UNIVERSITÉ PARIS-SUD ÉCOLE DOCTORALE 517 : PARTICULES, NOYAUX ET COSMOS Laboratoire : CSNSM-IN2P3-CNRS, UMR 8609 THÈSE DE DOCTORAT PHYSIQUE par Vladimir MANEA Penning-trap mass measurements of exotic CERN-THESIS-2014-351 29/09/2014 rubidium and gold isotopes for a mean-field study of pairing and quadrupole correlations Date de soutenance : 29/09/2014 Composition du jury : Directeur de thèse : David LUNNEY Directeur de Recherche CNRS, CSNSM, Orsay, France Rapporteurs : Héloïse GOUTTE Ingénieure Physicienne, CEA/DSM, Centre de Saclay, France Piet VAN DUPPEN Professeur, KU, Leuven, Belgique Examinateurs : Brigitte ROUSSIÈRE Directrice de Recherche CNRS, IPN, Orsay, France Hervé SAVAJOLS Chargé de Recherche CNRS, GANIL, Caen, France Nigel ORR Directeur de Recherche CNRS, LPC, Caen, France Abstract The most complex nuclei are situated between the magic and the mid-shell ones, in regions known for sudden changes of the trends of nuclear observables. These are the so-called shape-transition regions, where the nuclear paradigm changes from the vibrational liquid drop to the static rotor. With few exceptions, nuclei in these regions are radioactive, with half-lives dropping into the millisecond range. Complementing the information obtained from the low-lying excitation spectrum, nu- clear binding energies and mean-square charge radii are among the observables most sensitive to these changes of nuclear structure. In the present work, a study of the shape- transition phenomenon is performed by measurements of radioactive nuclides produced by the ISOLDE facility at CERN. The masses of the neutron-rich rubidium isotopes 98−100Rb and of the neutron-deficient gold isotopes 180;185;188;190;191Au are determined us- ing the Penning-trap mass spectrometer ISOLTRAP. The mass of 100Rb is determined for the first time. Significant deviations from the literature values are found for the iso- topes 188;190Au. A new experimental method is presented, using a recently developed multi-reflection time-of-flight mass spectrometer as a beam-analysis tool for resonance- ionization laser spectroscopy. The new method opens the path to measurements of atomic hyperfine spectra with ISOLTRAP, from which charge radii and electromagnetic moments of radioactive nuclides can be extracted. The properties of the studied nuclides map the borders of two prominent regions of quadrupole deformation, which constrain the fine balance between pairing and quadrupole correlations in the nuclear ground states. This balance is studied by the Hartree-Fock- Bogoliubov (HFB) approach. The sensitivity of the shape-transition phenomenon to the strength of pairing correlations is demonstrated. In particular, the strong odd-even staggering of charge radii in the mercury isotopic chain is shown to result in the HFB approach from the fine interplay between pairing, quadrupole correlations and quasi- particle blocking. Contents Acknowledgements 1 Preamble 3 1 Nuclear observables 9 1.1 Binding energy ................................. 9 1.2 Trends of binding energies ........................... 11 1.2.1 Decomposition and extension of the binding energy function . 12 1.2.2 Mass filters ............................... 14 1.3 Complementary nuclear data .......................... 25 2 Experimental method and data analysis 31 2.1 Charged-particle traps ............................. 31 2.2 Penning trap .................................. 32 2.2.1 Dynamics of a trapped ion ....................... 32 2.2.2 Driving the ion's motion ........................ 35 2.2.3 Detecting the ion's motion ....................... 37 2.3 From cyclotron frequency to mass: procedure, precision, systematic errors . 42 2.4 Production and preparation of the ion ensemble . 47 2.5 Complementary applications of the MR-TOF MS . 55 2.6 Experimental results .............................. 59 2.6.1 Neutron-rich rubidium isotopes .................... 59 2.6.2 Neutron-deficient gold isotopes .................... 64 3 Nuclear-theory concepts 71 3.1 Nuclear forces .................................. 71 3.2 Many-body calculations ............................ 72 3.3 The Hartree-Fock-Bogoliubov approach .................... 74 3.3.1 Hartree-Fock field ............................ 74 3.3.2 Pairing field ............................... 77 iii 3.4 Competition between particle-particle and particle-hole correlations in nuclei ....................... 80 3.5 Theoretical analysis of the measured nuclear data . 82 3.5.1 Aim ................................... 82 3.5.2 HFODD code .............................. 84 3.5.3 Tests of the method ........................... 86 4 Self-consistent mean-field calculations 93 4.1 Neutron-rich A ≈ 100 nuclei .......................... 93 4.2 Neutron-deficient gold-thallium nuclei . 103 4.3 Odd-even staggering of mercury isotopes . 109 4.4 Summary ....................................116 5 Conclusions and outlook 121 Appendices 125 A Finite-difference operators 127 B Motion of a charged particle in a Penning trap 131 C Publications related to thesis work 137 iv List of Figures 1.1 Experimental binding energies and different mass filters for the calcium isotopes ..................................... 16 1.2 Experimental two-neutron separation energies of neutron-rich A ≈ 100 nuclei 20 1.3 Experimental two-neutron separation energies and three-point estimator of the odd-even neutron gap for the bismuth and polonium isotopes . 24 1.4 Experimental two-proton separation energies of the thallium isotopes and three-point estimator of the odd-even neutron gap for the thallium and gold isotopes ................................... 25 1.5 Experimental N = 50 one-neutron and two-neutron gaps as a function of Z 26 1.6 Complementary nuclear data for the zirconium isotopic chain . 29 2.1 Idealized representations of ISOLTRAP's measurement Penning trap . 33 2.2 Excitation patterns of the radial eigenmotions of an ion in a Penning trap . 36 2.3 Scans of the frequencies of the main excitations of the ion motion applied at ISOLTRAP in the measurement trap ................... 39 2.4 Optimization of the phase and amplitude of some of the excitations of the ions' motion applied at ISOLTRAP in the measurement trap . 41 2.5 Schematic of the ISOLTRAP setup ...................... 50 2.6 Exemplary scans for the purification techniques used at ISOLTRAP . 53 2.7 Illustrative examples of applications of the MR-TOF MS as a beam analyzer 57 2.8 TOF-ICR resonance of 100Rb+ obtained with a Ramsey-type excitation pattern ...................................... 62 2.9 TOF-ICR resonance of 98Rb+ for with a 400 ms quadrupole excitation time 62 2.10 Two-neutron separation energies of rubidium isotopes using masses from the literature and this work .......................... 64 2.11 Two-neutron separation energies and mean-squared charge radii of the gold isotopes using data from the literature .................... 65 2 2 2.12 Resonance-ionization laser spectroscopy of the 6s S1=2 ! 6p P1=2 transi- tion in 185Au ................................... 68 2.13 Two-neutron separation energies and mean-squared charge radii of the gold isotopes from the literature and this work . 69 v 3.1 Calculated deformation energy of the prolate and oblate configurations, obtained using a spherical and a set of deformed harmonic oscillator bases for the krypton and gold isotopes ....................... 89 3.2 Theoretical mean-square charge radii of the prolate configurations along the krypton isotopic chain and oblate configurations along the gold isotopic chain 91 4.1 Deformation energy of the prolate and oblate configurations of the krypton isotopes, using different values of the pairing interaction . 94 4.2 Experimental two-neutron separation energies and mean-square charged radii of neutron-rich A ≈ 100 nuclei, compared to HFB-SLy4 calculations . 96 4.3 Experimental two-neutron separation energies and mean-square charge radii of even-Z, neutron-rich A ≈ 100 nuclei, compared to self-consistent mean- field calculations from the literature . 101 4.4 Theoretical values of the N = 50 two-neutron shell gap compared to ex- perimental values ................................102 4.5 Deformation energy of the prolate and oblate configurations of the gold isotopes using different values of the pairing interaction . 105 4.6 Experimental two-neutron separation energies and mean-square charge radii of neutron-deficient gold-thallium nuclei, compared to HFB-SLy4 calculations107 4.7 Experimental two-neutron separation energies and mean-square charge radii of neutron-deficient mercury isotopes, compared to self-consistent mean- field calculations from the literature . 110 4.8 Experimental values of the five-point empirical pairing gap for gold and mercury isotopes compared to the results of HFB-SLy4 calculations for mercury isotopes ................................112 4.9 Experimental values of the five-point empirical pairing gap for mercury and gold isotopes compared to the results of HFB-SLy4 calculations for mercury isotopes (only ground-state configuration) . 113 4.10 Experimental and theoretical two-neutron separation energies and mean- square charge radii of neutron-deficient gold and mercury isotopes, for a 3 pairing interaction of strength V0 = −200 MeV fm (with and without quasi-particle blocking) .............................114 4.11 Experimental and theoretical two-neutron separation energies and mean- square charge radii of neutron-deficient gold and mercury isotopes, for a 3 pairing interaction of strength V0 = −225 MeV fm (with and without quasi-particle blocking) .............................115