Rates of Light Neutron-Rich Nuclei for the r-Process Nucleosynthesis

116 Pages·2015·10.75 MB·English

by  Marcel Heine

γ
Measurement of (n, )-Rates of
Light Neutron-Rich Nuclei for the
r-Process Nucleosynthesis
Messungvon(n,γ)-ÜbergangsratenLeichterNeutronenreicherKernefürdie r-Prozeß
Nukleosynthese
ZurErlangungdesGradeseinesDoktorsderNaturwissenschaften(Dr.rer.nat.)
genehmigteDissertationvonDipl.-Phys. MarcelHeineausBadMuskau
2015—Darmstadt—D17
FachbereichPhysik
InstitutfürKernphysik
Measurementof(n,γ)-RatesofLightNeutron-RichNucleiforthe r-ProcessNucleosynthesis
Messung von (n, γ)-Übergangsraten Leichter Neutronenreicher Kerne für die r-Prozeß Nukleosyn-
these
GenehmigteDissertationvonDipl.-Phys. MarcelHeineausBadMuskau
1. Gutachten: Prof. Dr. ThomasAumann
2. Gutachten: ProfDr. Dr. h.cNorbertPietralla
TagderEinreichung: 27.05.2014
TagderPrüfung: 09.07.2014
Darmstadt—D17
Am Anfang gehts um explodierende Sterne.
Dann werden Formeln eingestreut.

Contents
1 Introduction 1
2 ExperimentalTechnique 3
2.1 Reaction Mechanism in Relativistic Electromagnetic Collisions . . . . . . . . . . . . . . . . . 3
2.2 Theoretical Calculation of Coulomb Dissociation Cross Sections. . . . . . . . . . . . . . . . . 7
2.2.1 The CDXS+ Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Experimental Spectroscopic Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Asymptotic Normalisation Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Neutron Capture Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 ExperimentalSetup 13
3.1 GSI Accelerator Facility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 R3B-LAND Setup in Cave C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Detection Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.2 Projectile Identification and Target Area. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.3 Fragment Branch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.4 Neutron Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 DetectorCalibration 23
4.1 The land02 Calibration Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Incoming Particle Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.1 Scintillator Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.2 Semiconductor Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 DataAnalysis 29
5.1 Selection of the Reaction Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1.1 Incoming Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1.2 Outgoing Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1.3 Neutron Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2 Data Normalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3 Background Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.3.1 Scaling of Target Runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.4 Efficiency Calibration of Detectors for Reaction Products . . . . . . . . . . . . . . . . . . . . . 38
5.4.1 Crystal Ball Simulations of a 60Co Calibration Source. . . . . . . . . . . . . . . . . . . 38
5.4.2 Response Function for De-excitation Spectra of Fragments . . . . . . . . . . . . . . . 43
5.4.3 XB Response to the De-excitation of 16C Fragments . . . . . . . . . . . . . . . . . . . . 43
5.4.4 XB Response to the De-excitation of 17C Fragments . . . . . . . . . . . . . . . . . . . . 44
5.4.5 LAND Efficiency Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.5 Invariant Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.6 DSSSD Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.6.1 Alignment Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.6.2 Three-Parameter Fit of an Empty-Target Run . . . . . . . . . . . . . . . . . . . . . . . . 48
i
5.6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6 Results 57
6.1 Coulomb Dissociation of 17C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.1 Nuclear Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.2 Integral Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.1.3 Differential Cross Section for 17C→16C(2+)+n . . . . . . . . . . . . . . . . . . . . . . 60
6.2 Coulomb Dissociation of 18C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.2.1 Nuclear Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.2 Coulomb-Dissociation Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.3 Neutron-Capture Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7 ConclusionsandOutlook 75
A DataAnalysis 77
A.1 Issues Related to XB Data for 18C Coulex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
A.2 Thermonuclear Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
B PhotogrammetricPositionMeasurement 85
B.1 Photo Shooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
B.2 Reconstruction of the Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
B.2.1 How to Do Photogrammetric Position Measurements . . . . . . . . . . . . . . . . . . . 87
B.3 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
B.3.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Literatur 97
ii Contents
List of Figures
1.1 R-process reaction flow along light nuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2.1 Electromagnetic excitation of a projectile in the field of a target nucleus. . . . . . . . . . . . 3
2.2 Field components of a lead target for 426 AMeV 18C beam. . . . . . . . . . . . . . . . . . . . 4
2.3 Frequency spectra for 426 AMeV 18C beam impinging on lead target. . . . . . . . . . . . . . 5
2.4 Virtual photon numbers for the E1/2 and M1 multipolarities. . . . . . . . . . . . . . . . . . . 7
3.1 GSI accelerator facility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 FRS areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 R3B-LAND setup at Cave C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.4 Signal flow along the electronics chain.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1 Data reconstruction flow with land02. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Time calibration data of a TDC channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3 Incoming ion charge for an N = Z calibration run. . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 Incoming particle identification plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.2 Correlation of the S8 times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3 Incoming PID plot with missing or invalid S8 times. . . . . . . . . . . . . . . . . . . . . . . . . 31
5.4 Tracking of a projectile-like fragment in the experimental setup. . . . . . . . . . . . . . . . . 32
5.5 Fragment-mass spectrum of 18C impinging on lead target. . . . . . . . . . . . . . . . . . . . . 33
5.6 Neutron background from the fragment arm in LAND. . . . . . . . . . . . . . . . . . . . . . . 33
5.7 Fragment charge distribution on the TFW for 18C projectiles. . . . . . . . . . . . . . . . . . . 35
5.8 Determination of the nuclear-scaling factor α . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Pb
5.9 Rescaling of the lead-target run for incoming 18C. . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.10 Representation of the XB detector in the R3BRoot toolkit. . . . . . . . . . . . . . . . . . . . . 39
5.11 Term schema of 60Ni related to the beta decay of 60Co. . . . . . . . . . . . . . . . . . . . . . . 39
5.12 Reconstruction of a 60Co source run from cosmics and simulations. . . . . . . . . . . . . . . 41
5.13 Reconstruction of coincident gammas from the 60Co source. . . . . . . . . . . . . . . . . . . . 42
5.14 LAND efficiency with respect to the relative energy. . . . . . . . . . . . . . . . . . . . . . . . . 45
5.15 Representation of the Target area in R3BRoot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.16 Straight-line fit residue of DSSSD 2 versus detector coordinate. . . . . . . . . . . . . . . . . . 49
5.17 Alignment of DSSSD 2 by means of a three-parameter fit. . . . . . . . . . . . . . . . . . . . . 50
5.18 Residue of DSSSD 2 with respect to a straight-line fit during the alignment. . . . . . . . . . 51
5.19 Position distributions of neutrons and projections on 18C projectiles on LAND. . . . . . . . . 53
5.20 Particle track with straggling in the DSSSDs and the target. . . . . . . . . . . . . . . . . . . . 54
6.1 Level scheme and shell-model neutron occupancy of 16C.. . . . . . . . . . . . . . . . . . . . . 57
6.2 Fit of the response function to the γ-spectrum for Coulomb dissociation of 17C. . . . . . . . 59
6.3 Differential Coulomb-breakup cross section for reactions to 16C(2+).. . . . . . . . . . . . . . 60
6.4 Level schemes of 18C and 17C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.5 Fit of the response function to the γ-spectrum for Coulomb dissociation of 18C. . . . . . . . 63
6.6 Exclusive differential Coulomb-dissociation cross sections for 18C. . . . . . . . . . . . . . . . 65
6.7 Exclusive neutron-capture cross sections on 17C. . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.8 Stellar reaction-rates for neutron capture on 17C to the ground state of 18C. . . . . . . . . . 67
iii
6.9 Differential Coulomb-dissociation cross sections for 18C in distorted-wave approximation. 70
6.10 Reduction of the measured nucleon-removal cross sections with respect to shell-model
calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.11 Ratio of reaction rates 17C(n,γ)18C from the Hauser-Feshbach model and present data. . . 72
A.1 Fit to the γ-sum spectrum for 18C Coulex for lead target. . . . . . . . . . . . . . . . . . . . . . 78
A.2 Fit to the γ-sum spectrum for 18C Coulex for carbon target. . . . . . . . . . . . . . . . . . . . 79
A.3 Fit to the γ-sum spectrum for 18C Coulex for the empty-target run. . . . . . . . . . . . . . . . 79
A.4 Fit to the γ-single spectrum for 18C Coulex for lead target in forward direction. . . . . . . . 80
A.5 Fit to the γ-single spectrum for 18C Coulex for lead target considering entire XB. . . . . . . 80
A.6 Fit to the γ-sum spectrum for 18C Coulex for lead target considering entire XB. . . . . . . . 81
A.7 Reaction rates for neutron capture in the ground state of 17C. . . . . . . . . . . . . . . . . . . 82
A.8 Reaction rates for neutron capture in the first excited state of 17C. . . . . . . . . . . . . . . . 83
A.9 Reaction rates for neutron capture in the second excited state of 17C. . . . . . . . . . . . . . 83
B.1 Marker for the photogrammetric position measurement. . . . . . . . . . . . . . . . . . . . . . 86
B.2 Co-planar condition in the photogrammetric position measurement. . . . . . . . . . . . . . . 86
B.3 Referencing between camera positions in the PhotoModeler. . . . . . . . . . . . . . . . . . . 87
B.4 Model of the detectors behind ALADiN.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
B.5 Model of the detectors in front of ALADiN.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
B.6 Model of the detectors in the target area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
B.7 CAD drawing of the experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
B.8 Active detector volumes in the R3B-LAND setup at Cave C. . . . . . . . . . . . . . . . . . . . . 92
B.9 Correlation of the uncertainties from the PhotoModeler and the construction drawing. . . 93
B.10 Angular distortion by means of the GFI housing. . . . . . . . . . . . . . . . . . . . . . . . . . . 94
B.11 Deviation of the positions in the CAD drawing and the PhotoModeler measurement. . . . 94
B.12 Angular distortion of the 3D-model for the GFIs and PDCs. . . . . . . . . . . . . . . . . . . . 95
iv ListofFigures
List of Tables
3.1 Incoming spill-rates and absolute ion-numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 List of inactive paddles in LAND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Trigger matrix of the S393 experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1 List of excluded XB crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Residue with respect to a straight-line fit of three DSSSDs. . . . . . . . . . . . . . . . . . . . . 48
5.3 Improvement of the residue in the DSSSDs with respect to a straight-line fit.. . . . . . . . . 51
5.4 Residue with respect to a straight-line fit from a two-step position alignment. . . . . . . . . 51
5.5 Full set of detector offsets from the DSSSD alignment routine. . . . . . . . . . . . . . . . . . 52
5.6 Mean values of position distributions of neutrons and 18C projectile projections on LAND. 53
5.7 Straggling in the target from experimental data and theoretical calculations. . . . . . . . . 54
5.8 Intrinsic position resolution of the DSSSDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.1 Integral cross sections for Coulomb dissociation of 17C. . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Experimental spectroscopic factors for the 17C→16C(2+)+n reaction. . . . . . . . . . . . . 61
6.3 Experimental cross sections and spectroscopic factors for Coulomb dissociation of 18C . . . 63
6.4 Parameters of the stellar reaction-rates for the parametrisation by Sasaqui et al.. . . . . . . 68
6.5 Parameters of the stellar reaction-rates for the parametrisation by Rauscher. . . . . . . . . . 69
6.6 Experimental spectroscopic factors for Coulomb-dissociation of 18C. . . . . . . . . . . . . . . 71
A.1 Accumulated detection efficiencies for gammas from the 1/2+ and 5/2+ levels in 17C. . . . 77
A.2 Dependence of the XB detection efficiency from the detector thresholds for Coulomb dis-
sociation of 18C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
B.1 Detector positions from the photogrammetric measurement. . . . . . . . . . . . . . . . . . . 91
B.2 Dimensions of the DSSSD wafers and the GFI and PDC housings. . . . . . . . . . . . . . . . . 91
v
Abstract
Exclusive neutron capture cross sections of 17C and associated stellar reaction rates have been derived
from Coulomb dissociation of 18C using the R3B-LAND setup at GSI in Darmstadt (Germany). The sec-
ondary beam of relativistic 18C at approximately 430 AMeV was generated by fragmentation of primary
40Aronaberylliumtarget. IntheFRagmentSeparator(FRS)thenucleiofinterestwereselectedandsub-
sequently guided to the experimental setup at Cave C. There the ions were excited electromagnetically
in the electric field of lead target nuclei and the de-excitation process was detected with the R3B-LAND
setup. Allreactionproductsoftheone-neutronevaporationchannelincludinggammasfromde-exciting
states of fragments were measured and the invariant mass was reconstructed. A similar measurement
of 17C Coulomb dissociation served as a benchmark to validate the accuracy of the present results with
respect to previously published data.
The measured relative energy spectra of 18C Coulomb dissociation to the ground state of 17C as well
as the first and second excited state in 17C qualitatively match theoretical calculations of the Coulomb-
dissociationprocessinanindependent-particlemodel. Inparticular,theshapesofexperimentaldataare
reproduced. The measured spectroscopic factors were compared to an exclusive one-neutron knockout
measurement on 18C, which is consistent within the respective uncertainties.
Theenergydifferentialcrosssectionswereconvertedintophoto-absorptioncrosssections18C(γ,n)17C
with virtual-photon theory. Subsequently, exclusive neutron-capture cross sections 17C(n,γ)18C to the
ground state were derived using the detailed-balance theorem. The neutron-capture cross sections were
used to calculate stellar reaction rates, where the neutron velocities follow a Maxwell-Boltzmann distri-
bution. The results were compared to thermonuclear reaction rates from a statistical Hauser-Feshbach
model (HF). The uncertainty of the experimental results is at maximum around 60% at T = 1 GK for
9
neutron capture in the ground state of 17C. This is accompanied by an uncertainty of a factor of ten in
the HF calculation.