Ground state properties of neutron-rich Mg isotopes [Elektronische Ressource] : the island of inversion studied with laser and β-NMR spectroscopy / Magdalena Kowalska

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• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2006
• Nombre de lectures: 19
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Ground state properties of neutron-rich Mg
isotopes – the “island of inversion” studied with
laser and β-NMR spectroscopy
Dissertation
zur Erlangung des Grades
“Doktor der Naturwissenschaften”
am Fachbereich Physik, Mathematik und Informatik
der Johannes Gutenberg-Universit¨at
in Mainz
Magdalena Kowalska
geb. in Poznan´, Polen
Mainz, August 2006Contents
Introduction 1
1 Motivation – “island of inversion” 3
1.1 Experimental evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Theoretical explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Decreased shell gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Correlation energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Known properties of neutron-rich Mg isotopes . . . . . . . . . . . . . . . . . . 12
2 Nuclear ground state properties 15
2.1 Charge radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Electromagnetic moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Magnetic dipole moment. . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.2 Electric quadrupole moment. . . . . . . . . . . . . . . . . . . . . . . . 20
3 Nuclear information from laser and β-NMR spectroscopy 21
3.1 Hyperfine structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 A-factor and the nuclear magnetic moment . . . . . . . . . . . . . . . 21
3.1.2 B-factor and the electric quadrupole moment . . . . . . . . . . . . . . 23
3.2 Isotope shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Field shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Mass shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
23.2.3 Determination of δhr i . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Nuclear magnetic resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 NMR and the nuclear electromagnetic moments. . . . . . . . . . . . . 29
3.4 Hyperfine splitting combined with NMR results: I and . . . . . . . . . . . 30I
4 Experimental techniques 33
4.1 Collinear laser spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Optical pumping and nuclear polarisation . . . . . . . . . . . . . . . . . . . . 34
4.3 Detection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.1 Fluorescence detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.2 β-decay asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 Experimental setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4.1 ISOLDE facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4.2 Collinear laser spectroscopy setup . . . . . . . . . . . . . . . . . . . . 49
5 Experimental results 53
5.1 Random and systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . 53
5.1.1 Random uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.2 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.1.3 Weighted average of several measurements . . . . . . . . . . . . . . . . 56
i24−265.2 Isotope shifts and change in charge radii for Mg . . . . . . . . . . . . . . 57
24−265.2.1 Isotope shifts of Mg . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.2 Considerations on the determination of changes in charge radii . . . . 59
29,315.3 Hyperfine structure and β-NMR resonances of Mg . . . . . . . . . . . . . 63
5.3.1 Simulations of the nuclear polarisation reached by optical pumping . . 63
5.3.2 Hyperfine structure observed in β-asymmetry . . . . . . . . . . . . . . 65
5.3.3 Results of β-NMR studies . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3.4 Combined hyperfine structure and β-NMR results – value of spin and
sign of the g-factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6 Interpretation and discussion of results 75
6.1 Charge radii of stable Mg isotopes . . . . . . . . . . . . . . . . . . . . . . . . 75
29,316.2 Magnetic moments of Mg – towards the island of inversion . . . . . . . . 76
6.2.1 Shell model calculations used for comparison with data . . . . . . . . 76
6.2.2 Comparison with theory and interpretation of measured spin and g-
29factor of Mg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2.3 Comparison with theory and interpretation of measured spin and g-
31factor of Mg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7 Summary and outlook 85
Bibliography 87
iiList of Figures
1.1 The nuclear chart around the “island of inversion” . . . . . . . . . . . . . . . 4
1.2 Ground state binding energies of sd and sd-pf nuclei . . . . . . . . . . . . . . 5
1.3 Two-neutron separation energies for nuclei around N =20 and Z =10−20. . 5
+1.4 Energies of first 2 states in even-even nuclei around “island of inversion”. . . 6
+ +1.5 B(E2;0 →2 ) values for neutron-rich even-even Ne and Mg isotopes. . . . 7
1.6 Electromagnetic moments and the constitution of the wave-function for the
ground states of neutron-rich Na isotopes. . . . . . . . . . . . . . . . . . . . . 8
1.7 Proton-neutron“spin-flip”interactionfornucleiaroundthe“islandofinversion”. 10
1.8 The orbital shift due to tensor force . . . . . . . . . . . . . . . . . . . . . . . 10
1.9 Sources of the correlation energy of the intruder and normal states . . . . . . 11
2.1 Mean radius and skin thickness of a nucleus.. . . . . . . . . . . . . . . . . . . 16
2.2 Level ordering in the nuclear shell model with the spin-orbit splitting . . . . . 17
2.3 Schmidt magnetic moments of odd-Z even-N nuclei . . . . . . . . . . . . . . . 19
2.4 Schmidt magnetic moments of odd-N even-Z nuclei . . . . . . . . . . . . . . . 19
29 +4.1 Optical pumping of Mg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
29 +4.2 Hyperfine pumping of Mg . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
294.3 Ground state hyperfine structure of Mg in strong and weak magnetic field . 36
29 314.4 β-decay of Mg and Mg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
294.5 Angular distribution of β particles for Mg . . . . . . . . . . . . . . . . . . . 40
4.6 S/N ratio for β-decay asymmetry versus opening angle . . . . . . . . . . . . . 41
4.7 Average β-decay asymmetry for states with different lifetimes . . . . . . . . . 43
4.8 Average S/N ratio for different lifetimes and relaxation times. . . . . . . . . . 44
4.9 Width and amplitude of NMR resonances versus the rf strength . . . . . . . . 45
4.10 Width and amplitude of NMR resonances for different effective lifetimes . . . 46
4.11 ISOLDE facility at CERN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.12 A schematic picture of the ISOLDE target with the laser ionisation and ex-
traction section.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.13 Time structure of ISOLDE proton pulses and of produced radioactive beams 49
4.14 Collinear laser spectroscopy and β-NMR setup . . . . . . . . . . . . . . . . . 50
24−265.1 Optical resonances in the D transition for Mg . . . . . . . . . . . . . . 581
24−265.2 Optical resonances in the D transition for Mg . . . . . . . . . . . . . . 582
24−265.3 King plot for D and D transitions in Mg . . . . . . . . . . . . . . . . . 601 2
2 24−265.4 Modified King plot δhr i versus isotope shifts for Mg . . . . . . . . . . . 61
5.5 Extrapolated modified difference in charge radii in D line . . . . . . . . . . . 621
5.6 Extrapolated modified difference in charge radii in D line . . . . . . . . . . . 631
5.7 Relaxation of β-decay asymmetry in different implantation crystals . . . . . . 65
5.8 β-decay asymmetry as a function of the laser power . . . . . . . . . . . . . . 66
295.9 Measured and simulated HFS of Mg . . . . . . . . . . . . . . . . . . . . . . 67
315.10 HFS of Mg seen in β-decay asymmetry . . . . . . . . . . . . . . . . . . . . . 68
315.11 Simulated HFS of Mg for I =1/2 . . . . . . . . . . . . . . . . . . . . . . . . 69
iii315.12 Simulated HFS of Mg for I =3/2 and 7/2 . . . . . . . . . . . . . . . . . . . 69
5.13 Width and amplitude of a Larmor resonance versus of rf-amplitude . . . . . . 70
295.14 Mg β-NMR signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
315.15 Mg β-NMR signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
26.1 Measured changes inhr i for Mg and Ne isotopes . . . . . . . . . . . . . . . . 76
6.2 Predicted effective single-particle energies for neutrons at N =20 . . . . . . . 78
6.3 Experimental g-factors in even-Z odd-N nuclei with 1 unpaired neutron in d 803/2
296.4 Measured and predicted excitation energies and g-factors for in Mg . . . . . 81
316.5 Measured and predicted excitation energies, spins, parities andg-factors in Mg 81
6.6 Single particle energies in the Nilsson model around N =20 . . . . . . . . . . 83
ivList of Tables
1.1 Ground state properties of neutron-rich Mg isotopes. . . . . . . . . . . . . . . 12
24−263.1 Mg charge radii from muonic atom transitions. . . . . . . . . . . . . . . 28
24−263.2 Differences in Mg charge radii based on transitions in muonic atoms. . . 29
29,31,334.1 Typical ISOLDE