New Techniques of Laser Spectroscopy on Exotic Isotopes of Gallium and Francium

CERN-THESIS-2013-040 30/04/2013 pcrsoyo xtcIooe of Isotopes Exotic on Spectroscopy hsssbitdt h nvriyo acetrfrtedge of degree the for Manchester of University the to submitted thesis A e ehiuso Laser of Techniques New alu n Francium and Gallium nteFclyo niern n hsclSciences Physical and Engineering of Faculty the in colo hsc n Astronomy and Physics of School hmsJh Procter John Thomas otro Philosophy of Doctor 2013 2 Contents

List of Figures 7

List of Tables 11

Abstract 13

Declaration 15

Acknowledgements 19

1 Laser Spectroscopy in Nuclear Physics 21 1.1 Introduction ...... 21 1.2 This Work ...... 23

2 Theory of Laser Spectroscopy 25 2.1 Hyperﬁne Structure ...... 25 2.1.1 Magnetic Dipole Moment ...... 28 2.1.2 Hyperﬁne Anomaly ...... 29 2.1.3 Electric Quadrupole Moment ...... 29 2.1.4 Spin Determination ...... 30 2.1.5 Angular Distribution of Fluorescence Photons ...... 31 2.2 Isotope Shift ...... 32 2.2.1 Mass Shift ...... 32 2.2.2 Field Shift ...... 33 2.2.3 Atomic Factors ...... 33 2.2.4 King Plot Method ...... 34 2.3 Experimental Considerations ...... 35 2.3.1 Photon Absorption ...... 35 2.3.2 Atomic Linewidths ...... 35 2.3.3 Power Broadening ...... 36 2.3.4 Doppler Broadening ...... 36 2.3.5 Experimental Lineshapes ...... 36

3 Laser Spectroscopy on Exotic Isotopes 39 3.1 Methods of Production ...... 39 3.1.1 Isotope Separation On-Line ...... 39 3.1.2 In-Flight Separation ...... 40

3 Contents

3.2 The ISOLDE Facility ...... 41 3.2.1 ISOLDE at CERN ...... 41 3.2.2 Production of Radioactive Isotopes ...... 43 3.2.3 Ion Cooling and Bunching ...... 45 3.3 Laser Spectroscopy Techniques ...... 46 3.3.1 Collinear Laser Spectroscopy ...... 46 3.3.2 Resonant Ionisation Spectroscopy ...... 48

4 The COLLAPS Beam Line 51 4.1 Beam Line Components ...... 51 4.2 Hyperﬁne Structure Measurements via Doppler Tuning ...... 54 4.2.1 Calibration of Scanning Voltages ...... 55 4.3 Cooling/Bunching with ISCOOL ...... 56 4.4 Experimental Procedure ...... 57

5 Laser Spectroscopy of Gallium Using COLLAPS 59 5.1 Previous Studies on the Neutron-Rich Gallium Isotopes ...... 59 5.2 Motivation for the Neutron-Deﬁcient Gallium Isotopes ...... 62 5.3 Experimental Setup at ISOLDE ...... 65 5.3.1 ISOLDE Target ...... 65 5.3.2 RILIS Ion Production ...... 66 5.3.3 ISCOOL ...... 66 5.3.4 Atomic Transition ...... 68 5.4 Experimental Data ...... 69 5.4.1 Analysis Technique ...... 69 5.4.2 Lineshape of Optical Transitions ...... 71 5.5 Hyperﬁne Structure Results ...... 73 5.5.1 70Ga...... 73 5.5.2 68Ga...... 76 5.5.3 64Ga and 66Ga...... 78 5.5.4 63Ga...... 80 5.5.5 Nuclear Moments of 63Ga and 70Ga ...... 82 5.5.6 Shell-Model Calculations of 63Ga ...... 83 5.6 Isotope Shift Analysis ...... 84 5.6.1 Extracting the Changes in Mean-Square Charge Radii . . . . . 84 5.6.2 Experimental Errors ...... 87 5.6.3 Interpretation of the Changes in Mean-Square Charge Radii . 88 5.7 Conclusion and Outlook ...... 90

6 The CRIS Beam Line 93 6.1 A Brief History of CRIS ...... 93 6.2 CRIS at ISOLDE ...... 94 6.3 Components of CRIS ...... 96 6.3.1 Laser Setup ...... 96 6.3.2 Charge-Exchange Cell ...... 97 6.3.3 Ion Detection Setup ...... 99 6.3.4 Ultra-High Vacuum Interaction Region ...... 102 6.3.5 Hyperﬁne Structure Scanning Methods ...... 103

4 Contents

6.3.6 Hardware Control ...... 104 6.3.7 Decay Spectroscopy Station ...... 106 6.3.8 Oﬀ-Line Ion Source ...... 107 6.3.9 Electrostatic Ion Optics and Faraday Cups ...... 108 6.4 Summary ...... 115

7 Laser Spectroscopy of Francium Using CRIS 117 7.1 Motivation for the Radioactive Francium Isotopes ...... 117 7.2 Experimental Setup at ISOLDE ...... 118 7.2.1 ISOLDE Target ...... 118 7.2.2 Ionisation Process ...... 119 7.2.3 Experimental Procedure ...... 123 7.3 Experimental Analysis ...... 124 7.3.1 Experimental Eﬃciency ...... 124 7.3.2 Components of Experimental Eﬃciency ...... 126 7.3.3 Background Rate ...... 130 7.3.4 Study of Experimental Error from the Analysis of 221Fr . . . . 131 2 207,211,220,221 7.3.5 A(7s S1/2) values and Isotope Shifts of Fr . . . . . 136 2 2 7.3.6 Atomic Factors for the 7s S1/2 → 8p P3/2 Transition . . . . . 139 7.3.7 Changes in Mean-Square Charge Radii ...... 140 7.4 Conclusion and Outlook ...... 141

Appendix A Publications 143

References 145

Final word count: 28 462

5 6 List of Figures

2.1 Precession of I and J about the coupled angular momentum, F ... 26 2.2 Example hyperﬁne structure of a spectral line in 69Ga ...... 27

3.1 Diagrams of the ISOL and In-Flight beam production methods . . . . 40 3.2 Layout of the ISOLDE facility at CERN ...... 41 3.3 Image of the ISOLDE facility and location within the CERN accelerator complex ...... 42 3.4 Schematic drawing of a surface ion source ...... 44 3.5 Photo of ISCOOL ...... 45 3.6 Diagram of the electrode potentials in ISCOOL ...... 46 3.7 Diagrams of the collinear ﬂuorescence and resonant ionisation spectroscopy methods ...... 47

4.1 Schematic diagram of the COLLAPS beam line ...... 52 4.2 Diagrams of the COLLAPS light collection region ...... 53 4.3 Diagram of the COLLAPS voltage scanning system ...... 54 4.4 Calibration of the voltage scanning system ...... 55 4.5 Variation of the ampliﬁcation factor of the voltage scanning system . 56 4.6 Diagrams of the COLLAPS timing triggers ...... 58

5.1 Shell model orbital occupations of the protons and neutrons within the gallium isotopes ...... 60 5.2 Previously measured optical spectra for the odd-A 67-81Ga isotopes . . 61 5.3 Previously measured optical spectra for the even-A 72−80Ga isotopes . 63 5.4 Excitation energies and matter radii of the gallium isotopes ...... 64 + + + 5.5 21 and 4 /2 energies in zinc and germanium ...... 65 5.6 ZrO2 target yields ...... 66 5.7 The RILIS ionisation scheme for gallium ...... 67 5.8 A ToF measurement of 69Ga bunches from ISCOOL ...... 67 5.9 The atomic transition chosen in gallium for fluorescence detection . . 68 5.10 Measured hyperfine structure of 69Ga ...... 70 5.11 Optimised fits of the gallium spectra using different lineshapes . . . . 72 5.12 Measured hyperfine structure of 70Ga ...... 74 5.13 Hyperfine structure fits of 70Ga for different hyperfine coefficient values 75 5.14 Simulated hyperfine structure of 68Ga using known moment values . . 76 5.15 Measured hyperfine structure of 68Ga ...... 77 2 68 70 2 5.16 χ values for fits of Ga and Ga with varying A(5s S1/2) values . . 78 5.17 Measured single component of 64Ga...... 79

7 List of Figures

5.18 Measured single component of 66Ga...... 79 5.19 Measured hyperfine structure of 63Ga ...... 80 2 2 5.20 A(5s S1/2)/A(4p P3/2) ratio values of the gallium isotopes ...... 81 5.21 Changes in mean-square charge radii of the gallium isotopes, calculated using different KMS values ...... 86 5.22 Changes in mean-square charge radii of the gallium isotopes using the initial and final KMS value ...... 87 5.23 Changes in mean-square charge radii of the gallium isotopes, plotted alongside neighbouring isotope chains ...... 89

6.1 3D drawing of the CRIS beam line ...... 94 6.2 Schematic drawing of the CRIS beam line ...... 95 6.3 Diagram of the CRIS laser locations within ISOLDE ...... 97 6.4 Technical drawing of the CEC ...... 98 6.5 Schematic drawing of the CEC ...... 98 6.6 Technical drawing of the MCP and dynode plate ...... 100 6.7 Circuit diagram of the MCP electronics ...... 101 6.8 Screenshot of the MCP detection oscilloscope ...... 101 6.9 Differential pumping of the interaction region from the CEC . . . . . 103 6.10 Drifting effects of an ion beam with voltages applied to the CEC . . . 105 6.11 Infrastructure of the control of the main components used for data collecting with CRIS ...... 106 6.12 Layout of the implantation site in the DSS ...... 107 6.13 Diagram of the off-line ion source ...... 107 6.14 3D drawing of the CRIS beam line ...... 108 6.15 3D drawing of the vertical steerers ...... 109 6.16 Schematic drawing of the quadrupole triplet ...... 109 6.17 3D drawing of the bending plates ...... 110 6.18 3D drawing of the quadrupole doublet ...... 111 6.19 3D drawing of the ion kicker ...... 112 6.20 3D drawing of the deflector plates ...... 112 6.21 3D drawing of the horizontal and vertical steering plates ...... 113 6.22 3D drawing of the MCP and dynode plate within the DSS ...... 114 6.23 Schematic drawings of electron suppressed and un-suppressed Fara- day cups ...... 114

7.1 Ionisation scheme for the francium isotopes ...... 120 7.2 Example hyperfine structure of a spectral line in 221Fr...... 121 7.3 Diagram of the laser setup for the ionisation of francium ...... 122 7.4 Diagram of timing sequences for the CRIS experiment ...... 123 7.5 Measured hyperfine structures of 218Fr and 219Fr...... 125 7.6 Ion counts for varying 423-nm pulse powers ...... 128 7.7 Ion counts for varying 1064-nm pulse powers ...... 129 7.8 Background ion counts in a scan of 202Fr ...... 130 7.9 Measured hyperfine structure of 221Fr...... 132 2 221 7.10 Extracted A(7s S1/2) values of Fr ...... 133 7.11 Extracted centroid values of 221Fr...... 134 7.12 Extracted FWHM values for 221Fr...... 135

8 List of Figures

7.13 Measured hyperﬁne Structures of 207,211,220,221Fr ...... 136 7.14 King plot of the 423-nm and 718-nm transitions in francium . . . . . 139

9 10 List of Tables

5.1 Previously measured ground-state spins, and magnetic dipole and electric quadrupole moments for the odd-A 67−81Ga isotopes . . . . . 62 5.2 Measured hyperfine coefficients and isotope shift of 70Ga ...... 75 5.3 Measured hyperfine coefficients and isotope shift of 63Ga ...... 82 5.4 Measured nuclear moments of 63Ga and 70Ga ...... 82 5.5 Experimental and shell model comparisons of the nuclear moments of 63Ga, with I = 3/2 and I = 5/2 ...... 83 5.6 Shell model calculations of the first three predicted energy levels in 63Ga...... 84 5.7 Measured isotope shifts and changes in mean-square charge radii of the gallium isotopes ...... 85

6.1 Operational pressures of the diﬀerent regions within the CRIS beam line...... 102

7.1 Yields of the francium isotopes from the ISOLDE UCx target . . . . . 119 2 207,211,220,221 7.2 Measured A(7s S1/2) values and isotope shifts of Fr . . . 137 2 207,211,220,221 7.3 Comparison of the measured A(7s S1/2) values of Fr with literature values ...... 137 7.4 Comparison of the measured magnetic moments of 207,211,220,221Fr with literature values ...... 138 7.5 Comparison of the changes in mean-square charge radii of 207,211,220Fr with literature values ...... 141

11 12 Abstract

ABSTRACT OF THESIS submitted to The University of Manchester by Thomas John Procter for the Degree of Doctor of Philosophy and entitled

New Techniques of Laser Spectroscopy on Exotic Isotopes of Gallium and Francium.

Date of submission: 28/03/2013

The neutron-deficient gallium isotopes down to N = 32 have had their hyperfine structures and isotope shifts measured via collinear laser spectroscopy using the COLLAPS (COllinear LAser sPectroScopy) beam line. The ground-state spin of 63Ga has been determined as I = 3/2 and its magnetic dipole and electric quadrupole moments were measured to be µ = +1.469(5) µN and Qs = +0.212(14) b respec- 70 tively. The nuclear moments of Ga were measured to be µ = +0.571(2) µN and Qs = +0.105(7) b. New isotope shift results were combined with previously measured values of the neutron-rich isotopes and the changes in mean-square charge radii of the entire gallium isotope chain were investigated. Analysis of the trend in the neutron-deficient charge radii demonstrated that there is no evidence of anomalous charge radii behaviour in gallium in the region of N = 32. A sudden increase of the charge radii was observed at the N = 50 shell gap and an inversion of the normal odd-even staggering effect was seen at N = 40.

The development of the CRIS (Collinear Resonant Ionisation Spectroscopy) beam line is reported, detailing the components that have been installed since its proposal in 2008. Results from the first experimental campaign on francium are discussed to present the current operational status of CRIS. Initial results demonstrate an experimental efficiency of 1:70, collisional background rate of 1:105 and a resolution of 1.5 GHz. Analysis of the 221Fr data provided an experimental accuracy 2 of measurements using CRIS, with 44 MHz for the A(7s S1/2) hyperfine coeffi- 2 cients and 360 MHz for the isotope shifts. The A(7s S1/2) hyperfine coefficients and isotope shifts were measured for 207,211,220,221Fr and show good agreement with literature values. The isotope shifts were combined with literature values to deter- 2 2 mine the atomic factors for the 7s S1/2 → 8p P3/2 atomic transition so that changes in the mean-square charge radii could be extracted and compared with literature. The results demonstrate the successful commissioning of the CRIS experiment.

13 14 Declaration

No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualiﬁcation of this or any other university or other institute of learning.

15 16 Copyright Statement

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II Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made.

III The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in the thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permis- sion of the owner(s) of the relevant Intellectual Property and/or Reproductions.

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17 18 Acknowledgements

Throughout the course of my Ph.D I have been fortunate enough to have received a great amount of support with my work and to have spent time with some truly great people. The contributions from these people, with special thanks to Kieran, have gone beyond anything I could have imagined and for their help I am incredibly grateful. To have made my last three and a half years so enjoyable, as well as manageable, I would like to thank the following:

Jon Billowes Paul Campbell Bradley Cheal Thomas Cocolios The Core CRIS/COLLAPS Collaborators Family & Friends Everyone I played Football with Kieran Flanagan Everyone I played Golf with H2ZZ Productions ISOLDE Staﬀ & Users Members of IKS Kara Lynch Manchester Physics Department Staﬀ & Students Anne Morrow Manchester Nuclear Physics Group Charlotte Rigby Andy Smith

19 20 Chapter 1

Laser Spectroscopy in Nuclear Physics

1.1 Introduction

Nuclear physics, as a field of scientific study, developed in the early 20th century as scientists investigated the possible internal structures of the atom. One of the early theories was that the atom was made up of spaced out electrons surrounded by a “cloud” of positively charged matter. This theory is often referred to as the “plum pudding model” and was proposed by J.J Thomson [1] in 1904. Soon after, Ernest Rutherford deduced that the atom was in fact made up of a highly dense, positively charged central structure, known as the “nucleus”, surrounded by electrons with orbits much larger than the size of the nucleus. This theory was based upon an experiment performed in Manchester in 1909 by Hans Geiger and Ernest Marsden under the supervision of Rutherford [2]. The experiment is commonly referred to as the Geiger-Marsden experiment and involved detecting the scattering of alpha particles that were directed onto a thin, gold foil. The majority of the alpha particles were detected directly opposite the alpha source after travelling through the foil unaffected. However, a few were detected to have scattered through large angles after being incident upon highly dense objects with large separations. These objects were nuclei and from this discovery the field of nuclear physics was born. The topic suddenly became one of the forefronts of scientific interest, leading to a dramatic acceleration in the understanding of the theory.

Soon after this emergence of nuclear physics, a developing topic of interest in atomic physics was the idea of an isotopic shift of spectral lines. In 1912, Russell and Rossi [3] attempted to find differences in the spectral lines of thorium that were characteristic of the individual isotopes. A bridge between nuclear and atomic physics was built in 1913 when Bohr [4] proposed a formula for this change in transition frequency, caused by the differences in recoil kinetic motion of the surrounding electrons with the different nuclear masses. This effect became known as the mass

21 1.1. Introduction shift. The first measurement of this effect was performed by Aronberg [5] in 1918 while investigating spectra from radiogenic lead and normal lead. In the experiment he observed the isotope shift of the spectral line, however, the magnitude of the shift was larger than what could be explained by kinematic effects alone. In 1932, Rosenthal and Breit [6] deduced that the isotope shift was also associated with the size and shape of the nucleus and this was confirmed in 1949 by Brix and Kopfer- mann [7]. In theory this was suggesting that the change in internal structure of the nucleus between isotopes altered the surrounding electric field, and therefore the atomic structure. This became known as the field shift. Due to all of these combined efforts and subsequent investigations into the topic, the effect of the isotope shift is now well understood and is used as a means to measure the mean-square charge radius of the nucleus.

Alongside the discovery and study of the isotope shift there was interest in another phenomenon present in spectral lines known as the hyperfine structure. This effect causes a “splitting” of a spectral line, where several components are observed for a single electronic transition. The first observation of the hyperfine structure was published in 1892 by Michelson and showed the green resonance line of thallium [8]. At the time, the physics behind the cause of this structure was not well known and it was not until 1924 that the first interpretation was put forward by Pauli [9]. He proposed that the hyperfine structure was due to the different couplings of the nuclear spin with the total angular momentum of the outer electrons to produce the total resultant angular momentum of the atom. It then took until 1931 for a firm grasp on the theory to be made where Hermann Schüler published a paper on the make up of the hyperfine structure [10]. In the paper, Schüler explained how the coupling of the nuclear and electron angular momenta can create different shifts in the energy levels of the electrons and how the different spectral lines observed are due to the transitions between these available levels. The interactions causing the hyperfine structure of spectral lines is now a well-understood theory and is widely used to investigate the nuclear moments, as well as a general method to determine the nuclear spin.

With the discovery and developing understanding of the isotope shift and hyperfine structure, experiments were proposed to measure the nuclear spin, moments and changes in mean-square charge radii of different isotopes to compare with the expanding level of nuclear theory. One of the popular methods for doing so was via optical spectroscopy. Optical spectroscopy experiments study the spectra of ra- diated energy from matter and, up until its involvement with nuclear physics, had widely been used as a method for identifying materials by their spectral lines. The method of optical spectroscopy for nuclear physics varied in and out of favour in the early-mid 20th century, but developments took a large step forward with the invention of the tuneable laser in the 1970s. Exploiting their monochromatic nature and the high power of the lasers, experiments could accurately and effectively target the behaviour of spectral lines, forming the technique of laser spectroscopy. The additional advantages of the narrow bandwidth and tunability of the laser paired with the refined knowledge of electron orbitals, from improved computing power, made laser spectroscopy a desirable technique and a popular method for nuclear

22 1: Laser Spectroscopy in Nuclear Physics physics experiments.

Since the invention of the technique many stable and long-lived isotopes have had their nuclear properties investigated. However, these isotopes only account for a small fraction of the total number in the nuclear chart that are available from nuclear reactions. Quickly it became desirable to have access to these nuclei to perform exotic laser spectroscopy measurements, as well as using other nuclear physics techniques. For this reason, radioactive ion beam facilities were constructed for the production and delivery of exotic isotopes for investigation. Experiments performed at these facilities, on radioactive isotopes, are known as on-line experiments. The ﬁrst on-line laser spectroscopy measurement was performed on sodium in 1975 by Huber et al. at the Orsay synchrocyclotron [11].

Today, after several decades of development, laser spectroscopy is still one of the leading techniques for the investigation of nuclear structure. Ongoing improvements in the sensitivity and resolution of the technique allow the most exotic nuclei to be investigated with increasing precision, to rigorously test the current understanding of nuclear theory.

1.2 This Work

This thesis will report on the contribution towards two different scientific projects within the field of laser spectroscopy. These are: (i) the investigation into the behaviour of gallium isotopes far from stability using collinear laser fluorescence spectroscopy and (ii) the development of the new collinear resonant ionisation spectroscopy (CRIS) beam line for the study of radioactive francium isotopes. Both of which are based at the ISOLDE radioactive ion beam facility at CERN.

For the fluorescence studies, Chapter 5 will give an overview of the data from the latest experimental campaign on gallium and present the analysis done for this thesis on the hyperfine structure and isotope-shift measurements of the neutron- deficient isotopes between A = 63 and A = 70. The measurement of the ground- state spin of 63Ga will be discussed and new magnetic dipole and electric quadrupole moments will be presented for 70Ga as well as 63Ga. The isotope shift data of the neutron-deficient isotopes will be collated with those measured previously for the neutron-rich isotopes and the behaviour of the extracted mean-square charge radii across the entire isotope chain will be investigated.

For the CRIS experiment, Chapter 6 will give the history of the technique and describe the individual components of the setup that allow for the study of highly exotic radioisotopes. Chapter 7 will introduce the current experimental campaign on the francium isotopes and use the analysis of the data obtained on selected isotopes to demonstrate the current operational status of CRIS.

23 24 Chapter 2

Theory of Laser Spectroscopy

The hyperﬁne structure and isotope shift of atomic spectral lines provide a means of extracting the nuclear properties of isotopes from experimental measurements. This chapter will present the theory behind these two phenomena and how laser spectroscopy can be used to measure the nuclear spin, magnetic dipole and electric quadrupole moments, and changes in the mean-square charge radius.

2.1 Hyperﬁne Structure

To understand the origin of the hyperfine structure it is helpful to first look at the gross structure of an atomic transition. The gross structure is the transition of an electron between two energy states, assuming that it has no spin. This structure can be observed by the detection of a photon that is emitted when an electron de- excites from the excited atomic state. The energy of the photon is determined by the difference in energies of the electronic states. The observation of these photons, which are characteristic of a particular transition within an atom, are referred to as spectral lines. The fine structure is the splitting of one of these spectral lines resulting in a difference in energies of the atomic states due to the different couplings of the individual electron spin, s, with the orbital angular momentum, l, forming the electron angular momentum, j. Laser spectroscopy is an ideal technique for observing these spectral splittings as the monochromatic photons from the laser can be used to excite the individual transitions in the atom. The incident photons can be tuned to a frequency to match the energy of the transition, referred to as the resonant frequency, so that the energy of the photon is transferred into exciting the atom. After excitation, the system relaxes back to its initial state through the release of a photon by spontaneous emission. These photons can then be detected and, by monitoring the frequency of the laser inducing the excitation, be used to infer the energy of the transitions within the atom. As the resolution of the spectroscopy technique increases, the fine structure can be studied in more detail and, in most cases, finer splittings are observed known as the hyperfine structure.

25 2.1. Hyperfine Structure

The hyperﬁne structure is produced by small shifts in energy of the electron states (which are otherwise degenerate) due to the interaction between the electromagnetic ﬁeld of the electron at the nucleus and the nuclear magnetic and electric moments. This interaction is best described in terms of a resultant angular momentum, F , of the atom, made up of the coupling of the nuclear spin, I, and the total electron angular momentum, J. The coupling of I and J cause them both to precess about F as shown in Figure 2.1.

Figure 2.1: Precession of I and J about the coupled angular momentum, F .

The angular momentum, F , is made up of a number of components depending on the values of I and J. The number of components is either (2I + 1) or (2J + 1) depending on which is smaller. These new F components are shifted in energy depending on the interaction of the electrons with the properties of the nucleus. The energy of the electrons are determined by the potentials of the nucleus given by, V = VMonopole + VDipole + VQuadrupole + VOctupole + ... (2.1) where VMonopole is the Coulomb potential that determines the electron energy levels and the remaining terms cause perturbations to the energies, given by ∆E. In general, as the order of the term increases the eﬀect on the electrons decreases. The total substate-weighted shifts of these perturbed F states cancel each other out to sum to zero, given by, X ∆EF (2F + 1) = 0. (2.2) F An electron in an atomic J state can have components of its combined wave function in any of these new F states. For electric dipole transitions, an electron can be excited from one of these F states to another F state in a higher orbital level, if angular momentum is conserved by ∆F = ±1, 0 and 0 9 0. Using laser spectroscopy the energies of the transitions between these F states can be measured and used

26 2: Theory of Laser Spectroscopy to infer the splittings in energies from the J states. An example hyperﬁne splitting diagram for 69Ga is shown in Figure 2.2, highlighting the allowed transitions between the upper and lower F states.

Figure 2.2: An example diagram of atomic energy splittings in 69Ga due to its hyper- ﬁne structure. Included is a simulated optical spectra to demonstrate how the hyperﬁne structure is observed experimentally. The F states are shifted in energy from their corresponding J states; therefore, the experimentally observed transitions are measured relative to the unperturbed transition frequency.

As mentioned earlier, the hyperfine interactions between the nucleus and orbital electrons are intrinsically linked to the nuclear electromagnetic multipole moments. It is these moment values that cause the shifts in the atomic energies of the F states. Each electromagnetic moment has a parity of (−1)L for electric moments and (−1)L+1 for magnetic moments (where L = 0 for monopole, L = 1 for dipole and L = 2 for quadrupole, etc.). From the computation of the expectation value of the moments, all odd-parity static multipole moments vanish [12]. Therefore, the moments that remain are the electric monopole, magnetic dipole and electric quadrupole, etc. The electric monopole moment is related to the total charge of the nucleus, Ze, and does not affect the hyperfine structure. The magnetic dipole and electric quadrupole interactions are the terms of interest for this thesis and will be discussed shortly. The effects of the higher order moments are several orders of

27 2.1. Hyperfine Structure magnitude smaller than the dipole and quadrupole moments and are generally too small to be observed by laser spectroscopy and usually deemed to be negligible.

2.1.1 Magnetic Dipole Moment

The interaction of the nuclear magnetic dipole moment, µ, with the magnetic field created by the orbital electrons at the nucleus, Be, produces the dipole term in the hyperfine splitting. The magnetic dipole moment is a measure of the tendency of a nucleus to align with an externally created magnetic field. In a nucleus a magnetic moment exists only if I is greater than 0. In atomic states where J 6= 0 an effective magnetic field is produced by the orbital electrons. This dipole interaction between the moment and the magnetic field creates a hyperfine energy [13], which can be written as, H = −|µ||Be|cosθ (2.3) where Be is the magnetic field in the direction of J and θ is the angle between I and J. This hyperfine energy leads to a shift in the atomic state energies of each F state by, AK ∆E = (2.4) 2 where K = F (F + 1) − I(I + 1) − J(J + 1) and A is the hyperfine coefficient given by, µ Be A = (2.5) I J where µ is the magnetic moment measured on the quantisation axis and Be is the magnitude of the magnetic field.

This shift in the atomic state energy can be experimentally measured via laser spectroscopy and used to deduce A. However, from a single measurement of A, the magnetic dipole moment is very difficult to extract using Equation 2.5, as the magnitude of the magnetic field caused by the electrons needs to be considered. Assuming this field is constant across an isotope chain, measurements of one isotope can be calibrated with known values of another to calculate new magnetic moments. As long as the measurements have been performed on the same atomic transition the A factors can be compared, removing the dependency of the magnetic field, as well as J. By equating the magnetic fields of two isotopes, as given in Equation 2.5, the relationship can be given by, µ AI 0 = 0 0 . (2.6) µ A I

0 0 Therefore, if both of the spins are known and A and µ have already been determined for one of the isotopes, a measurement of A can be used to deduce its magnetic dipole moment.

28 2: Theory of Laser Spectroscopy

2.1.2 Hyperﬁne Anomaly

In practice, Equation 2.6 does not account for an effect known as the hyperfine anomaly. The hyperfine anomaly was first suggested by A. Bohr and V. F. Weisskopf in 1950, and as such is also known as the Bohr-Weisskopf (BW) effect [14]. Bohr and Weisskopf postulated that the measured hyperfine coefficient A for some nuclei will be different from what is expected for a point nucleus. This effect arises due to the distribution of the nuclear magnetisation within its volume and reduces the A hyperfine coefficient by, A = Apoint(1 + A) (2.7) where A is the magnetic hyperfine anomaly. Taking this hyperfine anomaly into account, Equation 2.6 can be modified [15] and expressed as,

0 µI AI A ,A 0 = 0 0 (1 + ∆ ) (2.8) µI A I

0 A ,A where ∆ = A − A0 is the diﬀerential hyperﬁne anomaly for two isotopes.

In relation to the work on the gallium isotopes presented in this thesis, previous studies into their hyperﬁne anomaly values have been performed by Stroke [16]. In 0 the study it was shown that for the gallium isotopes, like most light nuclei, ∆A ,A is <0.1% and can be deemed negligible for experimental measurements. For heavier nuclei the larger nuclear size is not negligible compared to the electron wavefunctions and needs to be accounted for. The anomaly is usually within 1% and can be treated as a contribution to the ﬁnal error value.

2.1.3 Electric Quadrupole Moment

The nuclear electric quadrupole moment contributes to the hyperfine splitting by coupling to the electric field gradient of the orbital electrons produced at the nucleus. The spectroscopic quadrupole moment is an observable used to describe the charge distribution within a nucleus and exists for nuclei with spin I ≥ 1. The classical form is the intrinsic quadrupole moment, Q0, in the rest frame of the nucleus defined by, Z 2 2 Q0 = (1/e) (3z − r )ρ dτ (2.9) where e is the charge of the electron, ρ is the charge density, z is the direction in the symmetry axis, r2 = x2 +y2 +z2 and dτ is the volume element of the charged nucleus that the integral is carried over. The electric quadrupole moment is measured in −28 2 barns, where 1 barn (b) = 10 m . A positive Q0 represents a charge distribution that is stretched in the z-direction (prolate), a negative Q0 is stretched in the x and y directions (oblate) and a zero value describes a spherical nucleus.

In spectroscopy measurements Q0 cannot be directly measured as the value is aﬀected quantum mechanically by the rotation of the nucleus. Instead, the spectro-

29 2.1. Hyperfine Structure

scopic quadrupole moment, Qs, is measured, which is the projection of Q0 on the quantisation axis. For a well-deformed nucleus in its ground state, Qs can be related to Q0 [17] by, I(2I − 1) Qs = Q0. (2.10) (I + 1)(2I + 3)

To cause the energy splittings in the hyperfine structure, the spectroscopic quadrupole moment interacts with the electric field at the nucleus produced by the orbital electrons. This interaction leads to a shift in the atomic state energies [13], when J ≥ 1, represented by, 3 K(K + 1) − 2I(I + 1)J(J + 1) B 2 ∆E = (2.11) 4 I(2I − 1)J(2J − 1) where K = F (F + 1) − I(I + 1) − J(J + 1) and B is the hyperfine coefficient given by, ∂2V B = eQs (2.12) ∂z2 where h∂2V/∂z2i is the electric field gradient at the nucleus.

The spectroscopic quadrupole moment can be deduced from experimentally measuring B and then comparing it with known B and Qs values for a diﬀerent isotope. Assuming h∂2V/∂z2i is constant across an isotope chain isotopes, they can be equated to give a relationship between Qs and B for two isotopes by,

Qs B 0 = 0 . (2.13) Qs B

2.1.4 Spin Determination

As well as being able to extract nuclear moments, the nuclear spin can also be determined from the measurement of the hyperfine structure. In cases where the hyperfine structure is well resolved and the frequency of each transition can be accurately measured the nuclear spin can often be deduced from the shifts in atomic state energies. In others it may be as simple as counting the number of hyperfine transitions. For more complex hyperfine structures additional measurements can be used to help determine the nuclear spin.

Intensity of Hyperﬁne Transitions

To assist in the analysis of the hyperﬁne structure the relative intensities of each hyperﬁne transition can be taken into account to identify the individual transitions. The intensity of each transition is dependent on the nuclear spin I, as well as the F

30 2: Theory of Laser Spectroscopy and J values of the upper and lower atomic states. These values can be expressed in terms of a Wigner 6-j symbol of the coupling of the angular momenta involved in the transition [18] to give the intensities as, 2 Flower Fupper 1 Intensity = (2Flower + 1)(2Fupper + 1) . (2.14) Jupper Jlower I

These intensities can be calculated for each transition, normalised to obtain relative intensities and used in comparison to experimental data for diﬀerent I values.

Ratio of Hyperﬁne Coeﬃcients

If clarity cannot be obtained from the intensities of the transitions then it is possible to use the ratio of the hyperfine A coefficients of the upper and lower atomic states to assist in determining I. Using Equation 2.5, the ratio of the hyperfine coefficient A values, for the upper and lower atomic states involved in the transition, can be given as, Aupper Be upper Jlower = (2.15) Alower Be lower Jupper where the nuclear properties, I and µ cancel out as they are independent of the electronic configuration. This ratio value remains constant across an isotopic chain, assuming the absence of the hyperfine anomaly, as the magnetic field and spin of the electrons are unaffected by the nucleus in different isotopes. Therefore, if this value has already been measured for other isotopes, the ratio can be extracted using different nuclear spin values and the closest match can be used to infer I. This technique is used for the spin determination of 63Ga in Chapter 5.

2.1.5 Angular Distribution of Fluorescence Photons

For the investigation of the intensity of hyperfine transitions using collinear laser fluorescence spectroscopy the angular distribution of the photons needs to be taken into consideration. The angular distribution of gamma rays from an aligned nucleus [19, 20] can be given by, X W (θ) = AkPk(cosθ) (2.16) k=even where k ≤ 2L, L is the multipolarity of transition (ML, EL), Pk(cosθ) are the even Legendre polynomials and Ak are the angular distribution coefficients that take into account the angular distribution from angular momentum coupling and any attenuation due to spin dealignment. As an atomic system excited with polarised laser light is analogous to an aligned nucleus and atomic transitions are dipole (E1), the angular distribution of fluorescent photons can be expressed as,

W (θ) = 1 + A2P2(cosθ). (2.17)

31 2.2. Isotope Shift

Using this equation and tabulated coeﬃcients of Ak for the spin values of the upper and lower atomic states, the angular distribution of the emitted photons can be determined.

2.2 Isotope Shift

The isotope shift is the shift in frequency of a spectral line in one isotope compared to another caused by the eﬀects of the nucleus on the energies of the atomic states. For transitions with a hyperﬁne structure, the isotope shift is given as the shift of the unperturbed transition frequency, which will be referred to as the centroid frequency. In its simplest form, the isotope shift can be written as,

0 0 AA A A δνIS = ν − ν (2.18)

0 where νA and νA are the centroid frequencies of the same atomic transition in 0 isotopes A and A. This shift in frequency arises from two diﬀerent contributions between the isotopes, 0 0 0 AA AA AA δνIS = δνMS + δνFS (2.19) 0 0 AA AA where δνMS is the mass shift contribution and δνFS is the ﬁeld shift contribution.

2.2.1 Mass Shift

The mass shift is the mass dependent contribution to the isotope shift that arises due to the recoil kinetic energy of a nucleus with ﬁnite mass. The shift in the centroid frequency of an atomic transition between isotopes is caused by the kinetic energy change in the two systems [21] given by,

mA − mA0 X 2 X ∆T = ( pi + 2 pi · pj) (2.20) 2m 0 m A A i i>j

0 where mA and mA0 are the masses of isotopes A and A in atomic mass units, pi is the momentum of the ith electron and the sum runs over all electrons in the atom. 2 The pi term is referred to as the normal mass shift (NMS) contribution and the pi · pj term is referred to as the speciﬁc mass shift (SMS) contribution. These two terms can be combined linearly to express the total mass shifted frequency as,

0 0 0 AA AA AA δνMS = δνNMS + δνSMS. (2.21)

The NMS is the eﬀect of the nucleus recoiling with the atomic electrons while the SMS is a result of momentum correlations between electron pairs that either rein- forces or acts against the NMS.

32 2: Theory of Laser Spectroscopy

2.2.2 Field Shift

The field shift between isotopes arises from the change in the spatial extent of the nuclear charge distribution due to the addition or removal of neutrons in the nucleus. Although nuclei have small radii compared to the size of electron wave functions, the sizes still have an effect on atomic transitions. The field effect [21] can be determined from the energy of a non-point like nucleus in the electronic charge density generated by the electrons, |ψ(0)|, and is given by,

2 Ze 2 2 E = |ψ(0)| hrchi (2.22) 60

2 where the mean-square charge radius [22], hrchi, is deﬁned in terms of the nuclear charge distribution, ρ(r), by,

R ∞ 2 2 0 ρ(r) r dV hrchi = R ∞ . (2.23) 0 ρ(r) dV The field shift can then be expressed as the effect of this change in energy on a spectral line for different isotopes by,

2 0 Ze 2 2 AA δνFS = ∆|ψ(0)| δhrchi (2.24) 6h0 where ∆|ψ(0)|2 is the change in the electron density at the nucleus, between the 0 2 AA upper and lower atomic states, and δhrchi is the change in the nuclear mean- square charge radius of the isotopes.

2.2.3 Atomic Factors

As the isotope shift is dependent on the interaction of the atomic electrons with the nuclear charge distribution, measurements of this effect can be used to determine the change in the mean-square charge radii of different isotopes. Grouping the contributing effects into different factors and expressing the field-shift contribution in terms of the change in mean-square charge radius, the overall isotope shift [23] can be written as,

0 0 A,A mA0 − mA 2 A,A δνIS = KMS + Felδhrchi (2.25) mA0 mA where KMS is the mass-shift factor and Fel is the ﬁeld-shift factor. These factors are dependent on the electron conﬁguration and are unique for each atomic transition. The mass-shift factor is a linear combination of the NMS and SMS factors, KNMS and KSMS respectively, given by,

KMS = KNMS + KSMS. (2.26)

33 2.2. Isotope Shift

The KSMS is dependent on the momentum correlations of the electrons and is complex to determine. However, the NMS is directly calculable [24] and can be obtained via, KNMS = ν0 · me (2.27) where ν0 is the experimental transition frequency and me is the electron mass in atomic mass units.

If the isotope shifts have been measured for an isotope chain the changes in mean- square charge radii can be determined using Equation 2.25. In order to extract the change in mean-square charge radii, the mass-shift and field-shift factors need to be known for the transition under study. One such method of determining these factors is via the King plot method, which will be described in the next section. If sufficient experimental data is not available to perform this method then the factors can be theoretically calculated. An example of one of these techniques is the use of multi-configurational Dirac-Fock calculations [22]. These are required in the case of gallium and are used later in this thesis.

2.2.4 King Plot Method

A common method for determining atomic factors is the King plot method [21], where isotope shifts of one atomic transition are plotted against those of a different transition where the atomic factors are already known. The mass-shift and field- shift factors can be determined for an optical transition if at least three of the isotopes have had their isotope shifts measured on the second transition. Multiplying Equation 2.25 by a modification factor,

0 m 0 mA µA,A = A (2.28) mA0 − mA gives, for transitions a and b,

0 0 0 A,A a a A,A a 2 A,A µ δνIS = KMS + µ Felδhrchi (2.29)

and 0 0 0 A,A b b A,A b 2 A,A µ δνIS = KMS + µ Felδhrchi . (2.30)

0 2 A,A Since δhrchi will be the same for both transitions, they can be combined into one equation that describes a straight line,

0 a 0 a A,A a Fel A,A b a Fel b µ δνIS = b µ δνIS + KMS − b KMS (2.31) Fel Fel with a gradient of, a Fel gradient = b (2.32) Fel

34 2: Theory of Laser Spectroscopy and y-axis intercept of, a a Fel b intercept = KMS − b KMS. (2.33) Fel

Therefore, plotting the isotope shift data from two optical transitions (modi- 0 ﬁed by µA,A ) against each other and extracting the straight line properties, the relationships of the atomic factors can be determined.

2.3 Experimental Considerations

2.3.1 Photon Absorption

In laser spectroscopy, photons with frequency νl are scattered oﬀ an atom in order to excite one of the atomic transitions, ν0, of an electron. Resonant absorption of the laser light occurs at νl = ν0 and excites the electron into a higher energy state. The cross section of this resonant absorption [25] can be given by, c2 σ ≈ 2 . (2.34) 2ν0 For typical laser frequencies, this value is much greater than the size of the atom and is enormous in comparison to typical atomic or nuclear scattering cross sections of around 10−20 - 10−28 m2. For example, the 417 nm transition in gallium has a resonant absorption cross section of approximately 9 × 10−14 m2.

2.3.2 Atomic Linewidths

For an excited atomic state there is an associated homogeneous linewidth, known as the natural linewidth, due to the uncertainties in its energy and lifetime. This linewidth aﬀects the range of frequencies of the incident photons that can induce the resonant excitation. Using the uncertainty principle, ∆E ·∆t ≈ ~, and assuming the mean lifetime of the state, τ, is equal to the time uncertainty, the natural linewidth can be given by, ∆E 1 Γ0 ∆ν = = = (2.35) h 2πτ 2π where Γ0 is the total decay rate of the atomic state. The natural linewidth of an atomic state is given by a Lorentzian proﬁle with a full width at half maximum (FWHM) given by Γ0 and typically ranges from a few Hz to hundreds of MHz.

35 2.3. Experimental Considerations

2.3.3 Power Broadening

As well as spontaneous emission that takes place in the excited atomic state there is also the presence of stimulated emission induced by the incoming photons from the laser. As the laser power increases, the photons increase the rate of stimulated emission in the excited state, decreasing the lifetime of the state. This power broadening eﬀect [25] produces an increase in the atomic linewidth given by, p Γ = Γ0 1 + I/Is (2.36) where I is the laser intensity and Is is the saturating laser intensity, where the rate of absorption equals the rate of stimulated emission on resonance, given by,

3 hπν0 Γ0 Is = . (2.37) 3c2 The power broadening eﬀect is homogeneous and increases the linewidth by a Lorentzian lineshape. Typical power broadening values can range from a few MHz to a few GHz depending on laser power. For diﬀerent laser spectroscopy measurements a balance needs to be found between a substantial power to observe the atomic transitions and a suitable power to be able to resolve them.

2.3.4 Doppler Broadening

In addition to power broadening eﬀects, further lineshape broadening can be present due to the thermal velocity spread of the atoms. The atoms have a thermal energy spread associated with the Maxwell-Boltzmann distribution. In the rest frame of the atom, the frequency of the laser appears to be shifted depending on ν0(vz/c), where vz is the velocity of the atom in the direction of the laser beam. This leads to the Doppler broadening of the linewidth [20] given by,

8kT ln21/2 δνD = ν0 2 (2.38) mAc where mA is the atomic mass, k is the Boltzmann constant and T is the absolute temperature of the atoms in Kelvin. This thermal distribution broadens the linewidth of the observed atomic transition by a Gaussian proﬁle.

2.3.5 Experimental Lineshapes

For the analysis of the data presented in this thesis, the lineshapes of the Lorentzian proﬁles were constructed using,

2 1 γL f(ν) = 2 2 (2.39) 4 (ν − ν0) + (γL/2)

36 2: Theory of Laser Spectroscopy

where ν are the experimental frequencies, ν0 is the frequency of the hyperﬁne transition and γL is the FWHM of the Lorenztian proﬁle.

The Gaussian proﬁles were constructed using,

2 −(ν−ν0) f(ν) = e 2c2 (2.40) where, γG c = √ (2.41) 2 2ln2 and γG is the FWHM of the Gaussian proﬁle.

In experiments that have comparable contributions from Lorentzian and Gaus- sian factors, the experimental lineshape can be described as a Voigt proﬁle, which is a convolution of the two lineshapes.

37 38 Chapter 3

Laser Spectroscopy on Exotic Isotopes

Since its implementation, experiments using laser spectroscopy have investigated the nuclear properties of the majority of stable isotopes. To further the understanding of nuclear structure, it is desirable to be able to measure short-lived radioisotopes that are far from stability. In order to perform these experiments, radioactive ion beam facilities have been constructed to produce the exotic isotopes. Additionally, diﬀerent laser spectroscopy techniques have been developed to improve the resolution and sensitivity of the measurements. This chapter will introduce the common methods of ion beam production, present the ISOLDE facility and describe the laser spectroscopy techniques that were used for the work partaken in this thesis.

3.1 Methods of Production

In order to perform experiments in the exotic regions of the nuclear chart, experimental beam facilities have been built that can produce rare nuclei with the required yields for investigation. These facilities are known under different names, such as isotope separators or radioactive ion beam facilities, and each have varying techniques, but they all aim to provide the highest yields of exotic nuclei. Many facilities exist around the world that provide exotic isotopes for nuclear physics experiments, with the two most common methods using on-line and in-flight separation. Both techniques use an accelerated primary beam to initiate the production but differ due to their target types and beam extraction methods.

3.1.1 Isotope Separation On-Line

The isotope separation ion source (ISOL) method uses a high intensity primary beam of light particles that impinge onto a thick, hot target, see Figure 3.1.

39 3.1. Methods of Production

Figure 3.1: Diagrams of the ISOL and In-Flight ion beam production methods. The ISOL method utilises an accelerated, light ion beam on a thick target to produce reaction products whereas the In-Flight method uses a heavy ion beam on a thin target to generate beam fragments.

Within the target there are three main channels that produce the majority of the reaction products: spallation, fragmentation and fission [26]. These reaction products diffuse out of the hot target, are ionised and then subsequently accelerated by a potential placed on the target. This method produces a large yield (>1011/s) of nuclei, stable and non-stable; therefore, it is essential for these ions to be mass separated to pick the isotope of interest. Once mass selected, the ion beam can then be delivered to an experimental setup for investigation. The ISOL method has the advantage of being able to produce a wide variety of products that have excellent ion-optical properties. However, due to the time of extraction from the target, the production of isotopes is generally limited to cases with half-lives longer than 10 ms. Also, the method is chemistry-dependent due to chemical reactions within the target and the ionising potential of different elements.

3.1.2 In-Flight Separation

The in-ﬂight method is an inversion of the ISOL method, where accelerated heavy ion beams impinge onto a thin target, as shown in Figure 3.1. Here, the heavy ions are fragmented in the thin target and retain the majority of their forward momentum. These fragments then continue in their original path and enter an electromagnetic fragment separator before delivery of the selected beam to experimental setups. This method is independent of chemistry and, due to the fast production and exit of the fragments from the target, can produce ion beams with half-lives down to ∼ 1 µs. However, the technique is limited in scope by providing yields generally lower than those provided by the ISOL method and producing energetic beams with poorer ion-optic qualities.

40 3: Laser Spectroscopy on Exotic Isotopes

3.2 The ISOLDE Facility

The ISOLDE facility is an ISOL isotope separator based at the CERN particle accelerator facility in Switzerland [27]. ISOLDE stands for Isotope Separator On- Line DEvice. The facility utilises accelerated protons from the CERN accelerator complex in order to produce highly exotic nuclei. Currently, ISOLDE can produce over 600 isotopes of 70 different elements. The facility uses fixed targets that provide a wide array of reaction products that are ionised, extracted, accelerated, mass separated and then delivered to different experimental setups for study. The current arrangement of the ISOLDE facility, displaying the production sites, beam delivery system and experimental hall is shown in Figure 3.2.

Figure 3.2: Layout of the ISOLDE facility at CERN. 1.4 GeV protons from the CERN accelerator complex impinge onto two ISOLDE targets. The reaction products are then accelerated, mass selected and delivered to the experimental hall with the option of being cooled and bunched by a gas-ﬁlled linear Paul trap.

3.2.1 ISOLDE at CERN

The first demonstration of isotope separation was performed by Otto Kofoed- Hansen and Karl Ove Nielsen in 1951 at the Neils Bohr Institute [28]. They accelerated deuterons in a cyclotron and impacted them on to a beryllium target to produce neutrons. These neutrons were slowed down in paraffin and then used to induce fission in uranium. The fission fragments were ionised, accelerated and then mass separated. Krypton was one of the first elements to have been produced and separated using this setup [29]. Kofoed-Hansen and Nielsen continued development at the Institute and then in 1967, after the cyclotron had been removed, they assisted

41 3.2. The ISOLDE Facility in introducing a similar facility at CERN.

At CERN, a target and separator facility was constructed to utilise the 200 MeV external proton beam produced by the Synchro-Cyclotron (SC). This facility became known as ISOLDE. The facility was continually upgraded throughout the 1970s and 80s and a wealth of data and experience was obtained. After the SC shut down, the facility was transferred to a new site in 1992, in order to operate at its most eﬃcient within the developing high energy accelerators. The new site was chosen to allow 1 GeV protons from the proton synchrotron booster (PSB) to be delivered to the ISOLDE targets. The facility was then upgraded in 1999 to be able to receive 4 µA proton beams at 1.4 GeV from the PSB. The ISOLDE facility continues to be used as a 24 hour facility at this location and there are plans for a high intensity and energy upgrade in the near future known as HIE-ISOLDE [30]. The upgrade will prepare the target area to accept 2 GeV protons from the developed CERN accelerator complex, to increase the production yields of isotopes from the targets, and improve the energy of the post-acceleration system (REX-ISOLDE). An image of ISOLDE within the CERN accelerator complex is shown in Figure 3.3.

Figure 3.3: Image of the ISOLDE facility and accelerator complex. The linear accelerator facility [rectangle] ionises hydrogen and then accelerates the protons to 50 MeV for injection to the PSB [small circle]. Here, the protons are accelerated to 1.4 GeV and then delivered to the ISOLDE facility [square] or the proton synchrotron [large circle] for further acceleration.

42 3: Laser Spectroscopy on Exotic Isotopes

3.2.2 Production of Radioactive Isotopes

The ISOLDE facility consists of several specifically designed elements that allow it to provide many different beams of radioactive ions that are suitable for exper- imentation. Different targets, ion production techniques and separators are used, along with many electrostatic optics, to provide the optimised ion beam.

Radioactive Targets

In the ISOLDE facility there are two target areas that have been built for radioactive beam production. The two target areas are referred to as the GPS and HRS targets, due to the mass separators that follow them (see Mass Separation in this section for details). Within the target areas are stations where interchange- able targets can be installed and removed on demand. For ISOL facilities, such as ISOLDE, the type of target material is important in order to produce the ion beams of interest. Different target materials are used to provide the purest production of the radioactive isotope of interest, such as: molten metal, solid metal, carbide and oxide targets [31]. The choice of target material is dependent on the chemistry of the production of the element of interest and the efficiency of the extraction of the element from the target. 1.4 GeV protons from the PSB impinge onto the targets, producing the many reaction products. The PSB provides intense proton pulses with an average current of about 2 µA. The targets are heated up to over 2000℃ to allow the products to diffuse out of the target towards an ion source. Diffusion times are typically of the order of a few milliseconds and are dependent on the target material, temperature and point of production. The targets are held at a high potential, up to ∼ 60 kV, so that once the products have been ionised in the ion source they are accelerated away to the equivalent energy in keV.

Ion Sources

Within each target station are ion sources that ionise the reaction products so that they can be accelerated away as an ion beam. ISOLDE utilises three diﬀerent techniques for producing the ion beams:

i The surface ion source, shown in Figure 3.4, is the simplest of the ion production methods. The principle of the surface ion source is to ionise the atoms on a surface that has a work function higher than that of the atom. After the impact of the protons on the target, the atoms diﬀuse through the container, come into contact with the surface of the extraction line and transfer an electron. The extraction line is typically made of tantalum or tungsten and can be heated up to 2400℃.

ii The plasma ion source is used as an ion production method for atoms that cannot be surface ionised. In this set up the atoms diﬀuse into a plasma to be

43 3.2. The ISOLDE Facility

Figure 3.4: Schematic drawing of a surface ion source. The CERN protons impinge onto the target producing the reaction products. The products diﬀuse out of the target, ionise on the surface of the extraction line and are then accelerated away by the target potential.

ionised by electron collision. The plasma is produced by ionising a gas mixture, usually argon and xenon, by electrons accelerated between the transfer line and extraction electrode. iii The laser ion source is used to improve the yield and purity of the ion beam by resonantly ionising the produced atoms. In ISOLDE, the RILIS (Resonant Ionisation Laser Ion Source) [32] system has been implemented. In comparison to the other ion production techniques, the RILIS technique selectively chooses an atomic transition to resonantly ionise a speciﬁc element and can greatly improve its production out of the target. The RILIS setup sends pulsed lasers into the extraction line to stepwise ionise the atom of interest. The laser ion source is continuously being developed to incorporate new ionisation schemes for different radioactive isotopes and is now used in the majority of experiments at ISOLDE [33].

Mass Separation

After the ions have been produced and accelerated from the ISOLDE targets they are transported for mass separation. In ISOLDE there are two diﬀerent mass separators for the two target areas. These are the GPS (General Purpose Separator) and HRS (High Resolution Separator) separators [34]. The GPS allows three diﬀerent mass selected beams, within ± 15%, to be delivered simultaneously to experiments via individual beam lines (low mass, central mass and high mass). It consists of a single 70° magnet with a bending radius of 1.5 m and has a mass resolving power, M/∆M, of 2400. The HRS produces a single ion beam and utilises two separator magnets, of 90° and 60°, for higher mass resolution. During experimental runs the

44 3: Laser Spectroscopy on Exotic Isotopes

HRS routinely operates with a mass resolution of 3000 - 4500 [35]. It is to be noted that the mass separators do not completely remove all unwanted isotope masses. Collisions of the ion beam with gas molecules induce a spread in energy and change the direction of the ions. This results in a baseline acceptance of all nearby masses of a factor of ∼ 10−5 compared to the intensity of the selected mass beam [36].

3.2.3 Ion Cooling and Bunching

Before delivering the mass selected beam to the experimental setups, the ions can be cooled and delivered as bunches by a gas-ﬁlled linear Paul trap [37, 38], known as ISCOOL, pictured in Figure 3.5.

Figure 3.5: Photo of ISCOOL taken during its installation.

The cooling nature of ISCOOL is to minimise the energy spread and transverse emittance of the ion beam. The structure of the trap was designed by Petersson and Podadera [39] and consists of injection electrodes, a gas-filled radio-frequency quadrupole trap (RFQ) and extraction electrodes. The ion beam is cooled within the RFQ before being bunched and accelerated away by the extraction electrodes. The trap is floated on a high voltage (HV) platform, at a value slightly below the target potential, so that the ion beam is slowed down to ∼100 eV on entry. The platform voltage is connected to a high precision voltmeter, via a voltage divider, to monitor the voltage. This voltage determines the final energy of the re-accelerated/extracted beam. The RFQ is made up of four rods, which are oppositely paired with the same phase and voltage. The potential oscillates, providing a net force towards the central axis of the device. The inside cavity of the RFQ contains a helium buffer gas, typically 0.01 - 0.1 mbar, to slow and thermalise the ion beam to room temperature.

45 3.3. Laser Spectroscopy Techniques

The bunching operation of ISCOOL is to accumulate the ions within the trap so that they can be periodically delivered to experiments as bunches. ISCOOL is segmented into a series of electrodes, with graded steps in potential, to guide the ions to the end of the chamber. The electrodes at the extractor end of the trap control the bunching of the ion beam. A small DC potential (∼ +20 V) is applied to the end plate, compared to the rest of the electrodes, causing the ions to bunch up at the end of ISCOOL, shown in Figure 3.6. After a set amount of time the potential can then be dropped to release the ion bunch and then reapplied to start the collection of the next ion bunch.

Figure 3.6: Diagram of the electrode potentials in ISCOOL. Included are the two electrode potential settings used to trap the ions before they are released as bunches.

3.3 Laser Spectroscopy Techniques

Diﬀerent experimental methods have been developed at radioactive ion beam facilities in order to investigate the exotic nuclei that are produced. Two common laser spectroscopy techniques that are in practice at ISOLDE are: collinear laser spectroscopy and resonant ionisation spectroscopy.

3.3.1 Collinear Laser Spectroscopy

One of the main hindering factors of laser spectroscopy is the low experimental resolution due to the broadening of spectral lines, arising from the thermal motion of the ions under measurement. The extent of these eﬀects can be up to several GHz (∼ 4 GHz for neutron-rich Cu [40]) from the Doppler broadening of atoms within a

46 3: Laser Spectroscopy on Exotic Isotopes heated ion source. Therefore, it is desirable to have an experimental method that can minimise these eﬀects in order to improve the resolution of hyperﬁne structure measurements. Collinear laser spectroscopy (CLS) achieves this by accelerating the ions, to reduce their Doppler width, before collinearly overlapping them with a laser beam, as shown in Figure 3.7.

Figure 3.7: Diagrams of the collinear laser spectroscopy and resonant ionisation spectroscopy methods (see text for details).

The method was first demonstrated on the hydrogen molecular ion HD+ by Wing [41] and independently proposed by Kaufman [42] in 1976. CLS reduces the broadening effects by accelerating the ions to reduce their longitudinal velocity spread, δv. By differentiating the kinetic energy of the beam, the energy spread of the ions can be given as, δE = mAvδv (3.1) where δE is the energy spread of the ions, determined by the ion source, and v is the accelerated velocity. As δE remains constant under acceleration, an increase in the velocity leads to a reduction in the velocity spread of the ions. As the Doppler width of an observed optical transition frequency, ν0, is given by,

δνD = ν0(δv/c) (3.2) the reduction in the Doppler width caused by the acceleration can be expressed as, δE δν = √ ν D 2 0 (3.3) 2eUmAc where eU is the kinetic energy of the ions in eV. For a typical ISOL target with δE ≈ 1 eV, a beam of gallium, accelerated up to 60 keV, measured on an optical transition of 7 × 1014 Hz, will have a reduced Doppler width of ∼ 8 MHz.

47 3.3. Laser Spectroscopy Techniques

As well as the Doppler reduction of the ion beam, CLS has technical advantages that make it a popular method of laser spectroscopy. In non-collinear laser spectroscopy experiments the hyperfine structures are measured by manually scanning the frequency of the laser. In CLS it is possible to lock the laser to a reference frequency and scan the hyperfine structure by applying a secondary accelerating voltage to Doppler tune the ions. This technique is beneficial as it reduces the stability and systematic issues that are involved with changing the output from a laser system. For an ionic beam, the scanning voltage is usually applied to the laser/ion interaction region, whereas for atoms the voltage is applied to the point of neutralisation. Another advantage of the collinear method is that potentially every atom in the beam can contribute to the resonance signal. This is achieved by collinearly overlapping the atoms with the laser beam, shown in Figure 3.7, in theory allowing up to 100% of the beam to interact with the laser depending on the length of the interaction region and the experimental cross sections.

For CLS experiments, the main method of investigation is via the detection of resonant fluorescent photons using photo-multiplier tubes (PMTs). The PMTs are situated to maximise the solid angle for detecting the photons and to minimise background counts associated with scattered light. The spontaneous emission lifetime of the chosen atomic transition should be much shorter than the flight time of the ion through the interaction region to allow the upper state to de-excite to the lower state. CLS allows hyperfine structure measurements to be made with high resolution, however, the detection efficiency of the method is limited and re- stricts its sensitivity. The efficiency of a PMT varies for different wavelengths and the angular distribution of the fluorescence photons makes it impossible to detect all the events. Additionally, there are inherent detection problems associated with PMT dark counts and background counts from the scatter of laser light. Taking all these factors into account, the technique is generally limited to yields above 100 - 1000 atoms/s.

3.3.2 Resonant Ionisation Spectroscopy

Resonant ionisation spectroscopy (RIS) is a technique that has been developed for sensitive measurements of nuclei via laser spectroscopy. RIS has been successfully demonstrated on isotopes with yields as low as 0.01 ions/s [43]. For the technique, atoms are resonantly ionised within the ion source and then extracted, accelerated and delivered to a detection station, shown in Figure 3.7. The technique is performed by using lasers to resonantly excite the atom to a higher energy state and then ionising the atom via a Rydberg or auto-ionising state, or directly into the continuum. The ﬁrst demonstration of RIS was performed on a rubidium vapour in 1972 by Ambartzumian and Letokhov [44]. The advantage of RIS over CLS is the improvement in detection eﬃciency by detecting ions rather than photons. In theory, it is possible to detect 100% of the resonant ions compared to the limited sensitivity of detecting photons with CLS. The sensitivity is also assisted by a lower background rate, although background counts can still be present from non-resonantly ionised atoms as well as dark counts of the ion detector. The main disadvantage with RIS

48 3: Laser Spectroscopy on Exotic Isotopes is the low resolution available due to thermal Doppler broadening (for example ∼ 4 GHz for neutron-rich Cu [40]). A solution to this problem is to combine the geometry of CLS with the detection method of RIS to have a complementary pairing of high resolution and high sensitivity. This method forms the principal idea behind the CRIS beam line that is described in Chapter 6.

As the RIS technique has been demonstrated as a valuable tool for selectively ionising elements, it has been implemented at many radioactive ion beam facilities as a type of ion source (see Section 3.2.2). The ﬁrst laser ion source was demonstrated at the IRIS facility in 1991 and improved the ionisation eﬃciency of ytterbium from 0.2% (by surface ionisation) to 35% [45]. The method uses stepwise ionisation to select the isotope of interest, reducing isobaric contamination and can even select between ground and isomeric states, which would not be possible with mass separation.

49 50 Chapter 4

The COLLAPS Beam Line

The COLLAPS (COLlinear LAser sPectroScopy) beam line [46, 47, 48] is an experimental setup at ISOLDE for performing high precision collinear laser spectroscopy. The beam line was constructed in the early 1980s and was one of the ﬁrst on-line CLS experiments. COLLAPS utilises the collinear geometry to greatly reduce the Doppler broadening of spectral lines to perform high resolution measurements on accelerated beams. The setup was used for the measurements on the gallium isotopes presented in Chapter 5. This chapter will introduce the COL- LAPS beam line and describe its operation, in particular for the laser spectroscopy investigation of gallium.

4.1 Beam Line Components

A schematic diagram of the COLLAPS beam line is shown in Figure 4.1. For an on-line experiment the radioactive ion beam of interest is produced and mass selected in the ISOLDE target area and delivered to the COLLAPS setup. The ion beam, which has been accelerated up to typically 30 keV, is deflected 10° by two electrostatic deflector plates and collinearly overlapped with a co-propagating laser beam. Once overlapped with the laser beam the ions are neutralised in a charge-exchange cell filled with a hot alkali vapour (∼ 200℃). The neutral atoms then travel to a light collection region, where they are resonantly excited, and the emitted fluorescence photons are detected.

For hyperfine structure measurements an acceleration voltage is applied to the charge-exchange cell to Doppler tune the bunch (see Section 4.2). A set of post- acceleration ring electrodes are placed before the charge-exchange cell, which are stepped in voltage, so that the incoming ion bunch does not experience a sudden electric field. The photons from the fluorescence decays are detected by four PMTs at 90° with respect to the beam axis, which are assisted by four focusing lenses to improve the detection efficiency, see Figure 4.2. The PMTs can be changed for

51 4.1. Beam Line Components iue4.1: Figure hnrsnnl xie ntelgtcleto ein h yeﬁesrcue fteaoi rniin r cne yapyn a applying COLLAPS by to scanned delivered are transitions is atomic line the beam of central structures cell. hyperﬁne ISOLDE charge-exchange The the the region. to from collection voltage beam light tuning the ion Doppler in The excited resonantly line. then beam through COLLAPS bent the and of diagram Schematic 10 ° ob vrapdwt opoaaiglsrba.Tein r etaie nacag-xhnecl and cell charge-exchange a in neutralised are ions The beam. laser co-propagating a with overlapped be to

52 4: The COLLAPS Beam Line

Figure 4.2: Diagrams of the COLLAPS light collection region. [Top] Arrangement of the four PMTs situated after the charge-exchange cell. [Bottom] Detection region of ﬂuorescence photons, focused via 100 mm diameter aspheric lenses, into one of the PMTs.

each experiment depending on the wavelength of the ﬂuorescence photons. For the neutron-deﬁcient gallium experiment, 9814QSB and 9829QSA PMTs, manufactured by Electron Tubes, were used [49, 50] with typical dark count rates of 300/s.

An adjustable aperture (∼ 2 mm to >10 mm) is situated between the charge- exchange cell and light collection region to assist with optimising the transmission and spatial overlap of the atomic and laser beams. At the end of the beam line ions can be detected on a removable Faraday cup for transmission measurements and a Brewster window allows the laser beam to exit with minimal light scatter.

53 4.2. Hyperfine Structure Measurements via Doppler Tuning

4.2 Hyperﬁne Structure Measurements via Doppler Tuning

To make hyperﬁne structure measurements on the radioactive atoms, the beam is Doppler tuned across the frequency range by applying an accelerating voltage to the charge-exchange cell, altering the frequency of the laser in the atomic rest frame. The voltage is scanned over a range large enough to measure the hyperﬁne components of interest. For example, for 30 keV gallium isotopes measured on the 417 nm atomic transition, a scanning range of 300 V corresponds to a Doppler-shifted frequency range of ∼ 3.6 GHz.

To provide an accurate and reliable scanning voltage, a customised HV scanning system is used as part of the COLLAPS setup, shown in Figure 4.3.

Figure 4.3: Diagram showing the hardware used to apply voltages to the charge-exchange cell and post-acceleration electrodes to Doppler tune the ion beam. A scanning range of 0 → ±500 V can be used, oﬀset by up to ±10 kV.

The experiment control computer is connected to a fast scanning voltage supply unit (∼ 1 V/µs) that has a scanning range of −10 V to +10 V. This voltage is delivered to a high precision amplifier and amplified by a factor up to ×50. The amplified voltage is then connected to the ground of an isolated HV supply that can produce up to ±10 kV. This is a stable, high voltage supply and, by connecting the scanning voltage to the ground of the unit, allows the scanning volts to be applied on top of the static potential. The output of the supply is delivered to the charge-exchange cell and monitored during the experiment. The incoming ion beam

54 4: The COLLAPS Beam Line is accelerated/decelerated by this ﬁnal voltage before it is neutralised and enters the light collection region.

To be able to measure the hyperﬁne structure from an experimental run the applied voltage needs to be converted into the eﬀective frequency of the laser observed by the atom. The Doppler-shifted frequency of the observed laser light from the lab frame can be calculated using, √ 2 νobserved = νsource × (1 + α ∓ 2α + α ) (4.1) where, 2 α = eU/mAc (4.2) and eU is obtained by subtracting the scanning voltage applied to the charge exchange cell from the ISCOOL voltage. The minus sign is used for a co-propagating overlap of the atom and laser beams and the positive sign is for an anti-propagating overlap.

4.2.1 Calibration of Scanning Voltages

The voltage scanning setup is calibrated during experimental runs by measuring the voltage supplied to the charge-exchange cell for the range of output voltages from the fast scanning unit. An example of one of these calibration tests is shown in Figure 4.4.

Figure 4.4: A plot of the voltage on the charge-exchange cell against the scanning voltages supplied from the fast scanning unit taking during a calibration test. The gradient gives the ampliﬁcation factor. The read out voltage is oﬀset by the HV supply.

55 4.3. Cooling/Bunching with ISCOOL

As seen in the figure, the fast scanning unit is varied from −10V to +10V, to test the full range of the unit, and the gradient provides the modification factor of the amplifier. These scans are then taken several times during an experiment to monitor any drifts of the voltage supplies. An example of the fluctuations of this value is shown in Figure 4.5, which displays the amplifier factors measured during the neutron-deficient gallium experiment.

Figure 4.5: Amplification factors measured at different times during the neutron-deficient gallium experiment. The error bars for the amplifier factor are smaller than the data points. The weighted mean was 50.4304 with a standard deviation of 0.0083.

The scatter of the amplifier factor during the experiment was measured to be 0.0083, on a total value of 50.4304, which equates to an error of less than 0.01% on the final voltage experienced by the atom bunches. During on-line experiments, an error with the absolute value of the read out voltage is a possible contribution to the final error of nuclear measurements, in particular when investigating the isotope shift. An incorrect reading of this voltage will induce a systematic error in the experiment. This effect is discussed in the analysis of the gallium results in Chapter 5.

4.3 Cooling/Bunching with ISCOOL

The ISOLDE trap, ISCOOL, can be used in tandem with COLLAPS to improve the resolution and sensitivity of the experimental investigations. Cooling the ion beam minimises the energy spread of the ions before acceleration, leading to an increase of the experimental resolution, given by Equation 3.3. The sensitivity of the experiment can be improved by ISCOOL in two ways. The ﬁrst is from the improvement in emittance angle of the ions from ISCOOL. The improved focus of

56 4: The COLLAPS Beam Line the beam in the light collection region allows a lower power laser beam to be used, with the same power density, decreasing the number of photons that can scatter and contribute to the background. Secondly, by bunching the ions the data acquisition can be gated so that photons are detected only when the ion bunch is travelling in front of the PMTs. This reduces the background rate from continuous sources, dominated by laser scatter and dark counts, by a factor,

n = τacc/τbunch (4.3) where τacc is the accumulation time and τbunch is the temporal width of the ion bunch. For typical accumulation times and bunch widths, the background count rate can be reduced by up to a factor of 104.

4.4 Experimental Procedure

The experimental procedure of data collecting with the COLLAPS experiment is set up in order to efficiently measure hyperfine structures in the shortest time possible. This is achieved through using a computer system that controls the delivery rate of the radioactive ions while gating the detection of fluorescence photons to when the atom bunch is in the light collection region. A flow diagram and trigger diagram of the timing structure of the COLLAPS experiment are shown in Figure 4.6.

At the start of each acquisition the tuning voltage is applied to the charge- exchange cell before the arrival of the first bunch. The control computer sends a trigger signal to ISCOOL to dictate the accumulation and release times of the ion bunches. To limit space/charge effects within ISCOOL, adjustable slits within the ISOLDE target area can be used to limit the number of ions in each bunch to 107. The ion bunches travel to COLLAPS, are Doppler tuned by the accelerating voltage, neutralised in the charge-exchange cell and then atomically excited if on resonance with the co-propagating laser beam. The PMTs continually monitor the photon counts; therefore, a gate is set to match the arrival time of the bunch within the light collection region to reduce the number of background counts. The delay of the gate is determined by the time of flight (ToF) of the bunches from ISCOOL to the light collection region and the width is set by the temporal length (FWHM) of the bunch.

After the measurement of the atom bunch, the voltage is stepped up to the next value and the process is repeated. After reaching the top of the scanning range the tuning voltage is reset and the cycle is repeated until enough statistics are obtained. Scans can run for up to 2 hours while investigating exotic cases; after which, the acquisition should be halted to perform a calibration measurement on a reference isotope. These calibrations are taken to check for consistency and to ensure against any experimental drifts. This is important for isotope shift measurements as they are dependent on the change of transition frequency between isotopes and sensitive to any frequency drifts.

57 4.4. Experimental Procedure

Figure 4.6: Diagrams of the COLLAPS experimental procedure. [Top] Hardware components used in the experimental data collection and [bottom] the relative timings of the triggers and events with typical values. The control computer sets the Doppler tuning voltage to the charge-exchange cell, releases the ion bunch from ISCOOL and then gates the photon count signal from the PMTs to match with the arrival time of the bunch in the light collection region (see text for details).

58 Chapter 5

Laser Spectroscopy of Gallium Using COLLAPS

The neutron-deficient gallium isotopes, from A = 70 down to A = 63, were measured via collinear laser fluorescence spectroscopy using the COLLAPS beam line at ISOLDE. This chapter will introduce the previously performed measurements on the neutron-rich gallium isotopes and give the motivation for the work in this thesis to continue the campaign for the neutron-deficient cases. The setup for the neutron-deficient experiment will be explained before presenting the analysis of the measured isotopes. The hyperfine structures of the neutron-deficient isotopes will be discussed and the isotope shifts of the entire gallium isotope chain will be presented for the investigation into the behaviour of the mean-square charge radii.

5.1 Previous Studies on the Neutron-Rich Gallium Isotopes

The neutron-rich gallium isotopes were measured to investigate the behaviour of single particle energies along the isotope chain. The gallium isotopes are constructed of 31 protons, three of which lie outside the Z = 28 shell gap for the ground- state conﬁguration. See Figure 5.1 for the conventional shell model ordering of the nucleons in gallium. In the shell model these protons occupy the πp3/2 level, two of which will pair to give spin I = 0. This should leave the ground-state spin to be I = 3/2 for all odd-A gallium isotopes due to the resulting odd proton. In the neighbouring copper isotopes there are two protons fewer, so only one proton is present in the πp3/2 level outside Z = 28. Similar to the gallium case, the ground- state spin should be dependent on this proton, resulting in I = 3/2 for the odd-A copper isotopes. Recent experiments into the ordering of shell energies in copper have shown that after N = 40 a lowering of the πf5/2 level, relative to the πp3/2 level, occurs as neutrons ﬁll the νg9/2 orbital [51]. This can be explained by the tensor interaction between the νg9/2 and proton single particle energies, resulting

59 5.1. Previous Studies on the Neutron-Rich Gallium Isotopes

Figure 5.1: Shell model orbital occupations of the protons and neutrons within the gallium isotopes. Included, in italics, are the mass numbers of the isotopes to highlight the occupancy of the ﬁnal neutron.

60 5: Laser Spectroscopy of Gallium Using COLLAPS

75 in a lowering of the πf5/2 level with respect to πp3/2 [52]. By Cu (N = 46) the πf5/2 is seen to invert with πp3/2, resulting in I = 5/2 for the ground-state spin of 75Cu. The neutron-rich gallium isotopes were investigated to see how the two extra protons aﬀected the systematic behaviour of the πp3/2, πf5/2 and πp1/2 levels.

The hyperﬁne structures of the odd-A gallium isotopes between A = 67 and A = 81 were measured and used to determine the ground-state spin values as well as the magnetic dipole and electric quadrupole moments [53]. Example optical spectra of the neutron-rich odd-A gallium isotopes are shown in Figure 5.2.

Figure 5.2: Previously measured optical spectra for the odd-A67−81Ga isotopes, measured 2 2 on the 417.3 nm 4p P3/2 → 5s S1/2 transition, and [inset] the 403.4 nm 2 2 73 4p P1/2 → 5s S1/2 transition for Ga [53].

From the hyperﬁne structures the ground-state spins and moments of the isotopes were extracted, see Table 5.1. Prior to the measurements I = 3/2 had been assigned for all the ground-state spins up to 79Ga. From the experiment it was discovered that 73Ga actually has a ground-state spin of I = 1/2. It was postulated that this is due to the lowering of the πp1/2 level becoming the ground-state and quasi degenerate with the now low lying πp3/2 level. The inversion of the πf5/2 level 75 with the πp3/2 level, as seen in Cu, was also observed in the gallium isotopes with

61 5.2. Motivation for the Neutron-Deficient Gallium Isotopes

Table 5.1: Previously measured ground-state spins, and magnetic dipole and electric quadrupole moments for the odd-A 67−81Ga isotopes [53].

A I µ (µN) Qs (b) 67 3/2 +1.848(5) +0.198(16) 69 3/2 +2.018(4) +0.171(11) 71 3/2 +2.56227(2) +0.106(3) 73 1/2 +0.209(2) 0 75 3/2 +1.836(4) −0.285(17) 77 3/2 +2.020(3) −0.208(13) 79 3/2 +1.047(3) +0.158(10) 81 5/2 +1.747(5) −0.048(8)

I = 5/2 becoming the ground-state spin for 81Ga. Shape changes were also observed between the 67,69,71Ga and 75,77Ga isotopes, with the inversion of the sign of their electric quadrupole moments at 73Ga. This can be explained by two of the outermost 75,77 protons occupying the πf5/2 orbital in Ga leaving only one in the πp3/2 orbital, resulting in a particle like (oblate) conﬁguration, compared to a hole like (prolate) conﬁguration for 67,69,71Ga.

As well as the odd-A neutron-rich gallium isotopes, the even-A isotopes were investigated, yielding new ground-state spins and moments, as well as measuring their isotope shifts to complete the neutron-rich isotope chain. The measured hyperfine structures of the even-A 72−80Ga are shown in Figure 5.3. Experimental results confirmed the ground-state spin of 72Ga to be I = 3 and determined the ground-state spins of 74,76,78Ga to be I = 3,I = 2 and I = 2 respectively. In 80Ga a new isomer with a half-life greater than 200 ms was discovered. The outer structure was assigned I = 3 while the centre structure was determined to be I = 6, which, from the assistance of shell model calculations, is believed to be associated with the ground state. Additionally, the hyperfine structure and isotope shift of 82Ga was measured, allowing the mean-square charge radius information of the gallium isotope chain to extend across the N = 50 shell closure.

The isotope shifts measured for the neutron-rich isotopes during these previous experiments were not published and will be presented in this chapter along with the isotope shifts measured for the neutron-deﬁcient isotopes.

5.2 Motivation for the Neutron-Deﬁcient Gallium Isotopes

The extension of the gallium measurements into the neutron-deﬁcient isotopes was motivated by work done by Lépine-Szily et al. on the mean-square matter radii of the Ga, Ge, As, Se and Br isotopes [56]. The radii of each of the isotopes were obtained from the reaction cross-sections of a fragmented accelerated krypton

62 5: Laser Spectroscopy of Gallium Using COLLAPS

Figure 5.3: Previously measured optical spectra for the even-A 72−80Ga, measured on the 2 2 2 417.3 nm 4p P3/2 → 5s S1/2 transition, and [inset] the 403.4 nm 4p P1/2 → 2 74 5s S1/2 transition for Ga [54, 55].

beam on a 90 mg/cm2 thick nickel foil. For all cases they noticed an apparent increase in the matter radii with decreasing neutron number. The behaviour of the measurements they made for gallium is shown in Figure 5.4. The group investigated the I = Igs + 2 state energies of the gallium isotopes to see if this effect is related to a deformation of the nucleus, shown in the top plot in Figure 5.4. Generally, the higher the excitation energy of the I = Igs +2 state, the less deformed the nucleus is. From N = 37 downwards there is only a slight decrease in the excitation energy and does not represent a large enough change in deformation that would cause such an increase in the matter radius. To confirm that this possible effect is not associated with deformation change, the first 4+ and 2+ energies of the neighbouring even-even germanium and zinc isotopes were looked at. The changes in these energies from N = 50 down to N = 30 are shown in Figure 5.5. These energies often provide a reliable reflection of the behaviour of the shape of the nucleus [12]. On both plots there are sudden changes at N = 50 for germanium, in accordance with the magic number, as the more energetic νg9/2 level is filled. Around N = 40 both isotopes display changes in excitation energy levels due to the νp1/2 orbital. However, below N = 38 there is very little deviation in the excitation energies, suggesting very little

63 5.2. Motivation for the Neutron-Deficient Gallium Isotopes

Figure 5.4: Plots of the root-mean-square matter radii [squares] and E(7/2−) excitation energies [circles] of the gallium isotopes as a function of neutron number. Included in the lower plot are the root-mean-square proton radii [stars] of the stable isotopes and a projection of these radii by 0.95A1/3. Figure taken from Reference [56] change in deformation for these isotopes. As gallium lies between these two isotopes in proton number it may also suggest that little deformation changes occur as well below N = 38.

As there are no indications that this increase in matter radius was associated with deformation change, the group postulated that the eﬀect could be produced by the development of a proton skin. As neutrons are removed from the nucleus the repulsive force of the protons could act to push them further apart and actually increase the matter radius of the nucleus. If this is the case, it would be expected to cause a substantial change in the mean-square charge radius. As gallium has an accessible atomic transition it was decided to investigate this subject using laser spectroscopy. Laser spectroscopy is uniquely sensitive to charge re-distribution in the nucleus and would detect changes as small as 0.01 fm2. If the increase in the matter radius was due to changes in the proton distribution it would be expected

64 5: Laser Spectroscopy of Gallium Using COLLAPS

Figure 5.5: Plots of the ﬁrst 2+ [top] and 4+/2+ [bottom] energies in zinc [circles[ and germanium [triangles] against neutron number [57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68]. A large deviation from the general trend is observed at N = 50; however, no eﬀects are seen below N = 38 to imply any change in deformation.

to cause a change in the mean-square charge radius of almost 0.5 fm2 between isotope neighbours. If there is a development of a proton skin within the gallium isotopes with decreasing neutron number it will be clearly visible from the optical measurements. With this motivation, the neutron-deﬁcient gallium isotopes were investigated using collinear laser ﬂuorescence spectroscopy with the COLLAPS beam line at ISOLDE.

5.3 Experimental Setup at ISOLDE

5.3.1 ISOLDE Target

The production of the neutron-deﬁcient gallium isotopes required a specialised zirconium oxide, ZrO2, target heated at about 2000℃. From a ZrO2 target the release time of gallium is relatively rapid, τ ≈ 4 s, compared with τ ≥ 100 s for 2050℃ niobium and 2200℃ tantalum metal foil targets. The target was also chosen for its production rate of the neutron-deﬁcient isotopes compared to the other targets (1.2 × 106 atoms/µC for 63Ga compared to 2.1 × 103 atoms/µC from a uranium carbide target). The target was made with a reduced titanium content in

65 5.3. Experimental Setup at ISOLDE order to minimise any isobaric titanium oxide contamination [69]. The atoms were selectively ionised using RILIS and accelerated to 30 keV by a potential applied to the target area. A plot showing the yields and in-target production rates of the ZrO2 target with RILIS is shown in Figure 5.6.

Figure 5.6: In target production yields and extracted ion rates using RILIS of copper, zinc and gallium from the ZrO2 felt target [70].

5.3.2 RILIS Ion Production

To enhance the yields of the neutron-deﬁcient gallium isotopes the RILIS laser ion source system was used [71]. The yield of the gallium isotopes is improved by a factor of up to ∼ 100 using RILIS compared to surface ionisation. The stepwise ionisation scheme used by RILIS is shown in Figure 5.7. In the scheme the gallium atoms were resonantly excited from the ground state and the thermally populated 826.24 cm−1 metastable state (∼ 50% at 2000℃) using dye lasers pumped by a Nd:YAG laser. These states were then non-resonantly ionised from the 34781.67 cm−1 level with 532-nm YAG laser light. After ionisation, the gallium isotopes were accelerated away and mass separated in the HRS magnets before being delivered to ISCOOL.

5.3.3 ISCOOL

ISCOOL was used during the experiment to reduce the continuous background rate. The ions were accumulated in the trap for 50 ms and released for 100 µs. The delay of the photon detection gate was determined by the ToF of the ion bunch from ISCOOL to the light collection region. The width of the gate was determined by the temporal width of the ion bunch. Figure 5.8 shows the ToF spectrum of detected resonant ﬂuorescence photons from bunches of 69Ga.

66 5: Laser Spectroscopy of Gallium Using COLLAPS

Figure 5.7: The RILIS ionisation scheme used for the extraction of the gallium iso- 2 2 topes [32]. The atoms were resonantly excited from the 4p P1/2 and 4p P3/2 levels and then ionised into the continuum in a non-resonant step.

Figure 5.8: A ToF measurement of 69Ga bunches released from ISCOOL. The plot shows the number of resonant photon counts in the light collection region against the time of the photon signal since the bunch release from ISCOOL. The measurement was made with the photon gate in place to discriminate background counts. The photon signals were collected in 2.56 µs bins. The ToF was ∼ 63 µs and the FWHM was ∼ 10.5 µs.

67 5.3. Experimental Setup at ISOLDE

The figure shows the FWHM and ToF of the 69Ga bunches were about 10.5 µs and 63 µs in the light collection region respectively. The delay time of the photon detection gate was adjusted for different isotopes to compensate for the change in ToF. The background photon count rate of the PMTs during the experiment was between 500 and 10000 photons/s. The main contributions of this count rate were from scattered laser light and dark counts. By bunching the beam, this background rate was reduced by a factor of ∼ 5 × 103, given by Equation 4.3. The accumulation time was chosen to maximise the background suppression while limiting any space/charge effects within ISCOOL.

5.3.4 Atomic Transition

The bunched ion beam from ISCOOL was neutralised by passage through the charge-exchange cell containing a sodium vapour at 200℃ and then overlapped in a collinear geometry with continuous laser light. During the experiment the neutralisation efficiency was typically 70%. An additional acceleration potential was applied to the charge-exchange cell to allow the hyperfine structure of the atom to be scanned via the Doppler shift. As shown in Figure 5.9, there are two possible atomic transitions in gallium that can be used to measure its hyperfine structure:

2 −1 2 −1 • The 417 nm, 4p P3/2 (826.24 cm ) → 5s S1/2 (24788.58 cm ) transition

2 −1 2 −1 • The 403 nm, 4p P1/2 (0 cm ) → 5s S1/2 (24788.58 cm ) transition

Figure 5.9: The atomic transition chosen in gallium for ﬂuorescence detection. Atoms 2 2 in the 4p P3/2 state were resonantly excited to the 5s S1/2 state. The 2 2 systems then relaxed to the 4p P3/2 or 4p P1/2 states via an emission of a ﬂuorescence photon. The atomic information was obtained from [72].

2 2 During the experiment the population of the 4p P3/2 and 4p P1/2 states were found to be equally populated after neutralisation. The 417-nm transition was 2 chosen for the ﬂuorescence detection as the 4p P3/2 state allows for the measurement

68 5: Laser Spectroscopy of Gallium Using COLLAPS of the electric quadrupole moment. A frequency stabilised Ti:Sa laser was operated at 834 nm and frequency doubled to 417 nm in an external cavity to drive the atomic transition. The power of the second harmonic laser was typically 2.5 mW, reduced to minimise optical pumping effects but sufficient in order to measure the hyperfine structures, and the beam diameter was approximately 3 mm.

5.4 Experimental Data

5.4.1 Analysis Technique

The analysis of the gallium data was performed using a χ2 minimisation technique. Several scans were performed for each isotope, which were individually analysed, and the results from these were collated to obtain the final values. For each scan, a data file of photon counts against effective laser frequency was produced, which was used for the analysis. As explained in Section 4.2, the experimental frequency was calculated from the Doppler-tuning voltage using, √ 2 νobserved = νsource × (1 + α ∓ 2α + α ) (5.1) where, 2 α = eU/mAc . (5.2)

For each of the frequency values a simulated hyperfine structure was made using predicted shifts in energy calculated using Equations 2.4 and 2.11 with a fixed nuclear ground-state spin. An example simulated structure fitted to experimental data is shown in Figure 5.10. The hyperfine transitions were simulated using Lorentzian profiles (see next section) and the overall structure was produced using the following as free parameters:

2 • A(5s S1/2)

2 • B(4p P3/2) • Structure centroid frequency • FWHM of transition proﬁles (equal for all transitions) • Background level (assuming a ﬂat background) • Overall intensity (applied equally to all transitions)

2 2 A(4p P3/2) was constrained to A(5s S1/2) by the known ratio value of +5.592(9) from Reference [53], to assist with the ﬁtting routine.

The A and B hyperfine coefficient values define the shifts in energy of the hyperfine structure, dictating the magnitude of the separations between the peaks in the

69 5.4. Experimental Data optical spectra. The centroid frequency is an arbitrary value that is used to represent the unperturbed frequency of the atomic transition. This value is adjusted to provide the best match of the simulated hyperfine structure with the experimental data (this can be visualised by taking the fitted hyperfine structure in Figure 5.10 and moving it horizontally across the x-axis). This centroid frequency is extracted for each isotope scan and differences between these values yields the isotope shift. For the neutron-deficient experiment 69Ga was used for the reference scans; therefore, the measured isotope shifts are relative to this isotope.

The remaining free parameters shape the profiles of the simulated structure to provide the best fit of the experimental conditions. The individual profiles were assumed to have the same lineshape. The relative intensities of the hyperfine transitions were restricted to angular momentum coupling estimates. They were restricted to assist in identifying the peaks as well as assisting the fitting routine in cases where hyperfine transitions overlapped each other. The hyperfine structures of 69Ga measured during the experiment were fitted with the relative intensities of the peaks restricted to angular momentum coupling estimates to observe any differences between the fitted peak intensities and the data. One of these fits is shown in Figure 5.10.

Figure 5.10: The fitted hyperfine structure [solid blue line] of 69Ga, I = 3/2. The fit was made with the relative intensities of the peaks restricted to angular momentum coupling estimates. The fit shows good agreement with the relative intensities of the data.

The figure shows the fitted angular momentum coupling estimates agree well with the experimental data. Although there are slight differences in some of the peaks (for example the two peaks on the right) it was judged that it was more beneficial to the fitting procedure to use the restricted intensities than to have the individual intensities as free parameters.

70 5: Laser Spectroscopy of Gallium Using COLLAPS

Additionally, the intensities of the detected fluorescence photons are affected by their angular distributions, given by Equation 2.17. For the transition used 2 in this experiment, the upper atomic state is the 5s S1/2 level, which has an angular distribution coefficient of A2 = 0. Therefore, the angular distribution will be isotropic and will not have an affect on the observed intensities.

The simulated structure was iterated in a fitting routine that varied the free parameters until the best reproduction of the experimental data was made. The best simulated structure was set to be the fit which produced the smallest χ2 value, which is defined as, 0 2 X (Xi − X ) χ2 = i (5.3) σ2 i i 0 where Xi are the simulated counts, Xi are the experimental counts and σi are the p 0 errors on each experimental count given by, σi = Xi + 1. The reduced chi-square, 2 χr , was used in the analysis to determine the experimental errors and is defined as, χ2 χ2 = (5.4) r ν where ν is the number of degrees of freedom given by, ν = N − n, where N is the number of data points and n is the number of fitted parameters.

The free parameters were extracted at the end of the fitting routine and the hyperfine coefficients were used to determine the nuclear properties of the isotopes. For each free parameter the statistical error was produced by finding the limits 2 2 on the parameter that increased the χ by no more than the χr value. For the analysis of the gallium isotopes this χ2 minimisation fitting routine was used and any modifications made to the routine will be stated.

5.4.2 Lineshape of Optical Transitions

To provide the best representation of the experimental data, the lineshape for the hyperfine transitions in the simulated structure had to be determined. From the different possible causes of the observed lineshape, described in Section 2.3, the shape could be expressed as a Gaussian, Lorentzian or Voigt profile (convolution of the two). To find the appropriate profile, the single peak of the hyperfine structure of 64Ga was fitted using the χ2 minimisation technique, with Lorentzian, Gaussian and pseudo-Voigt profiles. The pseudo-Voigt profile is an approximation of the Voigt profile and is a variable combination of the Lorentzian and Gaussian profiles. This profile was used to observe the extent of any differences between the experimental data and the Lorentzian and Gaussian profiles. The scan performed on 64Ga was chosen to represent the experimental linewidth. As the ground-state spin is known to be I = 0, only a single optical transition is present, which avoids any influences from the tails of other peaks. The results from the fits are shown in Figure 5.11.

71 5.4. Experimental Data

Figure 5.11: Optimised fits of the 64Ga single component using Gaussian [top], Lorentzian [middle] and pseudo-Voigt profiles [bottom]. The pseudo-Voigt profile had an optimised combination of 88% Lorentzian and 12% Gaussian. 2 The χr values for the fits were 2.45, 1.33 and 1.32 respectively.

The results of the fitted hyperfine structures show a strong preference to the Lorentzian and pseudo-Voigt profiles, allowing the purely Gaussian profile to be 2 discarded. The χr values for the Lorentzian and pseudo-Voigt profiles were 1.33 and 1.32 respectively and for all the spectra tested they differed by no more than 0.01. The mixing ratios of the pseudo-Voigt profiles were strongly in favour of a Lorenztian distribution, with 88% being the lowest contribution seen from all of the fits. The dominance of the Lorentzian can be attributed to the natural linewidth and any power broadening effects of the resonant excitation that contributed more to the observed transition than the Gaussian contribution, reduced by the acceleration and cooling of the ion beam in ISCOOL. From these results the analysis of the gallium isotopes was performed using Lorentzian profiles.

For the linewidth of the optical transitions, the FWHM was left as a free parameter throughout the fitting routines to accommodate experimental fluctuations. 2 8 The decay rate of the 5s S1/2 state is ∼ 1.5 × 10 /s [72], which gives a natural width of approximately 25 MHz. The experimentally observed linewidth will be larger than this value√ due to contributions from Doppler (∼ 10 MHz at 30 keV) and power broadening (× 2 at saturation) effects. This would give an expected exper-

72 5: Laser Spectroscopy of Gallium Using COLLAPS imental linewidth of about 40 MHz. During the experiment the average resolution was ∼ 105 MHz, with a standard deviation of 20 MHz. This increased linewidth can be explained by a saturating effect caused by optical pumping. As there are two 2 2 2 possible paths for the 5s S1/2 state to decay to (the 4p P3/2 metastable or 4p P1/2 2 ground state), the “loss” of atoms to the 4p P1/2 state will decrease the saturation point of the experiment, causing a broadening effect as the laser power is increased. The extent of this effect has been investigated using an optical pumping simulation in Reference [73]. In the tests, the linewidths of the simulated transitions increased by a factor of 1.25 when the laser power was increased by a factor of 4. At the end of the gallium experiment the laser power was decreased from 2.5 mW to 0.8 mW and the experimental linewidth decreased from ∼105 MHz to ∼ 80 MHz, which is in agreement with the extent of the effect in the simulations. As this broadening effect of the linewidth is caused by optical pumping to a different fine structure component the effect will be of the same magnitude for all the isotopes, regardless of the nuclear spin.

5.5 Hyperﬁne Structure Results

From the hyperfine structures of the neutron-deficient isotopes, the hyperfine 2 2 coefficient values could be determined for the 4p P3/2 → 5s S1/2 atomic transition. 2 2 2 For the 5s S1/2 state, A(5s S1/2) could be measured, and for the 4p P3/2 state, 2 2 A(4p P3/2) and B(4p P3/2) could be measured. This section will present the results obtained from the analysis of these hyperfine structures.

During the experiment the hyperfine structures of 63,68,70Ga and the single components of 64,66Ga were measured. Due to technical difficulties, 65Ga and 67Ga were not investigated. One of the ISOLDE switchyards had recently developed a fault and was required to be fixed after the experiment; therefore, contamination within the ISOLDE central beamline had to be avoided. 65Ga decays to 65Zn, which has a half-life of ∼ 240 days and 67Ga has a half-life of ∼ 3 days.

5.5.1 70Ga

Prior to the experiment, the hyperfine coefficients of 70Ga were not known, but the ground-state spin had been measured to be I = 1 via the atomic beam magnetic resonance technique [74]. Due to the coupling of the nuclear spin with the electron angular momentum for this atomic transition, there are five hyperfine transitions between the lower and upper states. From the experimental measurements only three peaks were resolved (two of the peaks each contained the profiles of two transitions). However, the resolution was sufficient to resolve the strongest peak and extract the hyperfine coefficients from the locations of the other two. Two scans were performed for 70Ga and the optical spectra measured from one of them is shown in Figure 5.12.

73 5.5. Hyperfine Structure Results

Figure 5.12: Fitted hyperﬁne structure [solid blue line] of 70Ga, I = 1. The plot shows the number of photon counts for diﬀerent frequency values. The frequencies are relative to the unperturbed frequency of the atomic transition. Included are the contributions from the individual transitions that make up the total structure [dotted black lines].

As shown in the figure, the strongest transition was well resolved while the two transitions in each of the outer peaks were closely overlapped. Since there are different combinations of the A and B hyperfine coefficients that could represent the observed data, the structure was fitted over the range of possible values (as 2 fixed parameters in the fitting routine) to extract the χr values and see which values provided the best fit. The results from this investigation is shown in Figure 5.13.

2 From the figure it is clear to see two regions where the extracted χr value falls to a 2 2 minimum: at A(5s S1/2) ≈ 450 MHz and A(5s S1/2) ≈ 50 MHz. The combination 2 of A and B hyperfine coefficient values at A(5s S1/2) ≈ 50 MHz can be ruled out as 2 the average χr value from the runs with these values is 2.44, in comparison to 1.79 for the other region. Additionally, the hyperfine structure of 70Ga has been previously 2 2 observed using the 4p P1/2 → 5s S1/2 transition [73]. This transition is sensitive 2 only to the magnetic moment and the splitting observed was caused by a A(5s S1/2) hyperfine coefficient value of approximately 450 MHz. This is in agreement with 2 the region with the lowest fitted χr value. For the reasons stated, the hyperfine 2 structure was fitted using the hyperfine coefficients at A(5s S1/2) ≈ 450 MHz and the optimised fitted values were extracted.

Within the peaks that consist of two overlapping components, the extent of the horizontal movement of the individual transitions was determined within the fitting routine and are represented by the statistical errors of the extracted hyperfine coefficients. The weighted averages of the extracted hyperfine coefficients and isotope shifts from the scans performed are presented in Table 5.2.

74 5: Laser Spectroscopy of Gallium Using COLLAPS

Figure 5.13: Hyperfine structure fits of 70Ga, I = 1, for different hyperfine coefficient 2 2 values. The plot shows the fitted χr values for varying A(5s S1/2) and 2 2 B(4p P3/2). Two regions of minimum χr values are highlighted. The region 2 2 around A(5s S1/2) = 450 MHz has the lowest χr value and the region 2 around A(5s S1/2) = 50 MHz disagrees with previous observations (see text for details).

Table 5.2: The measured hyperfine A and B coefficients and isotope shift of 70Ga. The 2 2 A(5s S1/2) and B(4p P3/2) values were extracted from the fitted hyperfine 2 2 structure while A(4p P3/2) was scaled from A(5s S1/2).

2 2 2 69,A AIA(5s S1/2) A(4p P3/2) B(4p P3/2) δνIS (MHz) (MHz) (MHz) (MHz) 70 1 +454.0(11) [+81.2(2)] +38.3(11) −36(4)

75 5.5. Hyperfine Structure Results

5.5.2 68Ga

The ground-state spin of 68Ga is already known to be I = 1 and the magnetic dipole and electric quadrupole moments have been measured as +0.01175(5) µN and +0.0277(14) b respectively using the atomic beam magnetic resonance technique [75]. From these measurements, the hyperfine coefficient values for the atomic transition for 68Ga can be calculated and used to predict its hyperfine structure. The coefficients were calculated using Equations 2.6 and 2.13, and the hyperfine coefficients and moments of 71Ga [53, 75, 76] as reference values. The expected hyperfine coefficient values of 68Ga were determined to be:

2 • A(5s S1/2) = +9.34(6) MHz

2 • A(4p P3/2) = +1.67(2) MHz

2 • B(4p P3/2) = +10.1(8) MHz

These coeﬃcients are very small and only create slight energy shifts in the hyperﬁne structure, as seen in Figure 5.14.

Figure 5.14: Simulated hyperﬁne structure of 68Ga, I = 1 [solid blue line], plotted using previously measured magnetic dipole and electric quadrupole moments [75]. The individual transitions are also included [dotted black lines] with FWHMs of 25 MHz to demonstrate the collapsed nature of the structure.

In the figure the projected hyperfine structure of 68Ga has been plotted using 25 MHz for the transition linewidths. As the hyperfine profiles are overlapped with

76 5: Laser Spectroscopy of Gallium Using COLLAPS

25 MHz linewidths it would not be possible to resolve the transitions with the experimental resolution of ∼ 100 MHz. In the experiment several scans were made on 68Ga to measure the isotope shift value and to see if the expected hyperﬁne structure is reproduced. Five scans were made on 68Ga and these were individually analysed. An example of one of the spectra is shown in Figure 5.15.

Figure 5.15: Fitted hyperﬁne structure [solid blue line] of 68Ga, I = 1. Included are the contributions from the individual transitions that make up the total structure [dotted black lines].

As expected, the hyperfine structure was not resolved, consistent with the results from the previous work. Since the splittings are so small the individual transitions could be moved around relative to each other within the error allowed by the fitting routine. This leads to large statistical errors associated with the coefficient values. To investigate the extent of these variations the fitting routine was repeated with 2 2 A(5s S1/2) as the only free hyperfine coefficient parameter, with B(4p P3/2) fixed at 2 2 +10.1 MHz. The χ was extracted for each value to observe the range of A(5s S1/2) that produced suitable fits of the data. The analysis of one of the scans of 68Ga with 2 A(5s S1/2) values ranging from −100 MHz to +100 MHz is shown in Figure 5.16.

The figure shows a large dip in the χ2 values between around −50 MHz and +50 MHz, highlighting the range of values accepted by the fitting routine. This range demonstrates the accuracy of the hyperfine coefficient measurements possible from the data on 68Ga. To demonstrate the possible range of coefficient values, the result can be compared to a similar fitting routine for 70Ga, where the hyperfine structure is much more resolved, shown in Figure 5.16. As shown in the figure, there is a clear minimum for the 70Ga data that can be used to determine the statistical error compared to the large uncertainty of the χ2 seen for 68Ga.

77 5.5. Hyperfine Structure Results

2 68 70 2 Figure 5.16: χ values for fits of Ga [left] and Ga [right] for different A(5s S1/2) 2 68 70 values. B(4p P3/2) was set to +10.1 MHz and +34 MHz for Ga and Ga 2 respectively. The plots highlight the range of fitted A(5s S1/2) values for 68Ga compared to the more defined case of 70Ga.

From the analysis of the hyperfine structure of 68Ga the hyperfine coefficients of 68Ga were not extracted with more precision than the previously known values and the accuracy of the fitting routine showed no signs that they are any different from the literature values. The isotope shift could still be extracted and the weighted average value from the scans was determined to be:

69,68 • δνIS = +6(7) MHz

The variations of the hyperfine coefficients produced a negligible contribution to the statistical error of the isotope shift result. This was tested by comparing the extracted centroid values of the 68Ga data using ground-state spin values of I = 0 and I = 1. Between the single component from I = 0 and the hyperfine structure from I = 1 the centroid value changed on average across the scans by 1.5 MHz, in the largest case 2.5 MHz, smaller than the final error given.

5.5.3 64Ga and 66Ga

The ground-state spins of the odd-odd isotopes, 64Ga and 66Ga, are already known to be I = 0 from beta-gamma correlation and atomic beam magnetic resonance experiments [77, 74]. With I = 0 there should be no hyperﬁne splitting of the atomic state energies and only a single component should be observed. Scans were performed on 64Ga and 66Ga to obtain the isotope shifts and to see if there are any signs of a disagreement with the assigned spin values. The measured hyperﬁne structures of 64Ga and 66Ga are shown in Figure 5.17 and Figure 5.18 respectively.

The structures were analysed using the usual fitting routine with the ground- state spin set to zero, effectively setting the hyperfine coefficients to zero. This was so that the isotope shift could be measured, but also so that a single Lorentzian could be fitted, allowing the FWHM to be extracted and investigated. A larger

78 5: Laser Spectroscopy of Gallium Using COLLAPS

Figure 5.17: The measured single component of 64Ga, I = 0, with the ﬁtted structure [solid blue line].

Figure 5.18: The measured single component of 66Ga, I = 0, with the ﬁtted structure [solid blue line].

79 5.5. Hyperfine Structure Results

FWHM (>105 MHz) could suggest that the ground-state spin is not zero and that there is some structure to the observed spectra caused by the presence of overlapping hyperﬁne transitions. The data sets were analysed for both isotopes and the FWHM of the spectra were all of the order of ∼ 100 MHz, giving no suggestion that the spins could be anything except zero.

The transition centroid values were extracted from the single component ﬁts of 64Ga and 66Ga and their isotope shifts from 69Ga were measured to be:

69,64 • δνIS = +54(7) MHz

69,66 • δνIS = +54(5) MHz

5.5.4 63Ga

Before the experiment the ground-state spin of 63Ga was not known. In order to extract the hyperfine coefficient values from the hyperfine structure the ground- state spin first needed to be determined. Fourteen scans were performed on 63Ga and were individually analysed. For presentation, the summation of all the data obtained is shown in Figure 5.19.

Figure 5.19: The hyperfine structure [solid blue line] of 63Ga, I = 3/2, plotted on top of the summation of all data collected [black dots]. The structure was made using the weighted average of the hyperfine coefficients extracted from the individual data sets. Included are the contributions from the individual transitions that make up the total structure [dotted black lines].

80 5: Laser Spectroscopy of Gallium Using COLLAPS

From observation of the hyperfine structure, a ground-state spin of I = 1/2 was ruled out because more than three peaks were present and a χ2 analysis of the individual data sets reduced the possible spin values to I = 3/2 and I = 5/2. As described in Section 2.1.4, a valuable method to determine the ground-state spin is 2 via the ratio of the A hyperfine coefficient values. The A(4p P3/2) coefficient was 2 therefore set as a free parameter in the fitting routine as well as A(5s S1/2). The ratio between the two A coefficients were extracted for the two possible spin values and the results were compared with the known value for the isotope chain. The results of the different ratio values alongside values measured from the neutron-rich experiment are shown in Figure 5.20.

2 2 67,69,71,73,75−79,81 Figure 5.20: The ratio values of A(5s S1/2)/A(4p P3/2) for Ga from the neutron-rich experiment for comparison with those for 63Ga with I = 3/2 and I = 5/2. The horizontal lines represent the literature value of 5.592(9) [53].

The plot shows the variation and errors of the ratio values for the other gallium isotopes, so that they can be used as a comparison with those extracted for 63Ga. From the figure it is clear that I = 3/2 agrees with the trend across the isotope chain whereas I = 5/2 lies significantly away. The value produced for I = 5/2 differs from the ratio value by 4 standard deviations. From this analysis, the ground-state spin of 63Ga can be assigned as I = 3/2. Complimentary shell model calculations, discussed in Section 5.5.6, assist with the assignment of the spin value.

With the ground-state spin determined, the centroid value and hyperfine coefficients were extracted from the hyperfine structure using the standard fitting routine. The individual scans performed on 63Ga were independently analysed and the weighted average results are presented in Table 5.3.

81 5.5. Hyperfine Structure Results

Table 5.3: The measured hyperfine A and B coefficients and isotope shift of 63Ga. The 2 2 A(5s S1/2) and B(4p P3/2) values were extracted from the fitted hyperfine 2 2 structure while A(4p P3/2) was scaled from A(5s S1/2).

2 2 2 69,A AIA(5s S1/2) A(4p P3/2) B(4p P3/2) δνIS (MHz) (MHz) (MHz) (MHz) 63 3/2 +778.9(22) [+139.3(4)] +77.5(28) +81(6)

5.5.5 Nuclear Moments of 63Ga and 70Ga

With the measured hyperfine coefficients of 63Ga and 70Ga their magnetic dipole and electric quadrupole moments can be determined. In order to extract the moments from the measured hyperfine coefficient values, the results can be compared with those of a reference isotope, as described in Chapter 2. As a reminder, the new moment values were deduced using,

AIµref µ = (5.5) Aref Iref and, BQs ref Qs = . (5.6) Bref 2 2 For the calculations, the extracted A(5s S1/2) and B(4p P3/2) hyperﬁne coeﬃcient values from Tables 5.2 and 5.3 were used. For the reference isotope, the following values of 71Ga [53, 75, 76] were used:

• Iref = 3/2

2 • Aref (5s S1/2) = +1358.2(1.6) MHz

2 • Bref (4p P3/2) = +39(2) MHz

• µref = +2.56227(2) µN

• Qs ref = +0.107(1) b

Using these values, the new moments of 63Ga and 70Ga were extracted and are presented in Table 5.4.

Table 5.4: The magnetic dipole and electric quadrupole moments of 63Ga and 70Ga extracted from their hyperﬁne structures.

A I µ (µN) Qs (b) 70 1 +0.571(2) +0.105(7) 63 3/2 +1.469(5) +0.212(14)

82 5: Laser Spectroscopy of Gallium Using COLLAPS

5.5.6 Shell-Model Calculations of 63Ga

As a test of current nuclear shell models, the predictions of two independent models were compared with the experimental results of 63Ga. Two interactions were used for the shell model calculations: jj44b [78] and JUN45 [79]. The models were 56 developed for the (p3/2f5/2p1/2g9/2) model space, assuming a Ni core. The JUN45 model is constructed on a realistic interaction based on the Bonn-C potential. To make the model, 133 two-body matrix elements and four single-particle energies were empirically modified to fit 400 experimental energy data. The model uses data from 69 nuclei with A = 63 - 96. The jj44b model was obtained from a fit of about 600 binding and excitation energies in a method similar to that used for JUN45. Most of the energy data came from nuclei with Z = 28 - 30 and N = 48 - 50.

The ﬁrst test of the shell models was to compare the values of the magnetic dipole and electric quadrupole moments of the low-lying states in 63Ga. Using the shell models the moments were predicted for the ﬁrst I = 3/2 and I = 5/2 levels and compared to the results from Table 5.4. The comparison of these values is shown in Table 5.5.

Table 5.5: Experimental and shell model comparisons of the magnetic dipole, µ, and 63 electric quadrupole, Qs, moments of Ga, with I = 3/2 and I = 5/2. The shell model values were predicted using the jj44b [53] and JUN45 [79] interactions. The shell model results are in better agreement with I = 3/2 than I = 5/2 as the ground-state spin of 63Ga.

I Moment expt jj44b JUN45 3/2 µ (µN) +1.469(5) +1.605 +1.205 3/2 Qs (b) +0.212(14) +0.215 +0.259

5/2 µ (µN) +1.652(6) +0.909 +0.813 5/2 Qs (b) +0.424(25) −0.425 −0.423

Included in the table are moment values deduced from the hyperfine structure of 63Ga with the ground-state spin set to I = 5/2. The shell model values agree well with the experimental results for I = 3/2, with equal signs and similar magnitudes. The shell model values of the I = 5/2 level show a difference in magnitude of the magnetic moment values from the I = 5/2 fit of the hyperfine structure and the electric quadrupole moment has an opposite sign. These values support the wave function composition of the measured ground state to be I = 3/2 and assist in validating the conclusion from the experimental analysis of 63Ga.

For a further test of the models, the ordering of the predicted low-lying energy levels of 63Ga was investigated to see if they could reproduce the I = 3/2 ground state that was measured. The ordering of these states is listed in Table 5.6.

83 5.6. Isotope Shift Analysis

Table 5.6: Spins and energies of the ﬁrst three predicted energy levels of 63Ga, using the jj44b [53] and JUN45 [79] interactions.

Interaction Ground-State First Excited State Second Excited State Spin Spin & Energy Spin & Energy jj44b 3/2− 1/2− (118 keV) 5/2− (165 keV) JUN45 1/2− 3/2− (88 keV) 5/2− (237 keV)

Each interaction predicts three low-lying energy levels within a few hundred keV of each other from the ordering of protons within the πp3/2, πf5/2 and πp1/2 orbitals. The jj44b interaction correctly predicts I = 3/2 as the spin of the ground state, with I = 1/2 and I = 5/2 as the ﬁrst and second excited states. The JUN45 interaction incorrectly gives I = 1/2 for the ground state; however, this is very close to the I = 3/2 state, which is predicted to be within 88 keV. Both interactions have the I = 5/2 state at the highest energy of the three, further supporting the assignment of I = 3/2 for the ground state of 63Ga.

5.6 Isotope Shift Analysis

The isotope shifts of the gallium isotopes were measured in order to investigate the changes in mean-square charge radius. As described in Section 2.2, the isotope shift is the difference in the centroid frequency of the hyperfine structure, 0 0 A,A A A 0 δνIS = ν − ν , for a pair of isotopes with mass numbers A and A . During the analysis of the gallium isotopes the centroid frequencies were extracted from each run, compared with the nearest reference scan and then the weighted average was taken to accommodate for any experimental drifts. In the neutron-deficient experiment, 69Ga was used as the reference isotope and 71Ga was used for the previous neutron-rich experiments. The results from the neutron-deficient experiment presented earlier in this chapter were adjusted to be relative to 71Ga for consistency across the entire chain. The isotope shifts measured for the gallium isotope chain are 71,69 presented in Table 5.7. Prior to these experiments only δνIS = +39.6(3.5) MHz had been measured (via resonance fluorescence [80]) and is in excellent agreement with the value shown in the table.

5.6.1 Extracting the Changes in Mean-Square Charge Radii

To extract changes in mean-square charge radii from isotope shifts, the atomic factors need to be known for the transition under study. As a reminder these are the mass-shift, KMS, and ﬁeld-shift, Fel, factors that relate the isotope shift to the change in mean-square charge radius by,

0 0 A,A mA0 − mA 2 A,A δνIS = KMS + Felδhrchi . (5.7) mA0 mA

84 5: Laser Spectroscopy of Gallium Using COLLAPS

Table 5.7: Isotope shifts and changes in mean-square charge radii from 71Ga. The charge −2 radii were extracted using Fel = +400(60) MHz·fm , estimated from MCDF computations, and KMS = −211.4(210) GHz·u, “tuned” to match muonic data. Statistical errors are shown in parentheses and systematic errors are in square brackets (see text for details). * represents measurement from an isotope analysed in this thesis.

71,A 2 71,A 2 A δνIS (MHz) δhrchi (fm ) 63* +121(6)[18] −0.643(15)[135] 64* +94(7)[15] −0.579(18)[119] 66* +94(5)[11] −0.329(13)[75] 68* +46(7)[6] −0.214(18)[46] 69 +40(4)[4] −0.116(10)[28] 70* +4(4)[2] −0.096(10)[18] 71 0 0 72 +23(3)[2] +0.161(8)[26] 73 +15.5(15)[40] +0.243(4)[42] 74 −32(2)[6] +0.223(5)[45] 75 −45.3(16)[70] +0.285(4)[58] 76 −86(2)[9] +0.276(5)[64] 77 −109.4(15)[110] +0.308(4)[74] 78 −160(2)[13] +0.270(5)[78] 79 −186.2(19)[140] +0.290(5)[87] 80 −239(4)[16] +0.242(10)[91] 81 −271.8(15)[170] +0.242(4)[99] 82 −222(9)[19] +0.447(23)[120]

2 2 The atomic factors for the 4p P3/2 → 5s S1/2 transition in gallium are not known. Therefore, they need to be determined in order to extract the change in mean-square charge radii. Additional charge radii information, based on muonic atom data, only exists for the two stable gallium isotopes, 69Ga and 71Ga. These 2 71,69 2 values produce a single value of δhrchi = −0.116(20) fm [81], which alone is insufficient to calibrate both atomic factors simultaneously using the King plot method. For this reason multi-configurational Dirac-Fock (MCDF) calculations −2 were performed [82] and gave rise to the estimates Fel = +400 MHz·fm and KMS = −431 GHz·u for the field-shift and mass-shift factors respectively (their errors will be discussed later).

Using these estimated values, the changes in the mean-square charge radii were calculated. From the results the change in the mean-square charge radius of 69Ga from 71Ga was found to be −0.34(1) fm2, which differs significantly from the previously measured value of −0.116(20) from Reference [81]. This difference is due to an overestimation of the atomic mass-shift factor used in the calculations. While the computation of the field-shift factor appears to be quite stable for a systematically enlarged size of the MCDF wave functions, the mass-shift factor depends critically on correlations among the electrons, and no final convergence could be shown for this parameter. This mass-shift parameter comprises of two terms of different sign due

85 5.6. Isotope Shift Analysis to the normal (+396 GHz·u) and specific mass-shift (−825 GHz·u), and therefore suffers from an incomplete cancellation of different contributions. From the stability of the computations, an uncertainty of at least 15% was assigned to the specific mass-shift factor. Due to this uncertainty the mass-shift factor was re-evaluated, to find a more reliable specific mass-shift factor, so that the calculated value of 2 71,69 δhrchi agrees with the result from muonic data.

To observe the eﬀect of changing the mass-shift factor, the changes in mean- square charge radii were calculated using diﬀerent mass-shift factors. The results of these calculations with KMS values of −366 GHz·u, −431 GHz·u and −496 GHz·u are shown in Figure 5.21.

Figure 5.21: Changes in mean-square charge radii of the gallium isotopes, from 71Ga, calculated using diﬀerent KMS values. The plot highlights the eﬀect of changing KMS (see text for details).

In the figure it shows how a change in the magnitude of the KMS factor rotates the plot around the central, reference isotope. The plots retain the features of the changes in charge radii between isotopes regardless of the KMS value used. Therefore, adjusting the KMS factor will not alter the effects of physical changes that occur across the isotope chain; the gradient will only be adjusted to match the observed radii change observed in the muonic data. As this is the case, the mass-shift factor was tuned to provide a more accurate representation of the change in mean-square 2 71,69 charge radii. This was done by calculating the KMS value that produces a δhrchi value to match the muonic result. From this calculation, the new mass-shift factor was determined to be KMS = −211.4(210) GHz·u. With the normal mass-shift as +396 GHz·u, the new specific-mass shift is therefore −607.4(210) GHz·u. This new value represents a ∼ 25% difference from the initial specific mass-shift, in agreement with the error associated to the MCDF calculation. Using this new factor the charge radii could be more reliably extracted and the results are presented in Table 5.7.

86 5: Laser Spectroscopy of Gallium Using COLLAPS

A plot of the change in mean-square charge radii of the isotopes with the diﬀerent mass-shift factors is displayed in Figure 5.22.

Figure 5.22: Plot of the changes in mean-square charge radii of the gallium isotopes from 71Ga (N = 40). Results are shown using the estimated ﬁeld-shift factor −2 Fel = +400 MHz·fm from MCDF computations and two values of the mass-shift factor: KMS = −431 GHz·u obtained from MCDF computations [circles] and KMS = −211.4 GHz·u “tuned” to match muonic data [triangles] (see text for details).

The ﬁgure highlights the change in gradient of the change in mean-square charge radius but demonstrates how the characteristic changes between isotope neighbours still remains.

5.6.2 Experimental Errors

For the isotope shift measurements, the statistical errors are associated with the ﬁtting of the experimental data . The statistical errors are given by the variation 2 2 in the centroid frequency that allowed the ﬁtted χ value to deviate within the χr value. For the changes in mean-square charge radii, the statistical errors were found from the propagation of the isotope-shift errors used in the computation.

The systematic error for the isotope shifts arises from the uncertainty in the measurement of the voltage used to accelerate the atoms, the ISCOOL voltage. During the experiment the ISCOOL voltage was monitored by a high-precision voltage divider. An error in the read out of this voltage would cause a systematic shift to the measured centroid values. To calculate the extent of this systematic uncertainty, the

87 5.6. Isotope Shift Analysis

fitting routines were performed with different ISCOOL voltages until the extracted isotope shift of 71Ga from 69Ga changed to outside the error on the literature value, 3.5 MHz in +39.6 MHz [80]. It was found that the ISCOOL voltage could vary by 71,69 up to ±12 V until the extracted δνIS deviated too far from the known value. This ±12 V was extrapolated through the fitting routine used to determine the centroid values, providing the systematic error limits of the final measured isotope shifts.

For the mean-square charge radii, the systematic errors arise from the uncertainty in the atomic factors as well as the ISCOOL voltage used to measure the isotope shifts. The field-shift factor was given an uncertainty from the atomic factor computations of 60 MHz·fm−2 in 400 MHz·fm−2. The error in the final mass-shift 71,69 factor was determined from the propagation of the errors in the published δνIS [80] 2 71,69 and δhrchi [81] values used in its evaluation. Due to the mass dependence of the accelerating voltage on the isotope shift, the systematic effect caused by the uncertainty in the ISCOOL voltage acts in the same way as the uncertainties in the atomic factors. As the KMS factor was adjusted to match the literature value, the effects of the other errors are cancelled out in its evaluation, see Reference [83] for additional details. Therefore, the overall systematic error of the extracted charge radii is governed by the error in the determination of the final KMS factor. The systematic errors on the changes in mean-square charge radii were calculated using the limits of the KMS factor error and the extent of the uncertainty is shown in Figure 5.23.

5.6.3 Interpretation of the Changes in Mean-Square Charge Radii

With the ﬁnal mean-square charge radii evaluated from the isotope shifts, the trend of their changes across the entire gallium isotope chain can be investigated. Figure 5.23 displays the relative changes in the mean-square charge radii of the gallium isotopes, with the associated systematic error limits, plotted alongside those of the neighbouring nickel, zinc and krypton elements.

From the plot there are several visible effects that can be used to describe the structural nature of the gallium nuclei. Firstly, there is the behaviour of the charge radii in the neutron deficient isotopes, where the possible presence of a proton skin was proposed [56]. As described in Section 5.2, any development of a proton skin would cause an increase in the charge radii, up to ∼ 0.5 fm2, across isotope neighbours. By 63Ga, N = 32, there is no indication of any increase in the change in the mean-square charge radii from the downsloping trend observed from the heavier isotopes. Any developing rearrangement of the protons towards the surface of the nucleus would be clearly visible in the charge radii data; therefore, the results show that there are no signs to indicate a development of a proton skin in gallium by N = 32. Measurements beyond N = 32 may observe some substantial effects but the results from this campaign suggest that this would be unlikely. At the TRIUMF laboratory for particle and nuclear physics in Canada, there are plans to measure

88 5: Laser Spectroscopy of Gallium Using COLLAPS

Figure 5.23: Changes in mean-square charge radii of the gallium isotopes from 71Ga (N = 40), plotted alongside relative changes in the neighbouring nickel, zinc [84] and krypton [85] isotope chains. The neighbouring radii have been vertically oﬀset to avoid overlapping of data points and provide the best visible presentation for comparison. The systematic error limits on the gallium radii are represented by the dashed lines. The statistical errors are smaller than the data points. Included is an iso-deformation line for gallium taken from the droplet model [86]. the charge radius of 62Ga to assist with CKM unitarity tests [87]. This measurement will extend the charge-radii measurements of the gallium chain, allowing the most neutron-deﬁcient case to be investigated for any anomalous behaviour.

From the neutron-deficient side of the isotope chain the mean-square charge radii displays behavioural effects that can be described by conventional shell-model ordering as neutrons are added to the system. In 63Ga, the neutrons fully occupy the νp3/2 level, N = 32. As neutrons are added to the system they fill the νf5/2 then νp1/2 levels, resulting in a gradual increase of the mean-square charge radius. This rate of increase is similar to those experienced in the neighbouring zinc and nickel isotope chains. This increase remains fairly constant until around N = 40 where the gradient of the charge radii starts to flatten out, deviating from the previous trend. This occurs due to the total occupancy of the νp1/2 level and the subsequent filling of the νg9/2 level. From N = 41, the neutrons fill the νg9/2 level, returning the system to a more spherical shape. This is confirmed by the quadrupole moments of 72 the isotopes at the boundaries of the orbital, where Ga has Qs = +0.536(29) [54] 81 compared to Qs = −0.048(8) [53] for Ga. This same behaviour is observed in the krypton chain [85], but to a much larger degree, where the nucleus has a transition from strongly deformed around N = 40 to spherical at N = 50.

89 5.7. Conclusion and Outlook

On the neutron-rich side of the isotope chain a noticeable effect in the gradient of the charge radii is observed around N = 50. N = 50 is a well-known shell closure where there is a large difference in energy between the νg9/2 and νd5/2 orbitals. In the gallium chain, at N = 51 there is a sudden increase in the charge radii as the neutrons start to occupy the more energetic νd5/2 level. This was also observed in the krypton chain to a very similar degree. This sudden deviation highlights the significance of the N = 50 magic number and is typical of major shell closures.

Another effect that is present in the change in the charge radii, but in this case is observed across the entire chain, are deviations from the normal odd-N/even-N staggering effect. The normal odd/even staggering effect is where the mean-square charge radius of an isotope, with even-N, is larger than the average of its two, odd- N neighbours. In the gallium chain the majority of the isotopes follow the normal odd/even staggering trend. However, there are a couple of noticeable deviations. One of these is observed at N = 50 and is due to the major shell closure that was mentioned earlier. The second occurrence of the inversion of the odd/even staggering is observed at N = 40. This deviation suggests that there could be a possible sub- shell gap that occurs after the νp1/2 orbital. Anomalous behaviour has also been observed at this neutron number in the copper isotopes [88]. High-precision mass measurements have been performed on nickel, copper and gallium to investigate this N = 40 region [89]. The measurements showed no clear evidence of a shell closure at N = 40. However, there were some indications of a weak effect at this neutron number for Z = 28.

5.7 Conclusion and Outlook

From the experimental results presented in this chapter, the neutron-deﬁcient gallium isotopes down to N = 32 have had their hyperﬁne structures measured and the changes in mean-square charge radii extracted from their isotope shifts. The ground-state spin of 63Ga has been determined as I = 3/2 and its magnetic dipole and electric quadrupole moments have been measured to be µ = +1.469(5) µN and 70 Qs = +0.212(14) b respectively. The moments of Ga were also measured to be µ = +0.571(2) µN and Qs = +0.105(7) b.

Shell-model calculations were performed using the JUN45 and jj44b interactions. Calculations of the nuclear moments using both interactions showed good agreement with the experimental results, supporting their wave function compositions. The jj44b interaction correctly predicted I = 3/2 as the ground-state spin of 63Ga.

For the analysis of the change in mean-square charge radii of the gallium isotope chain, MCDF calculations were performed and the results were compared with non- 2 2 optical data to produce new atomic factors for the 4p P3/2 → 5s S1/2 atomic −2 transition. The factors were determined to be Fel = +400(60) MHz·fm and KMS = −211.4(210) GHz·u. Using these factors the changes in mean-square charge radii were extracted from the isotope shifts and investigated. Analysis of the trend in

90 5: Laser Spectroscopy of Gallium Using COLLAPS the neutron-deﬁcient radii demonstrated that there is no evidence of anomalous charge-radii behaviour in gallium in the region of N=32.

The results presented in this chapter have helped to complete the investigation into the gallium isotopes but have not closed the door on nuclear structure effects in this region. The work at TRIUMF into the measurement of 62Ga for CKM unitarity tests will provide results that will compliment those presented in this thesis. The reversal in the odd-N/even-N staggering effect of the charge radii highlights a possible sub-shell presence at N = 40 which has been suggested from other experiments. It will be interesting to observe the extent of the anomalous behaviour in the copper isotopes to investigate the effect of the number of protons in the system and see if further studies seem appropriate. The results of this experimental campaign of gallium have demonstrated how laser fluorescence spectroscopy is able to perform a wide range of high resolution measurements across an entire isotope chain for the investigation of nuclear structure effects.

91 92 Chapter 6

The CRIS Beam Line

The CRIS (Collinear Resonant Ionisation Spectroscopy) beam line is a new experimental setup situated at the ISOLDE isotope beam facility at CERN. CRIS was built to perform laser spectroscopy measurements on accelerated beams of highly exotic radioisotopes. This chapter will introduce the CRIS technique and describe the diﬀerent components of the experimental apparatus that have been installed over recent years.

6.1 A Brief History of CRIS

The CRIS technique is an experimental method that combines the resolution of collinear laser spectroscopy with the sensitivity of resonant ionisation spectroscopy. The combination of these methods was first proposed in 1982 by Kudryavtsev and Letokhov [90]. In their experiment they successfully demonstrated how the mass- dependent kinematic shift of all spectral lines of accelerated atoms could be used to increase the selectively of resonant ionisation of different isotopes within an atomic beam. To illustrate the sensitivity and future promise of the method they considered the possibility of being able to selectively ionise 26Al, which has a steady state abundance of ∼ 10−14. The first demonstration of CRIS at ISOLDE was performed in 1991 by Schulz et al. [91] and successfully investigated the hyperfine structures and isotope shifts of unstable ytterbium isotopes. The experiment achieved a low background rate of 1:108. However, the experimental efficiency was 1:105, limited mainly due to the duty-cycle losses associated with using a pulsed laser with a continuous atom beam.

With the development of ion-bunching techniques since these experiments, this duty-cycle loss can be eliminated, opening up the prospect of CRIS with an experimental efficiency improved by a factor of ∼ 104. The first demonstration of CRIS using bunched beams was in 2004 at the IGISOL facility and an experimental efficiency of 1:130 was achieved using bunches of 27Al [92]. In parallel to these tests,

93 6.2. CRIS at ISOLDE the installation of ISCOOL at ISOLDE was proposed [93], with CRIS one of the justiﬁcations for the project. ISCOOL was successfully established at ISOLDE in 2008 and a proposal for the new CRIS experiment at ISOLDE was submitted [94]. The project was accepted and development began with the main CRIS components designed and constructed in Manchester before being shipped to ISOLDE for installation in 2009. Between 2009 and 2012 the rest of the CRIS beam line was constructed and installed while tests were continuously performed to track the pro- gression of development. By October 2012 the CRIS beam line was ready for its ﬁrst on-line run and successfully demonstrated its capabilities for performing highly sensitive laser spectroscopy measurements on exotic francium isotopes.

6.2 CRIS at ISOLDE

The CRIS apparatus is a permanent experimental setup situated at the ISOLDE facility at CERN. Figure 6.1 shows a 3D drawing of CRIS and Figure 6.2 is a schematic drawing highlighting the major components of the setup.

Figure 6.1: 3D drawing of the CRIS beam line highlighting the major components of the apparatus.

For on-line experiments the HRS target is used for the production of the ion beam, in order to utilise the bunching and cooling capabilities of ISCOOL and the mass resolution of the HRS separator. The bunched ion beam (up to 50 keV) is delivered from ISCOOL to the CRIS setup via the ISOLDE central beam line. Within CRIS, the bunch passes through two pairs of vertical steering electrostatic plates to optimise the beam height and then is focused in an electrostatic quadrupole triplet. The CRIS beam line has several electrostatic focusing elements to assist in

94 6: The CRIS Beam Line Schematic drawing of the diﬀerent components of the CRIS beam line (see text for individual details). Figure 6.2:

95 6.3. Components of CRIS the transmission of the ion bunch. After the profile of the ion beam has been optimised it is bent through 34° to be overlapped with co-propagating laser beams and delivered to a charge-exchange cell to be neutralised via electron exchange with a heated alkali vapour. Any residual ions after neutralisation are deflected by an electrostatic kicker and the remaining atomic bunch travels towards the interaction region. Within this region the atom bunch is overlapped with the laser beams and ionised when on resonance with the laser frequency. Any remaining atoms continue undeflected to a beam dump area while the resonant ions are directed via electrostatic steering plates towards the end of the beam line for detection.

6.3 Components of CRIS

The experimental set up of CRIS contains many diﬀerent components in order to manipulate and control the ion beam, and provide the conditions necessary to make highly sensitive laser spectroscopy measurements. These components are:

• Laser Setup

• Charge-Exchange Cell

• Ion Detection

• Ultra-High Vacuum Interaction Region

• Voltage/Frequency Scanning

• Data Acquisition System

• Decay Spectroscopy Station

• Oﬀ-Line Ion Source

• Electrostatic Ion Optics and Faraday Cups

This section will provide descriptions of each of these components that contribute towards the operation of CRIS.

6.3.1 Laser Setup

For laser spectroscopy experiments it is important to have a suitable laser area to house the laser system and be able to deliver an optimised beam. For the CRIS experiment there are several possibilities for the location of the laser system. Adja- cent to the CRIS apparatus is a laser table, surrounded by an interlocked cage, that is used for the optimisation of laser beams before they are delivered into the beam line, see Figure 6.3. The CRIS laser table has space for the placement of several laser

96 6: The CRIS Beam Line

Figure 6.3: Diagram of the CRIS laser locations within ISOLDE. The CRIS beam line can accept laser beams delivered from the adjacent laser table, which in turn has the option to receive laser beams from the RILIS laser cabin or an external laser room. systems and is able to receive laser beams from external locations. Next to ISOLDE is a designated laser room (507-R-014 in Figure 6.3) for laser systems specifically operated for use on CRIS. The room has been utilised for various off-line tests with different laser systems that have been set up. As well as the external laser room, the CRIS beam line is able to receive laser beams from the RILIS cabin via an optical fibre. These options provide CRIS with access to several laser systems to be used for experimental studies, although there is currently no permanent system in place.

6.3.2 Charge-Exchange Cell

One of the major components of the CRIS beam line is the charge-exchange cell (CEC), to neutralise the ion beam for access to atomic transitions. The CEC is situated before the interaction region so that neutralisation occurs before the resonant ionisation process. Technical and schematic drawings of the CEC are shown in Figures 6.4 and 6.5 respectively.

97 6.3. Components of CRIS

Figure 6.4: Technical drawing of the CEC highlighting the locations of the ion/atom beam entry and exit points, the oil supply connections and the electrical feedthroughs.

Figure 6.5: Schematic drawing of the CEC. The alkali metal is heated up to about 150℃ to form a vapour for the charge-exchange process. The vapour condenses at the ends of the cell, which are cooled by oil circulation, and is recycled to pre- vent contamination in the rest of the beam line . The electrical feedthoughs are used to provide the heating current and monitor the central and end temperatures with thermocouples.

98 6: The CRIS Beam Line

The CEC is based on the COLLAPS design [46], constructed so that a constant alkali vapour is produced within the cell for the charge-exchange process, while minimising the release of the vapour particles into the rest of the beam line. For the vapour, an alkali metal is chosen due to its loosely bound electron and the typical collisional process can be given as,

B+ + A → B + A+ + ∆E (6.1) where B are the ion beam particles, A are the alkali vapour particles and ∆E represents any energy transfer, ranging from a few meV [46], for quasi-resonant neutralisation to an atomic ground state, to a few eV [92] if populating excited atomic states. For keV ion beams the charge-transfer cross-sections are generally of the order of 10−14 cm2, much larger than the collisional cross-section from the atomic radius, resulting in minimal momentum transfer and negligible phase-space distribution of the beam [46].

A central metal pipe, approximately 10 mm in diameter, is situated within a larger cylindrical unit so that the path of the ion beam travels through the centre of the pipe. There is a removable cap on the unit for loading the alkali metal into the cell. Heating cables are attached to the cylindrical housing unit via electrical feedthroughs to supply a heating current to the CEC. This heating current is then increased until the alkali metal produces a vapour that diﬀuses out, away from the centre. The ends of the cylindrical housing are cooled by oil circulation, causing the vapour to condense and recycle back towards the centre of the cell. This setup creates a dense vapour without contaminating the pressure within the rest of the beam line.

The neutralisation eﬃciency, ε, of the CEC can be estimated using,

ε = σneutNTLC (6.2)

−18 2 where σneut ≈ 10 m is the charge-transfer cross-section, NT is the density of vapour molecules and LC is the length of the vapour in the CEC. For the francium experiment, potassium was used and the vapour forms at approximately 150℃ with −4 19 −3 a vapour pressure of ∼ 8 × 10 mbar (NT ≈ 2 × 10 m ) [95]. If a constant vapour of ∼ 0.05 m is formed in the CEC then the neutralisation eﬃciency will approximately be 100%.

6.3.3 Ion Detection Setup

Resonant ions are detected in CRIS using a highly sensitive ion detection setup consisting of a two-stage Hamamatsu F4655-12 micro channel plate (MCP) [96] in combination with a negatively-charged copper dynode plate, shown in Figure 6.6. The MCP setup is ideal for ion detection as it has a high speed response (<1 ns timing), single ion sensitivity and a low dark count rate (∼ 2 /s). The resonant ions are transported from the interaction region, separated from the atoms, and steered

99 6.3. Components of CRIS

Figure 6.6: Technical drawing of the MCP and dynode plate. Included is the direction of travel of the ion beam and the resultant electron shower.

and focused towards the dynode plate. The ions impinge on the dynode plate and eject secondary electrons. The plate is biased with a negative potential in order to accelerate the electrons towards the MCP.

The MCP is biased for negative ion/electron detection in order to acquire a signal from the secondary electrons, shown in Figure 6.7. The front plate of the MCP is held at a low positive voltage to accelerate the electrons towards it. The electrons impinge onto the plate, creating subsequent electron showers. A positive potential (typically +2 kV) is applied across the MCP to guide the electrons towards the anode. The electrons collect on the anode and create an output voltage signal that can be connected to an external data acquisition system via a BNC connection. This signal can then be triggered on to provide a count for each ion that impacted on to the dynode plate. An example screenshot of the detection of an ion bunch with the data acquiring oscilloscope is shown in Figure 6.8.

100 6: The CRIS Beam Line

Figure 6.7: Circuit diagram of the MCP electronics. A potential divider is set up across the MCP to guide the electrons to the anode. The capacitors block the high DC voltage from the BNC connection, while the central capacitor acts as a high pass ﬁlter to allow the detection signal through.

Figure 6.8: Screenshot of the detection of a 238U ion bunch on the MCP oscilloscope. The y-axis is the height of the pulse signal, 2 mV/div and the x-axis is the time between ion counts, 1 µs/div. The vertical lines highlight the location of a trigger on the detected ion.

101 6.3. Components of CRIS

6.3.4 Ultra-High Vacuum Interaction Region

To reduce the amount of non-resonant collisional ionisation the interaction region is required to operate with an ultra-high vacuum (UHV). The background rate from collisional ionisation can be estimated [91] using,

Nback = σcollNTIPLI (6.3)

−19 2 where σcoll ≈ 10 m is the cross-section for collisional ionisation, NT is the density of target molecules, IP is the current of projectile atoms and LI is the length of the interaction region. For a bunched beam travelling through the 1.2-m interaction region, the collisional ionisation rate will be of the order of 1:103 for a pressure of −7 15 −3 5 −9 10 mbar (NT ≈ 2.5 × 10 m ), decreasing to 1:10 for a pressure of 10 mbar 13 −3 5 (NT ≈ 2.5×10 m ). For a 0.1 pA beam (∼ 2×10 atoms per bunch at 30 Hz) the number of collisional ions would be almost negligible at this pressure. Therefore, it is desirable for the interaction region to be as close to (if not below) 10−9 mbar to maximise the sensitivity of CRIS.

The CRIS experiment is operated at low pressure through the use of several turbo pumps, backed by roughing pumps, situated throughout the beam line. The general operating pressures of the regions within CRIS are presented in Table 6.1.

Table 6.1: Operational pressures of the diﬀerent regions within the CRIS beam line.

Region Pressure (mbar) Quadrupole Triplet <10−5 CEC <10−5 Interaction Region <10−8 Detection Region <10−7

As the interaction region is connected to the detection region and CEC it is necessary to have a pressure differential to maintain its UHV. This is particularly important for the separation from the CEC, to avoid the contamination of the pressure in the interaction region from any alkali vapour particles. The differential pumping apertures between the interaction region and CEC are shown in Figure 6.9. An additional differential pumping aperture is situated between the interaction region and the detection region. The apertures create a pressure differential by limiting the flow of particles from one region to the next. The conductance of molecular flow through a pipe, FM, is dependent on the radius of the aperture, a, and the length of the pipe, l, given by, 2 cπa¯ 3 FM = (6.4) 3 l where c¯ is the mean speed of the molecules [97].

The pumping apertures used in CRIS have a radius of 5 mm and a length of 20 mm. The dimensions were chosen to provide the best reduction in molecular

102 6: The CRIS Beam Line

Figure 6.9: Differential pumping of the interaction region from the CEC through the use of two differential pumping apertures. The apertures allow a ∼ 10−3 mbar pressure differential between the two regions.

ﬂow between the regions while avoiding any reduction in the transmission of the atom/laser beams through them. The apertures between the CEC and interaction region provides a pressure diﬀerential of ∼ 10−3 mbar, allowing the interaction region to operate at below 10−8 mbar.

6.3.5 Hyperﬁne Structure Scanning Methods

There are two methods that can be used to scan across the hyperfine structure of an atomic transition with CRIS. The first is by applying a scanning voltage to the CEC, to Doppler tune the atom onto resonances with a fixed-frequency laser. The second is to manually scan the output frequency of the resonant laser beam. The benefits of the voltage scanning method are: the setup is stable and repeatable, the voltage can be measured accurately and the voltage can be stepped quickly (<1 V/ms) to perform fast hyperfine scans. The method of manually scanning the laser frequency has the advantage of being able to scan over a large range (>25 GHz). However, it has problems in that the setup is more unstable (mode hopping for example) and it is difficult to perform repeat measurements.

To Doppler tune the beam in the CRIS setup, a tuning voltage is applied to the CEC so that the incoming ion bunch is either accelerated or decelerated before it is neutralised, adjusting the velocity of the atom beam in the interaction region. Scanning the voltage to Doppler tune the beam was tested oﬀ-line in 2011 to observe the stability of this method. The tests were performed using a bunched 238U beam,

103 6.3. Components of CRIS delivered to the MCP without neutralisation, to evaluate the steering eﬀects of the voltage on the ion beam as it passed through the CEC. The eﬀects on the beam by the applied scanning voltage is shown in Figure 6.10.

As is seen in the figure a slight steering effect was observed with negative voltages applied to the CEC and a more noticeable effect with positive voltages applied. When negative voltages are applied the ion beam is accelerated, minimising the steering effect, while there is an enhancement of the effect with positive voltages. Possible reasons for this effect were that the ion bunch was not well aligned as it travelled through the CEC or that the ions were poorly shielded from the external electrostatic ion optics. To attempt to solve this problem the vertical steering electrostatic ion optics, see Section 6.3.9, were installed to alter the height of the beam, so that it travelled through the CEC perpendicular to the electric field lines. Recent tests have shown an improvement, with the steering effect reduced. However, it is still a noticeable effect that would limit voltage ranges for hyperfine measurements. Therefore, the CRIS beam line currently operates by manually scanning the laser frequency, which is controlled by a computer system. In the future the beam steering effect will be addressed so that the experiment can perform measurements by scanning a tuning voltage. A new CEC will be constructed, which will be designed to minimise the observed steering effect.

6.3.6 Hardware Control

The CRIS experiment has a central computer system that it uses for the control of the components of the apparatus and to acquire the data for on-line measurements. The main components of the CRIS control system and how they are connected are shown in Figure 6.11. The operating programs for the computer control system have been written in LabVIEW. The system is connected to a voltage distribution rack that contains up to 24 HV supplies to supply and monitor the voltages for the electrostatic ion optics in CRIS. A high-precision ammeter (∼ 100 pA sensitivity) is connected to the CRIS Faraday cups to monitor the ion/atom beam intensities within the beam line. For laser-scanning measurements the computer system controls the laser frequency, while for voltage scanning experiments the system can control the voltage delivered to the CEC. A pulse generator is used to control the timing sequence of the experimental procedures and provide the trigger signals to be sent for the control of required components. (See section 7.2.3 for the timing set up of the data acquisition system for an on-line experiment). A LeCroy oscilloscope is connected to the MCP to continuously monitor the ion counts. A trigger is sent to the oscilloscope to dictate the expected arrival time of the resonant ion bunch and a window is placed on the oscilloscope to discriminate counts before and after the expected arrival time of the bunch. The ion count data is saved to the local machine and can be displayed within the control program during on-line experiments.

104 6: The CRIS Beam Line

Figure 6.10: Drifting eﬀects of a 238U ion beam after travelling through the CEC with negative [top] and positive [bottom] voltages applied. Within the plots the top boxes show the number of ion counts at each voltage, the right boxes show the timing structure of the beam and the central plot shows the combination of the two. The plots highlight the steering eﬀect of the CEC on the ion beam when voltages are applied (see text for details).

105 6.3. Components of CRIS

Figure 6.11: Infrastructure of the control of the main components used for data collecting with CRIS. Shown is the arrangement to manually scan the laser frequency for hyperﬁne structure measurements.

6.3.7 Decay Spectroscopy Station

As well as detecting the ions with the MCP, the beam can be delivered to a decay spectroscopy station (DSS), situated at the end of the CRIS beam line, for decay studies. The ions can be delivered onto one of ten 20 µg/cm2 carbon foils that are situated on a rotatable wheel, for the eﬃcient measurement of charged decay products. A technical drawing of the DSS implantation wheel is shown in Figure 6.12.

A pair of silicon detectors are placed either side of the implantation site for the detection of the decay products, as well as an additional pair situated further along the wheel, to investigate longer-lived species. Outside the chamber there is space for the placement of up to three high-purity germanium detectors. Recent publications, describing the results from initial development tests, can be found in References [98, 99, 100] for further information on the DSS.

The DSS compliments the CRIS beam line as it uses the high degree of selectivity offered by CRIS to perform decay spectroscopy on pure beams. It also offers the ability to distinguish between and identity the ground state and any isomeric states within a measured hyperfine structure.

106 6: The CRIS Beam Line

Figure 6.12: Layout of the implantation site in the DSS. For a more detailed description of the DSS see Reference [98].

6.3.8 Oﬀ-Line Ion Source

The CRIS beam line has its own oﬀ-line ion source for stable beam tests and measurements. The ion source is located within a HV cage, placed just before the quadrupole triplet. A schematic diagram of the ion source is shown in Figure 6.13.

Figure 6.13: Schematic diagram of the off-line ion source. The atoms diffuse out of the heated tantalum holder and surface ionise in the capillary tube. The ions drift through the tube by the potential difference of the heating current and are accelerated by the ion source potential.

107 6.3. Components of CRIS

Salt crystals are placed within a tantalum holder, which is heated by a high current (30 - 50 A), where the atoms diffuse out and are surface ionised in a ∼ 1 mm capillary tube. The ion source can be biased up to 30 kV so that the ions are accelerated and form a beam in a similar way to the ISOLDE targets. The accelerated ion beam is extracted from the capillary tube via an extractor plate, focused in an Einzel lens and then steered using horizontal and vertical steerers. After the beam has been optimised it is sent through a 90° bend and directed towards the quadrupole triplet. The ion beam can then be steered and used in CRIS in the same way as using an ion beam from ISOLDE. The ion source is not able to bunch the ion beam, to replicate the effects of ISCOOL, although for off-line tests it is not a necessary feature.

6.3.9 Electrostatic Ion Optics and Faraday Cups

Within CRIS, the ion beam is steered and focused using electrostatic ion optics and the beam intensity is monitored using several Faraday cups. Figure 6.14 shows the location of the ion optics [A - I] and Faraday cups [1 - 6] within CRIS. This section will describe the individual ion-optic components, labelled in Figure 6.14, and state the magnitude of the voltages than can be supplied to them.

Figure 6.14: 3D drawing of the CRIS beam line with the locations of the electrostatic ion optics [A - I] and Faraday cups [1 - 6].

108 6: The CRIS Beam Line

A Vertical Steerers ±5 kV Two pairs of plates, with opposite polarity, are used to control the height of the incoming ion beam, shown in Figure 6.15. The polarity of the HV supplies can be exchanged to increase or decrease the height of the beam. The plates were installed to assist with the transmission of the ion beam through the CEC when a tuning voltage is applied.

Figure 6.15: [Location A] 3D drawing of the vertical steerers situated at the front of CRIS. The plates are used in tandem to drop or raise the height of the ion beam.

B Quadrupole Triplet ±10 kV The quadrupole triplet acts as the ﬁrst focusing set of ion optics for transmission of the ion beam through CRIS. The front and rear quadrupoles share their positive and negative terminals, which are isolated from those of the central one, shown in Figure 6.16.

Figure 6.16: [Location B] Schematic drawing of the quadrupole triplet. Included are the connections of the four HV supplies.

109 6.3. Components of CRIS

C Bending Plates ±10 kV Two bending plates, see Figure 6.17, are situated after the quadrupole triplet to deflect the ion beam so that it can be collinearly overlapped with the laser beams. The housing for the bending plates has a connection that fits a laser window so the laser light can be delivered. Within the outer bending plate there is a machined slot to allow the laser beam to enter CRIS and travel towards the interaction region. Not included in the figure is a thin plate that runs above the path of the ion beam, between the bending plates. A voltage can be supplied to this plate to focus/defocus the beam before it enters the CEC.

Figure 6.17: [Location C] 3D drawing of the bending plates for steering the ion beam to the CEC. The laser beams enter CRIS via a laser window and are then overlapped with the ion beam via a machined slot in the outer bending plate.

D Correction Plates ±5 kV The bending plates are unable to produce a beam parallel to the axis of the beam line, creating a problem for the subsequent transmission of the beam. To solve this problem, there are a pair of electrostatic correction plates, see Figure 6.17, placed before the CEC to help correct the direction of the ion beam. The voltages on the correction and bending plates can be optimised in tandem to horizontally move the beam before it enters the CEC.

110 6: The CRIS Beam Line

E Quadrupole Doublet ±5 kV A quadrupole doublet, shown in Figure 6.18, is situated immediately after the correction plates to correct the focusing eﬀect of the bending plates and produce a tapering focus of the ion beam for transmission through the CEC and interaction region. It is important to have the beam well focused before it is neutralised as the CEC contains two 10 mm apertures and there are several 10 mm diﬀerential pumping apertures either side of the interaction region.

Figure 6.18: [Location E] 3D drawing of the quadrupole doublet located immediately before the CEC.

F Ion Kicker ±5 kV After the CEC is a kicker plate, shown in Figure 6.19, that is used to deﬂect away any remaining ions from the atom beam. The non-neutralised ions need to be removed from the atoms so that they are not detected on the MCP and misinterpreted as resonant ions. A positive voltage is applied to the plate to kick the ions into the side of the beam pipe. The ion kicker is situated just before the interaction region to reduce the number of collisional non-resonant ions.

G Resonant Ion Deflector Plates ±10 kV After the interaction region the resonant ions are steered towards the MCP or DSS for detection. This is done using the resonant ion deflector plates, shown in Figure 6.20, situated immediately after the interaction region. One of the deflector plates has a bend in it to avoid blocking the ion beam as it is steered through 20°. Along the axis of the interaction region is an extension beam pipe for the atoms to travel through and a laser window so the laser beams can exit the setup and be monitored on a photodiode.

111 6.3. Components of CRIS

Figure 6.19: [Location F] 3D drawing of the ion kicker used to deﬂect any remaining ions after the CEC. The ion kicker is placed immediately before the interaction region to minimise the eﬀect of collisional ionisation.

Figure 6.20: [Location G] 3D drawing of the deﬂector plates used to steer the resonantly ionised ions through 20° to the MCP or DSS for detection.

112 6: The CRIS Beam Line

H Second Quadrupole Doublet ±5 kV A second quadrupole doublet is installed before the DSS and MCP. The doublet is the same design as the one in location E and is used to correct for the focussing effect of the 20° bend. The doublet also provides a final, tight focus of the beam to optimise the transmission efficiency of the ions to the detector setups.

I Horizontal and Vertical Steerers ±5 kV The ﬁnal electrostatic ion optics in CRIS are the horizontal and vertical steerers, shown in Figure 6.21.

Figure 6.21: [Location I] 3D drawing of the horizontal and vertical steering plates used to guide the resonant ions to the MCP or DSS.

The steerers are required to deﬂect the resonant ion beam to switch between ion detection with the MCP or decay studies with the DSS. As the MCP setup is situated away from the beam axis the steerers are required to move the ions onto the dynode plate. The implantation site of the DSS is placed in the centre of the beam line; however, the steerers are still required to correct for any mis-steering caused by previous ion optics. For the path of the ion beam from the steerers to the MCP or DSS see Figure 6.22.

113 6.3. Components of CRIS

Figure 6.22: 3D drawing of the MCP and dynode plate within the decay spectroscopy station. The dynode plate is situated away from the centre of the beam line, requiring the ion beam to be deﬂected for detection.

1 - 6 Faraday Cups

The Faraday cups used in CRIS are a combination of suppressed and un-suppressed cups that are used to track the transmission eﬃciency of the ion beam, Figure 6.23.

Figure 6.23: Schematic drawings of the electron suppressed and un-suppressed Faraday cups used in CRIS. The ejection of electrons from the plate induces a diﬀer- ent current compared to the same beam hitting the plate where the ejection of electrons has been suppressed. Un-suppressed cups are also able to monitor neutral atom beam intensities.

114 6: The CRIS Beam Line

In the CRIS beam line, Cups 1, 2, 3, 5 and 6 are un-suppressed Faraday cups, whereas Cup 4 is a suppressed Faraday cup. As shown in the figure, suppressed Faraday cups include a plate that can have a negative voltage (up to −1 kV) applied to it, creating an electric field that repels the electrons that are sputtered from the surface, back onto the Faraday cup. This set up prevents the cup being able to monitor neutral atom beam intensities. With un-suppressed Faraday cups the electrons that are sputtered from the cup induce a current that is different to that caused solely by the impinging beam. Due to this difference in current it is not possible to compare the beam intensity between the two types of Faraday cup. Even between Faraday cups of a similar design it is difficult to compare the beam intensity due to the differences in surface area and material of the cups. For transmission tests in CRIS, the Faraday cups are mainly used to maximise the beam current at that part of the beam line.

6.4 Summary

This chapter has introduced the CRIS setup and described all the major components that are involved in the experiment. The CRIS experiment has passed its commissioning period and has been successfully installed in the ISOLDE facility, ready to perform high sensitivity laser spectroscopy measurements. The end of the commissioning period was marked by its ﬁrst on-line run on the investigation of exotic francium isotopes. The performance of CRIS during this experiment will be presented and discussed in the following chapter.

115 116 Chapter 7

Laser Spectroscopy of Francium Using CRIS

In October 2012, CRIS performed its first successful on-line laser spectroscopy measurements on the radioactive isotopes of francium. The experiment measured the hyperfine structures of the francium isotopes between A = 202 and A = 231. This chapter will describe the analysis of selected isotopes measured during the run to demonstrate the operational status of CRIS. The measured rates of resonantly ionised 202,218,219Fr performed at the peak period of the experiment allowed the efficiency and background rate to be estimated. The obtained scans of 221Fr were used to determine the current accuracy of hyperfine structure and isotope shift measurements using CRIS. The reference isotopes 207,211,220Fr were additionally analysed for comparison with literature values.

7.1 Motivation for the Radioactive Francium Iso- topes

Part of the initial proposal for the installation of the CRIS beam line was the physical motivation in the neutron-rich and neutron-deﬁcient francium isotopes. CRIS will be able to extend measurements of the magnetic moments and isotope shifts down to cases with yields below 100 atoms/s. Examples of interest in these measurements are for investigation into the possible onset of shape coexistence and −1 + 201,203 (πs1/2)1/2 isomeric states in Fr:

Possible onset of shape coexistence

The investigation into the phenomenon of shape coexistence has been of interest in nuclear physics for over 50 years [101]. A simple description of nuclear shape coexistence is the observation of diﬀerent types of deformation within the same

117 7.2. Experimental Setup at ISOLDE nucleus at low excitation energy. One of the avenues of experimental campaigns into this effect has been to investigate the region below the Z = 82 shell closure and near the N = 104 mid-shell. Here, the mercury isotopes have been measured using laser spectroscopy and an odd/even staggering effect of the charge radii was observed due to the competition between strongly and weakly deformed shapes [102]. Recently, in-source laser spectroscopy experiments have been performed using RILIS at ISOLDE on the Tl, Pb and Po isotope chains [103, 104, 105]. The francium isotope chain (Z = 87) is of interest as it lies close to this region and measurements can go down to N = 114. As francium is readily surface ionised there is little gain from performing in-source laser ionisation spectroscopy and laser measurements have not gone beyond 207Fr (N = 120) [106]. The CRIS technique will allow charge radii measurements to be extended down to N = 114, addressing how shape changes effect the nuclear structure in this region.

−1 + 201,203 (πs1/2)1/2 isomerici state in Fr

Above the Z = 82 shell closure several experiments have observed a reduction in single-particle energies with decreasing neutron number. In the astatine and bismuth −1 + isotope chains a (πs1/2)1/2 state has been seen to invert with the ground state in 195At and 185Bi [107, 108]. An isomeric state of spin 1/2+ has been discovered in 205Fr using the recoil-decay tagging technique [109] and alpha decay studies into 201,203 −1 + Fr show strong evidence of isomeric (πs1/2)1/2 states [110]. Using CRIS the ground and isomeric states of 201,203Fr will be studied with optical spectroscopy for the ﬁrst time and have their spins, moments and isotope/isomer shifts measured.

7.2 Experimental Setup at ISOLDE

7.2.1 ISOLDE Target

The francium isotopes were produced for the on-line experiment using a uranium carbide (UCx) target. Protons (∼ 2 µA) at 1.4 GeV impacted onto the thick target, producing francium atoms that were then surface ionised on a tungsten capillary tube and accelerated to 50 keV. At ISOLDE there are two targets that can be used for the production of francium: uranium carbide and thorium carbide. Both have advantages with higher yields for diﬀerent isotopes, but uranium carbide has the advantage of producing a wider range of francium isotopes without losing signiﬁcant yields in the rarer cases. A summary of measured francium yields from a uranium carbide target impacted with 0.6 GeV protons is shown in Table 7.1. Currently there are no documented measurements of the production of the isotopes with 1.4 GeV protons. However, the yield of 202Fr was measured immediately after the francium experiment and was found to be ∼ 100 atoms/µC [111]. Using this measurement, the increase in yield from 0.6 to 1.4 GeV can be projected throughout the other isotopes to provide a rough estimate of the francium yields during the experiment.

118 7: Laser Spectroscopy of Francium Using CRIS

These estimated yields are shown in the fourth column of Table 7.1.

Table 7.1: Measured yields of the francium isotopes from the ISOLDE UCx target with 0.6 GeV protons delivered from the synchro-cyclotron [112]. Included are estimated yields with 1.4 GeV protons from the PSB, projected from a yield measurement of 202Fr [111].

Isotope Half life Yield (atoms/µC) Estimated Yield (atoms/µC) [0.6 GeV Protons] [1.4 GeV Protons] 202 340 ms 7.1 × 101 1.0 × 102 203 550 ms 1.0 × 103 1.4 × 103 205 3.9 s 1.7 × 105 2.4 × 105 207 14.8 s 3.6 × 106 5.1 × 106 211 3.1 min 1.5 × 108 2.1 × 108 218 0.7 ms 4.3 × 103 6.1 × 103 219 21 ms 8.9 × 103 1.3 × 104 220 27.4 s 3.8 × 107 5.4 × 107 221 4.9 min 2.8 × 107 3.9 × 107 229 39 s 3.8 × 104 5.4 × 104

7.2.2 Ionisation Process

There are two atomic transitions that have been previously used to investigate the hyperﬁne structures of the francium isotopes [113, 106]. These involved excita- tions from the 7S to the 7P and 8P states, see Figure 7.1. For the ionisation scheme 2 in the CRIS experiment, the excitation step to the 8p P3/2 state was used. This transition was chosen to minimise the amount of background from non-resonant ionisation caused by the coupling of photons from the non-resonant step.

2 As shown in the figure, the 7s S1/2 electron was resonantly excited up to the 2 8p P3/2 orbit by the absorption of a 423-nm photon, providing the transition to measure the hyperfine structure of the francium isotopes. The second step involved a 2 non-resonant photon of wavelength 1064 nm to excite the electron from the 8p P3/2 state into the continuum. The expected hyperfine structure of 221Fr using this transition is shown in Figure 7.2.

Laser Powers

The required laser power for the resonant step in the experiment can be estimated from the saturation laser intensity, given by Equation 2.37. Using the mean 2 lifetime of the 8p P3/2 state, τ ≈ 80 ns [115], the saturation intensity of the 423 nm transition is approximately 0.03 mW/mm2. For the experiment a titanium sapphire (Ti:Sa) laser was used for the resonant 423-nm excitation step. The Ti:Sa laser was pumped by a 10 kHz 532-nm Nd:YAG laser producing a 10 kHz 845-nm pulse, which

119 7.2. Experimental Setup at ISOLDE

Figure 7.1: Ionisation scheme for the francium isotopes [114]. The resonant step excited 2 2 the 7s S1/2 electron into the 8p P3/2 state before being taken into the continuum by the non-resonant laser pulse [solid lines]. Included is a scheme 2 involving the 718 nm transition to the 7p P3/2 state that was not used in this experiment [dashed lines]. was then frequency doubled in a lithium triborate (LBO) crystal to 423 nm. With the 10 kHz repetition rate and an approximate beam diameter of 10 mm the saturation energy of the resonant transition will be ∼ 0.3 µJ per pulse. As the linewidth of the frequency doubled Ti:Sa will be much larger than the natural linewidth of the transition, the power of the laser will need to be comparatively larger for the experiment to reach saturation. Estimating the frequency doubled light to have a linewidth of ∼ 1.5 GHz, the experimental saturation energy of the transition will therefore be approximately 36 µJ per pulse.

The laser power required for the ionisation step is a lot more diﬃcult to calculate due to the non-resonant process of the photon absorption. As the step involves taking an electron into the continuum, the cross section for such a process is dependent on the atomic structure of the studied isotope. Previous investigations into the ionising cross sections of caesium and rubidium have found the photoionisation cross sections from excited states to range from 1 × 10−23 m2 [116] to 1.5 × 10−21 m2 [44]. These cross sections are signiﬁcantly smaller than the cross section of the resonant step (∼ 10−15 m2 from Equation 2.34), implying a much higher laser intensity is required. In the rubidium investigation it was found that saturation occurred at a laser energy density of ∼ 1022 photons/m2. For the 1064-nm process, this equates to an energy density of ∼ 1.8 mJ/mm2. The 1064-nm ionising laser pulse for the experiment was produced by a 30 Hz, neodymium-doped yttrium aluminium garnet (Nd:YAG) laser. With this repetition rate and an approximate beam diameter of

120 7: Laser Spectroscopy of Francium Using CRIS

2 mm, the required laser power for the ionising step can be estimated to be 0.2 mJ per pulse.

Laser Resolution

The experimental resolution of the hyperﬁne measurements is dependent on the linewidth of the laser pulse used for the resonant transition. As part of the staging of the CRIS project a low resolution Ti:Sa laser system was used that produced a 845-nm pulse with a linewidth of >800 MHz before frequency doubling. This setup was chosen to provide the experiment with a broadband system for locating the hyperﬁne structures in this early stage of operation and in the future a dedicated, narrowband laser system will be implemented.

For the current experiment, this linewidth will be the dominating contribution to the experimental resolution. The linewidth limits the experiment to the measure- 2 ment of the splitting of the 7s S1/2 atomic state. This constraint can be visualised by looking at the hyperﬁne splitting of 221Fr, shown in Figure 7.2.

2 2 221 Figure 7.2: The hyperﬁne structure of the 7s S1/2 → 8p P3/2 atomic transition in Fr. Included is an expected ion count hyperﬁne structure with the FWHM of the transitions comparable to the laser resolution. The splitting of the lower atomic state determines the spacing between the two observed peaks in the CRIS data.

121 7.2. Experimental Setup at ISOLDE

2 As shown in the figure, the splitting of the 8p P3/2 state is of the order of tens of MHz, so in the experiment these transitions will overlap each other and be viewed as 2 one structure. However, the 7s S1/2 state is split by about 19 GHz, which can easily 2 be resolved with this system. This allows the A(7s S1/2) hyperfine coefficient to be measured, providing a route to determine the magnetic moments of the isotopes.

Laser Setup

The laser setup for the on-line experiment is shown in Figure 7.3.

Figure 7.3: Diagram of the laser setup for the ionisation of the francium isotopes (see text for details).

The Ti:Sa laser system was provided by the ISOLDE, RILIS experimental group and was situated in the RILIS laser cabin. The frequency doubled 423-nm light was coupled into a multimode, large numerical aperture optical ﬁbre and transported to the CRIS optical table. On the optical table the Nd:YAG laser produced the 1064-nm beam. The energies of the laser pulses could be measured on the optical table before being delivered to CRIS. The 1064-nm light was overlapped with that at 423-nm and delivered to a laser launch platform to be sent to the interaction region. A photodiode was situated at the end of the beam line to monitor the arrival times of the laser pulses in the interaction region.

122 7: Laser Spectroscopy of Francium Using CRIS

7.2.3 Experimental Procedure

This section will describe how the experiment was performed in order to measure the hyperﬁne structures and isotope shifts of the francium isotopes. After the francium ions were extracted and accelerated from the HRS target they were accumulated and released in bunches by ISCOOL. The ions were accumulated every 32 ms and then the trapping potential was switched to the platform voltage for 100 µs to release ion bunches with a temporal length of ∼ 3 µs. The timing of the experiment was dictated by a trigger pulse generated from the 423-nm laser. The 423-nm laser has a repetition rate of 10 kHz, much faster than the bunching time possible with ISCOOL or the data acquisition rate. Because of this, the laser trigger was sent to a pulse generator that could skip 319 pulses to generate the appropriate trigger for ISCOOL and the 1064-nm laser. The triggers sent to the 1064-nm laser and ISCOOL were delayed so that the laser pulses and the atom bunch arrived in the interaction region simultaneously. A diagram of the timing sequences used for the experiment is shown in Figure 7.4.

Figure 7.4: Diagram of timing sequences for the CRIS experiment with typical delay times (see text for details).

The trigger delivered to ISCOOL was adjusted when a different mass was being studied to compensate for the difference in time of flight. Finally, a trigger was sent to the data acquiring oscilloscope that was monitoring the signal of resonant ion counts from the MCP. This trigger was delayed so that the oscilloscope looked for counts when it expected the resonant ion bunch to arrive at the MCP. A window

123 7.3. Experimental Analysis was placed on the oscilloscope (20 µs) to gate the data collection time. This window acts to exclude any counts outside of the expected arrival time of the ion beam.

For the hyperﬁne structure scans, the excitation laser pulse (423-nm) was set to a starting frequency while the ion bunches were being released from ISCOOL. The data acquisition was then started and counted the number of ions on the MCP. During this time ISCOOL was still continuously releasing the ion bunches every 32 ms. This was repeated for a set amount of time or the duration of a proton super-cycle from the PSB (typically 47 s) for the exotic isotopes. After the set time expired, the data collection would stop, the laser frequency was changed to the next value, left to settle, and then collection began again. This process was then repeated until the wavelength range for the hyperﬁne measurements was scanned across.

7.3 Experimental Analysis

In the experiment, laser spectroscopy measurements were made on the francium isotopes ranging from the neutron-rich 231Fr to the neutron-deficient 202Fr. The isotopes investigated covered new and previously studied isotopes, extracting nuclear observables on the ground states and long-lived isomeric states (>30 ms). The results from the neutron-deficient and neutron-rich isotopes will be independently analysed and presented in upcoming publications. The experimental efficiency and background rate of CRIS will be estimated from the investigation of the 202,218,219Fr isotopes. The hyperfine structure measurements of 221Fr will be used to determine the experimental accuracy while the reference 207,211,221Fr isotopes will be used for systematic and consistency checks with literature values.

7.3.1 Experimental Eﬃciency

The data obtained from the scans performed on 218Fr and 219Fr provided the best results to determine the current experimental eﬃciency of CRIS. These isotopes were investigated at the end of the on-line run when the experiment was at its most eﬃcient. The scans of 218Fr and 219Fr are shown in Figure 7.5.

To estimate the experimental eﬃciency, the number of resonant ions detected was compared to the number of ions that were delivered to CRIS. Using the values in Table 7.1, estimated yields of 218Fr and 219Fr are 6.1 × 103 atoms/µC and 1.3 × 104 atoms/µC respectively. For each step in frequency during the data collection the resonant ions were counted for one super-cycle. During the experiment, 16 proton pulses, with an average current of ∼ 2 µA, were delivered during each super-cycle. For the yields of 218Fr and 219Fr this equates to approximately 2 × 105 atoms/super- cycle and 4 × 105 atoms/super-cycle respectively. These estimated rates were used for the determination of the experimental eﬃciency since the ISOLDE Faraday cups are not sensitive enough to measure currents of this size and no yield measurements have been performed on these two isotopes.

124 7: Laser Spectroscopy of Francium Using CRIS

Figure 7.5: Measured hyperﬁne structures of 218Fr [top] and 219Fr [bottom]. The plots show the number of detected ions against the frequency of the 423-nm laser. The frequency is given relative to the unperturbed frequency of the atomic transition.

The total number of resonantly detected ions can be obtained from Figure 7.5 by taking the number of counts from the most intense peaks. For 218Fr the peak intensity was ∼ 2900 counts (left peak) and for 219Fr the peak intensity was ∼ 4800 counts (left peak). Using these values, and the estimated production rates stated earlier, the experimental eﬃciency rates from the 218Fr and 219Fr measurements were 1:70 and 1:85 respectively.

From the results the peak experimental eﬃciency that was achieved with CRIS can be stated as 1:70. However, it is to be stressed that this is a tentatively assigned value considering the assumptions that were made for the isotope yields from the ISOLDE target. The assumptions were that: the production cross section of the isotopes with 1.4 GeV protons in the ISOLDE target is the same as with 0.6 GeV protons, the release rates from the target are the same and the yield of 202Fr during

125 7.3. Experimental Analysis the experiment had not changed by the time the yield measurement was made af- terwards. With different targets, made of the same material, the production yields can vary by several orders of magnitude and within a single target the yields may fluctuate depending on: its temperature, total time of operation and random physical changes. For these reasons, it is vital to be aware that the measured yield of 202Fr is used as a guide for the expected yield during the on-line run. In future experiments it would be desirable to request a yield measurement for the investigated isotope immediately before and after the time of measurement, when the experiment is operating at its most efficient, so the experimental efficiency can be more reliably determined.

7.3.2 Components of Experimental Eﬃciency

During the on-line experiment there were several different efficiency components that contributed to the overall experimental efficiency. Each of these factors have varying magnitudes and it is important to account for their contributions to be able to improve the sensitivity of the CRIS technique in future designs.

Transport Eﬃciency

The transport efficiency of CRIS has been previously investigated using stable 238U and the Faraday cups within CRIS and the ISOLDE central beam line. In off- line experiments the transport efficiency was estimated to be 10% up to the MCP. Since these tests the vertical steerers (Section 6.3.9) have been installed to allow the beam to pass through the central axis of the CEC and they improved the transmission of the ion beam by a factor of ∼ 2. The realignment of the beam improved the transmission efficiency by reducing any cut-off associated with misalignment of the beam through the apertures in the CEC and the differential pumping apertures at either side of the interaction region. During the on-line experiment the transmission efficiency was increased, from improved ion optic focusing and steering parameters, and was measured to be ∼ 50% from the ISOLDE central beam line to the MCP.

Neutralisation Eﬃciency

The neutralisation efficiency of the CEC is a complicated measurement due to the sensitivity of Faraday cups and the differences in induced currents from the impact of atom and ion bunches. At its optimised operation the CEC has been able to achieve ∼ 100% neutralisation, with the accuracy on the measurement limited by the sensitivity of the Faraday cup. During the on-line experiment the neutralisation rate was kept below 100% so that the remaining ion beam could be accessed at any point to ensure it was still being delivered to the MCP. This was important during the optimisation stage of the experiment. When the stability and operation of CRIS is improved the CEC will be able to be run at 100% neutralisation efficiency.

126 7: Laser Spectroscopy of Francium Using CRIS

Using intensities from the Faraday cups and radioactivity measurements during the experiment, the operational neutralisation eﬃciency was estimated to be between 50% and 80%.

Detection eﬃciency

During the on-line run the detection efficiency of the MCP setup was not investigated. Once the experiment was optimised for data collection, the contributing factors of the neutralisation and transmission efficiencies, as well as the limitations of beam current readings with Faraday cups, meant it was not possible to accurately determine the detection efficiency. In June 2012 the detection efficiency of the MCP setup was tested off-line with a 238U beam and was estimated to be approximately 20%. From the overall experimental efficiency of the on-line run there is nothing to suggest that this value would have changed significantly since those tests but since it was not tested on-line it is extremely difficult to assign a current efficiency. As the detection setup has the potential to reach 100% efficiency it should be subject to a thorough off-line investigation to find how it can be improved for future experiments. The efficiency of the MCP can be dependent on factors such as: the trigger level set on the data acquisition oscilloscope, the voltage applied to the dynode plate, and the voltages applied to the MCP and anode. Using the result from the previous test, the detection efficiency for the on-line run is tentatively estimated to be 20%.

Ionisation Eﬃciency

The ionisation eﬃciency of the experiment has three main contributing factors:

• The spatial overlapping of the atom and laser beams

• The temporal overlap of the lasers with respect to the atom beam

• The powers of the resonant and ionisation laser pulses

During the experiment the typical ion bunch width was 2 - 3 µs. This corresponds to a spatial length of 40 - 70 cm for the francium atoms at 50 keV. This length easily allows for the entire bunch to be ionised by the lasers within the 1.2-m interaction region. During the on-line experiment the timing signals were optimised so that the atom bunch was in the centre of the interaction region when the laser pulses were delivered. The temporal overlap of the laser pulses was monitored by a photodiode after the interaction region and they were seen to drift during the experiment due to issues with the Ti:Sa pump laser. The arrival times of the pulses were corrected on-line by the manual adjustment of the Nd:YAG delay trigger; however, the issue would have effected the ionisation process of the previous bunches before it was corrected for. This effect dominates the uncertainty in the intensity of the hyperfine transitions observed during the experiment. In future experiments the temporal

127 7.3. Experimental Analysis stability of the laser systems should be increased to allow more precise measurements to be made, especially when the intensity of individual hyperﬁne transitions becomes more important in the data analysis.

The dependency of the resonant and non-resonant laser pulse powers on the ionisation efficiency was investigated during the experiment to observe any saturation effects. These tests are not able to determine how much the ionisation process contributed to the overall experimental efficiency; however, they will provide information on where improvements can be made. During the optimisation of the experiment, the 423-nm laser pulse was restricted to ∼ 3 µJ per pulse, (measured on the optical table). This was done to avoid any damage to the optical fibre that would have brought an end to the experiment. The transmission of the 423-nm light through the interaction region was measured to be ∼ 10% at the end of the beam line, mainly due to the optical quality of the beam from the optical fibre and its large spot size (∼ 10 mm in diameter). Using this transmission efficiency, the power of the laser pulses in the interaction region can be estimated to be approximately 10% of the powers measured on the table. During the optimisation stage of the experiment, the rate of resonantly produced 221Fr ions were counted for 423-nm powers between 0 and ∼ 3 µJ per pulse (measured on the optical table) and the results are shown in Figure 7.6.

Figure 7.6: Rate of resonant 221Fr ion counts for varying 423-nm pulse powers (measured on the CRIS optical table). The non-resonant 1064-nm pulse power was ﬁxed at 4 mJ. Included is a ﬁtted linear line through the data points to guide the eye.

To investigate the ionisation eﬃciency it is not advisable to directly compare the estimated pulse powers in the interaction region with the expected saturation power calculated in Section 7.2.2 (∼ 36 µJ), due to the uncertainties in the power density of the laser pulse and its spatial overlap with the atom bunch; however, they can be used as a general representation of what was experimental seen. The results

128 7: Laser Spectroscopy of Francium Using CRIS from Figure 7.6 show that during the tests the experiment was not saturated with the delivery of ∼ 3 µJ pulses, which was expected when compared to the estimated saturation power of ∼ 36 µJ. Towards the end of the on-line experiment the power of the 423-nm laser was increased from ∼ 3 µJ to ∼ 7 µJ per pulse to investigate the more exotic francium isotopes. This change in laser power improved the overall experimental eﬃciency by a factor of ∼ 2, suggesting the experiment was still not saturated. Unfortunately, due to the rest of the experimental time being used to obtain physics results, no further ionisation eﬃciency tests were performed, so it is unclear how close to saturation the experiment operated at this stage.

During the optimisation stage of the experiment the 1064-nm laser was limited to 4 mJ per pulse (measured on the optical table) due to problems with the focussing of the light at higher powers. The beam from the Nd:YAG laser was approximately 2 mm in diameter and had a transmission of ∼ 50% through the interaction region. A saturation test was performed during the optimisation time for pulse powers between 0 and 13 mJ and the results are shown in Figure 7.7. The higher powers could be reached to perform the tests but were not stable enough to operate normally.

Figure 7.7: Rate of resonant 221Fr ion counts for varying 1064-nm pulse powers (measured on the CRIS optical table). The resonant 423-nm pulse power was ﬁxed at 3 µJ. Included are ﬁtted linear [solid] and quadratic lines [dashed] through the data points to guide the eye.

The figure suggests that during the optimisation period the experiment was not saturated with the delivery of 13-mJ pulses. Unfortunately, due to valve problems and focussing issues of the 423-nm light, the test was limited to the four observed data points. Therefore, the measurement is in no way conclusive of how close the experiment was to saturation. At the end of the experiment the stability of the 1064- nm beam was improved and the measurements at the peak experimental efficiency were performed with ∼ 8 mJ per pulse delivered from the optical table. Due to the small diameter of the beam (∼ 2 mm), it is difficult to estimate how much of

129 7.3. Experimental Analysis the light overlapped with the atom bunch. Therefore, the magnitudes of the pulse energies cannot be compared directly with the 0.2 mJ per pulse value estimated in Section 7.2.2.

Using the estimated efficiencies of the different components mentioned earlier in this section and the peak experimental efficiency of 1:70, the ionisation efficiency of the experiment can be estimated to be around 30%. This value suggests that there should be room to improve the ionisation efficiency of the experiment. The results from the saturation tests, in particular those for the 423-nm transition (where the laser power used was ∼ 5 times smaller than the estimated saturating power) assist with the conclusion and provide an area of development for future experimental campaigns.

7.3.3 Background Rate

One of the main contributions to the background count rate of the experimental measurements is caused by collisional re-ionisation of the atoms with gas molecules in the interaction region. The data collected during the 202Fr run provided the best information for the calculation of the background rate due to the contamination of the beam with 202Tl. The hyperﬁne structure measurement of 202Fr is shown in Figure 7.8.

Figure 7.8: A hyperfine structure scan performed on the ground and isomeric states of 202Fr showing the number of resonant and background ion counts. Included is a fitted hyperfine structure of the ground and isomeric states (currently unas- signed). The fitted background rate was 0.097(65) per step, which equates to ∼ 6 counts throughout the entire scan.

From the fitted hyperfine structure shown in the figure, the background rate was measured to be 0.097(65) counts per super-cycle. Taking into account the ex-

130 7: Laser Spectroscopy of Francium Using CRIS perimental transport, neutralisation and detection eﬃciencies this equates to about 1.21(81) collisional ions per super-cycle. For this measurement there was an isobaric contamination of 202Tl, with a yield of around 104 ions/s [117]. During the data collection for 202Fr a beamgate was used that restricted the extraction of isotopes from the ISOLDE target to 1 s after the impact of a proton pulse. As 16 proton pulses were delivered per super-cycle, the number of 202Tl atoms present can be estimated at 1.6 × 105 atoms/super-cycle. This gives an estimation of the background rate of 1:105, which is of the magnitude similar to the rate predicted in Section 6.3.4. However, it should be noted that this value has been made with several assumptions, such as: the thallium contamination yield, the neutralisation eﬃciency of thallium and the presence of no additional background on the MCP. Additionally, not enough statistics were obtained to be able to perform a thorough analysis. Therefore, although the data can be used to provide a rough estimation of the collisional background rate further tests should be performed to fully understand the extent of this rate in CRIS. During the experiment the pressure in the interaction region was 1 × 10−8 mbar, mainly limited by a leak in the valve to the DSS. A base pressure of below 5×10−9 mbar has been previously achieved by baking out the beam line, which would further decrease the amount of background from collisional ionisation.

As well as background counts from collisional ionisation there are also additional contributions from dark counts and activity on the dynode plate. For the dark counts, with the MCP setup isolated from any incoming ion beam, there was on average one count every 20 s. As the gate for the measurements was 20 µs every 32 ms, the contribution from dark counts was reduced by a factor of 1.6 × 103 and deemed to be negligible. For residual activity on the plate, the largest contribution during the run was caused by activity from 221Fr (286 s half-life) and its daughters, which was used for the reference scans and optimisation of the experiment. In one case the background rate on the MCP was ∼ 220 /s during a hyperﬁne structure scan on 221Fr after at least 1 hour of intermittent implantation of 221Fr isotopes during optimisation tests. For future experiments it would be recommended to use isotopes with shorter half-lives for the reference scans so that activity can be minimised for the exotic cases.

7.3.4 Study of Experimental Error from the Analysis of 221Fr

The scans performed during the experiment on 221Fr were used to understand the accuracy of the measurements performed using the CRIS beam line. As 221Fr was used for the reference scans and experiment optimisation, nineteen scans were made that can be used to observe any scattering in the measured values. The hyperﬁne structure of one of the scans of 221Fr is shown in Figure 7.9.

The analysis of the experimental data was performed using an orthogonal distance regression technique in a similar way to the chi-square minimisation technique described in Section 5.4.1. The diﬀerence is that an additional error can be associated with the independent variable, in this case the error associated with the

131 7.3. Experimental Analysis

Figure 7.9: The measured hyperfine structure of 221Fr. The error bars for the frequency are smaller than the data points. During the experiment nineteen scans were performed on 221Fr. frequency of the laser. The chi-square is found from the difference between the fit and the experimental data and is minimised in the fitting routine to find the most suitable values. For more information on the fitting technique see Reference [118].

The free parameters for this ﬁtting routine were:

2 • A(7s S1/2)

• Structure centroid frequency

• FWHM of transition proﬁles (equal for all transitions)

• Background level (assuming a ﬂat background)

• Overall intensity (applied equally to all transitions)

For the individual transitions a pseudo-Voigt profile was initially used but this reduced to a pure Gaussian when compared to the experimental data. This was caused by the Gaussian lineshape of the 423-nm laser pulse providing the dominant contribution to the experimental resolution. The FWHM of the Gaussian profiles was left as a free parameter to determine the resolution of the experiment. The ratio of the A 2 2 factors for the atomic transition, A(7s S1/2)/A(8p P3/2), was fixed to 277.2 [106]. 2 B(8p P3/2) was set to the known value of −85.7 MHz [106] and the ground-state spin was set to I = 5/2 [119].

132 7: Laser Spectroscopy of Francium Using CRIS

An initial hyperfine structure was simulated and compared with the experimental data while the free parameters were iterated. The error on the ion counts was given as the square root of the number of counts plus one. The error on the laser frequency was set to cover the scatter observed during the experiment. For each data point, the laser frequency was monitored within the data collection program. The typical variation in the laser frequency was 20 MHz but was seen to increase up to 100 MHz during a scan at some occasions during the experiment. The fitting routine finished when the least-square difference was found with the optimised free parameters. The statistical errors of the parameters were given as one standard deviation. The fitting 2 routine was performed on all the scans and the A(7s S1/2) hyperfine coefficients, centroid values and FWHMs were extracted.

2 Extracted A(7s S1/2) Factors

2 Figure 7.10 shows the extracted A(7s S1/2) hyperﬁne values from all the scans performed on 221Fr.

2 221 Figure 7.10: Extracted A(7s S1/2) values of Fr measured throughout the experimental run. The error bars represent the statistical error of the ﬁtted A value from each run. Included is the weighted average value from all the runs [solid line] and the standard deviation of the scatter of the data points [dashed lines].

The error bars on each of the data points represent the statistical error of the A factor from the ﬁtting routine. The scatter of the data points represent the overall error on the A factor measurement due to random experimental uncertainties. From 2 all the measurements the weighted average value of A(7s S1/2) was determined

133 7.3. Experimental Analysis to be +6203 MHz. The standard deviation of the scatter of the data points was determined to be 44 MHz. This error represents the experimental error of the setup caused by random effects during the run. The origins of these random errors are not currently accounted for; therefore, the error on the exotic francium isotopes cannot be placed below 44 MHz until the issue has been fully addressed. Possible explanations for these errors could be attributed to: the error on the measured laser frequencies, the lineshape/asymmetry of the laser pulses and the spatial/temporal overlap of the laser pulses with the atom bunch. The intensities of the observed peaks measured during the experiment varied dramatically due to some of these effects. Fluctuations of these intensities will greatly affect the fitting routine and provide a large contribution to the experimental error. For future experiments this issue should be addressed to improve the accuracy of measurements achievable using CRIS.

Extracted Centroid Values

To determine the accuracy of the experiment for isotope shift measurements, the centroid values of all the 221Fr scans were measured to observe their deviations. The extracted centroid values are relative to an arbitrary value in MHz but the diﬀerence in frequency between isotopes provides the isotope shift information. Figure 7.11 shows the diﬀerent centroid values measured for the 221Fr scans.

Figure 7.11: Extracted centroid values of 221Fr measured throughout the experimental run. The error bars represent the statistical error of the ﬁtted centroid value from each run. Included is the weighted average value from all the runs [solid line] and the standard deviation of the scatter of the data points [dashed lines]. Also shown is the maximum scatter of the measured centroid values from the weighted average [dotted lines], given by 180 MHz.

134 7: Laser Spectroscopy of Francium Using CRIS

From the analysis the weighted average centroid value was determined to be −14234 MHz (arbitrary reference) with a standard deviation of 75 MHz. In Fig- ure 7.11, there appears to be a systematic increase in the centroid value during the experiment, the cause of which is currently unknown. When this drift can be accounted for, for example due to a drift in the measured ISCOOL voltage, then the isotope shift can be determined by calculating the diﬀerence between the centroid frequencies of exotic and reference isotopes measured at similar times. However, during this experiment the experimental uncertainties (mentioned previous for the A factor analysis) will dominate the error of the measurement beyond any systematic drift. This is highlighted in Figure 7.11, where the largest diﬀerence between data points, 180 MHz, was observed between neighbouring reference scans, Run 321 and 329. As this is the case, an error of 180 MHz has been associated with the mean centroid value. In order to account for these dramatic changes, the error on the measured isotope shifts between isotopes will be given as twice this error, 360 MHz. This value represents the limit on the current accuracy achievable with CRIS. De- tailed analysis of the individual scans for the more exotic isotopes may allow the level of accuracy to be improved.

Extracted FWHM

From each of the scans of 221Fr the FWHM was extracted to estimate the resolution of the experiment. For each of the ﬁts the FWHM was left as a free parameter to provide the best representation of the Gaussian proﬁle in the spectrum. The results from all the 221Fr scans are shown in Figure 7.12.

Figure 7.12: Extracted FWHM values for 221Fr measured throughout the experimental run. The error bars represent the statistical error of the ﬁtted FWHM from each run. Included is the weighted average value from all the runs [solid line] and the standard deviation of the scatter of the data points [dashed lines].

135 7.3. Experimental Analysis

The weighted average from all the runs gives an overall experimental resolution of ∼ 1.50(12) GHz. The scatter of the FWHM is caused by the thermal and pumping variations (random) in the set up of the Ti:Sa laser system and the variation of laser power used during the experiment. The resolution is in agreement with the expected output of the frequency doubled 423-nm light and there are no indications that it was aﬀected by power broadening due to the Gaussian nature of the observed line shape.

2 207,211,220,221 7.3.5 A(7s S1/2) values and Isotope Shifts of Fr

During the experiment the reference isotopes 207,211,220Fr were investigated as well as 221Fr. The measured hyperﬁne structures of these isotopes are shown in Figure 7.13.

Figure 7.13: Measured hyperﬁne structures of 207,211,220,221Fr. The size of the splittings 2 between the peaks are caused by the A(7s S1/2) values and the horizontal placement of the structures are due to the isotope shift.

2 207,211,220 The A(7s S1/2) values and isotope shifts of Fr were extracted from the measured hyperﬁne structures using the same ﬁtting routine used for 221Fr but with

136 7: Laser Spectroscopy of Francium Using CRIS

2 220 2 different B(8p P3/2) values. For Fr, B(8p P3/2) was set to the literature value of 2 207,211 +41.4 MHz [106]. Literature values of B(8p P3/2) do not exist for Fr so they were set to zero in the fitting routine. The analysis of 220Fr and 221Fr showed that 2 changing B(8p P3/2) between the literature value and zero affected the extracted 2 A(7s S1/2) and centroid values by the order of a few kHz, well below the accuracy 2 achievable in these measurements. The extracted A(7s S1/2) values and isotope shifts of 207,211,220,221Fr are shown in Table 7.2. 2 207,211,220,221 Table 7.2: Measured A(7s S1/2) values and isotope shifts of Fr.

2 221,A Isotope IA(7s S1/2) (MHz) δνIS (GHz) # of Scans 221 5/2 +6203(44) - 19 220 1 −6506(44) +2.66(36) 4 211 9/2 +8715(44) +24.09(36) 2 207 9/2 +8493(44) +28.50(36) 5

Comparisons with Previous Measurements

The demonstrated resolution of CRIS is not able to provide more accurate mea- 2 surements of the A(7s S1/2) values (44 MHz compared to ∼ 1 MHz) or the isotope shifts (360 MHz compared to ∼ 1 MHz) in comparison with earlier experiments. However, the results of the 207,211,220,221Fr isotopes can be compared with previous experiments for consistency and systematic error checks.

In 1985, A. Coc et al. [113] measured the hyperﬁne structures and isotope 207−213,220−228 2 2 shifts of Fr on the 7s S1/2 → 7p P3/2 (718-nm) atomic transition. In 1987, Duong et al. [106] measured the hyperﬁne structures and isotope shifts of 212,213,220,221 2 2 the Fr isotopes on the 7s S1/2 → 8p P3/2 (423-nm) transition. Due 2 to the transitions used, the A(7s S1/2) values can be compared from all experiments; however, the isotope shifts measured by CRIS can only be compared with 2 the measurements made by Duong. The A(7s S1/2) values of the francium isotopes measured from these experiments are shown in Table 7.4.

2 Table 7.3: A(7s S1/2) values measured on CRIS alongside literature values by Coc [113] and Duong [106].

2 2 2 Isotope IA(7s S1/2) (MHz) A(7s S1/2) (MHz) A(7s S1/2) (MHz) [CRIS] [Coc] [Duong] 221 5/2 +6203(44) +6204.6(8) +6209.9(1.0) 220 1 −6506(44) −6549.4(9) −6549.2(1.2) 211 9/2 +8715(44) +8713.9(8) - 207 9/2 +8493(44) +8484(1) -

2 The A(7s S1/2) results from CRIS show good agreement with those measured in the previous experiments. The results for 207,211,221Fr fall well within the errors

137 7.3. Experimental Analysis set on the measurements from the analysis, while the 220Fr result lies on the limit. This validates the current assigned accuracy of CRIS and highlights the need for the experimental uncertainties to be investigated in more detail before the precision can be decreased.

The isotope shift of 220Fr from 221Fr is the only result that has been previously 221,220 measured on the same atomic transition for comparison. The result of δνIS = +2.66(36) GHz measured during the CRIS experiment shows good agreement with +2.734(1) GHz from Duong. The magnitude of the error using CRIS and the diﬀer- ence from the literature value highlights how the experimental uncertainties of CRIS need to be further investigated before the accuracy of isotope-shift measurements can match those of previous studies.

Magnetic Moments

As described in Section 2.1.1, the magnetic moments of the francium isotopes can be calculated using known reference values. To determine the magnetic moments of the francium isotopes, 213Fr was used as the reference isotope [113, 75], with the nuclear properties:

• I = 9/2

2 • A(7s S1/2) = +8759.9(6) MHz

• µ = +4.02(8) µN

Using these values, the magnetic moments of the 207,211,220,221Fr isotopes measured by CRIS were calculated and are presented in Table 7.4.

Table 7.4: Magnetic moment values measured on CRIS alongside literature values from Stone [75].

Isotope µ (µN) µ (µN) [CRIS] [Stone] 207 +3.89 (9) +3.89 (8) 211 +4.00 (9) +4.00 (8) 220 −0.67 (2) −0.67 (1) 221 +1.58 (4) +1.58 (3)

These comparisons show that the largest error in the magnetic moments values calculated from CRIS arises from the uncertainty in the reference value, µ = +4.02(8) µN. Therefore, the resolution currently available with CRIS is more than suﬃcient to accurately measure the magnetic moments of the investigated isotopes.

138 7: Laser Spectroscopy of Francium Using CRIS

2 2 7.3.6 Atomic Factors for the 7s S1/2 → 8p P3/2 Transition

The isotope shifts can be used to determine the changes in the mean-square charge radii for a comparison with literature values. In order to extract the charge 2 2 radii, the atomic factors for the 7s S1/2 → 8p P3/2 transition in francium are required. The factors have been previously investigated by Duong [106]; however, they were evaluated using a King plot of only four isotope values.

In a bid to obtain more accurate values, the results from this experiment were added to the measurements by Duong to make a King plot using the information of six isotopes. The new atomic factors were evaluated using the known atomic factors 2 2 and isotope shifts of the 718-nm 7s S1/2 → 7p P3/2 transition as reference data. For this transition [24], the atomic factors have been previously evaluated to be:

718 −2 • Fel = −20.766(208) GHz·fm

718 • KMS = −85(113) GHz·u

The isotope shifts of 207,211,220Fr, with respect to 221Fr, from this experiment were collated with those measured on 212,213,220Fr by Duong to form the 423-nm transition values. These were plotted against isotope shifts for the same isotopes in the 718-nm transition by Coc [113], to make the King plot shown in Figure 7.14.

Figure 7.14: King plot of the 423-nm [x-axis] and 718-nm [y-axis] transitions for the 207,211,212,213,220Fr isotopes from 221Fr. The markers represent measurements made by CRIS [circle] and Duong [triangle]. The error bars for values from Duong are smaller than the data points (see text for details).

139 7.3. Experimental Analysis

From the King plot, the gradient of the line and y-intercept were calculated to be 1.0046(10) and −859(120) GHz·u respectively. As a reminder, the gradient and y-intercept relate the atomic factors for the two transitions by,

718 Fel gradient = 423 (7.1) Fel and, 718 718 Fel 423 intercept = KMS − 423 KMS . (7.2) Fel Using the evaluated King plot factors and the reference values, the atomic factors for the 423-nm transition were evaluated to be:

423 −2 • Fel = −20.671(208) GHz·fm

423 • KMS = +770(164) GHz·u

423 The errors on these results are smaller than those evaluated by Duong, where Fel 423 was assigned an error of 215 MHz and KMS had an error of at least 320 GHz associated with it.

As mentioned in Section 2.2.3, the normal mass-shift factor can be accurately calculated for an experimental frequency using,

νexpt KNMS = . (7.3) 1822.888

Therefore, for the 423-nm transition, the contribution to the mass-shift factor 423 from the normal mass shift can be calculated to be KNMS = +390 GHz·u. Using this 423 value then gives the speciﬁc mass shift contribution as KSMS = +380(164) GHz·u.

7.3.7 Changes in Mean-Square Charge Radii

With the determined atomic factors, the changes in mean-square charge radii of the francium isotopes can be calculated from the measured isotope shifts. The charge radii results from the CRIS experiment are shown in Table 7.5, alongside 2 2 literature values deduced using isotope shifts measured on the 7s S1/2 → 7p P3/2 transition [24].

The experimental error on the CRIS radii values arise from the random and statistical errors on the isotope shifts, explained earlier, propagated through the calculations. The systematic errors on the radii are caused by the uncertainties in the analysis of the atomic factors for the 423-nm transition. The magnitude of the errors were determined by calculating the change in charge radii using the error limits assigned to the atomic factors. The experimental accuracy for the isotope

140 7: Laser Spectroscopy of Francium Using CRIS

Table 7.5: Changes in mean-square charge radii measured on CRIS alongside literature values from Dzuba [24]. For the radii the parentheses give the errors propagated from the isotope shift errors and the square brackets give the systematic error from the evaluation of the atomic factors.

221,A 2 221,A 2 2 221,A 2 Isotope δνIS (GHz) δhrchi (fm ) δhrchi (fm ) [CRIS] [CRIS] [Dzuba] 220 +2.66(36) −0.129(18)[2] −0.133[2] 211 +24.09(36) −1.173(18)[14] −1.178[11] 207 +28.50(36) −1.390(18)[17] −1.386[14] shifts used by Dzuba was very high; therefore, only the systematic error is presented for the charge radii. The systematic errors arise from a 1% uncertainty in the theoretical calculation of the ﬁeld-shift factor.

The charge-radii values from the CRIS experiment presented in Table 7.5 show very good agreement with the literature values. The largest diﬀerence between the results is 3%, for 220Fr, which is well within the assigned experimental uncertainties and systematic errors of the CRIS value. The systematic errors from the experiments are also in agreement, with the magnitude slightly larger for the CRIS data due to the additional uncertainty of the atomic factors determined from the King plot analysis. These comparisons show that the current accuracy of CRIS is suﬃcient in order to investigate changes in mean-square charge radii of exotic nuclear isotopes.

7.4 Conclusion and Outlook

The hyperfine structures and isotope shifts of francium isotopes between A = 202 and A = 231 were investigated using CRIS, with the analysis of selected isotopes presented in this work. The sensitivity of CRIS was demonstrated for 202Fr, which has an estimated yield at ISOLDE below 100 ions/s. Due to the constraints of the laser system, high-precision hyperfine coefficient values could not be measured. However, it has been shown that the setup is able to perform extremely sensitive measurements and investigate the magnetic dipole moments and changes in mean- square charge radii of the francium isotopes. An experimental efficiency of 1:70 is estimated with a collisional background rate of 1:105 and a resolution of 1.5 GHz. The contributing factors to these values have been highlighted and areas for improvement have been suggested for future investigations.

Results for the previously studied isotopes of francium have demonstrated the 2 precision of measurements current achievable using CRIS. The A(7s S1/2) hyperfine coefficients were measured with an error of 44 MHz, dominated by random experimental uncertainties, and the isotope shift values have been conservatively assigned 2 a 360 MHz error value. The A(7s S1/2) hyperfine coefficients and isotope shifts were measured for 207,211,220,221Fr and show excellent agreement with literature values. An in-depth analysis of these results for future publications should decrease the

141 7.4. Conclusion and Outlook associated error values and allow for a detailed investigation of all the radioactive francium isotopes measured during the on-line run.

The isotope shifts measured during the experiment were combined with literature 2 2 values to determine the atomic factors for the 7s S1/2 → 8p P3/2 atomic transition. Using the King plot method the ﬁeld-shift and mass-shift factors were determined −2 to be Fel = −20.671(208) GHz·fm and KMS = +770 (164) GHz·u respectively. The atomic factors were used to extract the changes in mean-square charge radii of the reference isotopes and also showed very good agreement with literature values.

These results mark the successful operation of the ﬁrst on-line experiment with CRIS, demonstrating the setup as a highly sensitive experimental technique for laser spectroscopy measurements. In the future, the resolution of the experiment will be improved with the installation of a dedicated narrowband laser system for the resonant, excitation step. During the shutdown of the CERN accelerator complex from February 2013 the CRIS experiment will be able to be fully investigated allowing improvements to be implemented before on-line experiments start up again from 2014. The demonstration of CRIS presented in this thesis has showcased the appeal of the experiment, paving the way for the proposed copper [120] and polonium [121] investigations. This marks an exciting time for laser spectroscopy, with the sensitivity of experiments on exotic isotopes being continuously increased while allowing for high resolution nuclear measurements.

142 Appendix A

Publications

The experimental results of the gallium isotopes presented in this thesis and hardware developments of the CRIS beam line have been published in the following papers:

Nuclear mean-square charge radii of 63,64,66,68−82Ga nuclei: No anomalous behavior at N= 32 T. J. Procter e. al., Phys. Rev. C 86, 034329 (2012) [122]

Development of the CRIS (Collinear Resonant Ionisation Spectroscopy) beam line T. J. Procter et al., J. Phys.: Conf. Ser. 381(1), 012070 (2012) [123]

First on-line results from the CRIS (Collinear Resonant Ionisation Spec- troscopy) beam line at ISOLDE T. J. Procter and K. T. Flanagan, Hyperﬁne Interact. 381, 89 (2013) [124]

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