Download 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
© Szilárd Nagy, 2005 Stockholm University
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 S MILETRAP 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 24,26 Mg ions as well as the masses of the hydrogen- and lithiumlike 40 Ca 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 7 Li 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 µ u (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 4 He and 6 Li and have concluded that
the 6 Li(n,γ )7 Li reaction Q-value, used in the literature when calculating the
7 Li mass, is wrong by about 1 keV.
The mass difference between 3 He and 3 H (∆m(3 H −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 3 He1+ to previous mass
measurements of 3 H1+ and 3 He2+ , we have improved our previous Q-value
by a factor of 2. The current Q-value determined by S MILETRAP 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 24 Mg11+ and
26 Mg11+ 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 40 Ca17+ and 40 Ca19+ 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 7 Li,
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 70 Cu,
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. Tőkési, Z. Berényi,
B. Paripás, N. Stolterfoht, B. Sulik
Nucl. Instrum. and Meth. B, 235, 397–402 (2005).
vi
Contents
1
2
3
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comments on the author’s contribution . . . . . . . . . . . . . . . . . . . . .
Penning traps and their application for mass spectrometry . . . . . . .
3.1 Motion of ions in a Penning trap . . . . . . . . . . . . . . . . . . . . . . .
3.2 Cyclotron frequency measurement . . . . . . . . . . . . . . . . . . . . . .
4 Description of the experimental facility SMILETRAP . . . . . . . . . .
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 The electron beam ion source CRYSIS . . . . . . . . . . . . . . . . . .
4.3 The pre-trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 The precision trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 The control and data acquisition system . . . . . . . . . . . . . . . . . .
5 Mass measurement procedure at SMILETRAP . . . . . . . . . . . . . . . .
5.1 Calculation of the atomic mass and associated uncertainties . . .
6 Summary of the results and brief discussion . . . . . . . . . . . . . . . . . .
6.1 Accurate mass measurements of hydrogen-like 24 Mg and 26 Mg
ions and hydrogen-like and lithium-like 40 Ca ions . . . . . . . . . .
6.2 New mass value for 7 Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 The mass of 3 H and 3 He and the Q-value of the tritium β -decay
6.4 Proton mass evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Future outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Attached Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
5
7
8
10
15
15
15
18
19
20
23
29
33
33
36
38
41
43
45
47
49
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 increasing 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 S MILETRAP [14], or radioactive ions at I SOLTRAP [15].
The S MILETRAP 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 Pen1 In 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, muonneutrino 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 following simple reaction 3 H → 3 He + e− + νe the tritium (3 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 (K ATRIN) [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 (24 Mg, 26 Mg) and calcium (40 Ca) 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 gfactor. 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. Therefore we measured the mass of a few suitable candidates 24 Mg11+ , 26 Mg11+ ,
40 Ca17+ and 40 Ca19+ 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 11 Li [30]
which is attributed to a “halo” of neutrons around a compact core of nucleons [31, 32]. A halo state can be formed when bound states close to the continuum exist. Since 1985 a large amount of high-accuracy experiments have
been performed on 11 Li 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 7 Li 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 (1.1µ u) in the literature mass value confirmed by
measurements of the masses of 6 Li and 4 He. We found that this deviation is
due to a wrong Q-value used when calculating the mass.
The improved mass value of 7 Li 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 9,11 Li as well as 6,8 He. 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 7 Li.
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 S MILETRAP 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 specialists at MSL, however, the testing and debugging of the new system involving about 50 parameters for the S MILETRAP 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 S MILETRAP involved on one hand up keeping and on the other
hand further developing the experimental setup. During my time at S MILE 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 S AES St 707
NEG (Non-Evaporable Getter) strip has been added to three different locations of the experimental setup which provides additional pumping. Furthermore, 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 S MILETRAP. 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 operational 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-2510E) with an effective diameter of 18 mm and channel diameter of 10 µ m
(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
current needed for the creation of the H21+ 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 threedimensional trap. However, if a magnetic field B is applied parallel to the zaxis, 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 S MILETRAP.
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:
νc =
1 qB
,
2π m
(3.2)
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
Φ(x, y, z) =
8
U0
(2z2 − x2 − y2 ),
4d 2
(3.3)
where d is the characteristic trap dimension defined as
s 1 2 r02
d=
z0 +
.
2
2
(3.4)
The equipotential surfaces are hyperboloids generated by the electrodes of the
trap. The two end-cups have the geometrical form described by the equation
2z2 − x2 − y2 = 2z20 and the ring electrode 2z2 − x2 − y2 = −r02 . 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
− ω0 − ωz2 x = 0 ,
2
dt
dt 2
(3.6)
dx 1
d2y
+ ω0 − ωz2 y = 0 ,
dt 2
dt 2
(3.7)
d2z
+ ωz2 = 0 ,
dt 2
(3.8)
where
qB0
ω0 =
, ωz =
m
r
2qU0
.
md 2
(3.9)
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
+ iω0 − ωz2 u = 0 .
2
dt
dt 2
(3.10)
The general solution of this equation is found by setting u = exp(−iωt) which
leads to
1
ω 2 − ω0 ω + ωz2 = 0
(3.11)
2
The solutions ω+ and ω− of (3.11) are
q
1
ω+ =
ωc + ωc2 − 2ωz2 ,
2
(3.12)
9
and
q
1
2
2
ω− =
ωc − ωc − 2ωz .
2
(3.13)
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
ωc2 − 2ωz2 > 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| 2 4|U0 |
B > 2 qU0 > 0 .
m 0
d
(3.15)
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)
2ω+ ω− = ωz2 .
(3.17)
Furthermore it can be shown that
ω+2 + ω−2 + ωz2 = ωc2 ,
(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. Typically 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 phaseshifted 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 =
.
(3.20)
2Br02 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:
12
Z z1 m
Tr f =
dz ,
2[E0 − q ·V (z) − µ(ωRF ) · B(z)]
z0
(3.22)
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.
13
4. Description of the experimental
facility SMILETRAP
4.1
Overview
The S MILETRAP 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 S MILETRAP (Stockholm-Mainz-Ion-LEvitation-TRAP) started as a
collaboration between the Manne Siegbahn Laboratory at Stockholm University 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 S MILETRAP
project. The construction started at Mainz in the summer of 1990 and in December 1991 the first cyclotron resonance spectra was recorded. The apparatus was moved to Stockholm and connected to the electron beam ion source
(C RYSIS) [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 E BIS [50, 51]
named C RYSIS . 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 C RYSIS. 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 (C HORDIS, man15
Figure 4.1: The S MILETRAP Penning Trap mass spectrometer setup. The drawing
shows a portion of the C6 beamline coming from the electron beam ion source C RYSIS
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 C RYSIS.
A typical operation of the C RYSIS 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.
C RYSIS 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 S MILETRAP experiment, a typically 100 µ s 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 510 eV, which is estimated from the ion capture in the pre-trap since there is no
equipment near to C RYSIS to measure this. A lot has been learned during the
past years on how to set the parameters of C RYSIS 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 C R 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 C RYSIS the entire pre-trap is floated
on the same potential as the extraction potential of C RYSIS.
The present pre-trap has certain limitations, there is no possibility to mechanically 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 I SOLTRAP
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 endcup 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 S MILETRAP.
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 S MILETRAP 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
S MILETRAP control system. An additional ∼50 voltage parameters are needed
for the beam transportation from the exit of C RYSIS 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 S MILETRAP
control system is given in Fig. 4.3. The control system of S MILETRAP 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 µ V 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 (ATAO-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 digital (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
S MILETRAP are processed by using a NI PCI-4351 precision board installed
in PC-2.
20
Figure 4.3: A simplified illustration of S MILETRAP control and data acquisition system.
21
5. Mass measurement procedure at
SMILETRAP
The flow of a measurement is illustrated in Fig. 5.1. The experiment begins
at C RYSIS where the highly charged ions are produced as described in Section 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 µ s long C RYSIS pulse, a small fraction (1-2 µ s) 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 µ s) 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 µ s) 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 S MILETRAP
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-offlight 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 µ s. The capturing in the pre25
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 C RYSIS
can be from 20 ms to 2 s, depending on the requirements. The width of the extracted
pulse is 100 µs.
Injected into C RYSIS
∼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 C RYSIS, 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
frequencies, eliminating the dependence on B. Due to technical reasons H1+
2
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 S MILETRAP 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 S MILETRAP 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 S MILETRAP 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 S MILETRAP resonance. The main reasons are: a non full conversion of
magnetron into cyclotron motion during excitation and the short term instability of the magnetic field [52].
The center frequencies νc , and the corresponding uncertainty δ νc are derived from the fit. The obtained νcmain ± δ ν and νcre f ± δ ν 0 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:
R=
∑i ri σ12
i
∑i σ12
.
(5.1)
i
The weighted average (R) is given together with two errors, σint and σext .
2
σint
=
1
∑i σ12
i
2
σext
=
∑i σ12 (ri − R)2
i
(n − 1) ∑i σ12
.
(5.2)
i
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
29
7 5
7 0
T i m e o f f l i g h t / µs
6 5
6 0
5 5
5 0
4 5
G a u s s ia n fit
T h e o r e tic a l fit
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 lo tr 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:
νion
qion mre f
R=
=
.
(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 ):
M=
1 qmain
mre f + qmain me − EB .
R qre f
(5.4)
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
mass is me = 5.485 799 0945(24)×10−4 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 S MILETRAP are summarized in the following [14, 52, 61]:
• Reference mass
1+
By using H1+
2 as mass reference (m(H2 ) = 2.015 101 497 03(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 obtaining 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 C RYSIS 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 24 Mg and 26 Mg ions and
hydrogen-like and lithium-like 40 Ca ions
The mass measurements of the 24 Mg11+ , 26 Mg11+ , 40 Ca17+ and 40 Ca19+ 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 24 Mg and 26 Mg 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 24 Mg
and 26 Mg, 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 24 Mg and 26 Mg isotopes compared to the to the
literature values available prior to our measurements. The uncertainty in the case of
the 26 Mg isotope is larger due to the difference in statistics.
33
11 093,4
11 093,2
2 5
2 5
M g ( n , γ)
2 6
M g ( p , γ) - M g ( p , n )
T h is w o r k
S
n
/ k e V
11 093,0
11 092,8
11 092,6
11 092,4
11 092,2
11 092,0
Figure 6.2: 26 Mg neutron binding energies derived in different ways. Values taken
from [64]. The last point (H) is derived from our mass for 24 Mg and 26 Mg.
Our new mass values for 24 Mg and 26 Mg made also an impact in AME2003.
By using these mass values and several 24 Mg(n,γ ) reactions a new mass for
the 25 Mg was calculated. Our new mass values could be used to calculate the
26 Mg neutron binding energy (S ) which is compared to the values available
n
in the literature obtained in different ways, see Fig. 6.2.
Furthermore our new 24 Mg and 26 Mg mass values were used to conclude
that there is an uncertainty in the mass of 26 Al. The 26 Mg(p,n)26 Al reaction is
of special interest for problems connected with the intensity of allowed Fermi
β -transitions [64].
In Fig. 6.3 the mass of 40 Ca obtained from measurements using lithium-like
and hydrogen-like 40 Ca ions is compared to the literature value [64] published
prior to our experiment. The literature value of 40 Ca has been calculated using
the mass of 39 K and the 39 K(p,γ )40 Ca 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 40 Ca we have also improved the 40 Ca - 40 Ar
double β decay Q-value by one order of magnitude since the 40 Ar 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.
34
3 9 9 6 2 5 9 0 X X X / n u
1 200
4 0
C a
1 100
A M
T h
T h
T h
E 2
is w
is w
is w
0 0
o r
o r
o r
3
k 1 7 +
k 1 9 +
k a v e ra g e
1 000
900
800
700
A M E 2 0 0 3
T h is w o r k
Figure 6.3: The atomic mass of 40 Ca compared to the literature value AME2003 [64].
35
6.2
New mass value for 7 Li
The literature mass value for 7 Li is calculated using the 6 Li(n,γ )7 Li reaction
Q-value and the mass of 6 Li and has a relative uncertainty of 11 ppb [64].
The mass of 6 Li 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 7 Li as reference mass for
calibration purposes in high-accuracy Penning trap mass spectrometry [68] of
the short-lived radionuclides 9,11 Li and for laser spectroscopic studies of the
isotope shifts and nuclear-charge radii of both the stable 6,7 Li and short-lived
8,9,11 Li isotopes, a better knowledge of the mass was demanded.
By comparing the cyclotron frequency of 7 Li3+ to H1+
2 we measured the
7
mass of Li atom to an unprecedented uncertainty of 6.3×10−10 , see [Paper III.]. A large deviation from the literature value [64] has been observed,
see Fig. 6.4. The deviation is 1.1µ u 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 4 He and 6 Li. The 4 He measurement
did not result in any large systematical error. Our measured mass for 6 Li is in
agreement with the literature value within 2.4σ . From the masses of 6 Li and
7 Li measured by us the Q-value of the 6 Li(n,γ )7 Li 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 7 Li 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 7 Li mass.
Furthermore, note that the masses of 7 Be and 8 Li in AME2003 uses the 7 Li
mass as input data [64], therefore thanks to the new mass value these masses
are also improved.
36
2 0 0
7
U n c e r ta in ty / p p b
1 5 0
L i
1 0 0
5 0
0
-5 0
-1 0 0
-1 5 0
-2 0 0
A M E 9 3
A M E 8 5
A M E 2 0 0 3
T h is w o r k
Figure 6.4: The mass uncertainty of 7 Li compared to the values found in the literature.
7 251,4
7 251,2
7 251,0
Q - v a lu e / k e V
7 250,8
7 250,6
7 250,4
7 250,2
7 250,0
7 249,8
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 is w o r k
Figure 6.5: The Q-value of the 6 Li(n,γ)7 Li 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 6 Li and 7 Li.
37
6.3 The mass of 3 H and 3 He and the Q-value
of the tritium β -decay
By adding a new measurement of the 3 He1+ to the existing 3 H1+ and 3 He2+
data, we obtained a new value for ∆m(3 H −3 He) which is the Q-value of the
3 H → 3 He + e− + ν reaction.
e
The corresponding atomic mass of 3 H and 3 He 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 3 He 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 K ATRIN 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 retarding energy, the fitted β endpoint can be compared to the ∆m(3 H −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 K ATRIN experiment, further precision improvements are necessary and can be expected
soon.
38
3 016 049 282
3 016 049 280
3
H
A to m ic m a s s / n u
3 016 049 278
3 016 049 276
3 016 049 274
3 016 049 272
3 016 049 270
3 016 049 268
3 016 049 266
3 016 049 264
A M E -1 9 9 5
S M IL E -2 0 0 1
Figure 6.6: The mass of 3 H. The second point (H) is our measured value which was
used to obtain the Q-value.
3 016 029 326
A to m ic m a s s / n u
3 016 029 324
3
H e
3 016 029 322
3 016 029 320
3 016 029 318
3 016 029 316
3 016 029 314
3 016 029 312
3 016 029 310
A M E -1 9 9 5
S M IL E -2 0 0 1
T h is w o r k
V a n D y c k p r iv .
Figure 6.7: The mass of 3 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].
39
18 615
18 610
Q - v a lu e / e V
18 605
β- s p e c t r o m e t e r s
F T IC R
V a n D y c k ’9 3
T h is w o r k
18 600
18 595
18 590
18 585
18 580
18 575
Figure 6.8: The Q − value of the 3 H - 3 He reaction measured by using different techniques. The last point (H) has been obtained using 3 H1+ and 3 He1+ with S MILETRAP.
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 3 He mass from the Seattle group [73] and the 4 He
mass from AME2003 [64], I calculated the mass of H1+
2 from the measured
1+
+
3
1+
4
2+
frequency ratios of He / H2 and He / H2 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 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
m
fro m
fro m
p
m p / n u
1 007 276 467,5
3
H e
1 +
4
H e
2 +
1 007 276 467,0
1 007 276 466,5
1 007 276 466,0
A M E 2 0 0 3
T h is 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 3 He1+ /
H21+ and 4 He2+ / 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 S MILETRAP Penning Trap mass spectrometer and results obtained using the improved apparatus are presented.
The mass results obtained for 24 Mg11+ , 26 Mg11+ , 40 Ca17+ and 40 Ca19+ ions
are key input parameters for the g-factor experiments aiming to test the bound
electron QED. The new mass values for the 24 Mg and 26 Mg are valuable inputs
to solve problems in the atomic mass table.
By measuring the mass of 7 Li3+ we obtained a new mass value for 7 Li 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 6,7 Li and short lived 8,9,11 Li 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 K ATRIN. 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
4 He
3.016 029 321(26)
0.8
νe rest mass
7 Li
4.002 603 253 3(26)
0.7
systematics check
6 Li
7.016 003 425 6 (45)
0.6
reference ion
6.015 122 890(40)
7
related to 7 Li
24 Mg
23.985 041 690(14)
0.6
g-factor, QED test
26 Mg
25.982 592 986(34)
1.3
g-factor, QED test
40 Ca
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 S MILE TRAP and open the gates to yet unexplored experiments using very-heavy
highly charged ions up to hydrogen-like uranium (238 U91+ ), several measures
have to be taken.
Attaching SMILETRAP to REBIT.
Therefore the apparatus has to be dismantled and moved from its present location 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 S MILETRAP 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 S MILETRAP [54].
45
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 S MILETRAP. 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 S MILETRAP 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 S MILETRAP, 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 Babeş-Bolyai University, (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 S MILETRAP - a world class experiment. I
would like to thank my supervisor Prof. Reinhold Schuch for this opportunity.
Szilárd Nagy
19 December 2005, Stockholm
47
Bibliography
[1] F. W. Aston, “A New Mass Spectrograph and the Whole Number Rule,” Roy.
Soc. Proc. A 115, 487–514 (1927).
[2] A. J. Dempster, Proc. Am. Phil. Soc. 55, 755 (1935).
[3] K. T. Bainbridge and E. B. Jordan, “Mass Spectrum Analysis 1. The Mass Spectrograph. 2. The Existence of Isobars of Adjacent Elements,” Phys. Rev. 50,
282–296 (1936).
[4] J. Mattauch, “A Double-Focusing Mass Spectrograph and the Masses of N15
and O18 ,” Phys. Rev. 50, 617–623 (1936).
[5] A. O. Nier and T. R. Roberts, “The Determination of Atomic Mass Doublets by
Means of a Mass Spectrometer,” Phys. Rev. 81, 507–510 (1951).
[6] R. C. Barber, R. L. Bishop, H. E. Duckworth, J. O. Meredith, F. C. G. Southon,
P. V. Rookhuyzen, and P. Williams, “A High Resolution Mass Spectrometer for
Atomic Mass Determinations,” Rev. Sci. Instrum 42, 1–8 (1971).
[7] L. G. Smith and C. C. Damm, “Mass Synchrometer,” Rev. Sci. Instrum. 27,
638–649 (1956).
[8] L. G. Smith, “Measurement of Six Light Masses,” Phys. Rev. C 4, 22–31 (1971).
[9] Les Prix Nobel (Almqvist & Wiksell International, The Nobel Foundation,
1989).
[10] G. Gräff, H. Kalinowsky, and J. Traut, “A direct determination of the proton
electron mass ratio,” Zeitschrift für Physik A 297, 35–39 (1980).
[11] R. S. VanDyck, S. L. Zafonte, and P. B. Schwinberg, “Ultra-Precise Mass measurements Using the UW-PTMS,” Hyperfine Interact. 132, 163–175 (2001).
[12] S. Rainwille, J. K. Thompson, and D. E. Pritchard, “An Ion Balance for UltraHigh-Precision Atomic Mass Measurements,” Science 303, 3334–3338 (2004).
[13] J. K. Thompson, S. Rainwille, and D. E. Pritchard, “Cyclotron frequency shifts
arising from polarization forces,” Nature 430, 58–61 (2004).
49
[14] I. Bergström, C. Carlberg, T. Fritioff, G. Douysset, R. Schuch, and J. Schönfelder, “SMILETRAP - A penning trap facility for precision mass measurements
using highly charged ions,” Nucl. Instr. and Meth. in Phys. Res. A 487, 618–651
(2002).
[15] K. Blaum, F. Herfurth, A. Kellerbauer, H.-J. Kluge, M. Kucjein, S. Heinz, P.
Schmidt, and L. Schweikhard, “Recent developments at ISOLTRAP: towards a
relative mass accuracy of exotic nuclei below 10−8 ,” J. Phys. B 36, 921–930
(2003).
[16] M. P. Bradley, J. V. Porto, S. Rainville, J. K. Thompson, and D. E. Pritchard,
“Penning Trap Measurement of the Masses of 133 Cs, 87,85 Rb, and 23 Na with
Uncertainties ≤0.2 ppb,” Phys. Rev. Lett. 83, 4510–4513 (1999).
[17] C. Carlberg, T. Fritioff, and I. Bergtröm, “Determination of the 133 Cs and Proton Mass Ratio Using Highly Charged Ions,” Phys. Rev. Lett. 83, 4506–4509
(1999).
[18] F. DiFilippo, V. Natarajan, K. R. Boyce, and D. E. Pritchard, “Accurate Atomic
Masses for Fundamental Metrology,” Phys. Rev. Lett. 82, 3198–3201 (1994).
[19] I. Bergström, T. Fritioff, R. Schuch, and J. Schönfelder, “On the Masses of 28 Si
and the Proton Determined in a Penning Trap,” Physica Scripta 66, 1–7 (2002).
[20] G. Gabrielse, A. Khabbaz, D. Hall, C. Heimann, H. Kalinowsky, and W. Jhe,
“Precision Mass Spectroscopy of the Antiproton and Proton Using Simultaneously Trapped Particles,” Phys. Rev. Lett. 82, 3198–3201 (1999).
[21] A. Kellerbauer et al., “Towards high-precision mass measurements on 74 Rb for
a test of the CVC hypothesis and the unitarity of the CKM matrix,” Nucl. Phys.
A 746, 635–638 (2004).
[22] G. L. Greene, M. S. Dewey, E. G. Kessler, and E. Fischbach, “Test of special
relativity by a determination of the Lorentz limiting velocity: Does E = mc2 ,”
Phys. Rev. D 44, 2216–2219 (1991).
[23] M. Amoretti and et. al., “The ATHENA antihydrogen apparatus,” Nucl. Instrum.
and Methods A 518, 679–711 (2004).
[24] G. Gabrielse, X. Fei, K. Helmerson, S. L. Rolston, R. Tjoelker, T. A. Trainor, H.
Kalinowsky, J. Haas, and W. Kells, “First Capture of Antiprotons in a Penning
Trap: A Kiloelectronvolt Source,” Phys. Rev. Lett. 57, 2504–2507 (1986).
[25] H. Häffner, T. Beier, N. Hermanspahn, H.-J. Kluge, W. Quint, S. Stahl, J. Verdú,
and G. Werth, “High-accuracy measurement of the magnetic moment anomaly
of the electron bound in a hydrogen-like Carbon,” Phys. Rev. Lett. 85, 5308
(2000).
50
[26] J. Verdú, S. Djekic, S. Stahl, T. Valenzula, M. Vogel, G. Werth, T. Beier, H.J. Kluge, and W. Quint, “Electronic g-factor of hydrogenlike Oxygen 16 O17+ ,”
Phys. Rev. Lett. 92, 093002 (2004).
[27] Y. Fukuda and et. al, “Evidence for Oscillation of Atmosferic Neutrinos,” Phys.
Rev. Lett. 81, 1562 (1998).
[28] S. Eidelman and et. al, “Review of Particle Physics,” Phys. Lett. B 592, 1
(2004).
[29] J. Angrik and et al., “KATRIN Design Report,” FZKA Sci. Rep. 9090, 1–245
(2004).
[30] I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sugimoto,
O. Yamakawa, T. Kobayashi, and N. Takahashi, “Measurements of Interaction
Cross Sections and Nuclear Radii in the Light p-Shell Region,” Phys. Rev. Lett
55, 2676 (1985).
[31] B. Jonson, “Light dripline nuclei,” Phys. Rep. 389, 1–59 (2004).
[32] A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido, “Structure and reaction
of quantum halos,” Rev. Mod. Phys. 76, 215–261 (2004).
[33] G. Ewald et al., “Nuclear Charge Radii of 8,9 Li Determined by Laser Spectroscopy,” Phys. Rev. Lett 25, 113002 (2004).
[34] E. Arnold, J. Bonn, A. Klein, R. Neugart, M. Neuroth, E. W. Otten, P. Lievens,
H. Reich, and W. Widdra, “Quadrupole moment of 11 Li,” Phys. Lett. B 281, 16
(1992).
[35] C. Bachelet, G. Audi, C. Gaulard, C. Guénaut, F. Herfurth, D. Lunney, M. D. S.
Simon, and C. Thibault, “Mass measurement of short-lived halo nuclides,” Eur.
Phys. J. A 25, 31–32 (2005).
[36] R. C. Thompson, “Precision measurement aspects of ion traps,” Meas. Sci. Technol. 1, 93–105 (1989).
[37] F. M. von Penning, “Tiefdruckmanometer,” Philips Technische Rundshau 7,
201–208 (1937).
[38] J. R. Pierce, Theory and design of electron beams (D. Van Nostrand Company Inc., 1949).
[39] P. K. Ghosh, Ion Traps (Clarendon Press, Oxford, 1995).
[40] F. G. Major, V. N. Gheorghe, and G. Werth, Charged Particle Traps (Springer,
2005).
51
[41] L. S. Brown and G. Gabrielse, “Geonium theory: Physics of a single electron or
ion in a Penning trap,” Rev. Mod. Phys. 58, 233–311 (1986).
[42] L. S. Brown and G. Gabrielse, “Precision spectroscopy of a charged particle in
an imperfect Penning trap,” Phys. Rev. A 25, 2423–2425 (1982).
[43] M. Kretzschmar, “Single particle motion in a Penning trap: Description in the
Classical canonical formalism,” Phys. Scripta 46, 544 (1992).
[44] M. König, G. Bollen, H. J. Kluge, T. Otto, and J. Szerypo, “Quadrupole excitation of stored ion motion at the true cyclotron frequency,” Int. Jour. Mass Spec.
Ion Proc. 142, 95–116 (1995).
[45] F. Bloch, “Experiments on the g-factor of the electron,” Physica 19, 821–831
(1953).
[46] G. Bollen, R. Moore, G. Savard, and H. Stolzenberg, “The accuracy of heavyion mass measurements using time of flight ion cyclotron resonance in a Penning
trap,” J. Appl. Phys. 68, 4355 (1990).
[47] I. Bergström, In Proc. of Nobel Symposium 91 Lysekil, Sweden, August 1926, 1994, R. S. I. Bergström, C. Carlberg, ed., (World Scientific, Singapore,
1994).
[48] E. Beebe, L. Liljeby, Å. Engström, and M. Björkhage Physica Scripta 47, 470–
474 (1993).
[49] I. Bergström, M. Björkhage, H. Danared, H. Cederquist, T. Fritioff, L. Liljeby,
and R. Schuch, “Present status of the Stockholm electron beam ion source and
its scientific program,” In Electron Beam Ion Sources and Traps and Their
Applications: 8th International Symposium, K. Prelec, ed., (AIP Conference
Proceedings 572, Upton, New York, 2001).
[50] E. D. Donets, “USSR Inventor’s certificate No. 248860 16.03.(1967),” Bull.
OIPOTZ 24, 65 (1969).
[51] E. D. Donets, “Historical review of electron beam ion sources,” Rev. Sci. Phys.
69, 614 (1998).
[52] T. Fritioff, Phd thesis: Precision improvements of Penning trap mass measurements using highly charged ions (Stockholm University, 2002).
[53] G. Bollen, S. Becker, H. J. Kluge, M. König, R. B. Moore, T. Otto,
H. Raimbault-Hartmann, G. Savard, L. Schweikhard, and H. Stolzenberg,
“ISOLTRAP: a tandem Penning trap system for accurate on-line mass determination of short-lived isotopes,” Nucl. Instrum and Meth. A 368, 675–697
(1996).
52
[54] M. Suhonen, Licenciate thesis (Stockholm University, "to be published").
[55] R. T. Birge, “The calculation of errors by the method of least squares,” Phys.
Rev 40, 207 (1932).
[56] G. C. Rodrigues, M. A. Ourdane, J. Bieron, P. Indelicato, and E. Lindroth, “Relativistic and many-body effects on total binding energies of cesium ions,” Phys.
Rev. A 63, 012510 (2000).
[57] G. C. Rodrigues, P. Indelicato, J. P. Santos, P. Patté, and F. Parante, Atomic Data
and Nuclear Data Tables 86, 117 (2004).
[58] R. L. Kelly, J. Phys. Chem. Ref. Data 16, Suppl.1 (1987).
[59] J. H. Scofield, LLNL Internal Report UCID-16848 (1975).
[60] P. J. Mohr and B. N. Taylor, “CODATA recommended values of the fundamental
physical constants: 2002,” Rev. Mod. Phys. 77, 1–107 (2005).
[61] H. Borgenstrand, Phd thesis: An attempt to measure the proton mass using
a Penning trap and highly-charged ions (Stockholm University, 1997).
[62] M. Vogel, J. Alonso, S. Djekic, H.-J. Kluge, W. Quint, S. Stahl, J. Verdú, and G.
Werth, “Towards electronic g-factor measurements in medium-heavy hydrogenlike and lithium-like ions,” Nucl. Instrum. Meth. B 235, 7–16 (2005).
[63] G. Audi and A. H. Wapstra, “The 1995 update to the atomic mass evaluation,”
Nucl. Phys. A 595, 409–480 (1995).
[64] G. Audi, A. H. Wapstra, and C. Thibault, “The 2003 NUBASE Evaluation and
The 2003 Atomic Mass Evaluation,” Nucl. Phys. A 729, 1–676 (2003).
[65] S. W. Kikstra, C. V. D. Leun, P. M. Endt, J. G. L. Booten, A. G. M. van Hees,
and A. A. Wolters, “The 40 Ca level scheme investigated with the 39 K(p,γ )40 Ca
reaction,” Nucl. Phys. A 512, 425–465 (1990).
[66] T. P. Heavner, S. Jefferts, and G. H. Dunn, “Atomic mass of 6 Li using a Penningion-trap mass spectrometer,” Phys. Rev. A 64, 062504 (2001).
[67] P. J. J. Kok, K. Abrahams, H. Postma, and W. J. Huiskamp, “Investigation of
excited states of 7 Li by means of thermal neutron capture,” Nucl. Instrum. Meth.
B 12, 325 (1985).
[68] K. Blaum, Private communication, 2005.
[69] P. Spilling, H. Gruppelaar, H. F. de Vries, and A. M. J. Spits, “The reactions
12 C(n,γ )13 C and 19 F(n,γ )20 F,” Nucl. Phys. A 113, 395–411 (1968).
53
[70] A. M. F. Kamp and A. M. J. Spits, “Gamma rays from thermal-neutron capture
in natural and 39 K enriched potassium,” Nucl. Phys. A 180, 569–586 (1972).
[71] R. B. Firestone, R. M. Lindström, G. L. Molnar, S. M. M. A. V. R. Reddy, Z.
Revay, V. H. Tan, C. M. Zhou, and R. Paviotti-Corcuera, IAEA-Tecdoc (to be
published).
[72] T. Fritioff, C. Carlberg, G. Douysset, and I. Bergstr"om, “A new determination
of the 4 He and 3 He masses in a Penning trap,” Eur. Phys. J. D 15, 141–143
(2001).
[73] R. S. Van Dyck, Jr, Private communication, 2005.
[74] A. Solders, Licenciate thesis (Stockholm University, "to be published").
[75] G. Bollen, H. J. Kluge, T. Otto, G. Savard, and H. Stolzenberg, “Ramsey technique applied in a Penning trap mass spectrometer,” Nucl. Instr. and Meth. in
Phys. Res. B 70, 490–493 (1992).
[76] S. George, Diplomarbeit: Application of the Ramsey method in highprecision Penning trap mass spectrometry (Universität Münster, 2005).
54