert mit der Dicke der Neutronenhaut, die sich um die Kerne mit einem deut- ¨ lichen Uberschuss an Neutronen bildet. αD besitzt die M¨oglichkeit, eine Einschr¨ankungf¨urdie Taylorreihenausdehnung des Koeffizienten erster Ordnung der Symmetrieenergie um die S¨atti- gungsdichte zu setzen. Dieser Term wrid als \Steigung" und mit der Variablen L bezeichnet. Die Dipolpolarisierbarkeit kann erhalten werden, indem die St¨arke der Dipolantwort des Kernes auf alle Energien integriert wird. Dieses Integral wird jedoch mit der Energie gewichtet: Die Reaktion bei niedrigeren Energien spielt proportional eine gr¨oßereRolle als die bei h¨oheren. Ziel dieser Arbeit ist es, eine Dipolst¨averteilung f¨urein neutronenreiches Isotop von Zinn, 132Sn, zu erhalten und damit die dipole polarizability zu messen. Zu diesem Zweck wurden die an der GSI bei R3B in Darmstadt gewonnenen Daten verwendet, um zu zeigen, dass eine neuartige Methode zur Ermittlung der St¨arke der Dipolreaktion eines Kerns aus einem verrauschten Spektrum vielversprechend ist. Diese Methode kann auf andere Isotope und Experimente, bei denen ein Gamma-Array-Detektor verwendet wird, ¨ubertragen werden. Contents 1 Introduction 1 1.1 Motivation . .1 1.2 Theoretical overview . .2 1.2.1 The nuclear equation of state . .2 1.2.2 L and J parameters . .2 1.2.3 Relationship with αD, the static dipole polarizability . .3 1.2.4 Coulomb excitation . .5 1.2.5 Coulomb cross section and photo absorption cross section . .6 1.2.6 What about the oscillator strength? . .6 1.3 Experimental setup . .7 1.3.1 Beam . .8 1.3.2 Pre target tracking . 10 1.3.3 The Darmstadt-Heidelberg Crystal Ball . 13 1.3.4 Reaction fragment tracking . 22 1.3.5 Magnet assembly . 26 1.3.6 Targets and beams . 27 2 Analysis 28 2.1 Instruments . 28 2.1.1 Land02 . 28 2.1.2 The Toolkit . 29 2.2 Energy (and time) calibration . 42 2.2.1 Crystal Ball calibration . 42 2.3 Event selection . 43 2.3.1 Trigger matrices . 43 2.3.2 Incoming isotope identification . 45 2.3.3 Outgoing fragment . 48 2.4 Data preparation . 51 2.4.1 Front and back of the Crystal Ball . 51 2.4.2 Crystal thresholds . 53 2.4.3 Empty target contributions . 54 2.5 Simulations . 57 2.5.1 General setup and sbkg ........................... 57 2.5.2 The atomic background . 58 2.5.3 Event generation and abkg .......................... 58 CONTENTS 2.5.4 Experimental condition for the atomic background . 59 2.6 The whole background picture . 62 2.7 Calculations . 63 2.7.1 Cut efficiency, specificity and uncertainties . 63 2.7.2 Reaction probability . 65 2.7.3 Cross section . 67 2.7.4 Virtual photon number . 68 2.7.5 Coulomb excitation cross section from n-pole strength . 72 2.7.6 αD from dipole strength and photo absorption cross section distributions 74 3 Results 76 3.1 A landmark: 132Sn 2+ state . 76 3.1.1 Efficiencies involved . 77 3.1.2 Comparison with the data . 77 3.2 Target excitation . 80 3.2.1 Sensitivity (short) . 83 3.3 \Deconvolution" of 132Sn cascades . 83 3.3.1 Nuclear realisations . 85 3.4 Dipole polarizability . 87 3.4.1 Is it really just the dipole strength? . 88 4 Conclusions and Outlook 90 4.1 Sensitivity and target choice . 90 4.1.1 Sensitivity . 90 4.1.2 Target choice . 92 4.1.3 Outlook . 93 A Toolkit 95 A.1 Land02 . 95 A.2 XB programs . 95 A.2.1 Why not ROOT? . 95 A.2.2 Data structures . 96 A.2.3 File format . 97 A.2.4 Data conversion . 97 A.3 Octave tools . 98 A.3.1 "Manual fitter” . 99 B Clustering 101 B.1 What is \clustering"? . 101 B.2 Specificity of our problem . 101 CONTENTS B.2.1 Reasonable assumptions . 101 B.3 Nearest neighbour . 102 B.3.1 Problem of the nearest neighbour . 102 B.4 "Beading" . 104 B.4.1 Number of iterations . 105 B.4.2 Advantages of the beading algorithm . 105 B.4.3 Disadvantages of this algorithm . 106 C Thresholds of the Crystal Ball 107 D R3BRoot 109 D.1 FairSoft and FairRoot . 109 D.1.1 FairSoft . 109 D.1.2 FairRoot . 111 E sbkg 112 E.1 Simulation setup . 112 E.2 R3BRoot extensions . 112 E.2.1 Improved target geometry . 113 E.2.2 Tracking detectors . 113 F abkg 115 F.1 Atomic background spectrum breakup . 120 G Trigger flags and Tpat 126 List of Figures 138 List of Tables 139 Chapter 1 Introduction In this work, I'll attempt to extract the dipole polarizability of 132Sn from its Coulomb excita- tion. Because this quantity is proportional to an integral inversely weighted by the excitation energy, 1 I will concentrate on the region from zero to the (first) neutron separation threshold, Sn. 1.1 Motivation Among the many ways to describe and predict the behaviour of a nucleus, we find the nuclear equation of state (EoS). This expression aims to account for the properties of nuclear matter from common run-off-the-mill nuclei, such as those found in nature, to neutron stars and nuclei synthesized in laboratories far from stability. As we will see in the following, more detailed sections, the nuclear equation of state is.
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