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Towards a Nuclear Clock with the 229Th Isomeric Transition

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Towards a Nuclear Clock with the 229Th Isomeric Transition Dissertation SUBMITTED TO THE Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany FOR THE DEGREE OF Doctor of Natural Sciences Put forward by Pavlo V. Bilous Born in: Kherson, Ukraine Oral examination: 13.12.2018 Towards a nuclear clock with the 229Th isomeric transition The first referee: PD Dr. Adriana Pálffy-Buß The second referee: Prof. Dr. Klaus Blaum Zusammenfassung Der Kern 229Th mit seinem Isomerzustand bei 7.8 eV ist ein einzigartiger Kandidat für die erste nukleare optische Uhr mit außerordentlicher Genauigkeit von 10−19. Auf- grund der niedrigen Isomerübergangsenergie ist die Kopplung an die atomare Hülle bei den Prozessen der inneren Konversion (IK) oder Elektronenbrücke (EB) sehr stark. In dieser Arbeit untersuchen wir theoretisch die IK- und EB-Mechanismen und entwerfen neuartige lasergestützte Systeme, die auf (i) eine genauere Bestimmung der Isomerenen- ergie Em und (ii) effiziente Anregung des Isomers abzielen. Einerseits zeigen wir, wie die IK von angeregten elektronischen Zuständen von Th-Ionen zur Bestimmung der Iso- merübergangsenergie verwendet werden kann. Wir schlagen auch einen neuen Ansatz zur Messung der Isomerenergie mit Laserspektroskopie-Genauigkeit mit der laserinduzierten EB in 229Th3+ Ionen vor. Andererseits stellen wir mögliche Isomeranregungsschemata vor, die auf dem EB-Prozess in hochgeladenen Th-Ionen oder auf lasergestützter Ker- nanregung durch Elektroneneinfang des 29.19 keV-Kernzustands direkt über dem Isomer beruhen. Durch die Anwendung von hochgeladenen Ionen wird möglich, die EB optisch mit Hochleistungslasern zu treiben, was laut unserer Ergebnisse zu einer effizienten An- regung führen sollte. Ein solcher Aufbau mit Ionenfallen könnte für die zukünftige Entwicklung der Atomkernuhr relevant werden. Abstract The 229Th nucleus with its 7.8 eV isomeric state is a unique candidate for the first nuclear optical clock at an exceptional accuracy of 10−19. Due to the low isomeric transition energy, the coupling to the atomic shell in the processes of internal conversion (IC) or electron bridge (EB) is very strong. In this work we investigate theoretically the IC and EB mechanisms and design novel laser-assisted schemes aimed at (i) a more accurate determination of the isomer energy Em and (ii) efficient excitation of the isomer. On the one hand, we show how IC occurring from excited electronic states of Th ions can be used to determine the isomeric transition energy. We also propose a new approach to measure the isomer energy with laser spectroscopy accuracy via laser-induced EB in 229Th3+ ions. On the other hand, we put forward possible isomer excitation schemes based on the EB process in highly charged Th ions or on laser-assisted nuclear excitation by electron capture of the 29.19 keV nuclear state lying directly above the isomer. Our results show that EB in highly charged ions which allow optical driving with high-power lasers should lead to efficient excitation. Such a setup using ion traps might become relevant for the future development of the nuclear clock. Within the framework of this thesis, the following articles were published in refereed journals: • Internal conversion from excited electronic states of 229Th ions Pavlo V. Bilous, Georgy A. Kazakov, Iain D. Moore, Thorsten Schumm, and Adri- ana Pálffy. Phys. Rev. A 95, 032503 – Published 13 March 2017 • Laser-induced electronic bridge for characterization of the 229mTh → 229gTh nuclear transition with a tunable optical laser Pavlo V. Bilous, Ekkehard Peik, and Adriana Pálffy. New J. Phys. 20, 013016 – Published 10 January 2018 • Electric quadrupole channel of the 7.8 eV 229Th transition Pavlo V. Bilous, Nikolay Minkov, and Adriana Pálffy. Phys. Rev. C 97, 044320 – Published 25 April 2018 Articles in preparation: • Electronic bridge excitation of the 7.8 eV nuclear isomeric state in highly charged 229Th ions Pavlo V. Bilous, Hendrik Bekker, José R. Crespo López-Urrutia, and Adriana Pálffy. • Theory of laser-assisted nuclear excitation by electron capture Pavlo V. Bilous and Adriana Pálffy. to Daria Bilous, my love and my source of inspiration Contents Introduction3 1 Internal conversion (IC)7 1.1 IC theory....................................8 1.2 Dipole and quadrupole IC channels in 229Th................. 15 1.3 IC in a neutral 229Th atom.......................... 17 1.4 IC from excited electronic states of 229Th ions................ 23 2 Electronic bridge (EB) 31 2.1 EB theory.................................... 32 2.2 Dipole and quadrupole EB channels in 229Th................ 37 2.3 Laser-induced EB (LIEB)........................... 38 2.4 EB excitation in HCI.............................. 43 3 Laser-assisted nuclear excitation by electron capture (LANEEC) 51 3.1 LANEEC Theory................................ 52 3.2 LANEEC excitation of the nuclear state at 29.18 keV in 229Th...... 67 3.3 Direct two-photon excitation of the nuclear state at 29.18 keV in 229Th.. 68 4 Numerical methods 73 4.1 Calculations with GRASP2K and RATIP packages............. 73 4.2 Calculations for Th3+ ion in a cavity..................... 75 4.2.1 Solution of the DHF equations.................... 75 4.2.2 Expansion in the B-spline basis set................. 76 4.2.3 RPA calculations............................ 83 Summary and Outlook 87 Appendices 91 A Hamiltonian for the nuclear multipole moments’ coupling to an atomic elec- tron 93 B Graphical method in quantum theory of angular momentum 97 C Matrix elements of the electronic coupling operator 103 Bibliography 109 1 2 Introduction Frequency standards play an important role in modern science and technology. For in- stance, satellite-based systems of radionavigation such as the Global Positioning System (GPS) are able to provide a position determination with a few-meter accuracy due to a set of frequency standards operating onboard of satellites. In such systems the user to be located receives signals emitted synchronously by a number of satellites, typically at least four. The position is then determined by the time difference of the reception events. Frequency standards are employed in this scheme for achievement of a high level of synchronization in the signal emission. In the field of metrology, frequency standards are used first of all for precise measurements of time. The notions "clock" and "frequency standard" are often used as synonyms due to the fact that the time measurement proce- dure typically reduces to counting of the number of periods of some oscillating system. A second is defined as the duration of exactly 9 192 631 770 oscillations of a Cs atomic frequency standard, where the electronic transition between the two hyperfine levels of the ground state of the 133Cs atom is used as the oscillator [1]. The most accurate frequency standards today are atomic standards based on elec- tronic microwave or optical transitions. The first practical idea of implementation of a microwave clock was proposed by Isidor Rabi [2] based on the magnetic resonance method developed by Rabi and his collaborators in the end of 1930s [3]. The first pre- cise atomic frequency standard based on the microwave electronic transition in the 133Cs atom excited and interrogated by radiofrequency signals was built by Louis Essen and Jack Parry at the National Physical Laboratory in the UK in 1955 [4]. This opened an era of microwave atomic clocks which rapidly outperformed their quartz-based predeces- sor. During the 20th century the accuracy of the microwave frequency standards, i.e., the ratio of the time shift ∆T to the measured time interval T , reached 10−15 [5]. The next generation of atomic frequency standards is based on electronic transitions in the optical range. The operating frequency in such clocks is a few orders higher than in the Cs clock with the microwave transition. This brings the advantage that the same error in the number of counted oscillations is "collected" during a much shorter time allowing more efficient and simple correction of the systematic frequency shift of the standard. Started in the 1980s [6], the development of such optical frequency standards was boosted around the turn of the 21st century when an optical frequency comb was developed [7,8]. The frequency comb technique allows linking the optical frequency to a radiofrequency which can be then effectively measured by means of ordinary electronics. A proper choice of the electronic transition for the optical frequency standard is of crucial importance. It should have a narrow spectral width and be stable enough with respect to external perturbing fields. The excitation of the atomic system to the involved electronic states should be at the same time straightforward with laser sources available today. Such transitions have been found in a number of ions and neutral atoms. The most advanced frequency standards based on an electronic transition in a trapped single ion achieved the relative accuracy of 10−17 for ions 199Hg+ and 27Al+ [9, 10]. Clocks based on a few thousand neutral atoms placed in an optical lattice were a further breakthrough in optical frequency standards. The accuracy reached a few years ago in such clocks with atoms 171Yb [11] and 87Sr [12] was of the order 10−18. This year (2018) a record precision 3 of 2.5 · 10−19 obtained with the 87Sr-based standard has been reported in Ref. [13]. In order to fully exploit the technical opportunities rendered possible by the high accuracy of the 87Sr clock, it is important to make a comparison with another state-of-art frequency standard. An opportunity to develop such a standard is offered by the isotope 229 Th, which possesses a nuclear excited state at the energy Em = 7.8 ± 0.5 eV [14, 15]. In nuclear physics terms this state is a so-called isomer — denoted 229mTh — due to its long lifetime. The mere radiative lifetime of the state is estimated at 104 s. 229m Since the energy Em = 7.8 ± 0.5 of the isomer Th lies in the optical (VUV) range, 229Th is considered as a candidate for the first nuclear optical frequency standard at an unprecedented accuracy of 10−19 for a single Th ion [16–18].
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