New atomic massesrelated to fundamental physics

measured withSMILETRAP

Szilárd Nagy

AKADEMISK AVHANDLING

som med tillstånd av Stockholms Universitetframlägges till

offentlig granskning för avläggandet avfilosofie doktorsexamen

måndagen den 19 december 2005, kl. 13.00 i rum FA32,Alba Nova Universitetscentrum, Roslagstullsbacken 21, Stockholm.

Stockholm UniversityDepartment of Physics

2005

Doctoral DissertationNew atomic masses related to fundamental physics measured with SMILETRAPSzilárd NagyISBN 91-7155-166-2 pp.1-54

© Szilárd Nagy, 2005 Stockholm University

AlbaNova University CenterDepartment of PhysicsS–106 91 StockholmSWEDEN

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

Abstract

This thesis describes some recent improvements of the SMILETRAP Penningtrap mass spectrometer together with a number of interesting high precisionmass measurements, performed using the improved apparatus, which are rel-evant to several of today’s fundamental physics problems. The mass of thehydrogen-like 24,26Mg ions as well as the masses of the hydrogen- and lithium-like 40Ca ions have been determined, these values being indispensable whenevaluating g-factor measurements of the bound electron. In both cases theuncertainty in the mass was improved by at least one order of magnitude com-pared to available literature values.

The mass of 7Li has been measured and a new mass value has been obtainedwith an unprecedented relative uncertainty of 6.3×10−10. A large deviation of1.1 µu (160ppb) compared to the literature value has been observed. In orderto find the reason for this large deviation, and to look for possible systematicerrors, we have measured the mass of 4He and 6Li and have concluded thatthe 6Li(n,γ)7Li reaction Q-value, used in the literature when calculating the7Li mass, is wrong by about 1 keV.

The mass difference between 3He and 3H (∆m(3H−3 He)) is the Q-valueof the tritium β -decay. An accurate knowledge of the tritium Q-value is ofimportance in the search for a finite rest mass of the electron neutrino.

By adding an accurate measurement of the mass of 3He1+ to previous massmeasurements of 3H1+ and 3He2+, we have improved our previous Q-valueby a factor of 2. The current Q-value determined by SMILETRAP mass mea-surements is the most accurate and more importantly, it is based on the correctatomic mass values.

List of Papers

This thesis is based on the following papers

I High-precision mass measurements of hydrogen-like 24Mg11+ and26Mg11+ 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 aPenning Trap,Sz. Nagy, T. Fritioff, A. Solders, R. Schuch, M. Björkhage andI. 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).

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Publications not included in my thesis

I Contributions to fundamental physics and constants usingPenning trapsI. Bergström, Sz. Nagy, R. Schuch, K. Blaum, and T. FritioffProceedings of the fourth Tegernsee international conference onparticle physics beyond the Standard Model, BEYOND 2003,Castle Ringberg, Tegernsee, Germany, 9-14 June 2003Springer Verlag Berlin, Heidelberg, New York, ISBN3-540-21843-2 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. YazidjianPhys. Rev. Lett. 92, 112501 1-4 (2004).

III Accelerating multiple scattering of the emitted electrons incollisions of ions with atoms and moleculesT. Ricsóka, Gy. Víkor, Sz. Nagy, K. Tokési, Z. Berényi,B. Paripás, N. Stolterfoht, B. SulikNucl. Instrum. and Meth. B, 235, 397–402 (2005).

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Comments on the author’s contribution . . . . . . . . . . . . . . . . . . . . . 53 Penning traps and their application for mass spectrometry . . . . . . . 7

3.1 Motion of ions in a Penning trap . . . . . . . . . . . . . . . . . . . . . . . 83.2 Cyclotron frequency measurement . . . . . . . . . . . . . . . . . . . . . . 10

4 Description of the experimental facility SMILETRAP . . . . . . . . . . 154.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 The electron beam ion source CRYSIS . . . . . . . . . . . . . . . . . . 154.3 The pre-trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4 The precision trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.5 The control and data acquisition system . . . . . . . . . . . . . . . . . . 20

5 Mass measurement procedure at SMILETRAP . . . . . . . . . . . . . . . . 235.1 Calculation of the atomic mass and associated uncertainties . . . 29

6 Summary of the results and brief discussion . . . . . . . . . . . . . . . . . . 336.1 Accurate mass measurements of hydrogen-like 24Mg and 26Mg

ions and hydrogen-like and lithium-like 40Ca ions . . . . . . . . . . 336.2 New mass value for 7Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366.3 The mass of 3H and 3He and the Q-value of the tritium β -decay 386.4 Proton mass evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 Future outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Attached Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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1. Introduction

Mass measurements on an atomic scale were first performed by J. J. Thomsonat the Cavendish Laboratory of the University of Cambridge in the beginningof the 20th century using the parabola spectrograph. A number of differentmagnetic mass spectrometers combined with electrostatic devices were de-veloped by Aston [1], Dempster [2], Bainbridge and Jordan [3], Mattauchand 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 the50’s when L. G. Smith designed his rf mass synchrometer, which was the firstmass spectrometer that applied frequency measurements [7]. The accuracylevel achieved by Smith [8] could only be considerably improved by introduc-ing an entirely new technology. This occurred when Penning traps entered thefield of precision spectroscopy at the end of the 80’s thanks to the pioneeringwork of H. G. Dehmelt [9]. The first mass measurement using a Penning trapwas made by Gräff and coworkers [10].

The most accurate mass measurements today are accomplished by compar-ing cyclotron frequencies in a Penning trap using single ions at the WS-PTMSin Seattle [11], single ions and molecules at MIT 1 [12, 13], highly chargedions 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 beinginvestigated. High precision mass measurements have wide-ranging applica-tions in modern physics including the determination of fundamental constants[16, 17], metrology [18, 19], test of the fundamental charge, parity and timereversal (CPT) symmetry [20], the verification of nuclear models and test ofthe Standard Model [21]. Accurate mass comparisons in the 10−11 range canbe used to test Einstein’s mass energy relationship E = mc2 [22].

Beside mass measurements, Penning traps are used in various other experi-ments 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 measurewith high precision how much a single atom of a certain element weighs.

Rather than weighing the atom in a gravitational field, the "weighing" isdone in an electromagnetic field where the mass comparison is turned into afrequency comparison using a Penning trap.

A Penning trap is a combination of a homogeneous magnetic field and anelectrostatic quadrupole potential which makes it possible to hold and studyone or a few charged particle confined in a small volume of space. To measurethe mass of the atom of interest, one must first remove one or more electronsfrom the neutral atom so that it has a net charge. This is achieved using a de-vice called ion source. If we place this charged atom (an ion) in the magneticfield inside our Penning trap, the ion moves in circles. This motion is what wecall cyclotron motion. The number of revolutions per second is proportionalto the magnetic field strength and inversely proportional to the ion’s mass. Wecan place the ion of interest in the magnetic field and count how many revo-lutions per second it executes. Then we can place a different ion in the samemagnetic 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 ionshas 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 missingelectrons and their binding energies to the measured ion mass. This is a rathersimplified description, however, it gives the basic idea of our mass measure-ment using a Penning trap. In this way it is possible to determine the massof a single atom with a relative uncertainty better than 10−9 . This resolutionwould 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 inthis universe is interested in knowing the mass of atoms at such high preci-sion. One of the recent fundamental application of such accurate atomic massvalues 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 theatmosphere by cosmic rays, have given strong evidence for massive neutri-nos indicated by neutrino oscillations [27, 28]. Neutrinos with non-zero masshave an impact not only on our understanding of how particles interact witheach other but also at the larger scale of how the universe evolves in time, be-cause of the gravitational force of these nonzero mass neutrinos. In the follow-ing simple reaction 3H→ 3He + e− + νe the tritium (3H) atom spontaneouslyemits a single electron (e−) and an electron-neutrino (νe). By knowing themass difference between the tritium and helium atoms and the maximum en-ergy 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 mostaccurate Q-value based on the correct atomic masses. An ambitious experi-ment in Germany (KATRIN) [29] is going to measure the electron energy anddetermine the mass of the neutrino, where our mass could be used for cali-bration purposes. However, it seems that the accuracy achieved by us (1.2 eV)allows only to search for gross systematic errors. For an absolute calibrationeven higher precision is necessary. A more accurate value is expected in thenear future from the group of Prof. Van Dyck in Seattle.

The mass results for magnesium (24Mg, 26Mg) and calcium (40Ca) pre-sented in this thesis are a contribution to ongoing tests of a theory calledQuantum Electrodynamics (QED). QED is a quantum field theory of the elec-tromagnetic force. Taking the example of the force between two electrons,the classical theory of electromagnetism would describe it as arising from theelectric field produced by each electron. The force can be calculated fromCoulomb’s law. The QED theory treats the force between the electrons as aforce arising from the exchange of virtual photons. This theory is remarkabledue to the accuracy in predicting physical quantities like the g-factor of thefree electron. Electrons have magnetic moment that is characterized by the g-factor. The sea of transient virtual particles assumed by the QED theory, hasan effect on the magnetic moment of the electron. The QED theory allowed tocalculate the g-factor of the free electron. The calculated value turned to be inperfect agreement up to 10 digits with the experimentally measured g-factorvalue. This result illustrates the power of the QED.

The situation is more complicated when dealing with one electron bound toa nucleus of charge Z because of the very strong Coulomb field between theelectron and the nucleus. Experimental determinations of the bound electrong-factor in the case of the hydrogen-like ions C5+ and O7+ has recently beenperformed in an experiment in Mainz (Germany). In the evaluation of thisexperiment 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 aboutone order of magnitude in all cases.

The most intriguing discovery in the last twenty years related to atomic nu-clei 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 havebeen performed on 11Li in order to observe the halo character also in othernuclear ground state properties, e.g. in the nuclear charge-radii [33] and in thequadrupole moment [34] by laser spectroscopy and the neutron-separation en-ergy via direct mass measurements [35]. Common to all of these experimentsis 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 pre-cision by a factor of 18 compared to the previously accepted value. We haveuncovered a very large error (1.1µu) in the literature mass value confirmed bymeasurements of the masses of 6Li and 4He. We found that this deviation isdue to a wrong Q-value used when calculating the mass.

The improved mass value of 7Li presented in this work will be used asmass reference for on-line calibration purposes in high-accuracy Penning trapmass spectrometry on the short-lived radionuclides 9,11Li as well as 6,8He. Thelaser spectroscopic studies of the isotope shifts and nuclear-charge radii of thestable and short-lived Li isotopes will also benefit from the new, accurate massof 7Li.

4

2. Comments on the author’scontribution

I joined the SMILETRAP group as a graduate student in September 2001.After step by step learning the features of the SMILETRAP apparatus, I tookit over with all the accompanying tasks and responsibilities which includedupgrade of the vacuum system, building a new ion detector, replacing severalimportant parts of the electronics, the weekly routines of filling cryogenics inthe superconductive magnet and finally planning and performing new experi-ments.

The previous members of the group left me with a professional Labviewcontrol and data acquisition program which proved to be reliable and has beeneasy to use and maintain.

During my time the PDP-11 based beam transport system has been replacedby a commercial system named ConSys. The migration was done by the spe-cialists at MSL, however, the testing and debugging of the new system in-volving about 50 parameters for the SMILETRAP beam transport was done byme.

After an un-welcomed quench of the superconductive magnet in 2003 it wasmy responsibility to cool down and energize the magnet and tune the magneticand 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 otherhand further developing the experimental setup. During my time at SMILE-TRAP, I replaced or improved several important parts of the the trap electron-ics and vacuum system which are summarized in the following:

• Improved vacuum system. A number of new vacuum pumps, turbo pumpsand dry scroll pumps have been added. Altogether 15 m of SAES St 707NEG (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 addedto make the vacuum system more practical.

• New high voltage amplifier and pulser for the pre-trap. In collaborationwith 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 Iinstalled at SMILETRAP. It can generate a high voltage pulse of max. 4 kVwith a noise ∼10 mVrms by amplifying a user programmable waveform.

• New pre-trap electronics. A simple card with 3 protected summing ampli-fiers, to sum the DC voltages and the capture, boil-off and ejection signalsfor the pre-trap has been built. It has proper protections which save the op-erational amplifiers from breakdown due to high-voltage problems, thus, afrustrating problem has been eliminated.

• New RF frequency generator. A new commercial arbitrary wave form gen-erator Agilent 33250A (80 MHz) programmable via GPIB has been in-stalled which is used to generate the RF excitation in the precision trap. Inthe same way as the previously used HP3335A, this is also synchronizedto an external 10 MHz reference signal with a stability of 1×10−12 / daydelivered by an Epsilon Clock locked to GPS satellite.

• Building of a new detector with manipulator. To replace the most importantdetector which is used for the actual mass measurement I assembled a newMCP detector and added a detector manipulator which did not exist be-fore. 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 helpof the MSL electronic workshop, which amplifies the signal from the anodeplate of the detector. It has a 20 dB gain and a bandwidth of 100 MHz. Anextra SR430 Multichannel Scaler (Stanford Research Systems) used for thetime-of-flight measurement has been purchased and installed at the sametime.

• Rebuild of pre-trap high voltage insulation. The pre-trap insert has beenremoved and the electric insulation was improved considerably by addingnew insulator parts and it had been re-cabled using kapton insulated cablesinstead of naked copper and as a result, the pre-trap can take now 5 kVwithout problems.

• Remote control of reference ion creation. By installing a GPIBprogrammable Delta ES 03-10 power supply we can now fine tune thecurrent needed for the creation of the H1+

2 mass reference ion by electronbombardment.The above mentioned improvements had the objective to decrease further

the uncertainties in mass determinations as well as to reduce the preparationtime.

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3. Penning traps and their applicationfor mass spectrometry

The operation of a trap which aims to confine charged particles by electro-magnetic forces is limited by the fact that there cannot be a minimum of theelectrostatic potential in free space (Earnshaw’s theorem). The best that onecan do is to create a saddle-point in the potential, which is a minimum in onedirection and a maximum in another [36]. The lowest order potential of thisform 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 theshape of the equipotential surfaces of equation 3.1, which are hyperboloids ofrevolution about the z-axis, (Fig. 3.1). The potential given by eq. 3.1 withthe constant A positive will trap a positive ion in the z direction. But as thereis 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 closedorbit with three characteristic motions.

Such an arrangement of a homogeneous magnetic field and an electrostaticquadrupole 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 theelectric and magnetic field [37] similar to the trap. J. R. Pierce discuss in hisbook from 1949 [38] the usage of hyperbolic electrodes and axial magneticfield 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 andbuilt his first trap version in 1959. In 1989 H. G. Dehmelt and W. Paul wereawarded the Nobel prize in physics [9] for the development of the ion traptechnique together with N. F. Ramsey.

A comprehensive description of Penning traps can be found in the book ofGhosh [39] and in a recent book of Major et al. [40].

Most aspects of ion motion in a Penning trap has been described by Brownand Gabrielse in ref. [41]. Here only a brief introduction will be given, neces-sary for understanding the mass measurement procedure at SMILETRAP.

The Penning trap can be used as a mass spectrometer due to the fact that the

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Figure 3.1: Two realizations of a Penning trap. In both cases the electrodes define aquadrupole potential.

frequency of the ion motion is mass dependent. From the motional frequenciesof the trapped ion it is possible to determine the free cyclotron frequencywhich is related to the ion mass via the following equation:

νc =1

2π

qBm

, (3.2)

where m is the rest mass of a particle with charge q and B is the magnetic fieldstrength. This frequency can be determined either by measuring the imagecurrents 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-flighttechnique was used which is described in more detail in section 3.2.

3.1 Motion of ions in a Penning trapLet us consider a particle with mass m and charge q, in a Penning trap. Thehomogeneous magnetic field inside the ideal Penning trap is parallel with thez-axis, B= (0,0,B0) and the electric field E=−∇Φ is a result of the potential

Φ(x,y,z) =U0

4d2 (2z2− x2− y2), (3.3)

8

where d is the characteristic trap dimension defined as

d =

√12

(z2

0 +r2

02

). (3.4)

The equipotential surfaces are hyperboloids generated by the electrodes of thetrap. The two end-cups have the geometrical form described by the equation2z2−x2−y2 = 2z2

0 and the ring electrode 2z2−x2−y2 =−r20. U0 is a DC volt-

age applied between them, (Fig. 3.1). The force acting on the particle insidethe 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 ispurely electrostatic. The classical equations of motion can be written as:

d2xdt2 −ω0

dydt− 1

2ω

2z x = 0 , (3.6)

d2ydt2 +ω0

dxdt− 1

2ω

2z y = 0 , (3.7)

d2zdt2 +ω

2z = 0 , (3.8)

where

ω0 =qB0

m, ωz =

√2qU0

md2 . (3.9)

The motion in the z-direction is a simple harmonic oscillation with an axialfrequency 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 isintroduced. The radial equation of motion (3.6) and (3.7) then reduce to

d2udt2 + iω0

dudt− 1

2ω

2z u = 0 . (3.10)

The general solution of this equation is found by setting u = exp(−iωt) whichleads to

ω2−ω0ω +

12

ω2z = 0 (3.11)

The solutions ω+ and ω− of (3.11) are

ω+ =12

(ωc +

√ω2

c −2ω2z

), (3.12)

9

and

ω− =12

(ωc−

√ω2

c −2ω2z

). (3.13)

here ω+ is the modified cyclotron frequency and ω− is the magnetron fre-quency. The solutions of (3.11) must be real, which leads to the condition

ω2c −2ω

2z > 0 . (3.14)

Using (3.9) and (3.14) the conditions for stable confinement of charged parti-cle in a Penning trap can be deduced in terms of the applied fields

|q|m

B20 >

4|U0|d2 qU0 > 0 . (3.15)

It determines the minimum magnetic field required to balance the radial com-ponent of the applied electric field. Several useful relations exist between theeigen-frequencies of the trapped particle:

ω−+ω+ = ωc , (3.16)

2ω+ω− = ω2z . (3.17)

Furthermore it can be shown that

ω2+ +ω

2−+ω

2z = ω

2c , (3.18)

which is known as the invariance theorem [42].

3.2 Cyclotron frequency measurementIn the ideal case the three different motions are uncoupled and can be de-scribed by a quantized harmonic oscillator, as shown in ref. [41, 43].

An external electric radio frequency field can be used to enhance the energyof each individual motion by resonant excitation at the eigen-frequency. Typ-ically dipolar and quadrupolar excitations are used. For mass determinationpurpose, a coupling of the magnetron motion to the reduced cyclotron motionis achieved by a quadrupolar driving field at frequency ωRF = ωc = ω−+ω+which is applied simultaneously on the two pair of opposite segments of thering electrode as illustrated in Fig. 3.2.

The electric quadrupole field used for excitation can have the form:

Eq = Uq cos(ωqt−φq) ·

x

−y

0

. (3.19)

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Figure 3.2: Transverse cut of an eight-fold segmented ring electrode of a Penning trapshowing the connections for an azimuthal quadrupole excitation used in the case ofthe 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 anelectric quadrupole field is generated in the radial plane.

A continued excitation at the resonance frequency, ω− + ω+, will result ina periodic oscillation between the two motions [44]. The two radial motionswill be converting one into the other with the conversion frequency:

ωconv =URF

2Br20

(ωc

ω+−ω−

). (3.20)

It should be noticed, that, to the first order approximation, ωconv is independentof the ion mass since ωc ≈ ω+−ω−. A complete conversion of one motioninto the other is achieved after an excitation duration T = π/ωconv.

The time-of-flight (TOF) technique was proposed by Bloch [45] and firstapplied to precision mass measurements by Gräff et al. [10]. It is a destructivetechnique in the sense that one loses the captured ions in each detection cycle.

The cyclotron frequency is obtained by scanning the frequency of the exci-tation signal and measuring the time-of-flight of the ions flying from the trapto 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 theradial motions, since ωc � ω−. During the flight towards the detector, themagnetic moment due to the ions radial motion interacts with the gradient ofthe 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 decreasingB-field after it is ejected out of the trap, see Fig. 3.3.

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

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

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

Tr f =∫ z1

z0

{m

2[E0−q ·V (z)−µ(ωRF) ·B(z)]

} 12

dz , (3.22)

where E0 is the initial energy of the ion, V (z) and B(z) are the electric andmagnetic fields along the ion path from the trap at z0 to the detector at z1. Inthe resonance case ( ωRF = ωc) the magnetic moment µ(ωRF) has it’s maxi-mum value. By scanning the excitation frequency and recording the ions flighttime to the detector, the resonance can be observed as a well pronounced min-imum in the flight time spectrum, see Fig. 3.4. It can be shown [46] that thetheoretical Full Width at Half-Maximum (FWHM) is:

4νc ≈0.8TRF

. (3.23)

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

13

4. Description of the experimentalfacility SMILETRAP

4.1 OverviewThe SMILETRAP facility [14] includes a hyperboloid Penning trap mass spec-trometer with a superconductive magnet (Oxford Instruments, NMR Division,Type 200/130, Cryostat Family Type 3.) having 4.7 T central field. A sketchof the trap setup is presented in Fig. 4.1.

The SMILETRAP (Stockholm-Mainz-Ion-LEvitation-TRAP) started as acollaboration between the Manne Siegbahn Laboratory at Stockholm Uni-versity and the Physics Department of the Johannes Gutenberg University inMainz, Germany. The project was initiated by Prof. em. Ingmar Bergström.The main objective was to perform mass measurements relevant for funda-mental physics exploiting the precision gain by the usage of highly chargedions [47]. The 1989 Nobel Prize in Physics [9] was related to ion trap tech-nique, 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 appara-tus 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 CRYSISThe 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 beamwhich is compressed and confined by the ∼ 2 T magnetic field of a supercon-ductive solenoid in order to achieve high electron beam densities. The cryostatis cooled to liquid helium temperature (-269 °C) and is configured to providethe extremely high vacuum inside the source, which is necessary to preventrecombination of highly charged ions.

There are two ways of running CRYSIS. For the production of noble gas ionsand ions from molecular gases with a low melting point, a gas inlet is used andthe gas is injected more or less directly into the electron beam. The other wayis to use the external ion injector. The external ion injector is the compositionof a commercial Cold or HOt Reflex Discharge Ion Source (CHORDIS, man-

15

Figure 4.1: The SMILETRAP Penning Trap mass spectrometer setup. The drawingshows a portion of the C6 beamline coming from the electron beam ion source CRYSISand the 90◦ bending magnet, the pre-trap in a 0.25 T electromagnet and the precisiontrap in a 4.7 T superconductive magnet. The detector with a linear manipulator on thetop 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 pre-sented 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 witha high mass resolving power. Here, a wide variety of ions can be producedthrough gas-injection, sputtering, or evaporation from an oven. Typically thismethod is used for the production of metallic ions, where the gas inlet can notbe used. In this case the ion beam is injected through the electron collectorinto CRYSIS.

A typical operation of the CRYSIS ion source using external ions, involvesthree major steps. In the first step the isotope separated singly charged ionsare injected. The potential distribution is such that the ions overcome a po-tential barrier and get captured in a potential well created axially by a systemof 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 ionsare trapped. The charge state of the ions increases gradually by successivestrong electron impact ionization. During the time the ions stay confined, Hegas/ions can be used for cooling. After a selected confinement time the po-tential distribution is changed and the ions are extracted through the electroncollector.

The well defined ionization time in this type of ion source leads to a narrowcharge state distribution. The attainable charge state is limited by the electronbeam energy which must be greater than the ionization energy for the lastelectron. CRYSIS is designed for 50 keV electron energy which is sufficientfor the production of bare nuclei of all elements up to Xenon.

CRYSIS is built on a high-voltage platform, which means that the beamenergy can be varied independent of the electron energy between about 1qkeVand 45qkeV, where q is the charge state of the ion. When delivering beam tothe SMILETRAP experiment, a typically 100 µs long ion pulse is extracted atthe 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 noequipment near to CRYSIS to measure this. A lot has been learned during thepast years on how to set the parameters of CRYSIS to match the requirementsof the mass measurement experiment [52].

4.3 The pre-trapThe 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, whichconsists of seven cylindrical electrodes with an inner diameter of 10 mm andan entrance and an exit hole of 4 mm machined out of OFHC copper. Thevoltages on the four correction electrodes are tuned to create a near idealquadrupole field. The trap is placed inside an electromagnet which has a fieldof 0.25 T. To stop the beam coming from CRYSIS the entire pre-trap is floatedon 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 shorttime only (not due to charge exchange) and there is no ion cooling whichwould allow for colder ions in the precision trap.

18

4.4 The precision trapThe most important part of the mass spectrometer is a hyperboloidPenning 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 asuperconductive 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 elec-tric 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, cor-rection electrodes are used (Fig. 4.2). The voltages of the correction tubes andrings are tuned to achieve a near perfect trapping potential. The central ringelectrode is split into eight equal segments, which allows the use of dipole,quadrupole and octupole (2νc) excitation schemes. Four segments are used tocreate an azimuthal quadrupole radio-frequency field to couple the magnetronand cyclotron motions when performing mass measurements as described insection 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 entrancehole 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 materialis glass ceramics (MACOR) and aluminium oxide. The ring electrode is split in eightequal segments.

19

4.5 The control and data acquisition systemAt SMILETRAP one has to remotely control more than 50 parameters amongthem the voltages for the trap electrodes, the inter-trap optics and a numberof timing delays, waveforms and frequencies, which are implemented in theSMILETRAP control system. An additional∼50 voltage parameters are neededfor the beam transportation from the exit of CRYSIS to the pre-trap entrancewhich are accessed through a different control system available at the ManneSiegbahn Laboratory, named ConSys. A simplified scheme of the SMILETRAP

control system is given in Fig. 4.3. The control system of SMILETRAP is fullyimplemented in Labview, involving three personal computers (PC).

PC-1 is running the Graphical User Interface and all mass measurementsare 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 than50 µV and an absolute accuracy of±1 mV is used in order to obtain the stablevoltages needed for the precision trap. An analog voltage supply board (AT-AO-10) is used to remotely control the power supplies for the electrostatic de-flectors in between the two traps. The MIO-16-E4 board has 16 inputs whichare used to read in various analog signals.

The PC-3 is dedicated to control the pre-trap and therefore operates in ahigh-voltage cage. A high-speed analog output board (NI PCI-6713) is usedto generate the voltages for the pre-trap electrodes. By using optical TCP/IPconnection, the computer in the high-voltage cage and the voltage channeloutputs can be remotely programmed. It is possible to send additional digi-tal (TTL) signals and triggers (capture, boil-off, ejection) via separate opticalfibers.

To continuously monitor and stabilize external ambient parameters liketemperature and pressure the signals from a number of sensors placed aroundSMILETRAP are processed by using a NI PCI-4351 precision board installedin PC-2.

20

Figure 4.3: A simplified illustration of SMILETRAP control and data acquisition sys-tem.

21

5. Mass measurement procedure atSMILETRAP

The flow of a measurement is illustrated in Fig. 5.1. The experiment beginsat 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 adistance of about 15 m using conventional ion beam optics including a num-ber of electrostatic deflectors, quadrupole triplets and Einzel-lenses. Alongthe beam line, remotely controlled strip-detectors and Faraday-cups are usedto measure the beam profile and intensity. The beam energy is low, typically3.4 qkeV therefore it is quite an effort to transport this beam over the ratherlong distance to the trap setup.

Before entering the pre-trap, a charge state selection is done by scanningthe current of a 90◦ double focusing magnet which has a bending radius of500 mm. An example of a charge state spectra can be seen in Fig. 5.2(b). Thesame magnet also serves to deflect the beam vertically to the experiment. Outof the 100 µs long CRYSIS pulse, a small fraction (1-2 µs) is captured in thepre-trap due to the short length of the pre-trap compared to the length of thepulse. Typically a few thousand ions are captured here. The capturing is doneby applying a short negative voltage pulse (20 µs) on the lower end-cup of thepre-trap. When optimizing the capture in the pre-trap, the high voltage levelof 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 thenumber of ions was recorded can be seen in Fig. 5.2(c). After catching theions, the potential of the pre-trap is lowered to 0 V in a few milliseconds. Thisis 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. Theejection is achieved by applying a short negative voltage pulse (40 µs) on theupper end-cup of the pre-trap or by applying a positive voltage ramp on thering electrode.

The ion transfer in between the two traps is done through a series of drifttubes biased to -1 kV including a number of variable apertures, electrostaticdeflectors and lenses. A channeltron detector and a MCP-detector is used tooptimize the injection into the strong magnetic field, where the precision trapis located. These detectors can also be used to measure time of flight of theions ejected from the pre-trap, see Fig.5.2(d).

23

Figure 5.1: Schematic illustration of the mass measurement procedure at SMILETRAPPenning 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 toprevent ions with too large magnetron radii from entering the precision trap.The capturing in the precision trap is achieved by applying a short negativevoltage pulse on the lower end-cup and lower correction tube. Before the ionsare reflected out from the trap the voltage on these electrodes is restored backto 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 flightdiscrimination is usually applied, which means, that only ions arriving withina short time window are accepted. Out of the few thousand ions ejected fromthe pre-trap, typically about one hundred ions are captured in the precisiontrap. For a detailed ion balance see table 5.1.

To get rid of the high axial energy ions a so called boil-off technique isused. This involves lowering the trapping potential from 5 V to a few mVby ramping up the potential of the ring electrode. After the axially hottestions have left the trap, the potential is restored. The remaining cooler ions aresubject to an azimuthal quadrupolar radio-frequency excitation.

Table 5.1: Ion balance showing the average number of ions at different stages of theexperiment in a typical measurement. The width of the ion pulse injected into CRYSIScan be from 20 ms to 2 s, depending on the requirements. The width of the extractedpulse 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 couplewhich leads to a gain in the radial energy later converted into axial in thefringe field of the magnet as described in section 3.2. After excitation the ionsare gently ejected from the trap into the drift section and the time of flightto a detector 500 mm away is measured. To record the flight time, a MultiChannel Scaler & Averager (SR430, Stanford Research Systems) is used incombination with a Micro Channel Plate ion detector. A typical time-of-flightcyclotron resonance spectrum is shown in Fig. 5.2(f).

The coldest ion for the cyclotron frequency measurement is sorted out in aselection procedure involving four major stages. The first, is achieved alreadyin CRYSIS, due to the fact that the trapping voltage in the ion source is keptbetween 30 V to max. 70 V accompanied often with He cooling. The secondstage is the careful injection into the B-field of both traps. The ions are injectedas parallel to the B-field as possible to minimize the gain in radial energy of theions [53]. Furthermore, a selection is made by tuning the potential differencebetween the two traps to about 2 V. This measure limits the number of ionswhich 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 techniqueapplied in the precision trap.

In order to obtain the mass using eq. 3.2, in addition to the cyclotron fre-quency (νc), the B-field has to be measured as well. Since the B-field can notbe directly measured with high enough accuracy, the cyclotron frequency ofa reference ion is measured and the mass is obtained from the ratio of thesefrequencies, eliminating the dependence on B. Due to technical reasons H1+

2were used as reference ion since they could be easily produced by electronimpact 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, thecyclotron frequency of the main ion and the reference ion is alternately mea-sured within rather short time. The time for one scan including 21 equidistantfrequency steps is about 30-40 seconds. The switching to the reference ion isdone automatically and takes 1-2 seconds then the reference ion is scanned inthe same way. The total time of one measurement cycle including 2 scans ofthe main ion (each with 21 steps and 1 s exc. time) switching and 2 scans ofthe reference ion is less than 3 minutes.

A typical measurement with SMILETRAP involves a few thousand scanscorresponding to 20 000 or more ions of each species, requiring a measure-ment time from one day up to one week or more. Each ion is placed randomlyin a small volume of a few mm3 limited radially by the entrance hole withd=1 mm and axially by the boil-off procedure to <2.5 mm. Most of the imper-fections 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 andassociated uncertaintiesA measurement results in two interlaced series of frequency scans, one forthe ion of interest and one for the reference ion, as described in the previouschapter. The data is bunched and a resonance curve for each ion species isgenerated from 10-20 scans. The mass resolution in a Penning trap dependsdirectly 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 theresolving power of SMILETRAP is 3.6×107. The recorded time-of-flight datais fitted with a Gaussian curve using a least squares method and the centerfrequency is obtained to ∼ 1% of the linewidth. For the mass measurementspresented in this work an excitation time of 1 s has been used which results ina line width ≤1 Hz, and thus it is possible to reach a statistical uncertainty ofa few parts in 1010.

In Fig. 5.4 the Gaussian fitting is compared to a more correct fitting pro-cedure using the calculated theoretical line shape to fit the resonance pattern.It can be concluded that the two procedures result in center frequencies inagreement within the error bars however the fitting by the theoretical lineshapegives a slightly higher accuracy associated to the center frequency value [54].

The sidebands of the resonances which are related to the conversion ofmagnetron into cyclotron motion during excitation are suppressed in a typ-ical SMILETRAP resonance. The main reasons are: a non full conversion ofmagnetron 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-rived from the fit. The obtained νmain

c ±δν and νre fc ±δν ′ are divided to form

a frequency ratio ri±σi. The individual ratios ri are weighted together to forman average R which can be expressed as:

R =∑i ri

1σ2

i

∑i1

σ2i

. (5.1)

The weighted average (R) is given together with two errors, σint and σext .

σ2int =

1

∑i1

σ2i

σ2ext =

∑i1

σ2i(ri−R)2

(n−1)∑i1

σ2i

. (5.2)

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

29

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 83 54 04 55 05 56 06 57 07 5

G a u s s i a n f i t T h e o r e t i c a l f i tTim

e of fl

ight /

µs

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 theydiffer that is an indication for possible systematic errors.

The mass of the ion is calculated using the the weighted average ratio of themeasured frequencies:

R =νion

νre f=

qion

qre f

mre f

mion. (5.3)

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):

M =1R

qmain

qre fmre f +qmainme−EB. (5.4)

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

30

The remaining systematic effects that can be present when doing the massmeasurement with SMILETRAP are summarized in the following [14, 52, 61]:

• Reference massBy using H1+

2 as mass reference (m(H1+2 ) = 2.01510149703(27) u ) an un-

certainty of 0.18 ppb is introduced [14]. To use 12Cq+ the only uncertaintyintroduced would be the one resulting from the binding energy which is<10−11.

• Electron binding energiesThere is an error introduced when calculating the atomic mass using eq. 5.4due to the electron binding energies EB. This is usually≤0.1 ppb dependingon the mass and charge state. An error of 100 eV in binding energy wouldintroduce an error of 10−9 in case of a neutral atom with mass 100. Forlight masses Z < 20 the ionization energies of all charge states are knownto high accuracy, 10–20 eV, specially for closed atomic shells.

• Relativistic mass increaseThe measured ion mass is not the rest mass since the ion moves with anenhanced velocity after excitation, thus subject to measurable relativisticeffect when the precision reaches 1 ppb or better.The error related to relativistic effects is estimated by measuring the energybefore and after excitation by applying a deceleration potential as describedin [14]. The size of the error is usually <0.5 ppb.

• Ion number dependenceThe cyclotron frequency decreases with more ions inside the trap. By ob-taining cyclotron frequencies from 1,2,3 etc. simultaneously trapped ionsusing the off-line data analyzer program, it is possible to investigate shiftscaused by having more than 1 ion in the trap. We usually base the cyclotronfrequencies on events with 1 or maximum 2 simultaneously trapped ions.Not having 100% detection efficiency, what we regard as single ion eventmay arise from 2 or more simultaneously detected ions. There may be alsoa small difference in the detection efficiency of the main ion and the refer-ence ion, leading to uncertainties in the order of ∼0.1 ppb.

• q/A asymmetryIf the main ions charge to mass ratio (q/A) differs from the reference ionsq/A, the cyclotron frequency shift due to the misalignment between the Eand B-field axis is different therefore it does not cancel when calculatingthe cyclotron frequency ratio. It can not be excluded, that a frequency ratioshift up to 1 ppb may be present in cases where ion species are not q/Adoublets. Therefore, as much as possible, we try to perform mass measure-ments using q/A doublets.

• ContaminationsImpurities having the same q/A as the main ion may arise from CRYSIS orcreated 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 applyingdipolar excitation. The size of the error is typically about 0.1 ppb.

• Magnetic field driftInstabilities in the magnetic field can cause both a frequency shift and anincrease in the resonance line width. The natural decay of the current in oursuperconducting 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 pres-sure changes in the liquid He cryostat due to the daily air pressure fluctu-ations. This effect is known and after stabilization of the trap temperatureand the helium pressure, the frequency shifts due to changes in the mag-netic field is minimized to <0.1 ppb [52].

32

6. Summary of the results and briefdiscussion

6.1 Accurate mass measurements ofhydrogen-like 24Mg and 26Mg ions andhydrogen-like and lithium-like 40Ca ionsThe mass measurements of the 24Mg11+, 26Mg11+, 40Ca17+ and 40Ca19+ ionswere motivated by the g-factor experiment [25, 26] aiming to test the boundelectron QED [62].

In order to determine the g-factor of the bound electron in hydrogen-likeand lithium-like ions the mass of the ion is needed at an accuracy of typically1 ppb or better.

In Fig. 6.1 the atomic mass of the 24Mg and 26Mg obtained by us is com-pared to the literature values published prior to our experiment. The masseswere measured at a total relative uncertainty of 0.56 ppb and 1.3 ppb for 24Mgand 26Mg, respectively. The literature value had an uncertainty of ∼8 ppb inboth cases [63]. Thus we were able to considerably improve the mass preci-sion of both isotopes fulfilling the requirements of the g-factor experiment.Moreover, the masses presented here can allow for the observation of an iso-tope 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 theliterature values available prior to our measurements. The uncertainty in the case ofthe 26Mg isotope is larger due to the difference in statistics.

33

������������������������������������������������ 2 5 M g ( n , γ)

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

S n / k

eV

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

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 forthe 25Mg was calculated. Our new mass values could be used to calculate the26Mg neutron binding energy (Sn) which is compared to the values availablein the literature obtained in different ways, see Fig. 6.2.

Furthermore our new 24Mg and 26Mg mass values were used to concludethat there is an uncertainty in the mass of 26Al. The 26Mg(p,n)26Al reaction isof special interest for problems connected with the intensity of allowed Fermiβ -transitions [64].

In Fig. 6.3 the mass of 40Ca obtained from measurements using lithium-likeand hydrogen-like 40Ca ions is compared to the literature value [64] publishedprior to our experiment. The literature value of 40Ca has been calculated usingthe mass of 39K and the 39K(p,γ)40Ca reaction Q-value [65] and has a relativeuncertainty 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, thatour new value represents an improvement in the mass precision by a factor of10, see [Paper II.].

With the new mass value of 40Ca we have also improved the 40Ca - 40Ardouble β decay Q-value by one order of magnitude since the 40Ar mass isknown with a relative uncertainty of 0.07 ppb [64]. The obtained Q-value is193.5 keV with an uncertainty of 17 eV only.

34

���

���

���

�����

�����

�����

A M E 2 0 0 3

4 0 C a

A M E 2 0 0 3 T h i s w o r k 1 7 + T h i s w o r k 1 9 + T h i s w o r k a v e r a g e

39 96

2 590

XXX /

nu

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 7LiThe literature mass value for 7Li is calculated using the 6Li(n,γ)7Li reactionQ-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. Dunnwith a relative uncertainty of 2.7 ppb [66]. The Q-value used in the literature tocalculate the mass has an uncertainty of 80 eV [64]. A different Q-value withan uncertainty of 90 eV is available in the literature [67] which would result ina more than 100 ppb different mass. In order to use 7Li as reference mass forcalibration purposes in high-accuracy Penning trap mass spectrometry [68] ofthe short-lived radionuclides 9,11Li and for laser spectroscopic studies of theisotope shifts and nuclear-charge radii of both the stable 6,7Li and short-lived8,9,11Li isotopes, a better knowledge of the mass was demanded.

By comparing the cyclotron frequency of 7Li3+ to H1+2 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 about14σ .

To find the reason of the unexpectedly large deviation and to check forsystematics we measured the masses of 4He and 6Li. The 4He measurementdid not result in any large systematical error. Our measured mass for 6Li is inagreement with the literature value within 2.4σ . From the masses of 6Li and7Li measured by us the Q-value of the 6Li(n,γ)7Li reaction has been derivedand 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 fromthe 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 reads7251.02(9) keV. It seems that the Q-value in the literature is wrong which canexplain the deviation observed in the 7Li mass.

Furthermore, note that the masses of 7Be and 8Li in AME2003 uses the 7Limass as input data [64], therefore thanks to the new mass value these massesare also improved.

36

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

5 0

1 0 0

1 5 0

2 0 0

T h i s w o r kA M E 2 0 0 3A M E 9 3

Unce

rtaint

y / pp

b7 L i

A M E 8 5

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

������������������������������������������������������������������������������

T h i s w o r k2 0 0 31 9 8 51 9 7 2

Q-va

lue / k

eV

1 9 6 8

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

37

6.3 The mass of 3H and 3He and the Q-valueof the tritium β-decayBy 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 the3H → 3He + e−+νe reaction.

The corresponding atomic mass of 3H and 3He are presented in Fig. 6.6 andFig. 6.7, respectively. The mass values from the 1995 Atomic Mass Evaluation[63] deviate from our measurements by ∼5 ppb in both cases. The reasonof this deviation is understood, it is due to a day-to-night effect which wasunknown 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 Seattlegroup 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 mea-suring the energy spectrum of the β electrons with sensitivity of 0.2 eV. Aneutrino mass of 0.35 eV would be discovered with 5 σ significance [29]. Anon-zero neutrino mass would show up as a difference between the Q-valueand 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 anuncertainty of 1.2 eV which is enough only to find gross errors at the neutrinoexperiment. 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 ex-periment, further precision improvements are necessary and can be expectedsoon.

38

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���������

���������

���������

S M I L E - 2 0 0 1

Ato

mic m

ass /

nu

A M E - 1 9 9 5

3 H

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

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����������

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

Atomi

c mas

s / nu

A M E - 1 9 9 5

3 H e

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

39

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������

������ β - s p e c t r o m e t e r s F T I C R V a n D y c k ’ 9 3 T h i s w o r k

Q-

value

/ eV

Figure 6.8: The Q− value of the 3H - 3He reaction measured by using different tech-niques. The last point (H) has been obtained using 3H1+ and 3He1+ with SMILETRAP.

40

6.4 Proton mass evaluationFrom the mass measurements presented in this work, in two cases there wereaccurate mass values already available from other experiments.

By using the preliminary 3He mass from the Seattle group [73] and the 4Hemass from AME2003 [64], I calculated the mass of H1+

2 from the measuredfrequency ratios of 3He1+ / H1+

2 and 4He2+ / H+2 in both cases. From the

obtained H1+2 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 theproton mass.

Furthermore, this can be interpreted as a consistency check as well, if wehad any gross unaccounted systematics, it had shown up in this comparison.

������������

������������

������������

������������

�����������f r o m 3 H e 1 +

f r o m 4 H e 2 +

A M E 2 0 0 3

m p / n

u

T h i s w o r k

m p

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+ /H1+

2 and 4He2+ / H1+2 respectively. In the case of the latter two the error bars represent

only the statistical uncertainty.

41

7. Concluding remarks

In this work the improvements of the SMILETRAP Penning Trap mass spec-trometer and results obtained using the improved apparatus are presented.

The mass results obtained for 24Mg11+, 26Mg11+, 40Ca17+ and 40Ca19+ ionsare key input parameters for the g-factor experiments aiming to test the boundelectron QED. The new mass values for the 24Mg and 26Mg are valuable inputsto solve problems in the atomic mass table.

By measuring the mass of 7Li3+ we obtained a new mass value for 7Li andobserved a large deviation compared to the literature mass value. We correctedthe mass and improved the uncertainty in the mass by a factor of 18. The newmass can now be used as reference ion in future mass and nuclear charge-radiimeasurements 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 isthe most accurate value at present which allows to look for larger systematicsat the future neutrino experiment KATRIN. Further improvement of this valueis 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

3He 3.016 029 321(26) 0.8 νe rest mass4He 4.002 603 253 3(26) 0.7 systematics check7Li 7.016 003 425 6 (45) 0.6 reference ion6Li 6.015 122 890(40) 7 related to 7Li24Mg 23.985 041 690(14) 0.6 g-factor, QED test26Mg 25.982 592 986(34) 1.3 g-factor, QED test40Ca 39.962 590 858(19) 0.45 g-factor, QED test

43

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-heavyhighly charged ions up to hydrogen-like uranium (238U91+), several measureshave 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 movementhas alredy been started.

Installation of a new pre-trap.The installation of a new pre-trap with ion cooling implemented will removeseveral limitations which exist in the present setup. A new pre-trap has alreadybeen built and installed in a 1.1 T conventional electromagnet and testing isgoing 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 allowfor longer excitation times, thus higher resolution in the mass measurementis achievable. The proper fitting routine needed to analyze the data obtainedby the Ramsey excitation has already been developed [76] and it is beingimplemented at SMILETRAP [54].

45

Acknowledgements

My time in Stockholm has been a wonderful experience. The staff at MSL andAlbaNova have been beyond friendly and were always ready to offer a smile to thesmiling 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 andfor being by my side and helping me out whenever I got in trouble. I really enjoyedworking with you.Ingmar Bergström - for the confidence he has shown in me, for the endlessencouragement and strong support.Micke Björkhage - for all the ions delivered to SMILETRAP, for teaching me manyuseful 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 discussionsabout detectors and beam current measurement.György Vikor - for his advises and for being always ready to offer an extra pair ofhands when there was a need.Sven Leontein - for keeping me up to date with the latest features and bugs of the stripdetector 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" withsome cool guys from MSL: Mikael Blom, Gunnar Källersjö, Per Werner and PatrikLöfgren 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. Nagyfrom the Babes-Bolyai University, (Cluj-Napoca, Romania) for the confidence andsupport.

I am sure that the trap will find an even better new home at AlbaNova and in thehands 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. Iwould like to thank my supervisor Prof. Reinhold Schuch for this opportunity.

Szilárd Nagy19 December 2005, Stockholm

47

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54