New Atomic Masses Related to Fundamental Physics Measured with SMILETRAP

New atomic masses related to fundamental physics measured with SMILETRAP

Szilárd Nagy

AKADEMISK AVHANDLING

som med tillstånd av Stockholms Universitet framlägges till offentlig granskning för avläggandet av ﬁlosoﬁe doktorsexamen måndagen den 19 december 2005, kl. 13.00 i rum FA32, Alba Nova Universitetscentrum, Roslagstullsbacken 21, Stockholm.

Stockholm University Department of Physics 2005 Doctoral Dissertation New atomic masses related to fundamental physics measured with SMILETRAP Szilárd Nagy ISBN 91-7155-166-2 pp.1-54

AlbaNova University Center Department of Physics S–106 91 Stockholm SWEDEN

Printed by: Universitetsservice US AB, Stockholm 2005 www.us-ab.com Abstract

This thesis describes some recent improvements of the SMILETRAP Penning trap mass spectrometer together with a number of interesting high precision mass measurements, performed using the improved apparatus, which are relevant to several of today’s fundamental physics problems. The mass of the hydrogen-like 24,26Mg ions as well as the masses of the hydrogen- and lithium- like 40Ca ions have been determined, these values being indispensable when evaluating g-factor measurements of the bound electron. In both cases the uncertainty in the mass was improved by at least one order of magnitude compared to available literature values. The mass of 7Li has been measured and a new mass value has been obtained with an unprecedented relative uncertainty of 6.3×10−10. A large deviation of 1.1 µu (160ppb) compared to the literature value has been observed. In order to ﬁnd the reason for this large deviation, and to look for possible systematic errors, we have measured the mass of 4He and 6Li and have concluded that the 6Li(n,γ)7Li reaction Q-value, used in the literature when calculating the 7Li mass, is wrong by about 1 keV. The mass difference between 3He and 3H(∆m(3H −3 He)) is the Q-value of the tritium β-decay. An accurate knowledge of the tritium Q-value is of importance in the search for a ﬁnite rest mass of the electron neutrino. By adding an accurate measurement of the mass of 3He1+ to previous mass measurements of 3H1+ and 3He2+, we have improved our previous Q-value by a factor of 2. The current Q-value determined by SMILETRAP mass measurements is the most accurate and more importantly, it is based on the correct atomic mass values.

List of Papers

This thesis is based on the following papers

I High-precision mass measurements of hydrogen-like 24Mg11+ and 26Mg11+ ions in a Penning Trap, I. Bergström, M. Björkhage, K. Blaum, H. Bluhme, T. Fritioff, Sz. Nagy and R. Schuch, Eur. Phys. J. D 22, 41-45 (2003).

II Precision mass measurements of 40Ca17+ and 40Ca19+ ions in a Penning Trap, Sz. Nagy, T. Fritioff, A. Solders, R. Schuch, M. Björkhage and I. Bergström, Eur. Phys. J. D (submitted).

III A new mass value for 7Li, Sz. Nagy, T. Fritioff, M. Suhonen, R. Schuch, K. Blaum, M. Björkhage and I. Bergström, Phys. Rev. Lett. (submitted).

IV On the Q-value of the Tritium β-decay, Sz. Nagy, T. Fritioff, M. Björkhage, I. Bergström and R. Schuch, Europhys. Lett. (submitted).

v Publications not included in my thesis

I Contributions to fundamental physics and constants using Penning traps I. Bergström, Sz. Nagy, R. Schuch, K. Blaum, and T. Fritioff Proceedings of the fourth Tegernsee international conference on particle physics beyond the Standard Model, BEYOND 2003, Castle Ringberg, Tegernsee, Germany, 9-14 June 2003 Springer Verlag Berlin, Heidelberg, New York, ISBN 3-540-21843-2 Proceedings in Physics, Vol. 92, 397-418 (2004).

II Unambiguous identiﬁcation of three β-decaying isomers in 70Cu, J. Van Roosbroeck. C. Guénaut, G. Audi, D. Beck, K. Blaum, G. Bollen, J. Cederkall, P. Delahaye, H. De Witte, D. Fedorov, V.N. Fedoseyev, S. Franchoo, H. Fynbo, M. Gorska, F. Herfurth, K. Heyde, M. Huyse, A. Kellerbauer, H.-J. Kluge, U. Köster, K. Kruglov, D. Lunney, A. De Maesschalck, V.I. Mishin, W.F. Müller, Sz. Nagy, S. Schwarz, L. Schweikhard, N.A. Smirnova, K. Van de Vel, P. Van Duppen, A. Van Dyck, W.B. Walters, L. Weissmann, and C. Yazidjian Phys. Rev. Lett. 92, 112501 1-4 (2004).

III Accelerating multiple scattering of the emitted electrons in collisions of ions with atoms and molecules T. Ricsóka, Gy. Víkor, Sz. Nagy, K. Tokési,˝ Z. Berényi, B. Paripás, N. Stolterfoht, B. Sulik Nucl. Instrum. and Meth. B, 235, 397–402 (2005).

vi Contents

1 Introduction ...... 1 2 Comments on the author’s contribution ...... 5 3 Penning traps and their application for mass spectrometry ...... 7 3.1 Motion of ions in a Penning trap ...... 8 3.2 Cyclotron frequency measurement ...... 10 4 Description of the experimental facility SMILETRAP ...... 15 4.1 Overview ...... 15 4.2 The electron beam ion source CRYSIS ...... 15 4.3 The pre-trap ...... 18 4.4 The precision trap ...... 19 4.5 The control and data acquisition system ...... 20 5 Mass measurement procedure at SMILETRAP ...... 23 5.1 Calculation of the atomic mass and associated uncertainties ... 29 6 Summary of the results and brief discussion ...... 33 6.1 Accurate mass measurements of hydrogen-like 24Mg and 26Mg ions and hydrogen-like and lithium-like 40Ca ions ...... 33 6.2 New mass value for 7Li ...... 36 6.3 The mass of 3H and 3He and the Q-value of the tritium β-decay 38 6.4 Proton mass evaluation ...... 41 7 Concluding remarks ...... 43 8 Future outlook ...... 45 Acknowledgements ...... 47 Bibliography ...... 49 Attached Papers ...... 54

vii

1. Introduction

Mass measurements on an atomic scale were first performed by J. J. Thomson at the Cavendish Laboratory of the University of Cambridge in the beginning of the 20th century using the parabola spectrograph. A number of different magnetic mass spectrometers combined with electrostatic devices were developed by Aston [1], Dempster [2], Bainbridge and Jordan [3], Mattauch and Herzog [4], Nier and Johnson [5], Duckworth [6] etc. with rapidly in- creasing precision from 10−4 to 10−7. A breakthrough came at the end of the 50’s when L. G. Smith designed his rf mass synchrometer, which was the first mass spectrometer that applied frequency measurements [7]. The accuracy level achieved by Smith [8] could only be considerably improved by introducing an entirely new technology. This occurred when Penning traps entered the field of precision spectroscopy at the end of the 80’s thanks to the pioneering work of H. G. Dehmelt [9]. The first mass measurement using a Penning trap was made by Gräff and coworkers [10]. The most accurate mass measurements today are accomplished by comparing cyclotron frequencies in a Penning trap using single ions at the WS-PTMS in Seattle [11], single ions and molecules at MIT 1 [12, 13], highly charged ions at SMILETRAP [14], or radioactive ions at ISOLTRAP [15]. The SMILETRAP facility is unique due to the usage of highly charged ions. In fact, it is the only experiment in the world where ions with charges q>8+ have been used for mass measurement purpose. How accurate is "good enough"? -This always depends on the physics being investigated. High precision mass measurements have wide-ranging applications in modern physics including the determination of fundamental constants [16, 17], metrology [18, 19], test of the fundamental charge, parity and time reversal (CPT) symmetry [20], the verification of nuclear models and test of the Standard Model [21]. Accurate mass comparisons in the 10−11 range can be used to test Einstein’s mass energy relationship E = mc2 [22]. Beside mass measurements, Penning traps are used in various other experiments e.g. the production of antihydrogen at ATHENA [23] and ATRAP [24] (CERN) and g-factor measurements of the bound electron in Mainz [25, 26]. For the last four years as a PhD candidate I have been working with a Pen-

1In May 2003 the MIT lab was closed and the apparatus was moved to Florida State University, Tallahassee where it has been set up in a new ICR laboratory.

1 ning trap mass spectrometer, a powerful experimental apparatus to measure with high precision how much a single atom of a certain element weighs. Rather than weighing the atom in a gravitational field, the "weighing" is done in an electromagnetic field where the mass comparison is turned into a frequency comparison using a Penning trap. A Penning trap is a combination of a homogeneous magnetic field and an electrostatic quadrupole potential which makes it possible to hold and study one or a few charged particle confined in a small volume of space. To measure the mass of the atom of interest, one must first remove one or more electrons from the neutral atom so that it has a net charge. This is achieved using a device called ion source. If we place this charged atom (an ion) in the magnetic field inside our Penning trap, the ion moves in circles. This motion is what we call cyclotron motion. The number of revolutions per second is proportional to the magnetic field strength and inversely proportional to the ion’s mass. We can place the ion of interest in the magnetic field and count how many revolutions per second it executes. Then we can place a different ion in the same magnetic field and measure how many revolutions per second that executes. The ratio of the two numbers gives the ratio of the masses. If one of the ions has a well known mass the other ion mass can be obtained from this ratio. To get the mass of the neutral atom we have to add the mass of the missing electrons and their binding energies to the measured ion mass. This is a rather simplified description, however, it gives the basic idea of our mass measurement using a Penning trap. In this way it is possible to determine the mass of a single atom with a relative uncertainty better than 10−9 . This resolution would correspond to measuring a distance of 1000 km to better than ±1 mm. I am sure you would like to know what this is good for, why mankind in this universe is interested in knowing the mass of atoms at such high precision. One of the recent fundamental application of such accurate atomic mass values can be to determine how much a particle called a neutrino weighs. There are three known types of neutrinos called the electron-neutrino, muon- neutrino and tau-neutrino. Until recently, according to the Standard Model (SM) of particle physics, neutrinos were assumed to be massless. However, recent investigations of neutrinos from the sun and of neutrinos created in the atmosphere by cosmic rays, have given strong evidence for massive neutrinos indicated by neutrino oscillations [27, 28]. Neutrinos with non-zero mass have an impact not only on our understanding of how particles interact with each other but also at the larger scale of how the universe evolves in time, because of the gravitational force of these nonzero mass neutrinos. In the follow- 3 3 − 3 ing simple reaction H→ He + e + νe the tritium ( H) atom spontaneously − emits a single electron (e ) and an electron-neutrino (νe). By knowing the mass difference between the tritium and helium atoms and the maximum energy carried away by the electron, the mass of the neutrino can be obtained. I

2 am going to present in my thesis the mass measurements resulting in the most accurate Q-value based on the correct atomic masses. An ambitious experiment in Germany (KATRIN)[29] is going to measure the electron energy and determine the mass of the neutrino, where our mass could be used for calibration purposes. However, it seems that the accuracy achieved by us (1.2 eV) allows only to search for gross systematic errors. For an absolute calibration even higher precision is necessary. A more accurate value is expected in the near future from the group of Prof. Van Dyck in Seattle. The mass results for magnesium (24Mg, 26Mg) and calcium (40Ca) presented in this thesis are a contribution to ongoing tests of a theory called Quantum Electrodynamics (QED). QED is a quantum field theory of the electromagnetic force. Taking the example of the force between two electrons, the classical theory of electromagnetism would describe it as arising from the electric field produced by each electron. The force can be calculated from Coulomb’s law. The QED theory treats the force between the electrons as a force arising from the exchange of virtual photons. This theory is remarkable due to the accuracy in predicting physical quantities like the g-factor of the free electron. Electrons have magnetic moment that is characterized by the g- factor. The sea of transient virtual particles assumed by the QED theory, has an effect on the magnetic moment of the electron. The QED theory allowed to calculate the g-factor of the free electron. The calculated value turned to be in perfect agreement up to 10 digits with the experimentally measured g-factor value. This result illustrates the power of the QED. The situation is more complicated when dealing with one electron bound to a nucleus of charge Z because of the very strong Coulomb field between the electron and the nucleus. Experimental determinations of the bound electron g-factor in the case of the hydrogen-like ions C5+ and O7+ has recently been performed in an experiment in Mainz (Germany). In the evaluation of this experiment the mass of the hydrogen-like ion is a key input parameter. There- fore we measured the mass of a few suitable candidates 24Mg11+, 26Mg11+, 40Ca17+ and 40Ca19+ and improved the uncertainty in these masses by about one order of magnitude in all cases. The most intriguing discovery in the last twenty years related to atomic nuclei is the large nuclear matter distribution of the short lived nuclide 11Li [30] which is attributed to a “halo” of neutrons around a compact core of nucle- ons [31, 32]. A halo state can be formed when bound states close to the con- tinuum exist. Since 1985 a large amount of high-accuracy experiments have been performed on 11Li in order to observe the halo character also in other nuclear ground state properties, e.g. in the nuclear charge-radii [33] and in the quadrupole moment [34] by laser spectroscopy and the neutron-separation energy via direct mass measurements [35]. Common to all of these experiments is the need of a proper mass reference in order to calibrate the measurement

3 device and to look for systematic uncertainties. To provide such a reference, we measured the mass of 7Li and we corrected the mass and improved the precision by a factor of 18 compared to the previously accepted value. We have uncovered a very large error (1.1µu) in the literature mass value conﬁrmed by measurements of the masses of 6Li and 4He. We found that this deviation is due to a wrong Q-value used when calculating the mass. The improved mass value of 7Li presented in this work will be used as mass reference for on-line calibration purposes in high-accuracy Penning trap mass spectrometry on the short-lived radionuclides 9,11Li as well as 6,8He. The laser spectroscopic studies of the isotope shifts and nuclear-charge radii of the stable and short-lived Li isotopes will also beneﬁt from the new, accurate mass of 7Li.

4 2. Comments on the author’s contribution

I joined the SMILETRAP group as a graduate student in September 2001. After step by step learning the features of the SMILETRAP apparatus, I took it over with all the accompanying tasks and responsibilities which included upgrade of the vacuum system, building a new ion detector, replacing several important parts of the electronics, the weekly routines of filling cryogenics in the superconductive magnet and finally planning and performing new experiments. The previous members of the group left me with a professional Labview control and data acquisition program which proved to be reliable and has been easy to use and maintain. During my time the PDP-11 based beam transport system has been replaced by a commercial system named ConSys. The migration was done by the spe- cialists at MSL, however, the testing and debugging of the new system involving about 50 parameters for the SMILETRAP beam transport was done by me. After an un-welcomed quench of the superconductive magnet in 2003 it was my responsibility to cool down and energize the magnet and tune the magnetic and electric fields to optimum condition and get the experiment running again. I have been responsible for the mass measurements presented in this thesis, including planning of the experiment, preparing and transporting the beam, the data acquisition, data analysis and paper writing. My work at SMILETRAP involved on one hand up keeping and on the other hand further developing the experimental setup. During my time at SMILE- TRAP, I replaced or improved several important parts of the the trap electronics and vacuum system which are summarized in the following: • Improved vacuum system. A number of new vacuum pumps, turbo pumps and dry scroll pumps have been added. Altogether 15 m of SAES St 707 NEG (Non-Evaporable Getter) strip has been added to three different lo- cations of the experimental setup which provides additional pumping. Fur- thermore, three VAT all metal gate valves, bakable up to 300°C were added to make the vacuum system more practical. • New high voltage amplifier and pulser for the pre-trap. In collaboration with A. Paal from the MSL electronic workshop a low noise high voltage

5 amplifier and pulser for the pre-trap has been designed and built, which I installed at SMILETRAP. It can generate a high voltage pulse of max. 4 kV with a noise ∼10 mVrms by amplifying a user programmable waveform. • New pre-trap electronics. A simple card with 3 protected summing amplifiers, to sum the DC voltages and the capture, boil-off and ejection signals for the pre-trap has been built. It has proper protections which save the op- erational amplifiers from breakdown due to high-voltage problems, thus, a frustrating problem has been eliminated. • New RF frequency generator. A new commercial arbitrary wave form generator Agilent 33250A (80 MHz) programmable via GPIB has been installed which is used to generate the RF excitation in the precision trap. In the same way as the previously used HP3335A, this is also synchronized to an external 10 MHz reference signal with a stability of 1×10−12 / day delivered by an Epsilon Clock locked to GPS satellite. • Building of a new detector with manipulator. To replace the most important detector which is used for the actual mass measurement I assembled a new MCP detector and added a detector manipulator which did not exist before. The detector consists of two micro-channel plates (TOPAG MCP-25- 10E) with an effective diameter of 18 mm and channel diameter of 10 µm (OAR=63%) which are mounted in a Chevron configuration. • Building of a pre-amplifier. A low noise preamplifier was built with the help of the MSL electronic workshop, which amplifies the signal from the anode plate of the detector. It has a 20 dB gain and a bandwidth of 100 MHz. An extra SR430 Multichannel Scaler (Stanford Research Systems) used for the time-of-flight measurement has been purchased and installed at the same time. • Rebuild of pre-trap high voltage insulation. The pre-trap insert has been removed and the electric insulation was improved considerably by adding new insulator parts and it had been re-cabled using kapton insulated cables instead of naked copper and as a result, the pre-trap can take now 5 kV without problems. • Remote control of reference ion creation. By installing a GPIB programmable Delta ES 03-10 power supply we can now fine tune the 1+ current needed for the creation of the H2 mass reference ion by electron bombardment. The above mentioned improvements had the objective to decrease further the uncertainties in mass determinations as well as to reduce the preparation time.

6 3. Penning traps and their application for mass spectrometry

The operation of a trap which aims to confine charged particles by electromagnetic forces is limited by the fact that there cannot be a minimum of the electrostatic potential in free space (Earnshaw’s theorem). The best that one can do is to create a saddle-point in the potential, which is a minimum in one direction and a maximum in another [36]. The lowest order potential of this form with axial symmetry is the quadrupole potential given by : Φ = A(2z2 − x2 − y2) (3.1) where A is a constant. This potential can be generated by electrodes having the shape of the equipotential surfaces of equation 3.1, which are hyperboloids of revolution about the z-axis, (Fig. 3.1). The potential given by eq. 3.1 with the constant A positive will trap a positive ion in the z direction. But as there is no restoring force in the xy-plane this is not sufficient for a stable three- dimensional trap. However, if a magnetic field B is applied parallel to the z- axis, the trajectory of a particle attracted toward the ring will become a closed orbit with three characteristic motions. Such an arrangement of a homogeneous magnetic field and an electrostatic quadrupole potential is called a Penning trap in the honor of F. M. von Penning (1894-1953). He invented a novel vacuummeter using the superposition of the electric and magnetic field [37] similar to the trap. J. R. Pierce discuss in his book from 1949 [38] the usage of hyperbolic electrodes and axial magnetic field to confine electrons, here he also presents the so called magnetron trap. Based on this idea H. G. Dehmelt developed a simple description of the axial, magnetron, and cyclotron motions of an electron in such a magnetron trap and built his first trap version in 1959. In 1989 H. G. Dehmelt and W. Paul were awarded the Nobel prize in physics [9] for the development of the ion trap technique together with N. F. Ramsey. A comprehensive description of Penning traps can be found in the book of Ghosh [39] and in a recent book of Major et al. [40]. Most aspects of ion motion in a Penning trap has been described by Brown and Gabrielse in ref. [41]. Here only a brief introduction will be given, necessary for understanding the mass measurement procedure at SMILETRAP. The Penning trap can be used as a mass spectrometer due to the fact that the

7 Figure 3.1: Two realizations of a Penning trap. In both cases the electrodes define a quadrupole potential. frequency of the ion motion is mass dependent. From the motional frequencies of the trapped ion it is possible to determine the free cyclotron frequency which is related to the ion mass via the following equation: 1 qB ν = , (3.2) c 2π m where m is the rest mass of a particle with charge q and B is the magnetic field strength. This frequency can be determined either by measuring the image currents created in the trap electrodes [12, 11] or by a time-of-flight technique [10]. For the mass measurements presented in this work the the time-of-flight technique was used which is described in more detail in section 3.2.

3.1 Motion of ions in a Penning trap Let us consider a particle with mass m and charge q, in a Penning trap. The homogeneous magnetic ﬁeld inside the ideal Penning trap is parallel with the z-axis, B= (0,0,B0) and the electric ﬁeld E= −∇Φ is a result of the potential U Φ(x,y,z) = 0 (2z2 − x2 − y2), (3.3) 4d2

8 where d is the characteristic trap dimension deﬁned as s 1 r2 d = z2 + 0 . (3.4) 2 0 2

The equipotential surfaces are hyperboloids generated by the electrodes of the trap. The two end-cups have the geometrical form described by the equation 2 2 2 2 2 2 2 2 2z −x −y = 2z0 and the ring electrode 2z −x −y = −r0. U0 is a DC voltage applied between them, (Fig. 3.1). The force acting on the particle inside the trap is the Lorentz-force F = q(v × B) − q∇Φ. (3.5) where v is the velocity vector of the particle. The z component of the force is purely electrostatic. The classical equations of motion can be written as: d2x dy 1 − ω − ω2x = 0, (3.6) dt2 0 dt 2 z

d2y dx 1 + ω − ω2y = 0, (3.7) dt2 0 dt 2 z

d2z + ω2 = 0, (3.8) dt2 z where r qB 2qU ω = 0 , ω = 0 . (3.9) 0 m z md2

The motion in the z-direction is a simple harmonic oscillation with an axial frequency ωz, decoupled from the transverse motion in the x- and y-directions. To describe the motion in the (x,y)-plane the complex variable u = x + iy is introduced. The radial equation of motion (3.6) and (3.7) then reduce to d2u du 1 + iω − ω2u = 0. (3.10) dt2 0 dt 2 z

The general solution of this equation is found by setting u = exp(−iωt) which leads to 1 ω2 − ω ω + ω2 = 0 (3.11) 0 2 z

The solutions ω+ and ω− of (3.11) are 1 q ω = ω + ω2 − 2ω2 , (3.12) + 2 c c z

9 and 1 q ω = ω − ω2 − 2ω2 . (3.13) − 2 c c z here ω+ is the modiﬁed cyclotron frequency and ω− is the magnetron frequency. The solutions of (3.11) must be real, which leads to the condition 2 2 ωc − 2ωz > 0. (3.14)

Using (3.9) and (3.14) the conditions for stable confinement of charged particle in a Penning trap can be deduced in terms of the applied fields |q| 4|U | B2 > 0 qU > 0. (3.15) m 0 d2 0 It determines the minimum magnetic field required to balance the radial component of the applied electric field. Several useful relations exist between the eigen-frequencies of the trapped particle:

ω− + ω+ = ωc , (3.16)

2 2ω+ω− = ωz . (3.17)

Furthermore it can be shown that 2 2 2 2 ω+ + ω− + ωz = ωc , (3.18) which is known as the invariance theorem [42].

3.2 Cyclotron frequency measurement In the ideal case the three different motions are uncoupled and can be described by a quantized harmonic oscillator, as shown in ref. [41, 43]. An external electric radio frequency field can be used to enhance the energy of each individual motion by resonant excitation at the eigen-frequency. Typ- ically dipolar and quadrupolar excitations are used. For mass determination purpose, a coupling of the magnetron motion to the reduced cyclotron motion is achieved by a quadrupolar driving field at frequency ωRF = ωc = ω− + ω+ which is applied simultaneously on the two pair of opposite segments of the ring electrode as illustrated in Fig. 3.2. The electric quadrupole field used for excitation can have the form:  x    Eq = Uq cos(ωqt − φq) ·  −y . (3.19) 0

10 Figure 3.2: Transverse cut of an eight-fold segmented ring electrode of a Penning trap showing the connections for an azimuthal quadrupole excitation used in the case of the mass measurement. The voltage applied to one pair of opposite segments is phase- shifted by 180o with respect to the voltage applied to the other pair. In this way an electric quadrupole ﬁeld is generated in the radial plane.

A continued excitation at the resonance frequency, ω− + ω+, will result in a periodic oscillation between the two motions [44]. The two radial motions will be converting one into the other with the conversion frequency: URF ωc ωconv = 2 . (3.20) 2Br0 ω+ − ω−

It should be noticed, that, to the first order approximation, ωconv is independent of the ion mass since ωc ≈ ω+ − ω−. A complete conversion of one motion into the other is achieved after an excitation duration T = π/ωconv. The time-of-flight (TOF) technique was proposed by Bloch [45] and first applied to precision mass measurements by Gräff et al. [10]. It is a destructive technique in the sense that one loses the captured ions in each detection cycle. The cyclotron frequency is obtained by scanning the frequency of the excitation signal and measuring the time-of-flight of the ions flying from the trap to a detector located outside the strong magnetic field as illustrated in Fig. 3.3. The excitation enhances the radial kinetic energy due to the conversion of the radial motions, since ωc ω−. During the flight towards the detector, the magnetic moment due to the ions radial motion interacts with the gradient of the magnetic field. The ions, thus, will experience an axial force: ~F = −µ(∇ ·~B). (3.21)

The radial energy will be converted into axial as the ion moves in a decreasing B-ﬁeld after it is ejected out of the trap, see Fig. 3.3.

11 Figure 3.3: The B-ﬁeld variation along the time-of-ﬂight tube (thick line) and the voltage on the two drift tubes (thin line) are plotted as a function of the distance to the detector.

Figure 3.4: Theoretical lineshape of a cyclotron resonance and the energy gain [44].

12 The time of ﬂight of the ions can be calculated [44] from:

1 Z z1 m 2 Tr f = dz, (3.22) z0 2[E0 − q ·V(z) − µ(ωRF ) · B(z)] where E0 is the initial energy of the ion, V(z) and B(z) are the electric and magnetic fields along the ion path from the trap at z0 to the detector at z1. In the resonance case ( ωRF = ωc) the magnetic moment µ(ωRF ) has it’s maximum value. By scanning the excitation frequency and recording the ions flight time to the detector, the resonance can be observed as a well pronounced minimum in the flight time spectrum, see Fig. 3.4. It can be shown [46] that the theoretical Full Width at Half-Maximum (FWHM) is: 0.8 4νc ≈ . (3.23) TRF

To obtain the center frequency the measured resonance curve is ﬁtted using a least squares method to a Gaussian lineshape. In this way the center frequency can be obtained to ∼1% of the FWHM.

4. Description of the experimental facility SMILETRAP

4.1 Overview The SMILETRAP facility [14] includes a hyperboloid Penning trap mass spectrometer with a superconductive magnet (Oxford Instruments, NMR Division, Type 200/130, Cryostat Family Type 3.) having 4.7 T central field. A sketch of the trap setup is presented in Fig. 4.1. The SMILETRAP (Stockholm-Mainz-Ion-LEvitation-TRAP) started as a collaboration between the Manne Siegbahn Laboratory at Stockholm Uni- versity and the Physics Department of the Johannes Gutenberg University in Mainz, Germany. The project was initiated by Prof. em. Ingmar Bergström. The main objective was to perform mass measurements relevant for fundamental physics exploiting the precision gain by the usage of highly charged ions [47]. The 1989 Nobel Prize in Physics [9] was related to ion trap technique, therefore it had a great importance for the financing of the SMILETRAP project. The construction started at Mainz in the summer of 1990 and in De- cember 1991 the first cyclotron resonance spectra was recorded. The apparatus was moved to Stockholm and connected to the electron beam ion source (CRYSIS)[48, 49] at MSL in 1993.

4.2 The electron beam ion source CRYSIS The trap setup is connected to an electron beam ion source EBIS [50, 51] named CRYSIS . It consists of an electron gun to produce an electron beam which is compressed and confined by the ∼ 2 T magnetic field of a superconductive solenoid in order to achieve high electron beam densities. The cryostat is cooled to liquid helium temperature (-269 °C) and is configured to provide the extremely high vacuum inside the source, which is necessary to prevent recombination of highly charged ions. There are two ways of running CRYSIS. For the production of noble gas ions and ions from molecular gases with a low melting point, a gas inlet is used and the gas is injected more or less directly into the electron beam. The other way is to use the external ion injector. The external ion injector is the composition of a commercial Cold or HOt Reflex Discharge Ion Source (CHORDIS, man-

15 Figure 4.1: The SMILETRAP Penning Trap mass spectrometer setup. The drawing shows a portion of the C6 beamline coming from the electron beam ion source CRYSIS and the 90◦ bending magnet, the pre-trap in a 0.25 T electromagnet and the precision trap in a 4.7 T superconductive magnet. The detector with a linear manipulator on the top of the apparatus is used for the time of ﬂight measurement.

16 Table 4.1: Typical CRYSIS parameters used in the case of mass measurements presented in this work.

Parameter Value

Electron beam energy 14.5 keV Electron beam current 70–145 mA Magnetic field 1.5 T Ion energy 3.4 keV×q Charge per pulse 0.5–2 nC Ion pulse length 100 µs Confinement time 20 ms–2 s ufactured by DANFYSIK) on a 20 kV platform and an isotope separator with a high mass resolving power. Here, a wide variety of ions can be produced through gas-injection, sputtering, or evaporation from an oven. Typically this method is used for the production of metallic ions, where the gas inlet can not be used. In this case the ion beam is injected through the electron collector into CRYSIS. A typical operation of the CRYSIS ion source using external ions, involves three major steps. In the first step the isotope separated singly charged ions are injected. The potential distribution is such that the ions overcome a potential barrier and get captured in a potential well created axially by a system of tube electrodes around the beam and radially by the electron space charge. When the trap is full, the potential distribution is changed again and the ions are trapped. The charge state of the ions increases gradually by successive strong electron impact ionization. During the time the ions stay confined, He gas/ions can be used for cooling. After a selected confinement time the potential distribution is changed and the ions are extracted through the electron collector. The well defined ionization time in this type of ion source leads to a narrow charge state distribution. The attainable charge state is limited by the electron beam energy which must be greater than the ionization energy for the last electron. CRYSIS is designed for 50 keV electron energy which is sufficient for the production of bare nuclei of all elements up to Xenon. CRYSIS is built on a high-voltage platform, which means that the beam energy can be varied independent of the electron energy between about 1qkeV and 45qkeV, where q is the charge state of the ion. When delivering beam to the SMILETRAP experiment, a typically 100 µs long ion pulse is extracted at the end of each production cycle, containing about 108 ions. The extraction

17 is done at 3.4 kV. The energy spread of the beam is rather small, typically 5- 10 eV, which is estimated from the ion capture in the pre-trap since there is no equipment near to CRYSIS to measure this. A lot has been learned during the past years on how to set the parameters of CRYSIS to match the requirements of the mass measurement experiment [52].

4.3 The pre-trap The main role of the pre-trap is to retard and capture the ion pulse from CR- YSIS. The so called pre-trap is an open-ended cylindrical Penning trap, which consists of seven cylindrical electrodes with an inner diameter of 10 mm and an entrance and an exit hole of 4 mm machined out of OFHC copper. The voltages on the four correction electrodes are tuned to create a near ideal quadrupole field. The trap is placed inside an electromagnet which has a field of 0.25 T. To stop the beam coming from CRYSIS the entire pre-trap is floated on the same potential as the extraction potential of CRYSIS. The present pre-trap has certain limitations, there is no possibility to me- chanically align the E and B field axis. The ions can be stored only for short time only (not due to charge exchange) and there is no ion cooling which would allow for colder ions in the precision trap.

18 4.4 The precision trap The most important part of the mass spectrometer is a hyperboloid Penning trap named precision trap with r0 = 13 mm and z0 = 11.18 mm, (Fig. 3.1) placed inside a 4.7 T homogeneous B-field generated by a superconductive coil. It is similar to the trap used in the ISOLTRAP experiment (ISOLDE/CERN, Switzerland) [53]. To minimize the magnetic and electric field inhomogeneities the trap is built in gold plated OFHC copper of low susceptibility. To compensate for the electric field imperfections introduced by the entrance and exit holes on the end- cup electrodes of the trap, and for the finite size of the ring and end-cups, correction electrodes are used (Fig. 4.2). The voltages of the correction tubes and rings are tuned to achieve a near perfect trapping potential. The central ring electrode is split into eight equal segments, which allows the use of dipole, quadrupole and octupole (2νc) excitation schemes. Four segments are used to create an azimuthal quadrupole radio-frequency field to couple the magnetron and cyclotron motions when performing mass measurements as described in section 3.2.

Figure 4.2: A detailed sketch of the hyperboloidal Penning trap used at SMILETRAP. The hole on the upper end-cup has a diameter d=5 mm, the lower end-cup entrance hole is reduced to 1 mm. The trap is machined out of oxygen free high conductivity (OFHC) copper, and it is coated ﬁrst with silver than with gold. The insulator material is glass ceramics (MACOR) and aluminium oxide. The ring electrode is split in eight equal segments.

19 4.5 The control and data acquisition system At SMILETRAP one has to remotely control more than 50 parameters among them the voltages for the trap electrodes, the inter-trap optics and a number of timing delays, waveforms and frequencies, which are implemented in the SMILETRAP control system. An additional ∼50 voltage parameters are needed for the beam transportation from the exit of CRYSIS to the pre-trap entrance which are accessed through a different control system available at the Manne Siegbahn Laboratory, named ConSys. A simplified scheme of the SMILETRAP control system is given in Fig. 4.3. The control system of SMILETRAP is fully implemented in Labview, involving three personal computers (PC). PC-1 is running the Graphical User Interface and all mass measurements are set up from here. About 10 instruments are addressed via GPIB interface. A NI PCI-6704 analog voltage supply board with an average noise less than 50 µV and an absolute accuracy of ±1 mV is used in order to obtain the stable voltages needed for the precision trap. An analog voltage supply board (AT- AO-10) is used to remotely control the power supplies for the electrostatic deflectors in between the two traps. The MIO-16-E4 board has 16 inputs which are used to read in various analog signals. The PC-3 is dedicated to control the pre-trap and therefore operates in a high-voltage cage. A high-speed analog output board (NI PCI-6713) is used to generate the voltages for the pre-trap electrodes. By using optical TCP/IP connection, the computer in the high-voltage cage and the voltage channel outputs can be remotely programmed. It is possible to send additional digi- tal (TTL) signals and triggers (capture, boil-off, ejection) via separate optical fibers. To continuously monitor and stabilize external ambient parameters like temperature and pressure the signals from a number of sensors placed around SMILETRAP are processed by using a NI PCI-4351 precision board installed in PC-2.

20 Figure 4.3: A simpliﬁed illustration of SMILETRAP control and data acquisition system.

5. Mass measurement procedure at SMILETRAP

The flow of a measurement is illustrated in Fig. 5.1. The experiment begins at CRYSIS where the highly charged ions are produced as described in Sec- tion 4.2. The extracted ion beam is transported to the trap experiment over a distance of about 15 m using conventional ion beam optics including a number of electrostatic deflectors, quadrupole triplets and Einzel-lenses. Along the beam line, remotely controlled strip-detectors and Faraday-cups are used to measure the beam profile and intensity. The beam energy is low, typically 3.4 qkeV therefore it is quite an effort to transport this beam over the rather long distance to the trap setup. Before entering the pre-trap, a charge state selection is done by scanning the current of a 90◦ double focusing magnet which has a bending radius of 500 mm. An example of a charge state spectra can be seen in Fig. 5.2(b). The same magnet also serves to deflect the beam vertically to the experiment. Out of the 100 µs long CRYSIS pulse, a small fraction (1-2 µs) is captured in the pre-trap due to the short length of the pre-trap compared to the length of the pulse. Typically a few thousand ions are captured here. The capturing is done by applying a short negative voltage pulse (20 µs) on the lower end-cup of the pre-trap. When optimizing the capture in the pre-trap, the high voltage level of the pre-trap has to be scanned in order to match the beam transport energy. Such a figure when the high voltage of the pre-trap has been scanned and the number of ions was recorded can be seen in Fig. 5.2(c). After catching the ions, the potential of the pre-trap is lowered to 0 V in a few milliseconds. This is achieved by using a programmable low noise high voltage ramp generator. As a result, the energy of the ions is changed from +q×3.4 keV to 0 keV. The ejection is achieved by applying a short negative voltage pulse (40 µs) on the upper end-cup of the pre-trap or by applying a positive voltage ramp on the ring electrode. The ion transfer in between the two traps is done through a series of drift tubes biased to -1 kV including a number of variable apertures, electrostatic deflectors and lenses. A channeltron detector and a MCP-detector is used to optimize the injection into the strong magnetic field, where the precision trap is located. These detectors can also be used to measure time of flight of the ions ejected from the pre-trap, see Fig.5.2(d).

23 Figure 5.1: Schematic illustration of the mass measurement procedure at SMILETRAP Penning trap mass spectrometer.

24 Figure 5.2: In this figure (a) is a typical mass spectrum, (b) is a charge spectrum, (c) is a pre-trap high voltage scan, (d) is a time-of-flight spectrum (e) is another time-of- flight spectrum with excited ions and (f) is a cyclotron resonance, see text.

The ions are retarded to ground potential before entering the precision trap. An aperture with a hole of 1 mm in diameter is placed at the trap entrance to prevent ions with too large magnetron radii from entering the precision trap. The capturing in the precision trap is achieved by applying a short negative voltage pulse on the lower end-cup and lower correction tube. Before the ions are reﬂected out from the trap the voltage on these electrodes is restored back to the nominal value (approx. 5 V) within <1 µs. The capturing in the pre-

25 cision trap is synchronized to the ejection from the pre-trap. A time of ﬂight discrimination is usually applied, which means, that only ions arriving within a short time window are accepted. Out of the few thousand ions ejected from the pre-trap, typically about one hundred ions are captured in the precision trap. For a detailed ion balance see table 5.1. To get rid of the high axial energy ions a so called boil-off technique is used. This involves lowering the trapping potential from 5 V to a few mV by ramping up the potential of the ring electrode. After the axially hottest ions have left the trap, the potential is restored. The remaining cooler ions are subject to an azimuthal quadrupolar radio-frequency excitation.

Table 5.1: Ion balance showing the average number of ions at different stages of the experiment in a typical measurement. The width of the ion pulse injected into CRYSIS can be from 20 ms to 2 s, depending on the requirements. The width of the extracted pulse is 100 µs.

Injected into CRYSIS ∼50 nC Extracted pulse, (all charge states) ∼500 pC Charge separated pulse 10–20 pC Captured in pre-trap ∼2000 ions Captured in precision trap ∼100 ions After boil-off 1–5 ions

During the excitation the magnetron and reduced cyclotron motion couple which leads to a gain in the radial energy later converted into axial in the fringe field of the magnet as described in section 3.2. After excitation the ions are gently ejected from the trap into the drift section and the time of flight to a detector 500 mm away is measured. To record the flight time, a Multi Channel Scaler & Averager (SR430, Stanford Research Systems) is used in combination with a Micro Channel Plate ion detector. A typical time-of-flight cyclotron resonance spectrum is shown in Fig. 5.2(f). The coldest ion for the cyclotron frequency measurement is sorted out in a selection procedure involving four major stages. The first, is achieved already in CRYSIS, due to the fact that the trapping voltage in the ion source is kept between 30 V to max. 70 V accompanied often with He cooling. The second stage is the careful injection into the B-field of both traps. The ions are injected as parallel to the B-field as possible to minimize the gain in radial energy of the ions [53]. Furthermore, a selection is made by tuning the potential difference between the two traps to about 2 V. This measure limits the number of ions which have gained radial energy before excitation to enter the precision trap. In the third stage the selection is achieved by the d=1 mm aperture in front

26 of the precision trap. The last stage is the boil-off ion evaporation technique applied in the precision trap. In order to obtain the mass using eq. 3.2, in addition to the cyclotron frequency (νc), the B-field has to be measured as well. Since the B-field can not be directly measured with high enough accuracy, the cyclotron frequency of a reference ion is measured and the mass is obtained from the ratio of these 1+ frequencies, eliminating the dependence on B. Due to technical reasons H2 were used as reference ion since they could be easily produced by electron impact ionization of the residual gas in the pre-trap. The timing diagram of one step in the measurement cycle is given in Fig. 5.3. In order to eliminate a possible time dependent B-field fluctuations, the cyclotron frequency of the main ion and the reference ion is alternately measured within rather short time. The time for one scan including 21 equidistant frequency steps is about 30-40 seconds. The switching to the reference ion is done automatically and takes 1-2 seconds then the reference ion is scanned in the same way. The total time of one measurement cycle including 2 scans of the main ion (each with 21 steps and 1 s exc. time) switching and 2 scans of the reference ion is less than 3 minutes. A typical measurement with SMILETRAP involves a few thousand scans corresponding to 20 000 or more ions of each species, requiring a measurement time from one day up to one week or more. Each ion is placed randomly in a small volume of a few mm3 limited radially by the entrance hole with d=1 mm and axially by the boil-off procedure to <2.5 mm. Most of the imperfections in E and B averages out in this procedure.

27 Figure 5.3: A time scheme of a measurement cycle at SMILETRAP mass spectrometer.

28 5.1 Calculation of the atomic mass and associated uncertainties A measurement results in two interlaced series of frequency scans, one for the ion of interest and one for the reference ion, as described in the previous chapter. The data is bunched and a resonance curve for each ion species is generated from 10-20 scans. The mass resolution in a Penning trap depends √directly on the charge state, the magnetic field, the excitation time and the N of the number of detected ions. In the case of an ion with q/A = 0.5 the resolving power of SMILETRAP is 3.6×107. The recorded time-of-flight data is fitted with a Gaussian curve using a least squares method and the center frequency is obtained to ∼ 1% of the linewidth. For the mass measurements presented in this work an excitation time of 1 s has been used which results in a line width ≤1 Hz, and thus it is possible to reach a statistical uncertainty of a few parts in 1010. In Fig. 5.4 the Gaussian fitting is compared to a more correct fitting procedure using the calculated theoretical line shape to fit the resonance pattern. It can be concluded that the two procedures result in center frequencies in agreement within the error bars however the fitting by the theoretical lineshape gives a slightly higher accuracy associated to the center frequency value [54]. The sidebands of the resonances which are related to the conversion of magnetron into cyclotron motion during excitation are suppressed in a typical SMILETRAP resonance. The main reasons are: a non full conversion of magnetron into cyclotron motion during excitation and the short term insta- bility of the magnetic field [52]. The center frequencies νc, and the corresponding uncertainty δνc are de- main re f 0 rived from the fit. The obtained νc ±δν and νc ±δν are divided to form a frequency ratio ri ±σi. The individual ratios ri are weighted together to form an average R which can be expressed as: 1 ∑i ri 2 σi R = 1 . (5.1) ∑i 2 σi

The weighted average (R) is given together with two errors, σint and σext . 1 2 ∑i 2 (ri − R) 2 1 2 σi σint = 1 σext = 1 . (5.2) ∑i 2 (n − 1)∑i 2 σi σi

The internal error σint is the error of the weighted average of the individual frequency ratio measurement. The external error σext is the distribution of the individual measurement ri around the weighted average R. If the distribution of ri is purely statistical, and if the uncertainty in the ﬁt of the resonance curve

7 5

7 0

6 5 s µ

6 0 t h g

i 5 5 l f

f 5 0 o

e 4 5 m

i G a u s s i a n f i t

T T h e o r e t i c a l f i t 4 0

3 5 8 3 1 0 3 8 3 1 0 4 8 3 1 0 5 8 3 1 0 6 8 3 1 0 7 8 3 1 0 8 C y c l o t r o n F r e q u n e n c y / 3 6 0 X X X X X / H z

Figure 5.4: Gaussian versus theoretical lineshape, see text. has been calculated correctly, both errors should be equal [55]. In case they differ that is an indication for possible systematic errors. The mass of the ion is calculated using the the weighted average ratio of the measured frequencies: ν q m R = ion = ion re f . (5.3) νre f qre f mion

To obtain the atomic mass M one has to add to the ion mass given by eq. 5.3 the mass me of the missing q electrons and their total binding energy (EB):

1 qmain M = mre f + qmainme − EB. (5.4) R qre f

Where EB is the total ionization energy which can be calculated [56] or is already available with high accuracy [57, 58, 59]. The value of the electron −4 mass is me= 5.485 799 0945(24)×10 u with a relative standard uncertainty of 4.4×10−10 [60] and therefore this contribution to the ﬁnal uncertainty in the mass can be neglected.

30 The remaining systematic effects that can be present when doing the mass measurement with SMILETRAP are summarized in the following [14, 52, 61]: • Reference mass 1+ 1+ By using H2 as mass reference (m(H2 ) = 2.01510149703(27) u ) an uncertainty of 0.18 ppb is introduced [14]. To use 12Cq+ the only uncertainty introduced would be the one resulting from the binding energy which is <10−11. • Electron binding energies There is an error introduced when calculating the atomic mass using eq. 5.4 due to the electron binding energies EB. This is usually ≤0.1 ppb depending on the mass and charge state. An error of 100 eV in binding energy would introduce an error of 10−9 in case of a neutral atom with mass 100. For light masses Z < 20 the ionization energies of all charge states are known to high accuracy, 10–20 eV, specially for closed atomic shells. • Relativistic mass increase The measured ion mass is not the rest mass since the ion moves with an enhanced velocity after excitation, thus subject to measurable relativistic effect when the precision reaches 1 ppb or better. The error related to relativistic effects is estimated by measuring the energy before and after excitation by applying a deceleration potential as described in [14]. The size of the error is usually <0.5 ppb. • Ion number dependence The cyclotron frequency decreases with more ions inside the trap. By ob- taining cyclotron frequencies from 1,2,3 etc. simultaneously trapped ions using the off-line data analyzer program, it is possible to investigate shifts caused by having more than 1 ion in the trap. We usually base the cyclotron frequencies on events with 1 or maximum 2 simultaneously trapped ions. Not having 100% detection efficiency, what we regard as single ion event may arise from 2 or more simultaneously detected ions. There may be also a small difference in the detection efficiency of the main ion and the reference ion, leading to uncertainties in the order of ∼0.1 ppb. • q/A asymmetry If the main ions charge to mass ratio (q/A) differs from the reference ions q/A, the cyclotron frequency shift due to the misalignment between the E and B-field axis is different therefore it does not cancel when calculating the cyclotron frequency ratio. It can not be excluded, that a frequency ratio shift up to 1 ppb may be present in cases where ion species are not q/A doublets. Therefore, as much as possible, we try to perform mass measurements using q/A doublets. • Contaminations Impurities having the same q/A as the main ion may arise from CRYSIS or created via charge exchange in the precision trap. The amount of impurities

31 of the kind q-1 and q-2 etc. can be checked and even cleaned by applying dipolar excitation. The size of the error is typically about 0.1 ppb. • Magnetic field drift Instabilities in the magnetic field can cause both a frequency shift and an increase in the resonance line width. The natural decay of the current in our superconducting coil is <0.1 ppb/h. Therefore, this effect can be neglected, considering the fact that the measuring cycle is about 3 min. Other sources for the change of the magnetic field exist, such as the pressure changes in the liquid He cryostat due to the daily air pressure fluctuations. This effect is known and after stabilization of the trap temperature and the helium pressure, the frequency shifts due to changes in the magnetic field is minimized to <0.1 ppb [52].

32 6. Summary of the results and brief discussion

6.1 Accurate mass measurements of hydrogen-like 24Mg and 26Mg ions and hydrogen-like and lithium-like 40Ca ions The mass measurements of the 24Mg11+, 26Mg11+, 40Ca17+ and 40Ca19+ ions were motivated by the g-factor experiment [25, 26] aiming to test the bound electron QED [62]. In order to determine the g-factor of the bound electron in hydrogen-like and lithium-like ions the mass of the ion is needed at an accuracy of typically 1 ppb or better. In Fig. 6.1 the atomic mass of the 24Mg and 26Mg obtained by us is compared to the literature values published prior to our experiment. The masses were measured at a total relative uncertainty of 0.56 ppb and 1.3 ppb for 24Mg and 26Mg, respectively. The literature value had an uncertainty of ∼8 ppb in both cases [63]. Thus we were able to considerably improve the mass precision of both isotopes fulﬁlling the requirements of the g-factor experiment. Moreover, the masses presented here can allow for the observation of an isotope effect in the g-factor measurements, see [Paper I.].

Figure 6.1: Our mass results for the 24Mg and 26Mg isotopes compared to the to the literature values available prior to our measurements. The uncertainty in the case of the 26Mg isotope is larger due to the difference in statistics.

11 093,4 2 5 M g ( n , γ) 2 5 M g ( p , γ) - 2 6 M g ( p , n ) 11 093,2 T h i s w o r k

11 093,0

V 11 092,8 e

/ 11 092,6

S 11 092,4

11 092,2

11 092,0

Figure 6.2: 26Mg neutron binding energies derived in different ways. Values taken 24 26 from [64]. The last point (H) is derived from our mass for Mg and Mg.

Our new mass values for 24Mg and 26Mg made also an impact in AME2003. By using these mass values and several 24Mg(n,γ) reactions a new mass for the 25Mg was calculated. Our new mass values could be used to calculate the 26 Mg neutron binding energy (Sn) which is compared to the values available in the literature obtained in different ways, see Fig. 6.2. Furthermore our new 24Mg and 26Mg mass values were used to conclude that there is an uncertainty in the mass of 26Al. The 26Mg(p,n)26Al reaction is of special interest for problems connected with the intensity of allowed Fermi β-transitions [64]. In Fig. 6.3 the mass of 40Ca obtained from measurements using lithium-like and hydrogen-like 40Ca ions is compared to the literature value [64] published prior to our experiment. The literature value of 40Ca has been calculated using the mass of 39K and the 39K(p,γ)40Ca reaction Q-value [65] and has a relative uncertainty of 5.5 ppb [64]. For the g-factor experiment this is not satisfactory, higher accuracy has been requested [62]. It can be seen from the ﬁgure, that our new value represents an improvement in the mass precision by a factor of 10, see [Paper II.]. With the new mass value of 40Ca we have also improved the 40Ca - 40Ar double β decay Q-value by one order of magnitude since the 40Ar mass is known with a relative uncertainty of 0.07 ppb [64]. The obtained Q-value is 193.5 keV with an uncertainty of 17 eV only.

4 0 1 200 C a A M E 2 0 0 3 T h i s w o r k 1 7 +

u T h i s w o r k 1 9 +

n 1 100 T h i s w o r k a v e r a g e /

X 1 000 X

9 900 5

2 6 9

800 9 3 700 A M E 2 0 0 3 T h i s w o r k

Figure 6.3: The atomic mass of 40Ca compared to the literature value AME2003 [64].

35 6.2 New mass value for 7Li The literature mass value for 7Li is calculated using the 6Li(n,γ)7Li reaction Q-value and the mass of 6Li and has a relative uncertainty of 11 ppb [64]. The mass of 6Li was measured in a Penning trap by the group of G. H. Dunn with a relative uncertainty of 2.7 ppb [66]. The Q-value used in the literature to calculate the mass has an uncertainty of 80 eV [64]. A different Q-value with an uncertainty of 90 eV is available in the literature [67] which would result in a more than 100 ppb different mass. In order to use 7Li as reference mass for calibration purposes in high-accuracy Penning trap mass spectrometry [68] of the short-lived radionuclides 9,11Li and for laser spectroscopic studies of the isotope shifts and nuclear-charge radii of both the stable 6,7Li and short-lived 8,9,11Li isotopes, a better knowledge of the mass was demanded. 7 3+ 1+ By comparing the cyclotron frequency of Li to H2 we measured the mass of 7Li atom to an unprecedented uncertainty of 6.3×10−10, see [Pa- per III.]. A large deviation from the literature value [64] has been observed, see Fig. 6.4. The deviation is 1.1µu or 160 ppb which corresponds to about 14σ. To ﬁnd the reason of the unexpectedly large deviation and to check for systematics we measured the masses of 4He and 6Li. The 4He measurement did not result in any large systematical error. Our measured mass for 6Li is in agreement with the literature value within 2.4σ. From the masses of 6Li and 7Li measured by us the Q-value of the 6Li(n,γ)7Li reaction has been derived and it is compared to other values from the literature in Fig. 6.5. Our Q-value is Q=7251.10(4) keV. This deviate by more than 1 keV from the value used to calculate the 7Li mass in the literature, 7249.97(8) keV [64]. However, it agrees perfectly with the value from ref. [67] which reads 7251.02(9) keV. It seems that the Q-value in the literature is wrong which can explain the deviation observed in the 7Li mass. Furthermore, note that the masses of 7Be and 8Li in AME2003 uses the 7Li mass as input data [64], therefore thanks to the new mass value these masses are also improved.

2 0 0 7 1 5 0 L i

b 1 0 0 p p

5 0 y t

n 0 i

a t

r - 5 0 e c

n - 1 0 0 U

- 1 5 0

- 2 0 0 A M E 8 5 A M E 9 3 A M E 2 0 0 3 T h i s w o r k

Figure 6.4: The mass uncertainty of 7Li compared to the values found in the literature.

7 251,4 7 251,2 7 251,0 7 250,8 7 250,6 V e

k 7 250,4

e 7 250,2 u l

a 7 250,0 v - 7 249,8 Q 7 249,6 7 249,4 7 249,2 1 9 6 8 1 9 7 2 1 9 8 5 2 0 0 3 T h i s w o r k

Figure 6.5: The Q-value of the 6Li(n,γ)7Li reaction in chronological order. The values are 1962 from [69], 1972 from [70], 1985 from [67], 2003 ﬁrst point is from [71] and the second from [64]. The last point is the value derived from our mass measurements using 6Li and 7Li.

37 6.3 The mass of 3H and 3He and the Q-value of the tritium β-decay By adding a new measurement of the 3He1+ to the existing 3H1+ and 3He2+ data, we obtained a new value for ∆m(3H −3 He) which is the Q-value of the 3 3 − H → He + e + νe reaction. The corresponding atomic mass of 3H and 3He are presented in Fig. 6.6 and Fig. 6.7, respectively. The mass values from the 1995 Atomic Mass Evaluation [63] deviate from our measurements by ∼5 ppb in both cases. The reason of this deviation is understood, it is due to a day-to-night effect which was unknown at the time of the measurement by the Seattle group in 1993 [72]. The agreement of our 3He mass with the latest value [73] from the Seattle group gives additional confidence in our result, see Fig. 6.7. Using the above mentioned reaction, the KATRIN experiment (Karlsruhe, Germany) intends to measure the rest mass of the electron-neutrino by measuring the energy spectrum of the β electrons with sensitivity of 0.2 eV. A neutrino mass of 0.35 eV would be discovered with 5 σ significance [29]. A non-zero neutrino mass would show up as a difference between the Q-value and the endpoint of the β-spectrum. To do an absolute calibration of the re- tarding energy, the fitted β endpoint can be compared to the ∆m(3H −3 He). Any significant difference will indicate unaccounted systematic errors. The Q-value derived from our masses is presented in Fig. 6.8. It has an uncertainty of 1.2 eV which is enough only to find gross errors at the neutrino experiment. Note, that at present this is the most accurate Q-value available, which is derived from the correct atomic mass values, see [Paper IV.]. In order to be comparable to the expected sensitivity of the KATRIN experiment, further precision improvements are necessary and can be expected soon.

3 016 049 282 3 3 016 049 280 H

3 016 049 278 u n

3 016 049 276 /

s 3 016 049 274 s a 3 016 049 272 m

c 3 016 049 270 i

m 3 016 049 268 o t

A 3 016 049 266

3 016 049 264

A M E - 1 9 9 5 S M I L E - 2 0 0 1

3 Figure 6.6: The mass of H. The second point (H) is our measured value which was used to obtain the Q-value.

3 016 029 326 3 3 016 029 324 H e

3 016 029 322 u n

/ 3 016 029 320

s 3 016 029 318 a

m 3 016 029 316

c i 3 016 029 314 m o

t 3 016 029 312 A 3 016 029 310

A M E - 1 9 9 5 S M I L E - 2 0 0 1 T h i s w o r k V a n D y c k p r i v .

3 Figure 6.7: The mass of He. The triangles (H) are our results from two different runs using 2+ and 1+ ions, the last point () is the preliminary value from the Seattle group [73].

18 615 β- s p e c t r o m e t e r s 18 610 F T I C R V a n D y c k ' 9 3 18 605 T h i s w o r k

V 18 600 e

18 595

e u l 18 590 a v - 18 585 Q

18 580

18 575

Figure 6.8: The Q − value of the 3H- 3He reaction measured by using different tech- 3 1+ 3 1+ niques. The last point (H) has been obtained using H and He with SMILETRAP.

40 6.4 Proton mass evaluation From the mass measurements presented in this work, in two cases there were accurate mass values already available from other experiments. By using the preliminary 3He mass from the Seattle group [73] and the 4He 1+ mass from AME2003 [64], I calculated the mass of H2 from the measured 3 1+ 1+ 4 2+ + frequency ratios of He /H2 and He /H2 in both cases. From the 1+ obtained H2 mass the proton mass could be derived in both cases, which is presented in Fig. 6.9, showing agreement with the literature value [64] of the proton mass. Furthermore, this can be interpreted as a consistency check as well, if we had any gross unaccounted systematics, it had shown up in this comparison.

1 007 276 468,0 3 1 + m f r o m H e p f r o m 4 H e 2 + 1 007 276 467,5

u 1 007 276 467,0 n

p m

1 007 276 466,5

1 007 276 466,0 A M E 2 0 0 3 T h i s w o r k

Figure 6.9: The ﬁrst point is the accepted value of the proton from the AME2003 [64] with error bars representing the total uncertainty. The second and third points (H, O) represent the proton mass derived from the cyclotron frequency ratio of the 3He1+ / 1+ 4 2+ 1+ H2 and He /H2 respectively. In the case of the latter two the error bars represent only the statistical uncertainty.

7. Concluding remarks

In this work the improvements of the SMILETRAP Penning Trap mass spectrometer and results obtained using the improved apparatus are presented. The mass results obtained for 24Mg11+, 26Mg11+, 40Ca17+ and 40Ca19+ ions are key input parameters for the g-factor experiments aiming to test the bound electron QED. The new mass values for the 24Mg and 26Mg are valuable inputs to solve problems in the atomic mass table. By measuring the mass of 7Li3+ we obtained a new mass value for 7Li and observed a large deviation compared to the literature mass value. We corrected the mass and improved the uncertainty in the mass by a factor of 18. The new mass can now be used as reference ion in future mass and nuclear charge-radii measurements on stable 6,7Li and short lived 8,9,11Li radio nuclides . In this work a newly determined tritium Q-value is also presented which is the most accurate value at present which allows to look for larger systematics at the future neutrino experiment KATRIN. Further improvement of this value is still necessary.

Table 7.1: The mass values presented in this thesis with the total relative uncertainty. In the last column the motivation for the mass measurement is indicated.

Isotope Mass/u Total Unc./ppb Motivation

3 He 3.016 029 321(26) 0.8 νe rest mass 4He 4.002 603 253 3(26) 0.7 systematics check 7Li 7.016 003 425 6 (45) 0.6 reference ion 6Li 6.015 122 890(40) 7 related to 7Li 24Mg 23.985 041 690(14) 0.6 g-factor, QED test 26Mg 25.982 592 986(34) 1.3 g-factor, QED test 40Ca 39.962 590 858(19) 0.45 g-factor, QED test

8. Future outlook

To push the limits further and improve the final precision achievable at SMILE- TRAP and open the gates to yet unexplored experiments using very-heavy highly charged ions up to hydrogen-like uranium (238U91+), several measures have to be taken. Attaching SMILETRAP to REBIT. Therefore the apparatus has to be dismantled and moved from its present lo- cation at MSL to its new place at AlbaNova. The planning of the movement has alredy been started. Installation of a new pre-trap. The installation of a new pre-trap with ion cooling implemented will remove several limitations which exist in the present setup. A new pre-trap has already been built and installed in a 1.1 T conventional electromagnet and testing is going on [74]. Implementation of the Ramsey-technique. Tests have shown that the implementation of the Ramsey excitation technique [75] will be of benefit for future SMILETRAP measurements which will allow for longer excitation times, thus higher resolution in the mass measurement is achievable. The proper fitting routine needed to analyze the data obtained by the Ramsey excitation has already been developed [76] and it is being implemented at SMILETRAP [54].

Acknowledgements

My time in Stockholm has been a wonderful experience. The staff at MSL and AlbaNova have been beyond friendly and were always ready to offer a smile to the smiling student at SMILETRAP. You are all acknowledged!

I would like to say a special big THANK YOU to the following people: Tomas Fritioff - for introducing me to the secrets of the SMILETRAP apparatus and for being by my side and helping me out whenever I got in trouble. I really enjoyed working with you. Ingmar Bergström - for the confidence he has shown in me, for the endless encouragement and strong support. Micke Björkhage - for all the ions delivered to SMILETRAP, for teaching me many useful swedish expressions, and for his support on both dark and bright days. Andras Paal - for the electronics he built for me, and for the many fruitful discussions about detectors and beam current measurement. György Vikor - for his advises and for being always ready to offer an extra pair of hands when there was a need. Sven Leontein - for keeping me up to date with the latest features and bugs of the strip detector system for the ion beam transport. Birgit Brandner - for her help in the lab and for the delicious Lebkuchens. Jan Weimer - for always finding for me the right screw or the necessary tool. I improved my swedish language skills a lot by having many lunch and "fika" with some cool guys from MSL: Mikael Blom, Gunnar Källersjö, Per Werner and Patrik Löfgren who were always interested in my work and ready to help. I thank Klaus Blaum from the Johannes Gutenberg University, (Mainz, Germany) for the fruitful collaboration. I would like to express my gratitude to my undergraduate supervisor Prof. L. Nagy from the Babe¸s-BolyaiUniversity, (Cluj-Napoca, Romania) for the confidence and support. I am sure that the trap will find an even better new home at AlbaNova and in the hands of Markus Suhonen and Andreas Solders it will be soon up and running again, delivering many new results. Lycka till! I consider myself lucky to have joined SMILETRAP - a world class experiment. I would like to thank my supervisor Prof. Reinhold Schuch for this opportunity.

Szilárd Nagy 19 December 2005, Stockholm

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