Carbon-Cluster Mass Calibration at SHIPTRAP Ankur Chaudhuri, M.Sc

Carbon-cluster mass calibration at SHIPTRAP

Inaguraldissertation zur Erlangung des akademischen Grades doktor rerum naturalium (Dr. rer. nat) an der Mathematisch-Naturwissenschaftlichen Fakult¨at der Ernst-Moritz-Arndt-Universit¨atGreifswald

vorgelegt von

Ankur Chaudhuri, M.Sc.

geboren am 1. Juli, 1975 in Raigunj, Indien

Greifswald, 2007

Dekan: Prof. Dr. Klaus Fesser

1. Gutachter: Prof. Dr. Lutz Schweikhard Ernst-Moritz-Arndt-Universit¨atGreifswald

2. Gutachter: Prof. Dr. Kumar Satish Sharma University of Manitoba, Canada

Tag der Promotion: 10.12.2007

Abstract

A carbon-cluster ion source has been installed and tested at SHIPTRAP, the Penning-trap mass spectrometer for mass measurements of heavy elements at GSI/Darmstadt, Germany. A precision mass determination is carried out by measuring the ion cyclotron frequency ωc = qB/m, where q/m is the charge-to-mass ratio of the ion and B is the magnetic field. The mass of the ion of interest is obtained from the comparison of its cyclotron frequency ωc with that of a well-known reference ion. Carbon clusters are the mass reference of choice since the unified atomic mass unit is defined as 1/12 of the mass of the 12 12 C atom. Thus the masses of carbon clusters Cn, n=1,2,3,... are multiples of the unified atomic mass unit.

12 + Carbon-cluster ions Cn , 5 ≤ n ≤ 23, were produced by laser-induced desorption and ionization from a carbon sample. Carbon clusters of various 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + sizes ( C7 , C9 , C10, C11, C12, C15, C18, C19, C20) were used for an investigation of the accuracy of SHIPTRAP covering a mass range from 84 u to 240 u. To this end the clusters were used both as ions of interest and reference ions. Hence the true values of the frequency ratios are exactly known. The mass-dependent uncertainty was found to be negligible for the case of −8 (m−mref ) < 100 u. However, a systematic uncertainty of 4.5×10 was revealed.

In addition, carbon clusters were employed for the ﬁrst time as reference ions in an on-line studies of short-lived nuclei. Absolute mass measurements 144 146 147 12 + of the radionuclides Dy, Dy and Ho were performed using C11 as reference ion. The results agree with measurements during the same run using 85Rb+ as reference ion. The investigated radionuclides were produced in the fusion-evaporation reaction 92Mo (58Ni,xpyn) at SHIP (Separator for Heavy Ion reaction Products) at GSI. Among the measured nuclei 147Ho has the lowest half life (5.8 s). A relative mass uncertainty of 5 × 10−8 was obtained from the mass measurements using carbon clusters as calibrants.

Contents

1 Introduction 1

2 Radioactive ion beam facilities and mass measurements 3 2.1 Production and separation of radioactive nuclei ...... 3 2.1.1 The in-ﬂight separation method ...... 3 2.1.2 The ISOL method ...... 4 2.2 Mass-measurement techniques ...... 5 2.2.1 Penning trap mass spectrometry : Time-of-ﬂight Ion Cy- clotron Resonance (TOF-ICR) ...... 5 2.2.2 Revolution-frequency measurement at ESR ...... 5

3 Penning trap Theory 9 3.1 The ideal Penning trap ...... 9 3.2 The real Penning trap ...... 13 3.2.1 Imperfection of the electric-quadrupole ﬁeld ...... 13 3.2.2 Misalignment ...... 15 3.2.3 Magnetic ﬁeld inhomogeneity and temporal stability . . . . 15 3.2.4 Storage of more than one ion ...... 17 3.3 Excitation of the ion motion ...... 18 3.3.1 Dipolar excitation ...... 18 3.3.2 Quadrupolar excitation ...... 19

4 The SHIPTRAP experiment 21 4.1 Experimental set-up ...... 21 4.1.1 Stopping cell ...... 23 4.1.2 RFQ buncher ...... 26 4.1.3 Reference ion source ...... 27 4.1.4 Quadrupole deflector ...... 28 4.1.5 Penning traps ...... 29 4.2 Buffer-gas cooling and mass selection ...... 32 4.3 Time-of-flight Ion Cyclotron Resonance (TOF-ICR) detection technique ...... 35 ii CONTENTS

5 Carbon-cluster ion source 39 5.1 Motivation for a carbon-cluster ion source ...... 40 5.2 Experimental set-up ...... 41 5.3 Carbon-cluster ion source characterization ...... 43 5.3.1 Optimization of electrode voltages ...... 43 5.3.2 Energy spread of the ions ...... 47 5.4 Experimental procedure ...... 48 5.4.1 Timing sequence for measurement cycle ...... 48 5.4.2 Time-of-Flight mass spectrum ...... 49 5.4.3 Cooling resonance ...... 51 5.4.4 Cyclotron frequency determination of cluster ion ...... 51

6 Study of the accuracy of SHIPTRAP 55 6.1 Statistical uncertainty ...... 56 6.2 Count-rate-class analysis ...... 57 6.3 Time dependence of resonance frequencies ...... 59 6.4 Investigation of the systematic uncertainty of SHIPTRAP . . . . 61 6.4.1 Cross-reference measurements ...... 61 6.4.2 Mass-dependent systematic eﬀect ...... 63 6.4.3 Systematic uncertainty ...... 64 6.4.4 Summary ...... 65

7 On-line mass calibration by carbon-cluster ions 67 7.1 On-line mass measurements around A = 147 ...... 67 7.2 Carbon-cluster ions for oﬀ-line mass comparisons ...... 69 7.3 Carbon-cluster ions for on-line mass comparisons ...... 71 7.4 Discussions of mass measurements around A = 147 ...... 75 7.4.1 Two-neutron separation energies ...... 77 7.4.2 Proton separation energies ...... 78

8 Summary and Outlook 81

A Principles of Time-of-ﬂight mass spectrometry 83

B Values for used auxiliary data 85 List of Figures

2.1 Overview of the Separator for Heavy Ion reaction Product (SHIP) facility at GSI, Darmstadt...... 4 2.2 Overview of Experimental Storage Ring at GSI, Darmstadt . . . . 7

3.1 Schematic drawing of a hyperbolic Penning trap...... 10 3.2 Eigenmotions of ion inside a Penning trap...... 11 3.3 Eigenfrequencies of ion motion and parametric frequency (normalized to cyclotron frequency) as a function of trapping parameter. . 12 3.4 Relative magnetic ﬁeld deviation as a function of time measured at SHIPTRAP...... 17 3.5 Dipolar and Quadrupolar excitation scheme ...... 19 3.6 Conversion of the radial motions of ion in a Penning trap due to the external radiofrequency quadrupole excitation...... 20

4.1 Photograph of SHIPTRAP facility at GSI...... 22 4.2 Schematic layout of SHIPTRAP...... 23 4.3 Technical drawing of the SHIPTRAP set-up...... 24 4.4 Stopping cell and extraction RFQ of SHIPTRAP...... 25 4.5 Segmented RFQ cooler and buncher...... 26 4.6 Schematic diagram of the quadrupole deflector...... 27 4.7 Photograph of the quadrupole deflector...... 28 4.8 Schematic diagram of the SHIPTRAP Penning trap electrode system...... 31 4.9 Photograph of the SHIPTRAP Penning trap system...... 32 4.10 Ion motion in a buffer gas filled Penning trap...... 33 4.11 Schematic of the TOF-ICR detection technique...... 35 4.12 Theoretical line shape of time-of-flight ion cyclotron resonance. . . 36 4.13 Resonant and non-resonant ions in a time-of-flight ion cyclotron 12 + resonance of C11...... 38 5.1 Nuclear chart indicating reference ions ...... 40 5.2 Schematic diagram of carbon-cluster ion source...... 41 5.3 Photograph of carbon-cluster ion source at SHIPTRAP...... 42 iv LIST OF FIGURES

5.4 Photograph of rotatable sample-holder of carbon-cluster ion source. 42 5.5 Photograph of Sigradur°R target after and before laser ablation. . 43 5.6 Ion-optical simulation of cluster-source using Simion ...... 44 5.7 Ion counts from the cluster source as a function of extraction electrode voltage...... 46 5.8 Ion counts from the cluster source as a function of central electrode voltage...... 46 5.9 Ion counts from the cluster source as a function of outer electrodes voltage...... 47 5.10 Number of ions observed per laser pulse as a function of the blocking voltage at cluster source...... 48 5.11 Timing sequence of cluster measurement at SHIPTRAP...... 49 5.12 Typical time-of-flight (TOF) mass spectrum of carbon-cluster ions and some contaminants...... 50 5.13 Time-of-flight mass spectrum of carbon-cluster ions (A) without and (B) with dipolar and quadrupolar excitation...... 52 12 + 5.14 Cooling resonance of C11...... 53 12 + 5.15 Time-of-flight ion cyclotron resonance of C11...... 53 6.1 Determination of the constant c of equation 6.1...... 57 6.2 Count rate dependence of the observed cyclotron frequencies for 144Dy++ ions ...... 58 6.3 Count rate dependence of the observed cyclotron frequencies for 12 + C11 ions ...... 59 6.4 Interpolation of the cyclotron frequencies of reference ion . . . . . 60 6.5 Ideograms of all carbon-cluster cross-reference measurements. . . 62 6.6 Deviation of the weighted mean of the frequency ratios from the true values as a function of (m − mref )...... 63 6.7 Deviation of the weighted mean of the frequency ratios of different carbon clusters...... 65

7.1 Nuclear chart displaying measured radionuclides...... 68 7.2 Cooling resonance of isobars around A = 147...... 69 7.3 Time-of-ﬂight ion cyclotron resonance of 144Dy++, 146Dy++, and 147Ho++...... 72 7.4 Mass excess of 144Dy, 146Dy and 147Ho ...... 74 7.5 Two-neutron separation energies as a function of the neutron number...... 77 7.6 Chart of the nuclides showing the location of the proton drip-line. 79 List of Tables

4.1 Typical operating voltages of the quadrupole deflector...... 29 4.2 Typical voltages of different electrodes of the purification trap of SHIPTRAP...... 30 4.3 Typical voltages of different electrodes of the measurement trap of SHIPTRAP...... 30 4.4 Ion mobilities Kion for different ion and buffer-gas combinations. . 34 5.1 Voltages of different electrodes of the cluster ion source from the ion-optical simulation...... 45 5.2 Voltages of different electrodes of the cluster ion source after the optimization...... 45

6.1 Matrix of cross-reference measurements...... 61

7.1 Summary of the results of the off-line mass measurements of 133Cs and 85Rb...... 70 7.2 Comparison of the mass excess values from the off-line mass measurements of 133Cs and 85Rb...... 70 7.3 Summary of the results of the on-line mass measurements of 144Dy, 146Dy and 147Ho...... 73 7.4 Comparison of the mass excess values from the on-line mass measurements of 144Dy, 146Dy and 147Ho...... 73 7.5 Uncertainty in the frequency ratio due to the magnetic field changes. 75 7.6 Results of the atomic mass evaluation ...... 76 7.7 Proton separation energies of measured Ho and Tm isotopes. . . . 79

B.1 Values for used auxiliary data ...... 85

Chapter 1

Introduction

Precise mass measurements of atomic nuclei help to advance our understanding in several discipline of physics. By measuring the mass of a nuclide its binding energy can be precisely determined since proton and neutron masses are well- known. Thus, precise mass values of nuclei are an important parameter for the study of nuclear structure [Lunn03]. Nuclear astrophysics is another important discipline of physics in the context of high-precision mass measurements. For example, the study of the production of chemical elements in stellar nucleosynthesis needs precise mass values of radionuclides as input parameters for the reaction network calculation [Scha06]. Furthermore, the knowledge of the precise mass values supports stringent tests of fundamental symmetries such as the conserved vector current (CVC) hypothesis in super allowed β decays [Hard05]. However, the required accuracy of the mass value depends on the physics under investigation and generally varies from 10−5 to 10−11 [Blau06]. Today Penning traps are the most accurate tools for high-precision mass spectrometry [Schw06]. The pioneering work for the on-line mass measurement of short-lived nuclei using Penning trap started at ISOLTRAP/CERN [Stol90], [Boll96], [Mukh07]. Many other on-line Penning trap mass spectrometers have been installed world-wide following the success of the ISOLTRAP experiment. The currently working Penning trap mass spectrometers for the mass measurements of short-lived nuclei include CPT at the Argonne National Laboratory [Sava01], JYFLTRAP in University of Jyväskylä[Kohl04], LEBIT at the National Superconducting Cyclotron Laboratory at Michigan State University [Boll04a], and SHIPTRAP at GSI Darmstadt [Dill00]. Penning traps are also going to be used in many upcoming projects for mass measurements [Dill03], [Szer03], [Wada03]. Penning trap mass spectrometry reached relative uncertainties of 1 × 10−11 for stable nuclei [Rain04] and of 8 × 10−9 for radionuclides [Kell03], [Boll06] where the uncertainty is limited by the half-life of the investigated nuclide. Other than Penning trap experiments, the revolution frequency measurements at the storage ring facility at GSI Darmstadt [Fran87] plays an important role in 2 Introduction the context of the direct mass measurements of short-lived nuclei. SHIPTRAP is a Penning trap mass spectrometer which was set up at GSI, Darm- stadt for the investigation of transuranium nuclei and neutron-deficient nuclei in the medium-mass region. High-precision mass measurements of the radioactive ions produced in fusion-evaporation reactions at the in-flight facility SHIP at GSI is the primary goal of SHIPTRAP. It is one of the pioneering installations aiming for direct high-precision mass measurements of super-heavy elements. Further- more, other experiments at low energy such as ion-chemical reactions and in-trap decay experiments on heavy ions are also planned at SHIPTRAP. The energy of the SHIP beam is very large in comparison to that of other on-line Penning trap experiments like ISOLTRAP or JYFLTRAP. The necessity of a gas-stopping cell in this production scheme results in additional problems, which make this experiment even more challenging. For a high-precision mass spectrometer like SHIPTRAP, it is essential to study the limit of the mass-accuracy. A carbon-cluster ion source was designed and installed at SHIPTRAP for this purpose in the framework of this thesis. A large number of comparative measurements between laser-produced carbon-cluster species of different sizes (known as cross-reference measurements) have been performed to determine the accuracy and reveal the systematic uncertainty of the SHIPTRAP mass spectrometer. The accuracy of SHIPTRAP is experimentally determined for the first time by the present work. 12 Carbon cluster ions Cn, n=1,2,3,... are the ideal species for mass calibration, since the unified atomic mass unit is defined as 1/12 of the mass of the 12C atom. Thus, the masses of carbon clusters are multiples of the unified atomic mass unit. The molecular binding energy per atom of few eV can be neglected at the present state of accuracy. In the course of this study carbon-cluster ions were used for the first time as reference ions in an on-line mass measurement, namely during an experiment on the radionuclides 144Dy, 146Dy and 147Ho. The results agree well with the those where 85Rb was used as reference. In chapter 2 of this thesis different production schemes and mass measurement techniques of radioactive nuclei are discussed. Chapter 3 gives an account of the theory of Penning trap. An overview of the SHIPTRAP experiment is given in chapter 4. Chapter 5 gives an account of the experimental set-up, optimization and experimental procedure involving the carbon-cluster ion source. The measurements and analysis for the determination of the accuracy of SHIPTRAP are explained in chapter 6. The first absolute mass measurement of the short-lived nuclei using carbon cluster as reference is presented in chapter 7. The results and discussion about the on-line mass measurements around A = 147 at SHIPTRAP are also described in the same chapter. Chapter 2

Radioactive ion beam facilities and mass measurements

2.1 Production and separation of radioactive nuclei

In recent years the availability of radioactive ion beams has facilitated the investigation of the structure and dynamics of nuclear species studied in the laboratory. Radioactive ion beams of energies ranging from a few 10 keV to the relativistic regime are produced in the laboratory by various nuclear reactions with an energetic primary beam impinging a target. There are different production mechanism for the creation of exotic nuclei: fusion-evaporation, fission, projectile fragmentation, spallation and nuclear transfer reaction. In all these mechanisms not only the nuclide of interest but also other contaminant nuclei are produced. Hence mass separation is crucial. The method depends on the production mechanism. There are two complementary methods available, the in- flight separation technique and the Isotope Separation On-Line (ISOL) technique. In the following, these two techniques are briefly discussed. A More detailed discussion about the radioactive ion beam production and the separation of reaction products from the primary beam can be found in [Geis95].

2.1.1 The in-flight separation method During the past three decades the velocity filter SHIP (Separator for Heavy Ion reaction Products) at GSI has been used for in-flight separation of neutron deficient nuclei of intermediate and heavy masses. The primary beam is an ion beam at an energy of 3-6 MeV/u. It impinges a thin target (typically 500 µg/cm2) to initiate fusion evaporation reactions forming compound nuclei which recoil out of the target while evaporating a few neutrons or protons or α particles. Since the target used is thin the reaction products penetrate the ion-optical system 4 Radioactive ion beam facilities and mass measurements with high velocity. A combination of electric and magnetic fields which are or- thogonal to each other is applied for in-flight separation. For example, a Wien filter consisting of electric deflectors and dipole magnets as shown in figure 2.1 is used at the SHIP facility at GSI. It allows a separation of ions according to the velocity, independent of the mass-to-charge ratio. However, reaction products at relativistic energies are isotopically separated by magnetic dipoles. The projectile Fragment Separator (FRS) at GSI is an example of this technique. A detailed overview of FRS can be found in [Geis92] and of the SHIP separator in [Munz79], [Hofm00]. Separation of the primary beam and the reaction products is the main feature of such in-flight separator. A major advantage of this method is that the limits in half-lives for the nuclei of the separated secondary beam are given only by the time-of flight through the ion-optical system. It is typically in the order of a few microseconds.

TO SHIPTRAP

TOF- Si- ELECTRIC DETECTORS DETECTORS FIELD

BEAM TARGET STOP WHEEL MAGNETS

QUADRUPOLE PROJECTILES LENSES FROMUNILAC

Figure 2.1: Overview of the Separator for Heavy Ion reaction Product (SHIP) facility at GSI, Darmstadt.

2.1.2 The ISOL method The ISOL (Isotope Separation On-Line) method for the production and sepa- rations of radioactive nuclei is a widely applied technique. A typical example is the ISOLDE (Isotope Separator On-Line DEvice) [Kugl00] facility at CERN, Geneva. A high-energy proton beam with energies around 1 GeV or light ion 2.2 Mass-measurement techniques 5 beam with a few 100 MeV/u impinges a target which is thick enough to stop the products. The target material and its thickness is selected depending upon the nuclide of interest. The target is usually contained in a tantalum cylinder which is heated to 1000-2000K. This causes the radioactive products to evapo- rate and diffuse into an ion source. The atoms are ionized in the ion source by either surface, plasma or laser ionization. The ion source is an important part for the on-line purification process. A special combination of target-ion source is developed in order to obtain the ion beam of the isotopes of a particular element of interest. Isobaric contamination can be suppressed by, e.g. element-specific ionization like resonant laser ionization. The ions are electrostatically accelerated up to typically 60 keV at ISOLDE. They fly through a magnetic field for isotopic (mass) separation. About 600 isotopes of more than 60 elements can be produced via proton induced spallation and fission.

2.2 Mass-measurement techniques

Nuclear masses can be determined employing various techniques. The so-called indirect techniques involve the mass determination from nuclear reaction or radioactive decay. The mass of a unknown nulide can be determined by measuring the Q-value or by detecting the kinematics of the reaction products of a nuclear reaction [Peni01]. Radioactive decay Q-values also provide the mass difference between the parent and the daughter nuclei. Mass values can be derived by link- ing these mass difference to a known mass [Lunn03]. A recent example is given by [Bart03]. The direct mass measurements are performed either with storage rings or with Penning traps. In the following, different principles for direct mass measurements are briefly outlined.

2.2.1 Penning trap mass spectrometry : Time-of-flight Ion Cyclotron Resonance (TOF-ICR) Penning trap mass spectrometry with time-of-flight cyclotron resonance detection technique has been used as the most accurate tool for high-precision mass measurements. This technique involves the cyclotron-frequency measurement of an ion in a magnetic field. The TOF-ICR technique is employed in the SHIP- TRAP experiment for the high-precision mass measurement. The method and theory will be discussed in detail in section 4.3.

2.2.2 Revolution-frequency measurement at ESR A combination of a heavy ion synchrotron (SIS), a fragment separator (FRS) [Geis92] and an experimental storage ring (ESR) [Fran87] provides the opportunity of mass measurements of exotic nuclei at GSI, Darmstadt. Stable-isotope 6 Radioactive ion beam facilities and mass measurements ions which are accelerated in SIS, hit a target at the entrance of the FRS, where exotic nuclei are produced by in-flight projectile fragmentation. Fragments having a narrow band of magnetic rigidity are selected and transported to the ESR (shown in figure 2.2) which is used for storing exotic nuclei. Two complementary methods are used for the precise mass measurements of stored ions circulating in ESR: (1) Schottky mode and (2) Isochronous mode. Both principles can be understood from the first order relations between the mass-to-charge ratio m/q, the revolution frequency f and the velocity v of the ion [Rado00], [Geis01],

∆(m/q) ∆f ∆v | |= γ 2 | | +(γ 2 − γ2) | | . (2.1) (m/q) t f t v

Here γ is relativistic Lorentz factor and γt is a dimensionless parameter which characterizes the ion-optical mode of the ring. From equation 2.1 it is obvious that either the cooling of ions (∆v → 0) or the isochronous condition (γ → γt) is the basis of precise mass measurements.

(A) Schottky mode By means of electron cooling the velocity spread ∆v of the stored ions can be minimized. An electron cooler included at ESR (as shown in figure 2.2) allows to decrease ∆v/v to 10−6 in a few seconds [Geis01]. This results in the revolution frequency of the stored ions to be directly dependent on the mass-to-charge ratio. Schottky noise spectroscopy [Bore74] is used for non-destructive beam diagnosis in storage rings. The stored highly-charged ions, circulating in the ESR with revolution frequencies of about 2 MHz, induce a mirror charge on electrostatic pick-up electrodes installed in the ring at each turn [Rado00]. These noises induced by the stored circulating ions are recorded and analyzed. The location of the Schottky pick-up system at ESR is schematically shown in figure 2.2. The revolution frequency is obtained from a Fourier transform of the time-dependent signal and hence, the mass-to-charge ratio of the ion can be determined using equation 2.1. A mass resolving power of about 7 × 105 has been achieved by this method [Geis01]. The Schottky mass measurement technique is very effective for a broad mass mapping of exotic nuclei since about 50 masses can be determined simultaneously. This technique is presently limited to nuclei with lifetimes of at least a few seconds, as this is the time needed for electron cooling.

(B) Isochronous mode A complementary technique for the mass measurement of uncooled short-lived nuclei using the storage ring is the isochronous mass spectrometry where γ → γt [Geis01]. This technique requires a properly adjusted ion-optics mode where the revolution frequency of the stored ion does not depend upon its velocity but 2.2 Mass-measurement techniques 7

Figure 2.2: Overview of Experimental Storage Ring at GSI, Darmstadt [Litv03].

only on the mass-to-charge ratio. The revolution periods for individual stored ions are measured by a time-of-flight technique for many turns of the ions in the ring, typically 100-1000 turns resulting in a time-of-flight path 10-100 km. A mass resolving power of only about 105 is typically achieved [Geis01] but very short-lived nuclei can be investigated as the total flight time is in the order of few micro-seconds.

The ESR measurements have achieved a relative mass uncertainty of 2 × 10−7 [Litv03]. However, this technique can not compete with Penning trap mass spectrometry concerning the mass accuracy, where a relative mass uncertainty of 8 × 10−9 has been already achieved in on-line mass measurement of short-lived nuclei [Boll06].

Chapter 3

Penning trap Theory

In recent years Penning traps have been widely used as very accurate tool for high- precision mass spectrometry [Schw06], [Blau06]. A charged particle is confined inside a Penning trap by the combination of a strong homogeneous magnetic field and a super-imposed quadrupolar electric field. The magnetic field provides the radial and the electric field provides the axial confinement of the charged particle. The ability to trap the charged particle in a small volume in a well-defined field is the key feature of the Penning trap which makes it most useful for a precision experiment like mass measurements. In this chapter a short introduction to the theory and the techniques used in Penning trap mass spectrometry are given. More detailed descriptions can be found in [Brow86], [Boll90], [Boll04], [Ghos95], [Gheo04].

3.1 The ideal Penning trap

An ideal Penning trap is accomplished by combining a homogeneous magnetic field B~ = Bzˆ and a quadrupolar electric potential U(z, r) as shown in figure 3.1. Let us first assume there is no electric field present. An ion with charge- to-mass ratio q/m in the magnetic field B~ = Bzˆ and with a velocity component v perpendicular to the direction of magnetic field, experiences a Lorentz force ~ ~ FL = q~v × B. This force generates a radial confinement of the ion. As a result the ion performs a circular motion with the cyclotron frequency

q ω = B. (3.1) c m

However, there is no binding along the direction of magnetic field line. Hence the ion will escape if it has any velocity component in this direction. Axial confinement in a Penning trap is achieved by applying a voltage difference U0 between the end caps and the ring electrode of a trap (as shown in figure 3.1) 10 Penning trap Theory

z upper calotte

ring electrode r0 U0 z0

lower calotte

Figure 3.1: Schematic drawing of a hyperbolic Penning trap.

which produces a quadrupolar electric potential U µ 1 ¶ U (z, r) = 0 z2 − r2 . (3.2) 2d2 2 The parameter d is known as characteristic trap dimension and it is given by, Ã ! 1 r2 d2 = z2 + 0 , (3.3) 2 0 2 where r0 is the inner ring radius and 2z0 is the closest distance between the two end caps. The electric field components are given by U µ U ¶ E = − 0 z and E~ = 0 ~r. (3.4) z d2 r 2d2 In such an ideal electric and magnetic field configuration the equations of motions of an ion are ³ ´ ¨ ~ ˙ ~ mz¨ = qEz and m~r = q Er + ~r × B . (3.5) Solving these equation of motions results in three motional modes. These are known as the axial oscillation, the magnetron motion and the cyclotron motion as shown in figure 3.2. These three motions are independent oscillations with the 3.1 The ideal Penning trap 11

axial (z)

magnetron (-) cyclotron (+)

Figure 3.2: Schematic drawing of the Eigenmotions of a single ion inside a Penning trap.

following eigenfrequencies, s s qU ω ω2 ω2 ω = 0 and ω = c ± c − z , (3.6) z md2 ± 2 4 2 where ωz, ω− and ω+ are known as axial frequency, magnetron frequency and modiﬁed cyclotron frequency, respectively. The position of an ion in a Penning trap can be described by

x = ρ+cos(ω+t + φ+) + ρ−cos(ω−t + φ−) (3.7)

y = ρ+sin(ω+t + φ+) + ρ−sin(ω−t + φ−) (3.8)

z = ρzcos(ωzt + φz), (3.9) where ρ+,−,z are the amplitudes of the radial and axial motions and φ+,−,z are the corresponding phases. 2 2 For the condition ωc − 2ωz ≥ 0 the real root of equation 3.6 leads to a stable trajectory of the ion inside a Penning trap. Using equations 3.1 and 3.6, this condition may be rewritten as,

d2 B2 m/q ≤ (m/q)crit = , (3.10) 2 U0 12 Penning trap Theory

where (m/q)crit is the critical mass-over-charge. The critical condition may also be expressed by introducing a dimensionless trapping parameter [Schw95]

2 ωz m 2U0 πtrap = 2 2 = 2 2 . (3.11) ωc q d B

Stable radial motion corresponds to the condition 0 < πtrap < 1. Figure 3.3

Figure 3.3: Eigenfrequencies of ion motion ν+, ν−, νz and parametric frequency νp (normalized to cyclotron frequency) as a function of trapping parameter πtrap [Schw95].

shows the eigenfrequencies of the three modes of ion motion (ν+, ν−, νz) and radial parametric frequency νp = ν+ − ν− as a function of the stability parameter πtrap.

For the typical operating conditions of a Penning trap, i.e. very strong magnetic ﬁeld and weak electric potential, the magnitude of the eigenfrequencies follow the order ω− < ωz < ω+. (3.12)

Assuming ωc >> ωz and expanding the root for the radial eigenfrequencies (equation 3.6) to ﬁrst order yields U ω ≈ 0 (3.13) − 2d2B 3.2 The real Penning trap 13

U ω ≈ ω − 0 , (3.14) + c 2d2B which shows that the magnetron frequency is approximately independent of the mass and charge of the ion. Other relations between the eigenfrequencies and the cyclotron frequency (independent of any approximation) are

ωc = ω+ + ω−, (3.15) 2 2 2 2 ωc = ω+ + ω− + ωz (3.16) and

2 2ω+ω− = ωz . (3.17)

Equation 3.15 plays a key role in context of the high-precision mass measurement with Penning traps. The direct determination of the sum of the radial eigenfrequencies allows to determine the mass of the ion as long as the magnetic ﬁeld strength B and the charge state of the ion q are known (equation 3.1). Equation 3.16 is the so-called invariance theorem [Brow86], since this relation is also valid in case of the ‘real Penning trap’ (section 3.2).

3.2 The real Penning trap

A real Penning trap deviates from the ideal one as described above in many aspects. Electric-quadruple field imperfection, misalignment of the trap axis with respect to magnetic field axis, magnetic field inhomogeneity etc. lead to shifts in the eigenfrequencies and hence, to systematic uncertainties in the mass determination. Accurate knowledge of these trap imperfections and their influences is essential to design a Penning trap mass spectrometer and to apply correction potential at shim electrodes. Such knowledge is also important to understand the systematic uncertainties in the mass determination. The most important trap imperfections are briefly described in the following subsections. More detailed discussions can be found in [Brow86], [Boll90]and [Boll96].

3.2.1 Imperfection of the electric-quadrupole field Electric-quadrupole field imperfections are the deviations from the pure electric- quadrupole field as defined by equation 3.2. They occur due to the geometrical imperfections of the trap construction such as holes in the end caps for injection and ejection of the ions or from the unavoidable truncation of the electrodes. De- viations from the ideal electric-quadrupolar field are commonly expressed in terms of multipole expansions of the trapping potential. Frequency shifts caused by the 14 Penning trap Theory octupole and dodecapole contributions have been calculated [Brow86],[Boll90]. elec For the sum frequency ωc = ω+ + ω− the frequency shift ∆ωc depends on the amplitudes ρ+, ρ− and ρz of the reduced cyclotron, the magnetron and the axial oscillation, respectively:

µ3 C 15 C ¶ ∆ωelec = Ωelec 4 (ρ2 − ρ2 ) + 6 (ρ2(ρ2 − ρ2 ) − (ρ4 − ρ4 )) , (3.18) c c 2 d2 − + 4 d4 z − + − + with elec ω− U0 Ωc = ≈ ω− ≈ 2 . (3.19) 1 − ω−/ω+ 2d B

C4 and C6 are the coefficients of the octupole and dodecapole components of the electric field. As it is seen from equations 3.18 and 3.19, the frequency shifts due to electric-quadrupole field imperfections can be minimized by using a trap with a large characteristic dimension d, a small trap potential U0 and by using cold ions with small motional amplitudes ρ+, ρ− and ρz. In addition, the frequency shift can be further reduced by omitting or correct- ing for sources of higher multipole terms (i.e. by minimizing C4 and C6). To this end, correction(shim) electrodes are added to the Penning trap configuration.

elec elec The frequency shift ∆ωc is practically mass independent since Ωc is to ﬁrst order mass independent (equation 3.19). It gives rise to a calibration error in the mass determination due to the use of a reference ion of mass mref for the magnetic ﬁeld calibration. The mass calibration issue is addressed in section 4.3. The relative mass-dependent uncertainty of an ion of mass m and cyclotron frequency ωc is given by [Boll96],

∆m ∆ωc(m − mref ) = ∝ (m − mref ). (3.20) m ωcm Hence, for the highest accuracy it is desired to have the mass of the reference ion as close as possible to the mass of the ion of interest. The ultimate solution is to use mass doublets i.e. mref ≈ m but in most cases such reference ions are not available or their masses are not known well enough. In this context, carbon 12 clusters Cn, n = 1, 2, 3, ... are the mass reference of choice. The use of carbon clusters as reference ion at SHIPTRAP is discussed in detail in the chapter 5.

The induced image charge of ions on the trap electrodes can give rise to another source of electric ﬁeld imperfections. The corresponding frequency shift scales inversely with the cube of the trap dimension. Hence, it is more pronounced in the case of small traps [Dyck89]. However, in case of SHIPTRAP, where the sum frequency ωc = ω+ + ω− is directly determined, no frequency shift will occur since ∆ω+ ≈ −∆ω− [Boll90]. 3.2 The real Penning trap 15

3.2.2 Misalignment A misalignment of the axis of the electrostatic trapping field with respect to magnetic field axis can give rise to a systematic error in the mass determination. Such a tilting shifts all the eigenfrequencies of the ion motion in a Penning trap. For the case of a small tilting angle, i.e. Θ << 1, the frequency shift due to the misalignment is [Brow86], 9 ∆ωtilt ≈ ω sin2Θ, (3.21) c 4 − where ω− is the magnetron frequency of the ion, and Θ is the tilt angle between the trap axis and the magnetic field.

The frequency shift is to ﬁrst order mass independent, but it gives rise to a systematic mass-dependent uncertainty in the mass determination as shown in equation 3.20. Therefore, the trap has to be aligned very carefully with respect to the magnetic ﬁeld axis. For example, a tilt angle of one milliradian corresponds to a relative shift of cyclotron frequency of 7 × 10−9 for an ion with A = 250 in case of SHIPTRAP [Bloc07].

3.2.3 Magnetic field inhomogeneity and temporal stability A high-precision mass measurement via a cyclotron resonance requires a high homogeneity and temporal stability of the magnetic field. The homogeneity of the magnetic field can easily be destroyed if materials with high magnetic susceptibility are introduced. Therefore, only materials with low susceptibility are used for the trap construction. Usually oxygen-free high-conductivity (OHFC) copper and glass ceramics are used. Nevertheless their susceptibilities are high enough for noticeable perturbations in the magnetic field. A stored ion experiences different average magnetic fields for different amplitudes of its motion. The lowest order inhomogeneity of interest is a magnetic hexapole component β2. It creates a frequency shift [Boll90]

magn 2 2 ∆ωc ≈ β2ωc(ρz − ρ−). (3.22) In contrast to the frequency shifts discussed for the imperfection of eletric- magn quadrupole ﬁeld ∆ωc is proportional to the cyclotron frequency of the stored ion. Hence, it does not give rise to a mass-dependent uncertainty provided the amplitudes of ion motion are equal for both the ion of interest and the reference ion. Since this can only be achieved within certain limits, it is very important to construct the trap such that the inhomogeneity is suﬃciently small. The intrinsic homogeneity of the SHIPTRAP super-conducting magnet in the region of the measurement trap center was measured to be ∆B/B = 10−7 over a volume 16 Penning trap Theory of 1 cm3 [Bloc07].

Temporal instability of the magnetic field is another point of concern in the context of high-precision mass determination. The magnetic field strength of a super-conducting magnet can be changed by different mechanisms:

1. The current in a super-conducting magnet is reduced steadily due to a phenomenon called ﬂux creep [Ande62], [Ande64]. The decrease of the magnetic ﬁeld strength follows a logarithmic decay. This logarithmic decay can be approximated by a linear decrease for long periods up to years.

2. The magnetic susceptibility of any material depends on its temperature. The temperature of the bore of the super-conducting magnet ﬂuctuates with the temperature of the experiment hall. Hence, the magnetic susceptibility of the material surrounding the Penning trap, such as the stainless-steel vacuum chamber, varies with temperature as well. Thus, the magnetic ﬁeld sensed by the trapped ions varies with the temperature of the experiment hall.

3. Pressure changes in the cryostat of the super-conducting magnet change the boiling point of liquid helium. Thus, the magnetic susceptibility of all materials inside the liquid helium bath changes which leads to a variation of the magnetic ﬁeld strength.

4. Any change in the ambient magnetic field, which are unavoidable in an accelerator laboratory, changes the field of the super-conducting magnet. For example, massive objects like crane in the experimental hall can cause significant variation of the magnetic field.

The demand for the magnetic field stability is determined by the desired mass accuracy and by the time needed to switch between the cyclotron frequency measurements of the reference ion and the ion of interest. For SHIPTRAP the stability of the magnetic field has been measured during a period of two days and the resultant magnetic field fluctuation ∆B/B is plotted in figure 3.4, where ∆B = (B − B0) and B0 is the weighted mean of the measured value of magnetic field B. A steady decrease as well as superimposed random fluctuations over short periods is observed. The slope of the slow decay is indicated by the dashed ∆B 1 −9 line and can be approximated by B × ∆t = −7 × 10 /h [Bloc07]. 3.2 The real Penning trap 17

-7

4.0x10

-7

3.0x10

-7

2.0x10

-7

1.0x10

0.0 B/B

-7

-1.0x10

-7

-2.0x10

-7

-3.0x10

0.0 0.5 1.0 1.5 2.0

time / days

Figure 3.4: Relative magnetic ﬁeld deviation as a function of time measured at SHIPTRAP. The line represents a linear least-squares ﬁt to the data. [Bloc07].

3.2.4 Storage of more than one ion

Ideally in a high-precision mass measurement there should be only a single ion stored in the Penning trap at a time. In SHIPTRAP, the cyclotron frequency measurement is performed with typically more than one ion in the precision trap. Hence, the effect of the Coulomb interaction on the ion motion must be taken into account to obtain the accurate cyclotron frequency. There will be no shift of the observed cyclotron or magnetron frequencies if the electric field used to excite or detect the ion motion interacts only through the center of mass of the ion cloud [Jeff83], [Boll90]. However, the presence of contaminant ions having ch different masses causes a frequency shift ∆ωc in the observed resonance. The effect of Coulomb interaction on the ion motion in a Penning trap has been in- ch vestigated in [Boll92], [Gabr93]. It was found that the sign of ∆ωc depends on the cyclotron frequency difference of the stored ion species compared to the ch line-width of the resonances. ∆ωc increases with the total number of trapped ions. In case the unperturbed resonances cannot be resolved, only a single resonance is observed, which is narrower than expected for a simple superposition of the individual resonances. The position of the resonance is determined by the average mass of all ions stored in the trap. In case of large mass difference between the trapped ion species, the measured cyclotron frequency of both species shift to lower frequencies. The size of the res- 18 Penning trap Theory onance shift for one species is found to be proportional to the number of trapped ions of the other species and vice versa. A quantitative description of the observed frequency shifts must take into account the coupling of all eigenmotions by Coulomb interaction. Until now no general analytical solution has been found for the equation of motion of several ions in a Penning trap. Nevertheless, it is possible to confirm the observations qualitatively by a three-dimensional simulation of the motion of simultaneously stored ions [Boll92]. In practice, it is therefore required to have a pure ion sample stored in the trap. If this is not possible, a careful analysis of the frequency shift has to be performed. To this end, the cyclotron frequency is extrapolated to a single stored ion in the trap, by analyzing the cyclotron frequencies for different numbers of stored ions (so-called count-rate-class analysis, discussed in section 6.2) [Kell03].

3.3 Excitation of the ion motion

The resonant excitation of the ion motion inside a Penning trap is crucial in order to determine the cyclotron frequency of a stored ion, to selectively remove unwanted ion species from the trap, for counteracting the effect of ion loss via a growing magnetron radius or during the buffer-gas cooling in a Penning trap. Ion- trajectory manipulation is achieved by driving the ion motion with an external radio-frequency (RF) electric field. The effect on the ion motion depends on the multi-polarity and the frequency of the driving field. For SHIPTRAP dipolar and quadrupolar RF fields in the radial plane are in use which are described briefly in the following sections. A detailed discussion can be found in [Boll90], [Koni95].

3.3.1 Dipolar excitation The ion motions can be excited at one of the eigenfrequencies by applying a dipolar RF field. A dipole field created by an RF voltage with amplitude Ud o and with frequency ωd applied with 180 phase difference between two opposing segments of the ring electrode (figure 3.5a) drives one of the radial motions if the corresponding frequency is used. The resulting potential includes a dipolar term

Ud Φd = a1 · cos (ωdt − φd) · x, (3.23) r0 where a1 is a geometric factor that includes the effect of the segmentation of the ring electrode. This type of excitation applied at any radial eigenfrequency can excite that eigenmotion almost without affecting the other. An increase of the amplitude of the eigenmotions is achieved in resonance for all modes, but the initial behavior depends on the initial position and velocity of the ion and the phase of the applied RF field. A dipole excitation at ω+ can be used at SHIPTRAP for removing unwanted species from the trap. If it is desired to 3.3 Excitation of the ion motion 19

-Uq

r r

+U -U +U d d q r +Uq r0 0

-Uq Figure 3.5: Dipolar radiofrequecy excitation applied to two opposite segments of ring electrode (a). Quadrupolar radiofrequency excitation applied to four segments of the ring electrode (b).

enlarge the magnetron radius of all ions simultaneously, a dipole excitation at ω− is applied which is practically mass-independent (see section 3.1).

3.3.2 Quadrupolar excitation Another important multipolar excitation used for the ion manipulation in a Pen- ning trap is the quadrupolar excitation. The most important case in the context of Penning trap mass spectrometry of short-lived nuclei is to excite the ion motion at the sum frequency ωc = ω++ω− which corresponds to a coupling of the reduced cyclotron oscillation and the magnetron oscillation. To this end, an azimuthal quadrupolar potential is required which can be approximated experimentally by the conﬁguration shown in ﬁgure 3.5b. It has the form

Uq 2 2 Φq = a2 2 · cos (ωqt − φq) · (x − y ), (3.24) r0 where a2 is the geometric factor originating from the shape of the electrode segment. This type of excitation is also known as side-band excitation and couples both radial oscillations. In ﬁgure 3.6, the eﬀect of the applied quadrupolar excitation at ωq = ωc on the radial ion motion is shown. In this example, the motion starts with a pure magnetron motion (a), indicated by the circle, and, as a consequence of the excitation, converts fully to cyclotron motion (b) in time Tconv = π/ωconv. There is a continuous conversion at a frequency ωconv between the two radial motions. A full conversion takes place at ωq = ωc. The conversion frequency ωconv 20 Penning trap Theory

(a) (b)

Figure 3.6: Radial motion with a quadrupolar excitation at ωq = ωc . The motion starts with pure magnetron motion (a), indicated by the circle, and converts fully to cyclotron motion (b) in time Tconv [Boll96].

is proportional to the amplitude of the applied RF ﬁeld,

a2 q Uq ωconv = · · 2 . (3.25) 2(ω+ − ω−) m r0

The dipolar and quadrupolar fields necessary for the manipulation of the ion motional modes can be achieved by segmenting the ring electrodes of the Penning trap in the azimuthal plane and application of the respective potentials as already discussed and shown in figure 3.5. Two and four-fold segments are necessary for dipolar and quadrupolar excitation, respectively. The ring electrode of the Penning traps of SHIPTRAP is split into eight segments (described in section 4.1.5) which allows to manipulate ions also with a octupolar fields [Elis07]. Chapter 4

The SHIPTRAP experiment

SHIPTRAP is a Penning-trap mass spectrometer for precision mass measurements of heavy radionuclides at GSI [Dill00], [Marx03], [Sikl03]. It has been built in particular to enable the investigation of transuranium nuclides and other neutron-deﬁcient nuclides in the medium mass region which are not accessible at ISOL or fragmentation facilities. Most of the masses of transfermium nuclei are only known with an uncertainty of few hundred keV from the extrapolation of systematic trends [Audi03]. The nuclear binding energy, an important parameter for the study of nuclear structure, can be determined from the mass. Mass measurements of rare-earth nuclei at the proton drip line [Raut07] and of medium-heavy nuclei related to the astrophysical rp process [Voro06] have been started at SHIPTRAP after the completion of on-line commissioning in July 2004 [Raha06a]. In the future laser spectroscopy, ion-chemical reactions and in-trap decay experiments on heavy ions are also planned to be performed at SHIPTRAP [Dill00].

4.1 Experimental set-up

Figure 4.1 shows a photograph of the SHIPTRAP facility at GSI. A schematic drawing of the SHIPTRAP experimental set-up is shown in figure 4.2 and a more detailed technical drawing in figure 4.3. Radioactive nuclei produced in fusion-evaporation reactions and separated by the velocity filter SHIP are delivered with a typical energy of a few 100 keV/u. They are stopped and thermalized inside a He buffer-gas stopping cell at a pressure of 50 mbar (part (1) in figure 4.1) [Neum06]. The ions are extracted from the stopping cell by a combination of gas flow and electrical fields. The subsequent section is an extraction RF quadrupole (RFQ) [Neum06] which allows for differential pumping and operates as ion guide. It transports the ions to the next section, a helium gas-filled RFQ cooler and buncher. The ions are cooled, accumulated and bunched and then extracted as a low-emittance bunched beam enhancing 22 The SHIPTRAP experiment the efficient injection of ions into the Penning traps. Two cylindrical Penning

Figure 4.1: Photograph of SHIPTRAP facility at GSI. Positions of diﬀerent components of SHIPTRAP are marked in the photograph: (1) Stopping cell, (2) extraction RFQ, (3) RFQ buncher, (4) puriﬁcation trap and (5) measurement trap.

traps within a 7-T super-conducting magnet are used for high-precision mass measurements. The ions are injected into the first Penning trap where the sample is purified by mass-selective buffer-gas cooling (section 4.2). The mass-selected ions are transferred into the measurement trap where the precision mass spectrometry is performed by measuring the cyclotron frequency, ωc, by a time-of-flight detection method (section 4.3). The magnetic field is calibrated using reference ions of well-known masses.

The diﬀerent components of SHIPTRAP are brieﬂy described in this chapter. 4.1 Experimental set-up 23

GasCell Buncher Penning Traps SHIP Surface ionbeam ionsource Quadrupole Entrance deflector Diaphragm window Measurementtrap

MCP-detector

Extraction Laser RFQ beam Purificationtrap

DCcage RFfunnel Carbon-cluster ionsource Superconducting magnet

Figure 4.2: Schematic layout of SHIPTRAP.

4.1.1 Stopping cell

The energy (∼ MeV) of the reaction products from SHIP is much larger than the low injection energy (∼ eV) required for the Penning trap of SHIPTRAP. An ion-catcher device [Neum06] consisting of a buﬀer-gas stopping cell and a radio-frequency quadrupole (RFQ) provides a novel approach to the production of low-energy ion beams for SHIPTRAP. The gas cell is designed to stop heavy-ion beams with a diameter of up to 50 mm and with energies between 500 and 1000 keV/u. The reaction products are slowed down and thermalized in collisions with helium atoms. High-purity (grade 4.6: purity 99.996% or grade 6: purity 99.9999%) helium is used in the gas cell because of its high ionization potential and thus for preventing the charge-exchange reactions. Figure 4.4 shows the stopping cell together with the extraction RFQ. They are connected by a nozzle with an inner diameter of about 0.6 mm. The stopping cell has a total length of 320 mm and a diameter of 250 mm. The reaction products from SHIP enter the stopping cell through a thin metal foil at the entrance window which serves as main degrader. Pinhole-free, ultra-high vacuum compatible and bakable foils are available typically from light metals like aluminium and titanium. Hence in reality there are not many choices for the material of window foils. Typically titanium foils with a thickness about 4 µm are used at SHIPTRAP. The window foil is supported by a grid of wires since it maintains the high pressure diﬀerence between the stopping cell (∼ 50 mbar) and the vacuum of the SHIP beam line (∼ 10−6 mbar). The remaining energy of the reaction products is dissipated in the helium gas. 24 The SHIPTRAP experiment STOPPING CHAMBER Turbopump 400l/s EXTRACTION Turbopump RFQ 1600l/s TRANSFER LENSES PUMPING BARRIER RFQIONBEAM COOLER& BUNCHER iue43 ehia rwn fteSITA set-up. SHIPTRAP the of drawing Technical 4.3: Figure Turbopump 1000l/s Turbopump 2 1 TRANSFERSECTION ~4.8m 400l/s VALVE Turbopump 400l/s Turbopump 1000l/s PURIFICATION TSUPERCONDUCTING 7T TRAP DOUBLEPENNING RPSYSTEM TRAP MAGNET PUMPING BARRIER MEASUREMENT TRAP MCP-DETECTOR Turbopump 1000l/s 4.1 Experimental set-up 25

FUNNEL EXTRACTION-RFQ

DC-VOLTAGE CAGE

TOWARDS ENTRANCEWINDOW SHIPTRAP RFQ-BUNCHER

BEAM FROMSHIP NOZZLE

Figure 4.4: Stopping cell and extraction RFQ of SHIPTRAP [Neum06].

After stopping and thermalization in helium, the ions are accelerated by a pure DC gradient. The DC field is achieved by a DC cage (figure 4.4), a cylindrical five- segmented wire structure. Typically voltages between 120-300 V (corresponding to a DC gradient of 4-12 V/cm) are applied at the electrode segments of DC cage to guide the ions into the RF-DC funnel. The RF-DC funnel is a cone-like stack of 40 ring electrodes with equal spacing between rings as shown in figure 4.4. Application of an RF voltage (phase shifted by π between the adjacent rings) creates an effective repulsive potential, which keeps the ions away from the rings. Typically, the applied RF amplitude is 160 Vpp and the frequency is 0.8 MHz on the RF-DC funnel. An additional DC-gradient is superimposed along the funnel which guides the ions towards the nozzle. Typical voltages between 90-120 V are applied at the electrode segments of funnel. The nozzle voltage is ∼ 90 V. Very close to the nozzle, the helium gas flow takes over as dominant force and the ions are swept out of the stopping cell through the nozzle by a supersonic helium gas jet. The subsequent section is an extraction radio-frequency quadrupole (RFQ) consisting of four rods with a total length of about 180 mm. Each rod is axially divided into 12 segments for the application of different DC potentials. The diameter of each rod is 11 mm and the aperture of the RFQ (minimum distance between opposing rods) is 10 mm [Neum06]. Typically applied RFQ frequency is 1 MHz and the RF amplitude is 400 Vpp. The extraction RFQ is operated as ion guide which transfers the ions from the stopping cell into the RFQ buncher. The helium gas is pumped away and hence the ions get separated from the helium 26 The SHIPTRAP experiment while they are kept confined transversally and dragged longitudinally towards the RFQ buncher. The gas cell and extraction RFQ are pumped by turbomolecular pumps with pumping speeds of 400 l/s and 1600 l/s, respectively, together with a oil-free scroll pump (20,000 l/h). The location of different pumps is shown in figure 4.3.

4.1.2 RFQ buncher The ions from the stopping cell, guided through the extraction RFQ, enter the SHIPTRAP RFQ buncher which is an 1 m quadrupole rod structure consisting of four rods. The RFQ is operated at a helium buffer gas pressure of typically 5 × 10−3 mbar. An electronic valve (BALZERS EVR 116), which is connected with a commercial gas-purification system (SAES Getters PSGC50R2), is used to inlet helium in the RFQ buncher. The ions are cooled within a few milliseconds in this buncher, accumulated and extracted as a low-emittance bunched beam, facilitating the injection into the Penning trap system. A schematic diagram of the RFQ buncher is shown in figure 4.5. The rods of the buncher are divided longitudinally into 29 segments to apply an axial DC field. The diameter of each rod is 9 mm, the distance between two opposite rods is 7.8 mm, and the length of the different segments vary from 4 mm to 80 mm [Rodr03]. The ions enter the RFQ buncher at one side

INJECTED EXTRACTED IONBEAM IONBUNCH

BUFFERGAS

RF + r0 TRAPPING IONBUNCH DC RF - EJECTION

Figure 4.5: Segmented RFQ cooler and buncher [Rodr03].

and are guided in radial direction by an RF voltage applied to the four-rod set. The typical applied RF amplitude is 180 Vpp and frequency is 850 kHz. Thus, the ions are radially confined in the pseudo-potential well of the RF quadrupole field while their energy is reduced in collisions with the helium buffer gas atoms. 4.1 Experimental set-up 27

The ions are dragged along the axial direction of the buncher by applying an additional axial dc ﬁeld to the segmented rods. The dc potential slope with a harmonic trap at the end is shown along the symmetry axis in ﬁgure 4.5. Voltages between 74-60 V are typically applied at the electrode segments of the buncher. A large number (up to about 103) of ions can be accumulated in the potential minimum at the end of the RFQ buncher. The DC voltage of the last segment is 90 V when the buncher is closed, and it is pulsed to 0 V to extract a narrow ion bunch. The typical width of the extracted ion bunch is approximately 2 µs. The buncher can also be used in continuous mode in case the last segment is always kept in lower state.

4.1.3 Reference ion source For a high-precision mass spectrometer an accurate mass calibration is necessary. Typically 85Rb+ and 133Cs+ are used as reference ions at SHIPTRAP. They are produced by a surface ion source. The surface ion source used at SHIPTRAP consists of a metal tube made of tungsten which has a higher work function than the atom to be ionized. The metal surface is heated indirectly by means of a current (∼ 10 A) passing through a ﬁlament. The atom removes its valence electron to the hot metal surface and thus get ionized. A carbon-cluster laser ion source was developed, tested and used at SHIPTRAP [Chau07] in the framework of this thesis. This has been used as reference ion source at SHIPTRAP as well. A detailed description of the carbon-cluster ion source will be presented in the next chapter.

Surfaceionsource

QD1 QD2

RFQBucnher Penningtrap

QD4 QD3

Carbon-clusterionsource Figure 4.6: Schematic diagram of the quadrupole deﬂector used at SHIPTRAP. 28 The SHIPTRAP experiment

4.1.4 Quadrupole deflector The quadrupole deflector [Zema77] used at SHIPTRAP is a four-rod structure; the radius of each rod is approximately 20 mm and the aperture of the quadrupole deflector (minimum distance between opposite rods) is approximately 45 mm. Both ion sources are installed at the quadrupole deflector (figure 4.6) such that the source of ions can be easily selected from the stopping cell, the carbon- cluster laser ion source or the surface ion source. Either the carbon-cluster beam or the ion beam from the surface ion source is deflected 90o, depending upon the applied voltages, and the ions are injected into the Penning trap. Typical operating voltages of the quadrupole deflector to deflect the ion beam of 60 eV is given in the table 4.1. A photograph of the quadrupole deflector mounted on a flange is shown in figure 4.7.

Figure 4.7: Photograph of the quadrupole deﬂector mounted on a ﬂange. 4.1 Experimental set-up 29

Table 4.1: Typical operating voltages of the electrodes of the quadrupole deflector for deflecting the ion beam of energy 60 eV from the carbon-cluster ion source. The values in the parenthesis are the voltage applied while deflecting the ion beam coming from surface ion source.

Electrode Voltage (V) QD1 -73 (73) QD2 73 (-73) QD3 -73 (73) QD4 73 (-73)

The quadrupole deﬂector also enables one to inject the ion beam of 60 eV from the RFQ buncher into the Penning trap. In this case all the electrodes of the quadrupole deﬂector are kept at -940 V.

4.1.5 Penning traps The SHIPTRAP Penning trap system consists of two orthogonalized cylindrical Penning traps [Brow86] within a 7-T superconducting magnet. The inner diameter of the cylindrical traps is 32 mm, the distance between the trap centers is 20 cm. The first trap, known as purification trap, with a mass resolving power of about 105 is utilized for isobaric purification. The measurement trap with a mass resolving power of 106 allows for high-precision mass measurements. They are separated by a diaphragm for differential pumping to ensure a pressure < 10−7 mbar at the measurement trap even if the purification trap is filled with helium at a pressure about 10−5 mbar. The diaphragm is of length 50 mm and diameter 3 mm.

A transverse cut of the SHIPTRAP Penning trap electrodes is shown in figure 4.8 (top). The electric field along the trap axis is shown in figure 4.8 (middle). The superconducting magnet has two homogeneous regions, where the traps are placed. The homogeneous magnetic field regions are marked in figure 4.8(bottom). A photograph of the Penning trap system is shown in figure 4.9.

The purification trap is of total length of 212 mm. It consists of one pair of end electrodes, two pairs of correction electrodes and a ring electrode. Each end electrode is axially three-fold segmented to apply different dc potentials to create an extended potential well for efficient capture of the ions. The inner correction electrodes are two-fold segmented in the azimuthal plane. 30 The SHIPTRAP experiment

Table 4.2: Typical voltages of diﬀerent electrodes of the puriﬁcation trap of SHIPTRAP for ion energy 60 eV. The values in the parenthesis are the voltages applied while opening the trap for injection or extraction of ions.

Electrode Applied Voltage (V) end-cap electrodes (PE1/PE2/PE3) 72 (20) correction electrode (PC1) 62.3 (38) correction electrode (PC2) 44.2 ring electrode (PR) 40 correction electrode (PC3) 44.2 correction electrode (PC4) 62.3 (-20) end-cap electrodes (PE4/PE5/PE6) 72 (-20)

Table 4.3: Typical voltages of diﬀerent electrodes of the measurement trap of SHIPTRAP for ion energy 60 eV. The values in the parenthesis are the voltages applied while opening the trap for injection or extraction of ions.

Electrode Applied Voltage (V) end-cap electrodes (ME1/ME2/ME3) 78 (-20) correction electrode (MC1) 42 ring electrode (MR) 37 correction electrode (MC2) 42 end-cap electrodes (ME4/ME5/ME6) 78 (21) 4.1 Experimental set-up 31

CORRECTION CORRECTION ELECTRODES ELECTRODES 50mm ENDCAP RING ENDCAP ENDCAP RING ENDCAP 3mm

PurificationTrap Diaphragm MeasurementTrap 80 60 40 20 injection ejection 0 electricpotential(V) transfer -20

7.001

7.000

6.999

magenticfield(T)

6.998 -20 -15 -10 -5 0 5 10 15 20 distancefromcenterofmagnet(cm)

Figure 4.8: Top: Schematic diagram of the SHIPTRAP Penning trap electrode system. Middle: Electric ﬁeld along the trap axis. Bottom: Magnetic ﬁeld plot of 7-T superconducting magnet (MAGNEX SCIENTIFIC MRBR 7.0/160/AS) along the symmetry axis.

The ring electrode is azimuthally divided into eight segments. This allows for the excitation of different motions in various configurations (e.g. dipole, quadrupole or octupole) for different purposes. Typical operating voltages of different electrode segments of the purification trap for an ion energy of 60 eV are summarized in table 4.2.

The second trap, the measurement trap, is also cylindrical with the same inner diameter and a length of 185 mm. It consists of one pair of end electrodes, one pair of correction electrodes and a ring electrode. Similar to the purification trap, the end electrodes are axially three-fold segmented. The correction electrodes are two-fold segmented in the azimuthal plane similar to the purification trap. The ring electrode is azimuthally divided into eight segments which allows exciting the trapped ions either by a dipolar, a quadrupolar, or an octupolar RF field. A more detailed description of the design and construction 32 The SHIPTRAP experiment

Figure 4.9: Photograph of the SHIPTRAP Penning trap system. Diﬀerent electrodes are marked by their commonly used abbreviations (refer to table 4.2 and table 4.3) .

of the SHIPTRAP Penning trap system is given in [Raha06, Sikl03a]. Typical operating voltages of diﬀerent electrode segments of the measurement trap for an ion energy of 60 eV are summarized in table 4.3. The trap electrodes are made of oxygen-free high conductivity (OFHC) copper. To avoid oxidization, which can distort the electric ﬁeld, the copper electrodes are gold-plated.

4.2 Buﬀer-gas cooling and mass selection

As mentioned in section 3.2.4, a necessary condition for a high-precision mass measurement is to have contaminants-free and isobarically clean ion samples in the measurement trap. This can be achieved by a mass-selective buffer gas cooling technique [Sava91]. The ions are loaded into the purification trap, where buffer gas is present (typically at a pressure of few times 10−6 mbar). Helium is used as the buffer gas due to its high ionization potential which prevents charge-exchange reactions. To inlet buffer gas into the purification trap, a clean helium feeding line is used. An electronic valve (BALZERS EVR 116) is in use for the regulation of the 4.2 Buffer-gas cooling and mass selection 33

(a) (b)

Figure 4.10: Ion motion in a buﬀer gas ﬁlled Penning trap, (a)without and (b) with quadrupolar excitation [Sava91].

helium pressure inside the purification trap. The buffer-gas cooling mechanism for a large mass difference and a low relative velocity between the ion and the buffer-gas atom is well approximated by considering a viscous damping force

F~ = −δm~v, (4.1) where m is the mass of the ion, v is the velocity of the ion with respect to the buffer gas, and δ is the viscous damping parameter describing the effect of the buffer gas: q 1 p δ = · · norm , (4.2) m Kion Tnorm where Kion is the ion mobility, q/m is the ion’s charge-to-mass ratio, pnorm and Tnorm are the normalized pressure and temperature respectively. The values of Kion have been measured for many different gas-ion combinations and tabulated [Elli76], [Elli78]. The ion mobility values for different ions in various noble gases are given in table 4.4.

An analytical expression for the eﬀect of buﬀer gas on the motional amplitude of an ion in a Penning trap is given by

−αt ρ(t) = ρ0e . (4.3) 34 The SHIPTRAP experiment

Table 4.4: Ion mobilities Kion for diﬀerent ion and buﬀer-gas combinations [Boll04]. The values are tabulated in units of 10−5m2V −1s−1

He Ar Kr K+ 216(6) 27.0(8) 18.3(9) Rb+ 200(6) 31.0(9) 14.5(4) Cs+ 183(4) 21(1) 13.0(4)

In case of an axial oscillation the damping parameter α = δ, but in the case of the radial modes ω± α± = ±δ . (4.4) ω+ − ω− The axial oscillation and the reduced cyclotron motion are damped by the collisions with the buffer gas atoms. However, a simple cooling of the magnetron motion leads to an increase of its amplitude due to the negative sign of α− and the ions are lost once the amplitude of the magnetron motion is larger than the dimension of the trap. This scenario is shown in figure 4.10(a). Thus, the instability of the magnetron motion due to the presence of buffer gas in a Penning trap has to be overcome for the buffer-gas cooling to work. This is achieved by coupling the magnetron motion and the cyclotron motion via applying a quadrupolar excitation at ωq = ωc = ω+ + ω− (by applying an RF field at the ring segments) as described in section 3.3.2. It continuously converts the magnetron motion into cyclotron motion, resulting in an overall centering of the ions of interest [Sava91], as shown in figure 4.10(b). This cooling and centering qB process is mass selective since the applied quadrupole excitation ωc = m depends on the charge-to-mass ratio of the ion. Hence, only the ions of interest are cooled down to a small radius in the center of the trap. The cooled and centered ions are then ejected out of the Penning trap through a small opening (3 mm diameter in case of SHIPTRAP). Isobarically clean samples for precision mass measurements are prepared at SHIPTRAP by this method. Typically a dipolar excitation of duration ∼ 50 ms, RF amplitude ∼ 0.8 V, frequency ∼ 500 Hz; and a quadrupolar excitation of duration ∼ 200 ms, RF amplitude ∼ 0.2 V is applied at the purification trap for the buffer-gas cooling at SHIPTRAP. 4.3 Time-of-flight Ion Cyclotron Resonance (TOF-ICR) detection technique 35

4.3 Time-of-ﬂight Ion Cyclotron Resonance (TOF-ICR) detection technique

A Time-of-ﬂight Ion Cyclotron Resonance (TOF-ICR) technique [Boll90],[Graf80] is used at SHIPTRAP for the cyclotron-frequency detection of the stored ions in the measurement trap. Though the TOF-ICR technique is a destructive detection method, its advantage is obvious: it can be used for a single ion or a very low number of stored ions in the trap.

The isobarically puriﬁed ion samples are injected into the measurement

MCP detector Trap

Z Figure 4.11: Schematic of the TOF-ICR detection technique.

Penning trap of SHIPTRAP from the puriﬁcation Penning trap so that they are very nearly at rest in the centre of the trap. A dipolar excitation of ions at their magnetron frequency leads to an increase of their magnetron radius. Then a quadrupolar excitation at ωc = ω+ + ω− converts the magnetron motion into the cyclotron motion at the same radius [Boll90]. Typically a dipolar excitation of duration ∼ 50 ms, RF amplitude ∼ 0.15 V, frequency ∼ 1330 Hz; and a qudrupolar excitation of duration ∼ 100-1200 ms, RF amplitude ∼ 0.2 V is applied at the measurement trap of SHIPTRAP. The radial energy of the ion increases in this process because the reduced cyclotron frequency is much higher than the magnetron frequency. After the excitation the ions are ejected out of the trap and after a drift section along the axis out of the magnetic ﬁeld, are 36 The SHIPTRAP experiment

340

320

300 s) µ 280 TOF ( 260

240

220 -6π -4π -2π 02π 4π 6π ω − ω ⋅ ( q c) T q Figure 4.12: Theoretical line shape of mean time-of-ﬂight from the trap to the detector as a function of the frequency detuning ∆ω = ωq − ωc [Webe04].

detected at an MCP detector as shown in the figure 4.11. The magnetic moment of the ions E µ = r , (4.5) B which is acquired due to their radial motion, interacts with the magnetic field gradient and hence the ions experience an axial force. This force is proportional to the magnetic moment µ and hence to the radial energy Er of the ions and it is given by, E ∂B F~ = −~µ(∇~ · B~ ) = − r zˆ (4.6) B ∂z Due to this force, radial energy of the ion is converted into longitudinal energy when the ions fly through the magnetic field gradient [Graf80]. The ions which are excited resonantly have a higher longitudinal energy than the other ions. Thus, they reach the detector earlier than the other ions and hence have a shorter time-of-flight. A scan of the frequency of the quadrupolar excitation ωq yields a resonance curve from which the value of the cyclotron frequency ωc can be determined. The theoretical line shape for such a resonance as shown in figure 4.12 is well understood [Koni95]. Figure 4.13 shows a 12 + typical time-of-flight resonance of C11 ion recorded at SHIPTRAP (a), the corresponding time-of-flight distribution (b) and the corresponding time-of-flight distribution of resonant and non-resonant ions (c). The time-of-flight spectra in 4.3 Time-of-flight Ion Cyclotron Resonance (TOF-ICR) detection technique 37

figure 4.13 (b) are the sum of the individual spectra of all the data points that are in figure 4.13 (a). The time-of-flight spectra in figure 4.13 (c) are the sum of the individual spectra of the data points that are in the corresponding circles in figure 4.13 (a).

The line width of the resonance ∆νc ≈ 0.9/Tq is to ﬁrst order given by the Fourier limit of the applied quadrupole excitation of duration Tq. At SHIPTRAP, Tq is chosen between 100 ms and 1200 ms depending on the half-life of the nuclide to be measured. However, an upper limit of the excitation time is set by damping since the contrast of the TOF resonance is reduced for longer excitation time. An accurate mass measurement requires a precise knowledge of the magnetic ﬁeld strength B, which is achieved by measuring the cyclotron frequency ωc,ref of an ion with well-known mass mion,ref . From equation 3.1 the resulting ratio of the ionic masses can be derived as Ã ! m µω ¶ q ion = c,ref ion . (4.7) mion,ref ωc qref In case of singly-charged ions, the atomic mass m of the ion of interest is calculated from the cyclotron frequency of the ion of interest ωc, the cyclotron frequency of the reference ion ωc,ref , the atomic mass of reference ion mref and the electron mass me, by

m = r(mref − me) + me, (4.8) where ω r = c,ref (4.9) ωc is the cyclotron frequency ratio. The primary result of the mass measurement is the measured frequency ratio r. Since the knowledge of the value of the reference mass, i.e. the literature value, may change over time, r is usually tabulated in the corresponding publications. In the case where a carbon cluster 12 Cn, n=1,2,3,... is used as reference this reference mass is absolute as its mass has by deﬁnition no uncertainty. The molecular binding energy of only a few eV per atom of carbon-cluster can be neglected within the uncertainty level of about 1-10 keV aimed at with SHIPTRAP. 38 The SHIPTRAP experiment

(a) 124

122

120

118

116

114

112 ieo-lgt/Time-of-Flight µs 110

108

-3 -2 -1 0 1 2 3 ExcitationFrequency-815098.9/Hz (b) 60

30 Ion Count 20

0 60 70 80 90 100 110 120 130 140 150 160 Time-of-Flight/µs

Ion Count 6

0 60 70 80 90 100 110 120 130 140 150 160 Time-of-Flight/µs

12 + Figure 4.13: (a): Time-of-flight of C11 as a function of the excitation frequency applied in the measurement trap. The solid line represents an fit of the expected resonance curve [Koni95] to the data points. Resonant ions are marked by a red circle and non-resonant ions are marked by a blue circle. (b) Corresponding time-of-flight spectrum of ions. (c): Corresponding time-of-flight spectrum of resonant ions (red) and non-resonant ions (blue). Chapter 5

Carbon-cluster ion source

Clusters consisting of a few atoms build the bridge between individual atoms and the condensed phase of matter and they are thus of high general interest. Consid- erable progress has already been made in the study of their properties. However, there are still many aspects of the cluster properties to be investigated. Ion- storage techniques, in particular Penning traps, are important tools for advanced investigations of cluster properties [Schw06a]. Vice versa, cluster ions can serve as probes to explore the properties of ion traps. In particular, carbon-cluster ions are ideal for the calibration of mass spectrometers and for investigations of the uncertainties of the mass determinations, including the search for systematic deviations in high-precision mass measurements since the unified atomic mass unit is defined as 1/12 of the mass of the 12C atom. The use of carbon clusters as reference mass in Penning trap mass spectrometry was suggested in [Lind91] and [Jert93]. The mass of 28Si was determined by 12 + 12 + comparing the cyclotron frequencies of the singly charged ions C , C3 and 28Si+ in a Penning trap mass spectrometer [Jert93]. Doublet measurements of the 28 12 isobars Si3 and C7 were reported by use of a Penning trap mass spectrometer and the Fourier transform ion cyclotron resonance technique (FT-ICR) [Lind91]. The cluster ions were produced by laser ablation. The use of carbon clusters as reference mass for the on-line measurement of short- lived nuclei is more challenging. A carbon-cluster laser ion source was built and tested at ISOLTRAP/CERN, Geneva towards that direction [Blau02, Sche02]. Carbon-cluster ions were produced by laser desorption, fragmentation and ionization of C60 fullerenes. They have been used for the investigation of systematic uncertainties of ISOLTRAP [Kell03]. Along this line at SHIPTRAP a carbon-cluster ion source has been installed and 12 + tested in the framework of this thesis. Carbon-cluster ions Cn , 5 ≤ n ≤ 23, were produced by laser-induced desorption and ionization from a Sigradur°R sample. They were tested for the first time as reference ions in an on-line mass measurement of the short-lived radionuclides 144Dy, 146Dy and 147Ho. In addition, carbon clusters of various sizes were used for an investigation of the systematic 40 Carbon-cluster ion source uncertainty of SHIPTRAP covering a mass range from 84 u to 240 u [Chau07].

5.1 Motivation for a carbon-cluster ion source

For a high-precision mass spectrometer like SHIPTRAP an accurate mass calibration is an essential ingradient. Absolute mass measurement is possible against the microscopic mass unit in case carbon clusters are used as mass calibrants. The estimated values of the molecular binding energy/atom of the carbon clus- 12 12 ters vary from 3.1 eV in C2 to 7.0 eV in C60 [Toma91] which corresponds to an uncertainty ≈ 10−9 (for lower masses) and is negligible within the present uncertainty level at SHIPTRAP. Furthermore, carbon clusters can be chosen such that their mass is at most six mass units away from any nuclide (ﬁgure 5.1).

3985133 CKRb212019181716151413121110987654321Cs

C21

C20 C C18 19

C17 C16 C15 C14

C13

C12

C11

C10

C7 133 C6 Cs

C4 C 3 85Rb C2

39K

Figure 5.1: Nuclear chart of the known nuclei. The decay modes of the nuclei are indicated: stable nuclide (black squares), α decay (yellow squares), β+ decay (pink squares), β− decay (blue squares), and spontaneous ﬁssion (green squares). Magic numbers are indicated by black solid lines. The diagonal red solid lines indicate the position of the reference ions typically used (39K, 85Rb, 133Cs) at SHIPTRAP and diagonal black solid lines indicate the position of 12 carbon-cluster ions Cn.

Thus, a possible systematic uncertainty due to the mass diﬀerence between the measured ion and the calibrant is reduced (section 3.2). These features give 5.2 Experimental set-up 41 the carbon-cluster ion source a natural advantage over alternative ion sources for mass calibration [Blau02, Schw05]. In addition, cross-reference measurements between cluster ions of diﬀerent size can reveal systematic uncertainties over a wide range of masses [Kell03]. They allow determining the present uncertainty limit for mass measurements performed at SHIPTRAP (section 4.3).

5.2 Experimental set-up

The vacuum part of the carbon-cluster laser ion source consists of a sample holder, an extraction electrode and an einzel lens. A schematic diagram of this ion source is shown in figure 5.2. A photo of the ion source mounted to the quadrupole deflector of SHIPTRAP beam line is shown in figure 5.3.

Einzellens

Vacuumhousing

Deflector Laserbeam Extractionplate Sigradursample

Sampleholder

Figure 5.2: Schematic diagram of carbon-cluster ion source.

The main features of this ion source are high ion-transport efficiency, the pos- sibility to simultaneously use different samples and a fast exchange of the sample. To change the laser-spot position on the sample (continuously or in steps) the sample holder is mounted on a rotatable feed-through as shown in the figure 5.4. In the present study, commercially available Sigradur°R has been used as target material for the production of carbon clusters by laser-induced desorption, fragmentation and ionization. Sigradur°R is pure carbon synthesized from phenolic 42 Carbon-cluster ion source

rotatable carbon-cluster quadrupole telescopiclens feed-through ionsource bender systemforlaser

Figure 5.3: Photograph of carbon-cluster ion source at SHIPTRAP.

rotatablefeed-through sampleholder Sigradursample

Figure 5.4: Photograph of rotatable sample-holder of carbon-cluster ion source. 5.3 Carbon-cluster ion source characterization 43

Targetafter Targetbefore laserablation laserablation

Figure 5.5: Photograph of Sigradur°R target after and before laser ablation.

resin, which has fullerene-related micro structures [Harr04]. It has been already used for the production of carbon clusters at University of Mainz [Blau03]. A Sigradur°R sample (disc-shaped, 10 mm diameter, thickness 2 mm) is placed upon the rotatable sample holder. A frequency-doubled beam of an Nd:YAG laser (Minilite II) is focussed off-center on the rotating sample, such that a single sample can be used for about a week. The laser-pulse duration is 3-5 ns and the typical pulse energy is 4-12 mJ. The beam is focussed to about 1 mm diameter at the target position by a telescope lens system. The Sigradur°R sample after and before the laser ablation is shown in figure 5.5. The sample is kept at an electrical potential of 60 V with respect to ground, which corresponds to the energy of ions coming from the SHIPTRAP RFQ buncher. The source is installed in front of a quadrupole deflector (figure 4.2) as described in section 4.1.4. The carbon-cluster beam is deflected 90o by the quadrupole deflector and the ions are injected into the purification Penning trap.

5.3 Carbon-cluster ion source characterization

5.3.1 Optimization of electrode voltages The appropriate electrode voltages of the cluster ion source have been optimized with respect to the ion transfer eﬃciency of the carbon clusters from the creation 44 Carbon-cluster ion source point to the Penning traps of SHIPTRAP. Ion optical simulation studies have been performed using Simion 7 software prior to the actual experimental optimization. The simulations were performed for randomly created ions of mass 120 u having an initial energy between 0.01 eV and 1.9 eV and an angular distribution for the ion-creation between 0o-180o. The value for the electrode voltages from the simulation are tabulated in the table 5.1. Figure 5.6 shows equipotential line and ion-trajectory for these voltages.

Apertureof Cluster-source quadrupolebender

100mm

Figure 5.6: Ion-optical simulation of cluster-source using Simion. Equipotential lines are shown by red solid lines. The ion-trajetory is described by the blue area.

An experimental optimization of the electrode voltages of the carbon-cluster ion source was performed at SHIPTRAP. At the beginning, the central-electrode voltage (Vce) of the Einzel lens system was kept at -50 V and both the inner (Vie) and outer electrode voltages (Voe) were kept at -300 V according to the best value obtained from the simulation. The ion counts per laser pulse were recorded at the MCP detector behind SHIPTRAP (figure 4.2) for different values of the extraction-electrode voltage (Vee). The best value was found for Vee < −600 V as it is shown in figure 5.7. Next, Vce of the einzel lens was varied keeping Vee=-1500 V, Vie=-300 V, and Voe=-300 V. It was found that the ion count is maximum when Vce=0 V (figure 5.8). For the rest of the experiment Vce was kept at 0 V. Finally keeping Vee=-1500 V and Vce=0 V, both Vie and Voe were varied together. The best value was found at Vie=Vie=-400 V (shown in figure 5.9). The applied voltages to different electrode segments are summarized in table 5.2. 5.3 Carbon-cluster ion source characterization 45

Table 5.1: Voltages of diﬀerent electrodes of the cluster ion source from the ion-optical simulation.

Electrode Applied Voltage (V) Extraction electrode -1500 deﬂector segments -300 inner electrode -300 central electrode -50 outer electrode -300

Table 5.2: Voltages of diﬀerent electrodes of the cluster ion source after the optimization.

Electrode Applied Voltage (V)

Extraction electrode (Vee) < −600 deﬂector segments -400 inner electrode (Vie) -400 central electrode (Vce) 0 outer electrode (Voe) -400 46 Carbon-cluster ion source

15 Ion Counts/ pulse

0 -200 -400 -600 -800 -1000 -1200 -1400 -1600 -1800

Extraction Voltage (V ) /V

Figure 5.7: Ion counts as a function of the extraction-electrode voltage Vee keeping Vce=-50 V and Vie=Voe=-300 V.

20 Ion Counts/ pulse Counts/ Ion

0 -50 -100 -150 -200 -250 -300 -350 -400

Central-electrode Voltage (V )/V

Figure 5.8: Ion counts as a function of the central-electrode voltage Vce keeping Vee=-1500 V and Vie=Voe=-300 V. 5.3 Carbon-cluster ion source characterization 47

30 Ion Counts/ pulse Counts/ Ion

0 -50 -100 -150 -200 -250 -300 -350 -400 -450 -500 -550

Outer-electrode Voltages(V ,V )/ V

ie oe

Figure 5.9: Ion counts as a function of the inner and outer-electrodes voltage (Vie and Voe) keeping Vee=-1500 V and Vce=0 V.

5.3.2 Energy spread of the ions

A test setup, where a copper grid was mounted between the cluster source and an MCP detector, was used to measure the energy spread of the cluster ions after production. This experiment was performed at University of Greifswald. The sample was kept at an electrical potential of 90 V with respect to ground. The energy distribution of the ions was obtained by applying a blocking voltage to the copper grid. The solid line in figure 5.10A represents a fit to the experimental data points. The fit was performed by use of Origin with the Boltzmann function [Orig],

A1 − A2 y = + A2. (5.1) 1 + e(x−x0)/dx

The derivative of the fit curve is shown in figure 5.10(B). The energy spread of the ions extracted from the cluster source is determined from the FWHM of the peak in the derivative to be 3.4 eV. The measured energy spread of the produced ions is small enough for the efficient loading of the ions in the purification Penning trap of SHIPTRAP (see table 4.2). 48 Carbon-cluster ion source

(A)

2 Ion Counts /pulseIon

(B)

-1

-2 Derivative

-3

-4

0 10 20 30 40 50 60 70 80 90 100 110

Blocking Voltage / V Figure 5.10: Number of ions observed per laser pulse as a function of the blocking voltage applied to a copper grid in front of the detector. The solid line (A) is a ﬁt to the data points, (B) the derivative of the ﬁt curve.

5.4 Experimental procedure

5.4.1 Timing sequence for measurement cycle Timing sequence of the measurement cycle used for the carbon-cluster measurement is similar to the measurement cycle used for the radioactive ions. Figure 5.11 shows the timing sequence that is used within a complete measurement cycle for the cyclotron determination of a cluster ion. The cycle is started by triggering the flash lamp of the Nd:YAG laser (1). After a delay (typically of the order of 70 µs), the Q switch of the laser is triggered (2) and hence a laser pulse (pulse duration 3-5 ns) is directed on-to the Sigradur°R sample. After a drift time depending on the mass of cluster ion, the ions are captured in the purification trap (3). Then the ions are cooled for 100 ms (4). This is followed by a dipolar magnetron excitation for 50 ms (5), a quadrupolar cyclotron excitation of 200 5.4 Experimental procedure 49 ms (6) and a waiting period of 60 ms for further radial and axial cooling (7). Then the mass-selected ions are ejected from the purification trap (8). A similar time sequence is used for the measurement trap: After capturing the ion (9), a dipolar magnetron excitation for 50 ms (10) is applied. Finally a quadrupolar cyclotron excitation of 1200 ms (11) is applied before the ion is ejected out (12) of the measurement trap.

Cluster-SourceLaser FlashLamp 50m s (1) QSwitch 50m s (2) Purification Trap

Capture 20m s (3)

Axialcooling 100ms (4)

RFMagnetron 50ms (5)

RFCyclotron 200ms (6)

WaitingPeriod 60ms (7)

Extraction 35m s (8) Measurement Trap

Capture 35m s (9) RFMagnetron 50ms (10) RFCyclotron 1200ms (11)

Extraction 5ms (12)

Figure 5.11: Timing sequence used within a complete measurement cycle for the cyclotron determination of a cluster ion. A detailed discussion is given in text.

5.4.2 Time-of-Flight mass spectrum The carbon-cluster ions are captured in flight in the purification Penning trap and cooled by collisions with the helium buffer-gas atoms. The large mass accep- tance of the capturing process in the purification trap allows to capture several different masses at once. To identify the captured cluster ions, the ion sample is ejected from the first trap towards the MCP detector (figure 4.2). A typical time-of-flight (TOF) mass spectrum of singly-charged carbon-cluster ions and some contaminants is shown in figure 5.12. There was no dipolar or quadrupolar excitation applied to the purification trap in this particular example. The storage time was 380 ms. In a first order approximation the masses of the ions were 50 Carbon-cluster ion source calibrated from their time-of-flight using the method described in appendix A. 12 + The spectrum shows mainly carbon clusters Cn , 5 ≤ n ≤ 23 which agrees with earlier measurements [Blau03]. Each of the carbon-cluster species ranging from 12 + 12 + C5 to C23 were later confirmed by cyclotron frequencies determined from their individual time-of-flight ion cyclotron resonances. + + He and H2O were identified as main contaminants. As already mentioned helium was used as buffer gas in the purification trap. Although the buffer gas is fed to the trap through a gas purifier, sometimes contaminations by water vapor + + is observed [Raha06]. It has been supposed that He and H2O ions were created in the purification trap. The ionization may take place via charge-exchange. The other low-mass impurities observed in the time-of-flight spectrum are as yet not identified. It was noticed during the measurement that the laser power has an influence on the abundance of the observed cluster species. Higher laser power produced mainly lower-size clusters and vice versa. This finding is useful for tuning the cluster-source to produce clusters of the sizes of interest.

He +

H O +

C 2

+ 18

+ 5

2 Intensity /Arbitrary Unit /Arbitrary Intensity

0 25 50 75 100 125 150 175 200 225

TOF/ s

Figure 5.12: A typical time-of-ﬂight (TOF) mass spectrum of carbon-cluster ions and some contaminants detected after trapping and cooling in the puriﬁ- cation trap of SHIPTRAP. 5.4 Experimental procedure 51

5.4.3 Cooling resonance As explained in section 4.2, the cooling and centering technique in the purification trap is mass selective [Sava91], hence cluster ions of a specific size can be selected. A time-of-flight mass spectrum of carbon-cluster ions detected after trapping and cooling in the purification trap is shown in figure 5.13. It should be mentioned that the drift time between the laser pulse and the opening of the purification trap (section 5.4.1) is 90 µs in the example of the time-of-flight mass spectrum in figure 5.13 whereas 130 µs in the example of figure 5.12. Hence, the time-of-flight distributions are not similar. The capture time (time sequence (3) of figure 5.11) in purification trap is 20 µs for both the cases. The time duration while the trap is opened and can capture the ions into the trap is commonly known as capture time. However, it is not possible to capture single cluster species in the purification trap.

There was no dipolar or quadrupolar excitation applied to the purification 12 + trap in the example of figure 5.13(A). Next, C11 ions are cooled and centered by applying dipolar and quadrupolar excitation in the purification trap. Time- 12 + of-flight spectrum in the figure 5.13(B) shows only C11 ions, other species present in the TOF spectrum of figure 5.13(A) are removed by the buffer-gas cooling mechanism.

The number of extracted ions as a function of the quadrupolar excitation 12 + frequency, for an excitation time of 200 ms and for the cluster species C11 is shown in ﬁgure 5.14. The mass resolving power was about 70,000 in this example.

5.4.4 Cyclotron frequency determination of cluster ion The mass-selected cluster ions are then transferred to the measurement trap. The time-of-flight ion cyclotron resonance technique [Boll90, Graf80] as described in section 4.3 was employed to measure the cyclotron frequency. An example of 12 + a typical time-of-flight ion cyclotron resonance for C11 ion is shown in figure 5.15. Here the mean TOF as a function of the applied quadrupolar excitation frequency is plotted. The solid line is a least-square fit of the expected line shape [Koni95] to the data points. The resolving power in this case was about 830,000. 52 Carbon-cluster ion source

(A) 11

(B)

8 Intensity/Arbitrary unit Intensity/Arbitrary

0 25 50 75 100 125 150 175 200 225

TOF/µs Figure 5.13: Time-of-ﬂight mass spectrum of carbon-cluster ions detected after trapping and cooling in the puriﬁcation trap (A) without and (B) with RF excitation. 5.4 Experimental procedure 53

12 +

FW HM=11.4 Hz

2 Intensity /Arbitrary Unit /Arbitrary Intensity

-50 -40 -30 -20 -10 0 10 20 30 40 50

Excitation frequency - 815294.2 /Hz

12 + Figure 5.14: Number of carbon-cluster ions C11 ejected from the puriﬁcation trap as a function of the excitation frequency. The solid line is a Gaussian ﬁt to the data points. The duration of the cyclotron excitation was 200 ms.

142

140

138

136

134

12 +

132

130 TOF / µS

128

FW HM =0.98 Hz

126

124

122

120

-3 -2 -1 0 1 2 3

Excitation frequency - 815099.7 /Hz

12 + Figure 5.15: Time-of-ﬂight of C11 as a function of the excitation frequency applied in the measurement trap for an excitation time of 900 ms. The solid line represents a ﬁt of the expected resonance curve [Koni95] to the data points.

Chapter 6

Study of the accuracy of SHIPTRAP

Undoubtedly Penning traps are the most precise tools for the direct mass determination available today. This fact has been demonstrated most recently by a direct test of E = mc2 using a Penning trap at MIT1 [Rain05]. Penning trap mass spectrometry of stable nuclei can reach relative uncertainties below 1×10−11 by simultaneously confining two different ions on the same magnetron orbit in a Penning trap, and hence balancing out many sources of noise and error (such as fluctuations of the magnetic field)[Rain04]. Another way to improve the relative precision of the mass measurements is to use q higher charge states of the ions. As seen from equation 3.1 (i.e. ωc = m B), higher charge states result in higher cyclotron frequencies and hence a smaller relative uncertainty. Mass measurements of highly-charged stable ions at SMILETRAP [Berg02] can reach relative uncertainties of a few parts in 1 × 10−10 or better. Multiply-charged ions are also expected to be used in the TITAN facility [Dill03]. However, high-precision mass spectrometry of short-lived radionuclides is more challenging due to the low production rates, short half-lives and the accelerator laboratory environment to create them. As an example, the limit of mass accuracy for ISOLTRAP has been determined to be 8 × 10−9[Kell03]. The SHIPTRAP experiment at GSI is a more recent facility for the investigation of short-lived radionuclides. It is designed for precision experiments of fusion- evaporation residues of transfermium nuclei and other neutron-deficient nuclei. Typical reference ions used at SHIPTRAP are 85Rb and 133Cs. Their masses have been measured with relative uncertainties below 1 × 10−10 using Penning traps [Brad99]. However, for the mass measurement of transfermium nuclei, as intended at SHIPTRAP, the ion of interest differs by many mass units from those reference ions. This could lead to a mass-dependent systematic uncertainty in the mass measurement procedure as it is discussed in section 3.2.

1This system has since been moved from MIT to Tallahassee. 56 Study of the accuracy of SHIPTRAP

In this chapter a test of the performance of SHIPTRAP with respect to a mass- dependent systematic effect and systematic uncertainties is reported. Carbon- cluster ions from the carbon-cluster laser ion source provide an excellent test bed for this investigation. The measurements, their evaluation, and analysis are discussed in this chapter. Furthermore, carbon clusters have been tested as reference ion for the first time in an on-line mass measurement at SHIPTRAP during the present study (chapter 7). In the next sections a few topics related to the data evaluation (e.g. statistical uncertainty, count-rate class analysis, time dependence of resonance frequencies) are briefly discussed.

6.1 Statistical uncertainty

The relative statistical uncertainty of the experimentally determined cyclotron frequency employing the TOF-ICR method (section 4.3) can be described by an empirical relation proposed in [Boll01]:

δν c c = √ . (6.1) νc νcTRF N

Here, N is the total number of ions detected, TRF is the quadrupolar excitation duration in the Penning trap, νc is the cyclotron frequency and c is a dimensionless constant. For short-lived nuclei, the excitation time TRF is limited by their half-life. Typically, a quadrupolar excitation is applied for up to 1.2 s in the measurement trap of SHIPTRAP. In case of the carbon-cluster cross-reference measurements the duration of the quadrupolar excitation in the measurement trap was always 1.2 s and the relative statistical uncertainty obtained was about 2 × 10−8 for individual resonance. A q higher ion-mass results in a lower cyclotron frequency ωc = m B. Hence, for same excitation time TRF , one has to record more ions for heavier ions than the lighter ions to get same precision1. For future SHIPTRAP mass measurements of heavy ions in the transfermium region this is also a matter of concern. A quantitative discussion for the achievable precision for mass number A = 250 can be found in [Bloc07]. By the cyclotron frequency measurements of diﬀerent carbon-cluster species 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + ( C7 , C9 , C10, C11, C12, C15, C18, C19, C20) used for the cross- reference measurements (section 6.4.1), the constant c of equation 6.1 is determined. The results of these measurements as a function of the number of ions

1Precision of the measurement means the closeness of agreement between independent test results obtained under stipulated conditions. The measure of precision is usually expressed in terms a standard deviation of the test results and this should be clearly distinguished from accuracy of measurement. Accuracy of measurement is deﬁned as the closeness of the agreement between the result of a measurement and the value of the measurand [Tayl94]. 6.2 Count-rate-class analysis 57

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8 c

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

0 1000 2000 3000 4000 5000 6000 7000 8000

Number of detected ions

Figure 6.1: Determination of the constant c of equation 6.1 from the cyclotron frequency measurements of diﬀerent carbon-cluster ions. The solid line indicates the average value of c and the dashed lines indicate its one sigma standard deviation.

detected (N) are shown in ﬁgure 6.1. From these measurements, the average value is found to be c = 0.79(14). This value is comparable to the measured value of c=0.898(8) at ISOLTRAP [Kell03].

6.2 Count-rate-class analysis

The storage of more than one ion species in the measurement Penning trap leads to a shift in the cyclotron frequency of the ion (section 3.2.4). In order to correct for this frequency shift a special technique called count-rate-class analysis [Kell03] is employed. The data set is divided into different count-rate-classes depending upon the number of simultaneously trapped ions (observed counts) and the cyclotron frequency is determined individually for each class. The cen- troid frequencies are plotted as a function of the center of gravity of the count rate distribution of that classes. A linear least-square fit is extrapolated to the case of a single ion stored in the measurement trap. Figure 6.2 and 6.3 shows the count rate dependence of the observed cyclotron frequencies for 144Dy++ and 12 + C11 ions respectively which were measured at SHIPTRAP during the present investigation. The linear fit is extrapolated to one ion in the trap taking the effect into account that the MCP-detector efficiency is 35% [Raut07a]. Though care 58 Study of the accuracy of SHIPTRAP was taken for each carbon-cluster measurement so that only the selected cluster species was transferred from the purification trap to the measurement trap, the count-rate-class analysis was also employed to check for the presence of any contaminants. There was no such frequency shift observed within the uncertainty level for any of the cluster measurements. However, the count-rate-class analysis increases the uncertainty of the cyclotron frequency obtained from the TOF ion cyclotron resonance of cluster ions. The frequency shift for the radioactive ion 144Dy++ arises from the presence of contaminants which are most-likely produced due to the charge-exchange reactions in the stopping cell.

1494985.35

144 ++

1494985.30

1494985.25

1494985.20

1494985.15

1494985.10

1494985.05 Cyclotron f requency /f Hz requency Cyclotron

1494985.00

0 1 2 3 4 5 6 7 8

Count rate class / average# of ions

Figure 6.2: Cyclotron frequency as a function of the count-rate class. The measurement was made with 144Dy++ ions at SHIPTRAP. The dotted lines represent the one-sigma conﬁdence band.

6.3 Time dependence of resonance frequencies 59

815099.80

12 +

815099.75

815099.70

815099.65

815099.60 Cyclotron f requency /f Hz requency Cyclotron

815099.55

0 10 20 30 40 50 60

Count rate class / average# of ions

Figure 6.3: Cyclotron frequency as a function of the count-rate class. The mea- 12 + surement was made with C11 ions at SHIPTRAP. The dotted lines represent the one-sigma conﬁdence band.

6.3 Time dependence of resonance frequencies

The cyclotron frequency and its associated experimental standard deviation is obtained from the individual TOF resonance. The cyclotron frequency of the ion of interest νc,1 ± δνc,1 is recorded at time t1. The cyclotron frequency of the reference ion is recorded twice; νc,0 ± δνc,0 at time t0 and νc,2 ± δνc,2 at time t2 (ﬁgure 6.4). The cyclotron frequency of the two reference measurements are linearly interpolated to the time t1.

(t1 − t0) νc,ref (t1) = νc,0 + (νc,2 − νc,0) (6.2) (t2 − t0) and its standard deviation is given by s µ ¶2 µ ¶2 2 t2 − t1 2 t1 − t0 δνc,ref (t1) = (δνc,0) + (δνc,2) . (6.3) t2 − t0 t2 − t0 The result of the measurements is represented in terms of the cyclotron frequency ratio r = νc,ref (t1) and its relative statistical uncertainty is calculated to νc,1 be v uÃ ! Ã ! δr u δν 2 δν 2 stat = t c,ref + c,1 . (6.4) r νc,ref νc,1 60 Study of the accuracy of SHIPTRAP

Interpolated line

c,0

c,1

c,ref Cyclotron frequency

c,2

t t t

0 1 2

Time of measurement

Figure 6.4: Interpolation of the cyclotron frequencies of reference ion

At this end, a relative time-dependent uncertainty of 3 × 10−9 per hour due to the non-linear magnetic ﬁeld ﬂuctuation [Raut07a] was quadratically added to the statistical uncertainty of the frequency ratio. The combined uncertainty is given by,

q 2 −9 2 δrB = (δrstat) + [(t2 − t0)r(3 × 10 )] . (6.5)

In case of more than one measurements, the weighted mean of the frequency ratio r is given by

Pn i=1 wiri 1 r = Pn , wi = 2 . (6.6) i=1 wi δri and the uncertainty obtained is ,

1 δr = q (6.7) Pn i=1 wi 6.4 Investigation of the systematic uncertainty of SHIPTRAP 61

Table 6.1: Matrix of cross-reference measurements. The clusters given in the ﬁrst column were taken as ‘reference ion’ and clusters in the ﬁrst row were taken as ‘ion of interest’. A pair of cluster sizes is marked by ‘*’ in case a cross measurement was performed.

12 + 12 + 12 + 12 + 12 + 12 + 12 + C10 C11 C12 C15 C18 C19 C20 12 + C7 ** 12 + C9 *** 12 + C10 *** 12 + C11 ****

6.4 Investigation of the systematic uncertainty of SHIPTRAP

6.4.1 Cross-reference measurements To investigate the achievable precision of a mass spectrometer and to reveal possible systematic uncertainties, ions with well-known mass covering a large mass range are required. Carbon-cluster ions are well suited for such studies since they provide reference ions over the full mass range covered by SHIPTRAP with a spacing of only 12 atomic mass unit. Moreover, the use of cluster ions eliminates the uncertainty in the mass of the reference ions as long as the binding energies are small compared to the level of precision. Hence, the true value of the frequency ratios is exactly known, if cluster ions are measured using other cluster ions as reference. More than 100 such cross-reference measurements have been performed at SHIP- TRAP. For each individual TOF resonance, about 3000 ions were recorded in measurements between 15 minutes and one hour depending on the production rate of the cluster species under investigation. The duration of the quadrupolar excitation in the measurement trap was 1.2 s and the relative statistical uncertainty obtained was about 2 × 10−8 for each of the measurements. A matrix of the clusters which have been compared in the cross-reference measurements is shown in table 6.1. The results of the entire set of cross-reference measurements are represented in the ideograms [Agui86] shown in ﬁgure 6.5. Each experimental data point in the plot represents a Gaussian with a central value

er/r = (rmeasured − rtrue)/rmeasured, (6.8) a width δ(er/r) and an area proportional to 1/δ(er/r) where δ(er/r) is the uncertainty of the relative deviation. The ideogram of a cluster species is the sum 62 Study of the accuracy of SHIPTRAP

12 12 C10 C18 1.00

0.75

0.50

0.25

12 12C 1.00 C11 19

0.75

0.50

0.25

12C 12C 1.00 12 20

0.75

arbitraryunit

0.50

0.25

12 -6-4-20246 C15 1.00

0.75

0.50

0.25

-6-4-20246 -7 (er /r)/10 Figure 6.5: Ideograms of all carbon-cluster cross-reference measurements. The 12 + measurements with different reference ions are represented by symbols: C7 12 + 12 + 12 + (circles), C9 (triangles), C10 (rectangles) and C11 (inverted triangles). 6.4 Investigation of the systematic uncertainty of SHIPTRAP 63 of all such Gaussians associated with the individual cross-measurement, where that particular cluster was treated as the ‘ion of interest’. Different symbols are used in the ideograms to indicate different ‘reference ions’. The ideograms show that the distributions of the individual measurements are nearly Gaussian where a sufficient number of measurements was performed.

6.4.2 Mass-dependent systematic effect A cyclotron-frequency shift δν can arise for instance from the imperfection of the electric-quadrupole field or from a misalignment of the axis of the electrostatic trapping field and the magnetic-field axis in a Penning trap (see section 3.2). The frequency shift δν gives rise to an error in the calibration of B with a reference ion. As it is described in section 3.2 the relative error in the mass determination of an ion is δm/m = (δν/ν)((m − mref )/m). This mass-dependent effect can be studied using ions of well-known masses and large mass difference between ion of interest and reference ion. The carbon-cluster cross-reference studies have been performed to investigate mass-dependent systematic effects at SHIPTRAP. The results of the cross-reference measurements are shown in figure 6.6. Each

4 -8

-4 /r) / 10 r

-8

-12

-16

-20

0 12 24 36 48 60 72 84 96 108 120

m-m /u

ref

Figure 6.6: Deviation of the weighted mean of the frequency ratios from the true values as a function of (m − mref ).

data point represents the weighted mean of all individual measurements between 64 Study of the accuracy of SHIPTRAP two particular cluster species. The data analysis was performed as described in section 6.3. The mass-dependent uncertainty has been found to be in agreement with zero for small mass differences with (m − mref ) < 100 u. Hence, it is desirable to select the reference ion in the SHIPTRAP mass measurements such that the difference between the mass of ion of interest and reference ion is always less than 100 u. The n = 20 carbon cluster measurements suffer from a large scattering of the measured cyclotron frequencies as can be seen in figure 6.6. This might be the reason for the large deviation observed for the (m − mref ) > 100 u frequency ratios.

6.4.3 Systematic uncertainty The reduced χ2 of the distribution of the mean frequency ratio for the carbon- cluster species used in the cross-reference measurements was calculated to be χ2/N = 5.5 where " # X i 2 2 er χ = i (6.9) i δr and N is the total number of cross measurements. This high value might be due to the presence of a systematic uncertainty δrsys. The total uncertainty of a frequency ratio can be obtained by v u Ã ! u δr 2 δr = t(δr)2 + r × sys (6.10) total r

The one-sigma value of the systematic uncertainty was determined using equations 6.9 and 6.10 to be δr sys = 4.5 × 10−8 (6.11) r such that χ2/N is approximately one.

As seen from figure 6.6, there is a large deviation observed for the cross- reference measurements for the case of (m − mref ) > 100, which increases the systematic uncertainty. The one-sigma value of the systematic uncertainty was found to be 2.2 × 10−8 if the cross-reference measurements for the case of (m − mref ) > 100 u were excluded from the calculation. However, the value of systematic uncertainty has been considered according to equation 6.11 i.e. considering all cross-reference measurements to avoid an underestimation of the uncertainty. The frequency-ratio deviations after adding the systematic uncertainty are shown in figure 6.7, i.e. the deviations of the weighted mean of the frequency ratio from their true values is plotted for different carbon clusters which were 6.4 Investigation of the systematic uncertainty of SHIPTRAP 65

12 12 12 12 12 12

C C C C C C C 8 19

10 11 15 18 20 12

0 -8

-4

/r) /10 r

-8 (e

Ref erence C

-12

Ref erence C

Ref erence C -16

Ref erence C

-20

Figure 6.7: Deviation of the weighted mean of the frequency ratios of diﬀerent carbon clusters. The dashed lines indicate the systematic uncertainty, which was added quadratically for each measurement. The dotted lines indicate the systematic uncertainty if the data points for the case of (m − mref ) > 100 u were excluded from the calculation.

taken as the ‘ion of interest’ in the cross-reference measurements. The cause of the systematic uncertainty is not well-understood at present. A probable reason is the misalignment of the axis of the electrostatic trapping ﬁeld with respect to magnetic ﬁeld axis (section 3.2.2) at SHIPTRAP.

6.4.4 Summary The mass-dependent uncertainty was found to be in agreement with zero for small mass diﬀerences with (m − mref ) < 100 u. The one-sigma value of the systematic uncertainty has been found to be 4.5 × 10−8 for the SHIPTRAP mass measurement.

Chapter 7

On-line mass calibration by carbon-cluster ions

7.1 On-line mass measurements around A = 147

The neutron-deficient rare isotopes around A = 147 were investigated at SHIP- TRAP during two on-line experiments in October 2005 and December 2005, respectively. The on-line data presented in this chapter were collected from the above mentioned beamtimes. The investigated radionuclides were produced in the reaction 92Mo (58Ni,xpyn) at SHIP. The primary beam energy was 4.36 and 4.60 MeV/u during the two runs, respectively. The 58Ni primary beam hit a 0.626 mg/cm2 thick 92Mo target to produce radio-nuclei around 147Tm in a fusion evaporation reaction. The average intensity of the primary beam was around 200 particle-nA. The production cross sections of the reaction for the two used beam energies vary from 200 µb for 147Tm to 80 mb for 147Ho (estimated using HIVAP code [Reis81]). In total 18 nuclei were investigated in the two runs which are shown in figure 7.1. The masses of 9 nuclei were measured for the first time. The 147Tm measurement was most challenging because of the lowest production cross section (∼ 200 µb) and lowest half life (580 ms) among the measured nuclei. Only singly-charged ions were detected during the first run while in the second run doubly-charged ions were detected. This shows the improved vacuum condition and cleanliness in the stopping cell during the second run. Prior to the second beamtime pressure reached down to 10−10 mbar before the gas cell was filled with helium buffer gas. As mentioned in chapter 4, the radioactive ions were stopped and thermalized inside the stopping cell. The ions were cooled, accumulated and bunched in the buncher and then transferred into the purification trap. An isobaric selection of the nuclei was performed there by the mass-selective buffer gas technique (section 4.2). Figure 7.2 shows an example of a cooling resonance of isobars around 147Ho obtained at SHIPTRAP in the beam-time in October 2005 [Raut07]. An 68 On-line mass calibration by carbon-cluster ions

Figure 7.1: Nuclear chart displaying measured eighteen radionuclides. The masses of nine nuclides (red colored) were measured for the ﬁrst time, the masses of nine other were known before. [Raut07a].

quadrupolar RF excitation was applied for 200 ms in the purification trap to get a mass resolving power about 50000 in this example. Only one particular isobar was selected in the purification trap by fixing the cyclotron frequency. The selected nuclide was then transferred to the precision measurement trap where the mass was measured. As mentioned earlier (section 4.1.3), typical reference ions used in SHIPTRAP are 133Cs+ and 85Rb+. Hence, 133Cs+ was used as reference ion for singly-charged radioactive ions in the first run. To reduce the difference in m/q values between the ion of interest and reference ion, 85Rb+ was used as reference for the doubly- charged radioactive ions in second run. One of the aim of the present study was to test the carbon-cluster ions produced from the carbon-cluster ion source as reference ion in on-line mass measurement. 7.2 Carbon-cluster ions for off-line mass comparisons 69

147

147 147 147 Er

Ho Tb Dy

Ion countsIon

732350 732400 732450 732500

Excitation frequency / Hz

Figure 7.2: Cooling resonance of isobars around A = 147. An excitation time of 200 ms was used to resolve the isobars [Raut07].

Carbon-cluster ions were used for the first time as reference ions in the on-line mass measurement for short-lived nuclei during the second run in December 2005. 144 146 147 12 + Three radionuclides Dy, Dy and Ho were measured using C11 as refer- 133 + 85 + 12 + ence ion after off-line mass comparisons between Cs , Rb and C11. The results are presented in this chapter. In addition, the influence of the SHIPTRAP mass measurements on nuclear structure and the location of the proton drip-lines are also discussed.

7.2 Carbon-cluster ions for oﬀ-line mass comparisons

The masses of the stable nuclei 133Cs and 85Rb are known with relative uncertainties less than 1 × 10−10 [Brad99]. They are also easily produced at SHIPTRAP by means of the surface ion source (section 4.1.3). Hence, they are the ideal 70 On-line mass calibration by carbon-cluster ions candidate for the off-line test of the carbon-cluster ions. The masses 133Cs and 85 12 Rb were compared using C11 as reference prior to the on-line experiment using 12 C11 as reference. Table 7.1 summarizes the results of these off-line comparisons and table 7.2 gives the mass excesses ME = m−Au (where A is the atomic mass number and u is the unified mass unit). The measured mass excess of 85Rb was matching with the AME [Audi03] value within the uncertainty of SHIPTRAP measurement. The measured mass excess of 133Cs was found to deviate by 10 keV from AME which corresponds to a relative mass deviation of 8.3 × 10−8. However, it should be noted that only five TOF resonances were used to determine the mass excess of 133Cs and three TOF resonances were used to determine the mass excess of 85Rb.

Table 7.1: Summary of the results of the off-line mass measurements of 133Cs and 85Rb. Column one: measured ion; Column two: number of recorded scans Ns; column three: total number of ions Nion recorded in all scans; column four: measured frequency ratios r = νc/νref with their statistical (first bracket) and total uncertainty (second bracket) and Column five: relative total uncertainty.

−8 Ion Ns Nion Frequency ratio (δr/r)/10 r(σstat)(σtotal) 133Cs+ 5 9732 1.006859595(21)(50) 5.0 85Rb+ 3 4167 0.643269627(30)(42) 6.5

Table 7.2: Comparison of the mass excess values from the oﬀ-line mass measurements of 133Cs and 85Rb. Row one: measured nuclide; row two: resulting 12 + mass excess (and uncertainty) obtained at SHIPTRAP using C11 as reference ion and row three: mass excess as given by AME 2003 [Audi03].

Nuclide 133Cs 85Rb 12 + Mass excess/keV (Reference ion C11) -88060.8(6.2) -82170.4(5.1) Mass excess/keV (AME 2003) -88070.958(22) -82167.331(11) 7.3 Carbon-cluster ions for on-line mass comparisons 71

7.3 Carbon-cluster ions for on-line mass comparisons

The masses of the radionuclides 144Dy, 146Dy and 147Ho were measured using 12 C11 as reference during the beam-time in December 2005. Typical TOF resonances for these radio-nuclei obtained during the beam time are shown in the figure 7.3. It should be mentioned that the cluster ion source was tuned for the production 12 + of C11,12 since singly-charged ions were expected from the gas stopping cell. During the beam time it turned out that a large fraction of doubly-charged ions were extracted due to the improved cleanliness of the gas cell. Hence, they were used for the mass measurement. It was not possible to optimize the laser power (section 5.4.2) for the production of the appropriate low-size cluster due to the lack of time during the beamtime. Thus, the carbon-cluster ions did not match the m/q values of the ion of interest. The radionuclides were also measured using 85Rb+ as reference ion during the same beam time [Raut07] as the m/q 12 + value was closer. The results agree with those where C11 was used as reference ion. Table 7.3 summarizes the results and table 7.4 gives the mass excesses ME = m − Au (where A is the atomic mass numbers and u is the unified mass unit). It should be noted that the cluster measurements differed from rubidium and radionuclides measurements concerning the condition for buffer gas flow in the purification trap. Helium was directly fed into the purification trap using an electronic valve (BALZERS EVR 116) and the shutter-valve between the buncher and Penning trap was closed during all the carbon-cluster measurements. In case of rubidium and radionuclides measurements there was no direct flow of helium into the purification trap. The helium flow in the buncher was sufficient to reach into the purification trap via the beamline. These changes might have caused different conditions for damping in the Penning trap for the cluster and the rubidium/radionuclides measurement. The difference between the mass excesses of the investigated radionuclides as measured at SHIPTRAP and the values given in the literature (AME 2003) [Audi03] is plotted in figure 7.4. The measured mass excesses of 144Dy and 146Dy agree with [Audi03] which were mainly influenced by the values measured at GSI-ESR [Litv05]. The measured mass excess of 147Ho deviates from the previous value [Audi03], [Litv05]. Isomeric contamination in any one of the experiments could cause this deviation but the exact reason is not yet understood [Raut07]. However, the mass values obtained at SHIPTRAP with different reference ions agree with each other. The uncertainty of the primary result is tabulated in the table 7.3. The data evaluation followed the procedure described in chapter 6. The relative statistical uncertainty was about 2 × 10−8 for each measurement. The relative 72 On-line mass calibration by carbon-cluster ions

(a) (b)

(c)

Figure 7.3: (a) Time-of-flight of 144Dy++ as a function of the excitation frequency applied in the measurement trap for an excitation time of 900 ms. (b) Time-of-flight of 146Dy++ as a function of the excitation frequency applied in the measurement trap for an excitation time of 900 ms. (c) Time-of-flight of 147Ho++ as a function of the excitation frequency applied in the measurement trap for an excitation time of 600 ms. The solid line represents a fit of the expected resonance curve [Koni95] to the data points. 7.3 Carbon-cluster ions for on-line mass comparisons 73

Table 7.3: Summary of the results of the on-line mass measurements of 144Dy, 146Dy and 147Ho. Column one: measured ion; column two: half-life of the ra- dionuclei; column three: reference ion used for the mass calibration; Column four: number of recorded scans Ns; column ﬁve: total number of ions Nion recorded in all scans; column six: measured frequency ratios r = νc/νref with their statistical (ﬁrst bracket) and total uncertainty (second bracket) and column seven: relative total uncertainty.

−8 Ion T1/2 Reference Ns Nion Frequency ratio (δr/r)/10 r(σstat)(σtotal) 144 2+ 12 + Dy 9.1 s C11 3 2354 0.545222618(15)(29) 5.3 144Dy2+ 9.1 s 85Rb+ 6 3322 0.847580193(28)(45) 5.3 146 2+ 12 + Dy 33.2 s C11 5 6076 0.552774142(13)(28) 5.1 146Dy2+ 33.2 s 85Rb+ 13 13372 0.859319365(22)(43) 5.0 147 2+ 12 + Ho 5.8 s C11 4 14661 0.556589680(7)(26) 4.7 147Ho2+ 5.8 s 85Rb+ 9 11078 0.865250860(24)(44) 5.0

Table 7.4: Comparison of the mass excess values from the on-line mass measurements of 144Dy, 146Dy and 147Ho. Row one: measured nuclide; row two: 12 + resulting mass excess (and uncertainty) obtained at SHIPTRAP using C11 as reference ion; row three: resulting mass excess (and uncertainty) obtained at SHIPTRAP using 85Rb+ as reference ion and row four: mass excess as given by AME 2003 [Audi03].

Nuclide 144Dy 146Dy 147Ho Mass excess/keV -56570.5(7.1) -62536.5(6.9) -55738.7(6.4) 12 + (Reference ion C11)

Mass excess/keV -56570.1(7.1) -62554.7(6.7) -55753.6(6.9) (Reference ion 85Rb+)

Mass excess/keV -56580(30) -62554(27) -55837(28) (AME 2003) 74 On-line mass calibration by carbon-cluster ions

146 147 144

Dy Ho Dy

-20

-40

-60

AME2003

-80

Ref erence C

85 Mass Excess (AME2003-SHIPTRAP)/keVMass -100

Ref erence Rb

Figure 7.4: The mass excess of 144Dy, 146Dy and 147Ho measured with 85Rb 12 reference, measured with C11 reference, and as given by AME 2003 [Audi03].

time-dependent uncertainty due to magnetic ﬁeld changes was obtained to be 5 × 10−11 per minute from a measurement prior to the beam-time [Bloc07]. Its contribution to the primary result is tabulated separately in table 7.5 for each of the frequency ratio measurement during the beam-time where carbon-cluster was used as reference ion. Obviously, there is no contribution of uncertainty of the mass of the reference ion in case carbon-clusters are used as reference ion. The contribution to the mass-dependent systematic uncertainty is also negligible as described in section 6.4.2. However, a residual systematic δrsys −8 uncertainty of r = 4.5×10 was added in quadrature to the ﬁnal uncertainty.

The results also show that the carbon-clusters are useful as reference ion for the on-line mass measurements at SHIPTRAP. 7.4 Discussions of mass measurements around A = 147 75

Table 7.5: Uncertainty in the frequency ratio due to the magnetic field changes. Column one: measured ion; column two: reference ion; column three: time differences between the central time of the two reference measurements; column four: resulting relative uncertainty due to the magnetic field change.

δr −9 Ion of interest Reference ion δt(min)( r )B/10 144Dy2+ 12C+ 142.16 7.11 144Dy2+ 12C+ 49.1 2.45 144Dy2+ 12C+ 53.56 2.68 146Dy2+ 12C+ 71.83 3.59 146Dy2+ 12C+ 17.82 0.89 146Dy2+ 12C+ 18.79 0.94 146Dy2+ 12C+ 18.88 0.94 146Dy2+ 12C+ 142.16 7.11 147Ho2+ 12C+ 85.43 4.27 147Ho2+ 12C+ 21.39 1.07 147Ho2+ 12C+ 19.67 0.98 147Ho2+ 12C+ 1077.68 53.9

7.4 Discussions of mass measurements around A = 147

The results of the SHIPTRAP mass measurements for 18 radionuclides (ﬁgure 7.1), as obtained from the on-line experiments in October and December 2005, are included in the Atomic Mass Evaluation (AME). All available mass values not only from mass spectrometry but also from nuclear reactions and decays are used as input values in a least square evaluation of best values for atomic masses in AME [Waps03]. A detailed description of the atomic mass evaluation of the present work in collaboration with Georges Audi, CSNSM/Orsay, can be found in [Raut07a]. The ﬁnal results in terms of mass excess are summarized in the table B.1. The implication of the new mass values to the nuclear structure in that region of nuclear chart and also to pin down the position of the proton drip-line are discussed in this section. 76 On-line mass calibration by carbon-cluster ions

Table 7.6: Results of the atomic mass evaluation. Column one: measured nuclei; column two: resulting mass excess (and uncertainty) obtained at SHIP- TRAP [Raut07]; column three: mass excess (and uncertainty) as given in AME [Audi03]; column four: newly adjusted mass excess values(and uncertainty); column ﬁve: the rounded diﬀerences between the experimental data and the previous one from AME2003.

Nuclide Mass excess/keV Mass excess/keV Mass excess/keV ∆ M/keV (SHIPTRAP) (AME2003) (New) 143Tb -60420(50) -60430(60) -60420(50) 10(80) 147Tb -70740(11) -70752(12) -70746.2(8.1) 12(16) 143Dy -52169(13) -52320(200) -52169(13) 150(200) 144Dy -56570.1(7.1) -56580(30) -56570.1(7.1) 10(30) 145Dy -58242.6(6.5) -58290(50) -58242.6(6.5) 47(50) 146Dy -62554.7(6.7) -62554(27) -62554.9(6.7) 0(28) 147Dy -64197.9(8.8) -64188(20) -64194.7(8.1) -10(22) 148Dy -67861(13) -67859(11) -67860.2(8.2) -2(17) 144Ho -44609.5(8.5) -45200(300) -44609(8.5) 590(300) 145Ho -49120.1(7.5) -49180(300) -49120.1(7.5) 60(300) 146Ho -51238.2(6.6) -51570(200) -51238.2(6.6) 330(200) 147Ho -55757.1(5.0) -55837(28) -55757.1(5.0) 80(28) 148Ho -57990(80) -58020(130) -57990(80) 30(150) 146Er -44325.0(8.6) -44710(300) -44322.0(6.7) 390(300) 147Er -46610(40) -47050(300) -46610(40) 440(300) 148Er -51479(10) -51650(200) -51479(10) 170(200) 147Tm -35969.8(9.9) -36370(300) -35974.4(6.8) 400(300) 148Tm -38765(10) -39270(400) -38765(10) 500(400) 7.4 Discussions of mass measurements around A = 147 77

7.4.1 Two-neutron separation energies The two-neutron separation energy is expressed as

S2n(N,Z) = B(N,Z) − B(N − 2,Z), (7.1) where B(N,Z) is the binding energy of the nucleus with N neutrons and Z protons which is deﬁned as

2 B(N,Z) = [NMn + ZMp − M(N,Z)]c (7.2) for a nucleus of mass M(N,Z). Mn and Mp are the mass of a neutron and a proton, respectively. The two-neutron separation energy S2n is an important

Figure 7.5: Two-neutron separation energies of several neutron-deficient isotopes in the range Z ∼ 59−72 as a function of the neutron number N [Raut07a]. The solid black circles stand for the previously measured data and the open black circles stand for estimated data taken from [Audi03]. Data points marked by the red diamonds are the new data from SHIPTRAP and the blue circles 12 + indicate that the measurement has been performed using C11 ions as reference. parameter to visualize the nuclear shell structure effects through the mass sys- tematics in the case of neutron shells [Lunn03]. As a general trend S2n values 78 On-line mass calibration by carbon-cluster ions fall steadily with respect to the neutron number N for a given element. However, sudden drops in S2n values are observed at the magic numbers which mark shell closures. The two-neutron separation energy S2n as a function of N for the region around 147 Tm is shown in figure 7.5. The sudden drop in S2n is clearly visible for the magic number N = 82 followed by a plateau indicating the transition from spher- ical to deformed shape. In the figure 7.5 the solid black circles stand for the previously measured data and the open black circles stand for estimated data taken from [Audi03]. Those are connected by black dashed lines for a particular nuclide. The new data from SHIPTRAP beam-times which are included into AME are shown by red diamonds and are connected by solid red lines. Data points marked by blue circles indicate that the measurement has been performed 12 + 85 + using C11 ions as reference in addition to Rb . The new data confirm the trends obtained from the previous data but with lower uncertainty. The values of S2n for the isotones N = 81 are notably higher than the previously estimated values, which results in a flatter plateau for the elements Er, Ho and Dy.

7.4.2 Proton separation energies

In analogy with S2n(N,Z) the proton separation energy is deﬁned as

Sp(N,Z) = B(N,Z) − B(N,Z − 1). (7.3)

It is an important tool for determining the proton drip-line which is visualized as the locus of points corresponding to the minimum value of Z for which Sp < 0 at each value of N [Lunn03]. Figure 7.6 shows a chart of nuclide where the proton drip-line is indicated. The proton separation energies of measured Ho and Tm isotopes are tabulated 144,145 in the table 7.7. From data of the present work the Sp values of Ho and 147,148Tm were found to be negative and hence these nuclei are proton-unbound [Raut07b]. 147Tm is a known proton-emitter [Klep82], [Sell93]. However, the Sp values of the other three nuclei were estimated only with large uncertainties 147 [Audi03]. The new value conﬁrms the previously known Sp value of Tm [Sell93]. 147 The measurement of Ho slightly lowers its Sp value as compared to the earlier measurement. The measurement of 145Ho clearly shows that it is proton-unbound. The present mass measurement allowed to unambiguously determine the sign of Sp for these nuclei and hence to pin down the position of the proton drip-line. 7.4 Discussions of mass measurements around A = 147 79

protondrip-line

neutrondrip-line

Figure 7.6: Chart of the nuclides showing the location of the proton drip-line. The stable isotopes are indicated by solid squares [Wood97].

Table 7.7: Proton separation energies of measured Ho and Tm isotopes. Column one: measured nuclei; column two: half lives of the nuclei; column three: proton separation energies from SHIPTRAP measurements [Raut07b]; column four: proton separation energies from [Audi03].

Nuclide T1/2 Sp(keV) Sp(keV) (SHIPTRAP) (AME2003) 144Ho 700 ms -271(16) 160(360) 145Ho 2.4 s -161(10) -110(300) 146Ho 3.6 s 285(11) 570(200) 147Ho 5.8 s 492(10) 570(40) 147Tm 580 ms -1066(13) -1058(3) 148Tm 700 ms -560(40) -490(500)

Chapter 8

Summary and Outlook

In the frame of the present work, a carbon-cluster laser ion source for SHIP- TRAP was built up, tested, optimized, commissioned and employed for on-line 12 + mass measurements. Carbon-cluster ions Cn , 5 ≤ n ≤ 23, were produced by laser-induced desorption and ionization from a carbon sample. The thesis describes the design and use of a carbon-cluster ion source for the investigation of the accuracy of the SHIPTRAP Penning trap mass spectrometer. Also presented are the results of mass measurements of the radionuclides 144Dy, 146Dy and 147Ho for which carbon clusters were used for mass calibration. The description of systematic measurements with laser-produced carbon clusters is the main focus of this work. Carbon clusters covering a range of mass from 84 u to 240 u were used to test the performance of SHIPTRAP with respect to systematic uncertainties. A large number of measurements with cluster ions of diﬀerent sizes were performed, allowing a comparison over a wide range of frequency ratios. The measurements, their evaluation, and analysis are discussed. The mass-dependent uncertainty was found to be negligible for the −8 case of (m − mref ) < 100 u. However, a systematic uncertainty of 4.5 × 10 was revealed which is the present limit of mass accuracy of SHIPTRAP. In the course of this work, carbon clusters were utilized for the ﬁrst time as reference ions in an on-line mass measurement of short-lived nuclei. Absolute mass measurements of the radionuclides 144Dy, 146Dy and 147Ho were performed 12 + −8 using C11 as reference ion. A relative mass uncertainty of 5 × 10 was obtained. The results agree with measurements performed in the same run using 85Rb+ as reference ion. Thus, carbon clusters are useful as reference ions for on-line mass measurements provided the tuning of cluster ion source becomes easier. The major parts of the original contribution of this thesis can be summarized in the following points: • Development, installation, testing, optimization and use of a carbon-cluster ion source for the investigation of the accuracy of the SHIPTRAP mass spectrometer and for mass calibration (absolute mass measurement). 82 Summary and Outlook

• Cross-reference measurements between diﬀerent cluster species and their analysis to determine the limit of mass accuracy of SHIPTRAP. • Use of carbon cluster as reference ions in an on-line mass measurement for ﬁrst time.

It is important to understand the source for the observed systematic uncertainty at SHIPTRAP which is presently further investigated. In addition, further measurements with carbon clusters and other reference ions are foreseen. Especially the cases of large mass differences between the reference ion and the ion of interest shall be revisited. The lighter masses should be covered as well. The typically used SHIPTRAP reference 133Cs can cover the mass measurement of nuclei A < 233 without any additional mass-dependent uncertainty. However, in the near future SHIPTRAP will investigate heavy ions in the transfermium region. It is difficult to get any reference ion with well-known mass in this regime. For example, 219Rn can be easily accessible at SHIPTRAP from the radioactive ion source mounted at gas-cell, but its mass excess is known only by 8830.8 (2.5) keV. Carbon-clusters are the best choice for mass measurements of heavy ions because of their close mass values as well as only negligible uncertainty in their mass values. The full mass range of interest for SHIPTRAP is covered by the carbon clusters with a mass differences to the ion of interest of at most six mass units. Hence, the carbon-cluster ion source will play an important role in future SHIPTARP on-line mass measurements. There is always room for improvement. A better control over the laser power is desirable in the future use of cluster source. Furthermore, easy tuning for the cluster production of a particular size is required during the on-line measurement. Presently, the purification trap (originally meant for isobaric purification) is used to select the cluster size of interest out of the spectrum of different cluster sizes that are all coming simultaneously from the cluster-ion source. A quadrupole mass filter between the source and the purification trap would make the use of carbon-cluster as mass reference more convenient. A corresponding modification of the carbon-cluster ion source is planned for the near future. Appendix A

Principles of Time-of-ﬂight mass spectrometry

If a bunch of different ion species flies through an electrostatic beam transfer system, each ion of a particular charge-to-mass ratio q/m takes the same time to fly a fixed distance over that beam transfer system, assuming all the ions start to fly from the same position and fly in the same direction with approximately same initial energy. This describes the basic principle of the time-of-flight mass measurement method. If they are accelerated through a potential difference U, they have a kinetic energy 1 E = qU = mv2. (A.1) 2 Each ion flies with the same velocity v in the beam transfer system. Hence, to travel a distance l an ion takes time t is given by, Ã ! 1 l 2 qU = m (A.2) 2 t s m t = l (A.3) 2qU It is seen from equation A.3, for the ions which are accelerated through same potential difference U and having same charge state q, √ t ∝ m (A.4) Commonly, the unknown mass of an ion is determined by measuring its time- of-flight and also measuring time-of-flight of one or more ions of well known masses. However, this method is no longer used for precision mass measurement. The precision is typically in the order of 100 keV-1 MeV and isomeric states can not be resolved.

Appendix B

Values for used auxiliary data

Table B.1: Values for used auxiliary data from the NIST database [Nist].

1 u 1.660 538 782(83) x 10−27 kg Mass of proton 1.007 276 466 77(10) u Mass of neutron 1.008 664 915 97(43) u Mass of electron 5.485 799 0943(23) x 10−4 u

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Resume

Ankur Chaudhuri

Personal Details:

• Family Name: Chaudhuri

• Name: Ankur

• Date of birth: July 1, 1975

• Place of birth: Raigunj, India

• Nationality: Indian

Contact Information:

Institut fürPhysik Ernst-Moritz-Arndt-Universität Felix-Hausdorff-Str. 6 D-17487 Greifswald, Germany

Phone (Oﬃce): +49 3834 86 4755 Fax: +49 3834 86 4701 E-mail: [email protected]

Education:

• Ernst-Moritz-Arndt-Universit¨atGreifswald, Germany Ph.D. Candidate, Physics, 2007

• Banaras Hindu University, India M.Sc., Physics, 1999

• Malda College, University of North Bengal, India B.Sc. (Honours), Physics, 1996

Publications

in chronological order (backwards):

submitted:

• Direct mass measurements beyond the proton drip-line. C. Rauth, D. Ackermann, K. Blaum, M. Block, A. Chaudhuri, S. Eliseev, R. Ferrer, D. Habs, F. Herfurth, F. P. Hessberger, S. Hofmann, H.-J. Kluge, G. Maero, A. Martin,G. Marx, M. Mukherjee, J. B. Neumayr, W. R. Plass, W. Quint, S. Rahaman, D. Rodriguez, C. Scheidenberger, L. Schweikhard, P. G. Thirolf, G. Vorobjev, C. Weber, and Z. Di. submitted to Phys. Rev. Lett

• Mass measurements of neutron-deﬁcient radionuclides near the end-point of the rp-process with SHIPTRAP. A. Martin, D. Ackermann, G. Audi, M. Block, A. Chaudhuri, Z. Di, S. Eliseev, D.Habs, F. Herfurth, F. P. Hessberger, S. Hofmann, H.-J. Kluge, M. Mazzocco, M. Mukherjee, J. B. Neumayr, Yu. Novikov, W. Plass, S. Rahaman, C. Rauth, D. Rodriguez, C. Scheidenberger, L. Schweikhard, P. G. Thirolf, G. Vorobjev, and C. Weber. submitted to Eur. Phys. J. D

• Direct mass measurements around A=146 at SHIPTRAP. C. Rauth, D. Ackermann, G. Audi, M. Block, A. Chaudhuri, S. Eliseev, F. Herfurth, F. P. Hessberger, S. Hofmann, H.-J. Kluge, A. Martin, G. Marx, M. Mukherjee, J.B. Neumayr, W.R. Plass, S. Rahaman, D. Rodriguez, L. Schweikhard, P.G. Thirolf, G. Vorobjev, C. Weber, and the SHIPTRAP collaboration. submitted to Eur. Phys. J. A

2007:

• Carbon-cluster mass calibration at SHIPTRAP. A. Chaudhuri, M. Block, S. Eliseev, R. Ferrer, F. Herfurth, A. Martin, G. Marx, M. Mukherjee, C. Rauth, L. Schweikhard, G. Vorobjev. Eur. Phys. J. D 45, 47 (2007) 98 Publications

• Towards direct mass measurements of nobelium at SHIPTRAP. M. Block, D. Ackermann, K. Blaum, A. Chaudhuri, Z. Di, S. Eliseev, R. Ferrer, D. Habs, F. Herfurth, F.P. Hessberger, S. Hofmann, H.-J. Kluge, G. Maero, A. Martin, G. Marx, M. Mazzocco, M. Mukherjee, J.B. Neumayr, W.R. Plass, W. Quint, S. Rahaman, C. Rauth, D. Rodriguez, C. Scheiden- berger, L. Schweikhard, P.G. Thirolf, G. Vorobjev and C. Weber. Eur. Phys. J. D 45, 39 (2007)

• Mass measurements in the endpoint region of the rp-process at SHIPTRAP. M. Block, D. Ackermann, K. Blaum, A. Chaudhuri, Z. Di, S. Eliseev, R. Ferrer, D. Habs, F. Herfurth, F.P. Hessberger, S. Hofmann, H.-J. Kluge, G. Maero, A. Martin, G. Marx, M. Mazzocco, M. Mukherjee, J.B. Neumayr, W. R. Plass, W. Quint, S. Rahaman, C. Rauth, D. Rodriguez, C. Schei- denberger, L. Schweikhard, P. G. Thirolf, G. Vorobjev, C. Weber. Hyperﬁne Interactions (2007) DOI: 10.1007/s10751-007-9550-3

• Extraction eﬃciency and extraction time of the SHIPTRAP gas-ﬁlled stopping cell. S.A. Eliseev, M. Block, A. Chaudhuri, Z. Di, D. Habs, F. Herfurth, H.-J. Kluge, J.B. Neumayr, W.R. Plass, C. Rauth, P.G. Thirolf, G. Vorobjev, Z. Wang. Nucl. Instr. and Meth. B 258, 479 (2007)

• Octupolar Excitation of Ions Stored in a Penning Trap Mass Spectrometer - a Study Performed at SHIPTRAP. S. Eliseev , M. Block, A. Chaudhuri, F. Herfurth, H-J. Kluge, A. Martin, C. Rauth, G. Vorobjev. Int. J. Mass Spectrom. 262, 45 (2007)

2006: • Mass measurements of radionuclides near the endpoint of the rp-process at SHIPTRAP. G. Vorobjev, D. Ackermann, D. Beck, K. Blaum, M. Block, A. Chaud- huri, Z. Di, S. Eliseev, R. Ferrer, D. Habs, F. Herfurth, F. Hessberger, S. Hofmann, H.-J. Kluge, G. Maero, A. Martin, G. Marx, M. Mazzocco, J.B. Neumayr, Y. Novikov, W. Plass, C. Rauth, D. Rodriguez, C. Scheiden- berger, L. Schweikhard, M. Sewtz, P. Thirolf, W. Quint, C. Weber. Proc. of the Int. Symposium on Nuclear Astrophysics - Nuclei in the Cos- mos - IX, CERN, Geneva, Switzerland, June 2006, Proceedings of Science PoS(NIC-IX) 208, (2006)

• On-line Commissioning of SHIPTRAP. S. Rahaman, M. Block, D. Ackermann, D. Beck, A. Chaudhuri, S. Eliseev, Publications 99

H. Geissel, D. Habs, F. Herfurth, F.P. Hessberger, S. Hofmann, G. Marx, M. Mukherjee, J.B. Neumayr, M. Petrick, W.R. Plass, W. Quint, C. Rauth, D. Rodriguez, C. Scheidenberger, L. Schweikhard, P.G. Thirolf, C. Weber. Int. J. Mass Spectrom 251, 146 (2006)

• The ion-catcher device for SHIPTRAP. J.B. Neumayr, L. Beck, D. Habs, S. Heinz, J. Szerypo, P. G. Thirolf, V. Varentsov, F. Voit, D. Ackermann, D. Beck, M. Block, Z. Di, S. A. Eliseev, H. Geissel, F. Herfurth, F.P. Hessberger, S. Hofmann, H.-J. Kluge, M. Mukherjee, G. Mnzenberg, M. Petrick, W. Quint, S. Rahaman, C. Rauth, D. Rodriguez, C. Scheidenberger, G. Sikler, Z. Wang, C. Weber, W. R. Plass, M. Breitenfeldt, A. Chaudhuri, G. Marx, L. Schweikhard, A. F. Dodonov, Y. Novikov, M. Suhonen. Nucl. Instr. Meth. B 244, 489 (2006)

2005:

• The ion trap facility SHIPTRAP, Status and perspectives. M. Block, D. Ackermann, D. Beck, K. Blaum, M. Breitenfeldt, A. Chaud- huri, A. Doemer, S. Eliseev, D. Habs, S. Heinz, F. Herfurth, F.P. Hess- berger, S. Hofmann, H. Geissel, H.-J. Kluge, V. Kolhinen, G. Marx, J.B. Neumayr, M. Mukherjee, M. Petrick, W. Plass, W. Quint, S. Rahaman, C. Rauth, D. Rodriguez, C. Scheidenberger, L. Schweikhard, M. Suhonen, P.G. Thirolf, Z. Wang, C. Weber, and the SHIPTRAP collaboration. Eur. Phys. J. A 25, s01, 49 (2005)

Acknowledgements

First of all it is my pleasure to acknowledge my Ph.D. supervisor Prof. Dr. Lutz Schweikhard for providing me the opportunity to work under his supervision. My sincere thanks go to him for his scientific, moral, and financial support during the entire course of this work. I am specially grateful to him for his constant help, critical advices and active encouragement while working for the SHIPTRAP project despite the large geographical distance. I would like to specially thank Prof. Dr. H.-J. Kluge for his hospitality during my stay at GSI/Darmstadt. Many thanks to Dr. Gerrit Marx, not only for introducing me to the field of ion trapping, also for his guidance and friendly cooperation throughout the last four years. I am specially thankful to Dr. Michael Block for his guidance in the course of the SHIPTRAP experiment and also for reviewing the manuscript of the thesis. I would like to thank Dr. Frank Herfurth for many fruitful discussions with respect to the data evaluation. I thank Dr. Klaus Blaum and Dr. Manas Mukherjee for their valuable advices concerning the carbon-cluster experiment at SHIPTRAP. It has been my pleasure to be a part of the large SHIPTRAP collaboration. I especially like to thank my former colleagues Michael Dworschak, Dr. Sergey Eliseev, Ana Martin, Dr. Manas Mukherjee, Dr. Saidur Rahaman, Dr. Christian Rauth, Dr. Gleb Vorobjev, and Dr. Christine Weber for providing a friendly and stimulating working atmosphere at SHIPTRAP. I would like to thank my colleagues Martin Arndt, Sudarshan Baruah, Martin Breitenfeldt, Markus Eritt, Peter Grothkopp, Franklin Martinez, Hagen Ritter, Noelle Walsh, and Falk Ziegler for extending their help whenever I needed. I express my thank to my parents and Sudipta for providing me support and encouragement.

Declaration

Hiermit erkläre ich, daß diese Arbeit bisher von mir weder an der Mathematisch- Naturwissenschaftlichen Fakultätder Ernst-Moritz-Arndt-UniversitätGreifswald noch einer anderen wissenschaftlichen Einrichtung zum Zwecke der Promotion eingereicht wurde. Ferner erkläre ich, daß ich diese Arbeit selbständigverfaßt und keine anderen als die darin angegebenen Hilfsmittel benutzt habe.

Hereby I declare that, this work has so far neither been submitted to the Faculty of Mathematics and Natural Sciences at the Ernst-Moritz-Arndt- University of Greifswald nor to another scientiﬁc institution for the purpose of the degree of doctorate. Furthermore I declare that I have written this work by myself and that I have not used any other resources, other than those mentioned earlier in this work.

Ankur Chaudhuri