One of the interesting properties is the lifetime of each state and lifetime ... lifetime in Ti II measured in an ion storage ring. H. Hartman, D. ... Radiative Lifetime of a Bound Excited State of Teâ. A. Ellmann, P. ...... I truly love you. And now, the end ...
Laser Spectroscopic Investigations of Decay Properties in Stored Ions Peter Lundin
© Peter Lundin, Stockholm 2008 ISBN 978-91-7155-680-6 Distributor: Department of Physics, Stockholm University
To my family...
Abstract
Investigations and measurements of metastable states are in many ways very important. Spectroscopists, theorists and astrophysicists have all great interest and requirements regarding knowledge about such states and their properties. One of the interesting properties is the lifetime of each state and lifetime measurements are therefore of great importance. It is necessary to have a long observation time when performing investigations on metastable states in ions and there are some dierent methods to ful ll this requirement. One method to store ions is to use an ion storage ring in which the ions are bent in circle by a magnetic or an electrostatic eld. The storage ring method combined with a laser probing technique constitutes the basis for the papers described in this thesis. The thesis also contains some theoretical background to the experiments together with explanations regarding the experimental setup, the procedure for the laser probing technique and the systematic eects that have to be considered. The thesis includes results from nine different positive and negative singly charged ions. The experimental and theoretical results are presented and compared. The experiments have been done in collaboration with E. Biémont's theoretical group in Belgium, with S. Johansson's astrophysical group in Lund and D. Hanstorp's group in Gothenburg.
List of Papers
This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I
Importance of an M2 Depopulating Channel for a Kr II Metastable State E. Biémont, A. Derkatch, P. Lundin, S. Mannervik, L.-O.
Norlin, D. Rostohar, P. Royen, P. Palmeri and P. Schef Physical Review Letters 93, 063003 (2004) II
Disentanglement of magnetic eld mixing reveals the spontaneous M2 decay rate for a metastable level in Xe+ P. Schef, P. Lundin, E. Biémont, A. Källberg, L.-O. Norlin, P. Palmeri, P. Royen, A. Simonsson and S. Mannervik Physical Review A 72, 020501(R) (2005), Rapid Communication
III
Inclusion of Electric Octupole Contributions Explains the Fast Radiative Decays of Two Metastable States in Ar+ P. Lundin, J. Gurell, L.-O. Norlin, P. Royen, S. Mannervik, P. Palmeri, P. Quinet, V. Fivet and E. Biémont Physical Review Letters 99, 213001 (2007)
IV
The FERRUM project: an extremely long radiative lifetime in Ti II measured in an ion storage ring H. Hartman, D. Rostohar, A. Derkatch, P. Lundin, P. Schef, S. Johansson, H. Lundberg, S. Mannervik, L.-O. Norlin, and P. Royen J. Phys. B: At. Mol. Opt. Phys. 36, L197-L202 (2003)
V
The FERRUM project: experimentally determined metastable lifetimes and transition probabilities for forbidden [Ti II] lines observed in η Carinae H. Hartman, P. Schef, P. Lundin, A. Ellmann, S. Johansson, H. Lundberg, S. Mannervik, L.-O. Norlin, D. Rostohar and P. Royen Mon. Not. R. Astron. Soc. 361, 206-210 (2005)
VI
Experimental Oscillator Strengths for Forbidden Lines in Complex Spectra H. Hartman, S. Johansson, H. Lundberg, P. Lundin,
S. Mannervik and P. Schef Physica Scripta T119 40-44 (2005) VII
The FERRUM project: experimental and theoretical transition rates of forbidden [Sc II] lines and radiative lifetimes of metastable [Sc II] levels H. Hartman, J. Gurell, P. Lundin, P. Schef, A. Hibbert, H.
Lundberg, S. Mannervik, L.-O. Norlin and P. Royen Astronomy & Astrophysics 480, 575-580 (2008) VIII
Laser-probing measurements and calculations of lifetimes of the 5d 2 D3/2 and 5d 2 D5/2 metastable levels in Ba II J. Gurell, E. Biémont, K. Blagoev, V. Fivet, P. Lundin,
S. Mannervik, L.-O. Norlin, P. Quinet, D. Rostohar, P. Royen and P. Schef Physical Review A 75, 052506 (2007)
IX
Monitoring the weak collisional excitation of a stored ion beam reveals the radiative decay rate of extremely long-lived metastable levels P. Royen, J. Gurell, P. Lundin, L.-O. Norlin and S. Mannervik Physical Review Communication
X
A
76,
030502(R)
(2007),
Metastable levels in Sc II: lifetime measurements and calculations P. Lundin, J. Gurell, S. Mannervik, P. Royen, L.-O. Norlin, H. Hartman and A. Hibbert Physica Scripta, accepted for publication (2008)
10
Rapid
XI
Lifetimes of metastable levels of singly ionized titanium : theory and experiment P. Palmeri, P. Quinet, E. Biémont, J. Gurell, P. Lundin, L.-O. Norlin, P. Royen, K. Blagoev and S. Mannervik J. Phys. B: At. Mol. Opt. Phys., accepted for publication (2008)
XII
Radiative Lifetime of a Bound Excited State of Te− A. Ellmann, P. Schef, P. Lundin, P. Royen, S. Mannervik,
K. Fritio, P. Andersson, D. Hanstorp, C. Froese Fischer, F. Österdahl, D. J. Pegg, N. D. Gibson, H. Danared and A. Källberg Physical Review Letters 92, 253002 (2004) XIII
Radiative lifetimes of metastable states of negative ions P. Andersson, K. Fritio, J. Sandström, G. Collins, D. Hanstorp, A. Ellmann, P. Schef, P. Lundin, S. Mannervik, P. Royen, K. C. Froese Fischer, F. Österdahl, D. Rostohar, D. J. Pegg, N. D. Gibson, H. Danared and A. Källberg Physical Review A 73, 032705 (2006)
Contents
Part I: Introduction 1 2
The Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectroscopy and Lifetime Measurements . . . . . . . . . . . . . . . . . . .
17 19
2.1 Long lifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Part II: Theoretical Aspects 3 Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Forbidden Lines in Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27 31
Part III: Experimental Method 5 Experimental Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 CRYRING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 The data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 The Doppler tuning device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 The laser probing technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Systematic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Repopulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Simultaneous repopulation measurement . . . . . . . . . . . . . . . . . . . . . 7.1.2 Separate repopulation measurement . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Collisional quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Negative Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
35 37 38 38 39 40 43 47
47 48 49 50 53 55
Part IV: Summary of Papers 10 Kr II . . . . . . . . . . . . . 11 Xe II . . . . . . . . . . . . 12 Ar II . . . . . . . . . . . . . 13 The FERRUM Project
.... .... .... ...
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
13.1 Ti II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Ti II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Oscillator strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 Sc II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14 Ba II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Extremely Long-lived Metastable Levels . . . . . . . . . . . . . . . . . . . . . .
59 61 65 69
69 71 71 73 75 77
16 Sc II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Ti II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Negative Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1 Te− . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Se− , Si−
& Te− . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81 83 85
85 86
Part V: Summary and Discussion 19 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
Part VI: Author's contribution Part VII: Acknowledgements Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
Part I: Introduction
1. The Atom
The atom as a concept is very old and originates from the Greek philosopher Democritus (∼ 460-370 B.C.) who stated that all matter consists of very small, indivisible, elementary particles called atoms [1, 2]. Democritus' atomic concept fell into oblivion for a long time and was not revived until the English meteorologist John Dalton in the early 19th century proposed the Atomic Theory [3] where he among other things stated that dierent elements have dierent characteristic weights. In the beginning of the 20th century J.J. Thomson discovered the electron [4] and also showed that it was a subatomic particle (i.e. the atom was not indivisible after all). With this somewhat revolutionary result in hand Thomson proposed that the atom was composed of electrons surrounded by a positive medium (later called the plum pudding model ) [5]. This model was, however, soon revised by Rutherford who claimed that the electrons move in orbits around a positive nucleus which constitutes the larger part of the mass [6]. The Rutherford model had, however, a problem. Due to classical mechanics the electron will continuously loose energy when circulating around the atom's positive centre and it will nally collapse into the nucleus. In 1913 Niels Bohr presented a solution to this problem by suggesting that the electron only could travel in certain discrete orbitals [7]. This is today known as the Bohr model of the atom. The Bohr model has later been re ned by the development of quantum mechanics in the early 20th century. This led to a new understanding of the atom where it was realized that the atom instead should be seen as a nucleus surrounded by a cloud of electrons described by a wave function and this is the accepted model used today. There has always been an urge to sort the dierent elements in a reasonable and logical way. The increased knowledge about atoms and its structure has also developed and changed this sorting procedure over the years, from Aristotle's thought that everything was build by one or a mixture of the four elements (earth, water, air and re) until the modern periodic table that lists all elements (117 con rmed at the moment) in increasing atomic number, see Fig. 1.1.
17
1A 1
8A 2
Zn
7A 9
30.97
32.07
[Ar]4s23d104p4
Cl
10 neon
[He]2s22p6
Ne
18
20.18
Ar
36
xenon
[Kr]5s24d105p6
Xe
54
83.80
krypton
[Ar]4s23d104p6
Kr [Ar]4s23d104p5
Br
35
4.003
6A 8
helium
5A 7
fluorine
[He]2s22p5
carbon
14
boron
[Ne]3s23p2
phosphorus
P
13
silicon
As
34 [Ar]4s23d104p3
33
Ge
Se [Ar]4s23d104p2
79.90
bromine
53
78.96
selenium
52
74.92
51
72.58
germanium
arsenic
32
Si [Ne]3s23p1
28.09
Al
26.98
aluminum
31
Ga
[Ar]4s23d104p1
1s2
He
Cu
F
1
1s
H hydrogen
Periodic Table of the Elements
28
O
oxygen
[He]2s22p4
[Ne]3s23p6
4A 6
2A 4
[Ar]4s23d8
N
17
3A 5
3
1.008
8B 27
nitrogen
[He]2s22p3
16.00
[Ne]3s23p5
C
16
argon
[He]2s22p2
B
14.01
[Ne]3s23p4
39.95
[He]2s22p1
Be beryllium
[Ar]4s23d7
gallium
50
69.72
19.00
12.01
15
35.45
chlorine
[He]2s2
[He]2s1
Li lithium
26
zinc
49
65.39
copper
48
63.55
47
I
[Kr]5s24d105p5
Te
[Kr]5s24d105p4
Sb
[Kr]5s24d105p3
iodine
Sn
[Kr]5s24d105p2
In
[Kr]5s24d105p1
Cd [Kr]5s14d10
126.9
85
118 8
(222)
radon
[Xe]6s24f145d106p6
86
131.3 127.6
tellurium
84
121.8
antimony
83
tin
82
118.7
Rn [Xe]6s24f145d106p5
81
At [Xe]6s24f145d106p4
Po [Xe]6s24f145d106p3
astatine
Bi [Xe]6s24f145d106p2
(209)
polonium
Pb [Xe]6s24f145d106p1
208.9
bismuth
(?)
Uuo o
(210)
lead
(298))
Uuh h
116 6
207.2
(296))
71
Uuq q
114 4
204.4
thallium
Tl
114.8
indium
[Kr]5s24d10
Ag
80
112.4
cadmium
79
silver
[Xe]6s24f145d10
Hg
107.9
Au
[Xe]6s14f145d10
(277)
112
200.5
mercury
(272)
70
[Xe]6s24f145d1
69
[Xe]6s24f14
101
nobelium (254)
[Rn]7s25f14
102
lawrencium (257)
[Rn]7s25f146d1
Lr
103 [Rn]7s25f13
175.0
[Xe]6s24f13
Lu Tm
68
Yb
Er
lutetium
[Xe]6s24f12
ytterbium
100
mendelevium (256)
173.0
thulium
99
fermium (253)
[Rn]7s25f12
167.3
[Rn]7s25f11
168.9
erbium
98
einsteinium (254)
164.9
[Xe]6s24f11
67
Ho [Xe]6s24f10
66
Dy
holmium
[Rn]7s25f10
Fm Md No
97
californium (249)
Es [Rn]7s25f9
Cf berkelium (247)
162.5
S [Ne]3s23p3
sulfur
10.81
[Ar]4s23d6
12B 30
9.012
7B 25
[Ar]4s23d10
6.941
[Ar]4s23d5
58.69
11B 29
12 6B 24 58.93
[Kr]4d10
78
106.4
palladium
Pt
[Ar]4s13d10
[Ne]3s2
[Ar]4s13d5
Ca
24.31
20
5B 23
Ni
[Ar]4s23d3
cobalt
Co
4B 22 iron
Fe
[Ar]4s23d2
55.85
Mn
3B 21 54.94
manganese
Cr
[Ar]4s23d1
52.00
chromium
V
11
Ti
[Ne]3s1
Sc
[Ar]4s2
50.94
vanadium
Pd [Kr]5s14d8
77
102.9
rhodium
Ir
46
Rh [Kr]5s14d7
101.1
76
Os
45
Ru
[Kr]5s24d5
(98)
Re
[Xe]6s14f145d9
197.0
[Xe]6s24f145d7
111
gold
195.1
platinum
110
190.2
iridium
109
190.2
108
[Xe]6s24f75d1
96
dysprosium
Ds Uuu Uub darmstadtium (271)
[Rn]7s15f146d9
meitnerium (266)
[Xe]6s24f7
65 [Xe]6s24f6
terbium
[Rn]7s25f76d1
[Xe]6s24f9
[Xe]6s24f5
gadolinium
64
Tb
[Rn]7s25f146d7
Mt
osmium
[Xe]6s24f145d6
107
186.2
rhenium
[Xe]6s24f145d5
75
44
Tc
ruthenium
43
technetium
nickel
47.88
titanium
74
tungsten
[Xe]6s24f145d4
W
95.94
molybdenum
[Kr]5s14d5
42
44.96
41
scandium
40
73
[Kr]5s14d4
Zr 92.91
niobium
72
[Kr]5s24d2
Y 91.22
zirconium
57
Ta
[Xe]6s24f145d3
183.9
[Xe]6s24f145d2
106
[Xe]6s25d1
104
Hs
hassium (265)
[Rn]7s25f146d6
Bh
bohrium (262)
[Rn]7s25f146d5
Sg
seaborgium (263)
[Rn]7s25f146d4
63
dubnium (260)
62
[Rn]7s25f146d3
61
(257)
rutherfordium
59
Gd [Xe]6s24f4
europium
Bk [Rn]7s25f7
158.9
samarium (150.4)
95
americium (243)
157.3
promethium (147)
94
[Rn]7s25f6
152.0
144.2
neodymium
Pu Am Cm plutonium (242)
curium (247) neptunium (237)
[Rn]7s25f46d1
93
Np
92
U
Nd Pm Sm Eu
60
[Rn]7s25f146d2
Db
180.9
tantalum
89
138.9
actinium (227)
[Rn]7s26d1
58
Pr
140.9
[Xe]6s24f3
Ce
praseodymium
[Xe]6s24f15d1
cerium
140.1
91
Pa
uranium (238)
[Rn]7s25f36d1
90
[Rn]7s25f26d1
Th
105
hafnium
178.5
lanthanum
La* Hf
88.91
[Kr]5s24d1
yttrium
39
40.08
38
[Kr]5s2
Sr 56
87.62
strontium
Ba [Xe]6s2
88
[Rn]7s2
Nb Mo
calcium
magnesium
Na Mg 22.99
sodium
19
K
[Ar]4s1
39.10
potassium
37
[Kr]5s1
Rb 55
85.47
rubidium
Cs [Xe]6s1
barium
137.3
radium (226)
87
132.9
Ra Ac~ Rf
cesium
Fr [Rn]7s1
(223)
francium
Lanthanide Series*
Actinide Series~
protactinium (231)
232.0
thorium
[Rn]7s26d2
element names in blue are liquids at room temperature element names in red are gases at room temperature element names in black are solids at room temperature
Figure 1.1: The periodic table is a tabular method of displaying the chemical elements. Elements are listed in order of increasing atomic number, i.e. the number of protons in the atomic nucleus.
18
2. Spectroscopy and Lifetime Measurements
The year 1666 was the beginning of the scienti c method called spectroscopy as Isaac Newton introduced the word spectrum after he showed that white light from the sun could be divided into a continuous series of colors [8], see Fig. 2.1 for an illustration. It should be noted that the region visible for the eye in the electromagnetic spectrum (EM-spectrum) is rather small and the white radiation from the sun consists of many wavelengths invisible to the human eye. In Fig. 2.2 a schematic picture of the EM-spectrum is shown. In 1814 Fraunhofer observed the rst discrete spectral lines ever when he saw dark lines in the suns spectrum with his spectroscope. He could, however, not fully understand the origin of these lines but Kirchho and Bunsen later discovered that each element is related to certain spectral lines [9] and they concluded that the dark lines originated from absorbtion in the sun. Today it is well known that energy emitted by matter creates a spectrum and that each physical system (i.e. atoms and molecules) has a speci c level structure. Spectroscopical studies can be used to map and identify these structures.
Figure 2.1: Illustration of Newtons discovery that white light from the sun coluld be divided into a visible spectrum with a prism.
19
There are dierent types of spectroscopy but they can mainly be divided into three groups: Absorption spectroscopy - light of a well known wavelength travels through a medium. Depending on the atomic structure of the elements in the medium certain wavelengths will be absorbed and the wavelengths of the absorbed light can be observed in a spectra. Spectra from astrophysical objects are often of this type. Emission spectroscopy - the radiated energy (light) at dierent wavelengths from an element is observed directly. Scattering spectroscopy - the amount of light that is scattered at a certain wavelength, angle and polarization is measured. One useful application of this method is Raman scattering where e.g. vibrational and rotational modes in a system can be investigated. There are many important properties of atoms and ions to study and much work within this area is in progress. One interesting property is the lifetime of each energy level and lifetime measurements of these levels are therefore of great importance. Dierent methods and techniques can be used for lifetime measurements but a time-resolved spectroscopic method makes it possible to do high precision studies of this property. Which method that best suits the experiments depends on e.g. how long the lifetime is. For a normal radiative atomic lifetime of some nanoseconds there are several dierent techniques that can be used, for example the technique called linewidth measurement [10]. 1 where τ is Here the natural linewidth, which is de ned as ∆ν = 2πτ the radiative lifetime, of the state is measured. ∆ν yields the lifetime directly by simply observing the spectrum from the element of interest if there is no other broadening mechanism involved. Another technique for measuring short-lived states is the beam-foil technique [11, 12] which was frequently used 30 years ago. Here ions with a well de ned kinetic energy pass through a thin carbon foil (∼ 50nm) where an excitation of the ions occur. The excited ions will decay in ight after passing the foil and a time resolved spectrum can then be recorded with a spectrometer. However, the nonselective excitation leads to cascading eects from higher lying states and great caution during the analysis of the spectrum has to be taken. On the other hand non-selective excitation can be advantageous since a large amount of the states are populated.
20
The invention of lasers [13] opened up new doors for spectroscopy studies and lifetime measurements. There are a large number of laser techniques that can be applied in order to investigate the lifetime of a state and these methods are in contrast to the beam-foil technique state selective. Some examples are e.g. laser-induced uorescence [14, 15, 16, 17] and beam-laser experiment where the foil from the beam-foil experiment is changed to a laser beam [18].
21
2.1
Long lifetimes
If the lifetime of the state is long (milliseconds or seconds) the experimental procedure must, however, be dierent. If we consider a lifetime of ∼ 1 s and an ion energy of 40 keV the ion would travel ≈ 105 m within one lifetime which means that the beam-foil technique is excluded in this case. So what we need is a storage technique which gives us a long observation time within a reasonable spatial region. This requirement is ful lled by using either an ion trap (e.g. Paul or Penning) or an ion storage ring. The ion trap can be used in combination with lasers [19, 20, 21, 22] which makes this method state selective. However, a lifetime measurement at an ion trap facility often requires a number of dierent light sources and there can also be di cult to correct for some systematic eects, such as ion storage lifetime and collisional excitation. It is also possible to store the ion in a storage ring, magnetic [23, 24, 25] or electrostatic [26, 27]. A lifetime measurement of an ion in a storage ring can either be passive or in combination with lasers. Without a laser (that is passive) the ions are injected into the ring where they circulate and the uorescence from the decay is observed with e.g. a photomultiplier [28]. The experiments described in this thesis use a combination of a storage ring and lasers. The technique used has been developed during recent years [29, 30] and will be described in detail. Also, results from investigations on metastable states of nine dierent singly charged ions (six positive and three negative) will be presented. All experiments have been performed at the CRYRING storage ring at Stockholm University. The theoretical calculations presented together with the experimental results in the papers have been done by Emile Biémont's group in Belgium, Alan Hibbert in Northern Irland and Charlotte Froese Fisher in USA.
22
Figure 2.2: The EM-spectrum in the wavelengths range from several thousand meters down to fractions of the size of an atom. Note that the region visible to the eye is rather small.
23
Part II: Theoretical Aspects An atom in an excited state is not stable and it will decay radiatively to another state by emitting a photon. Without the presence of an external eld this process is spontaneous and the average time the atom stays in the excited state before it decays is called the radiative lifetime. Spontaneous emission, stimulated emission and absorption in atoms can be described by the Einstein coe cients. If a system of two states is considered we can denote the energy of the lower state E1 and its population N1 while the energy of the higher lying energy level is denoted E2 and its population N2 , see Fig. 2.3. The change of population in level 2 per unit time (the rate) can be formulated, using the Einstein coe cients A21 , B12 and B21 which denote the spontaneous emission, absorption and the stimulated emission respectively, as
−
dN1 dN2 = = A21 N2 − B12 ρ(ω)N1 + B21 ρ(ω)N2 dt dt
(2.1)
where ρ(ω) is the energy density of the radiation eld per frequency interval. If the radiation eld is absent then ρ = 0 and the solution to Eq. 2.1 is given by Eq. 2.2.
N2 (t) = N2 (0) · e−A21 t
(2.2)
A determines the lifetime and can be written as 1 (2.3) A21 = . τ If the excited state, denoted i, can decay to several states, see Fig. 2.4, the total radiative transition probability is the sum of all decay channels and the lifetime is then determined by the inverse of the sum of these rates according to Eq. 2.5. Atot =
X k
Aik
(2.4)
E
N2
2
A
B
21
B
12
21
E
N1
1
Figure 2.3: Spontaneous emission, absorption and stimulated emission between two energy levels denoted with the Einstein coe cients A21 , B12 and B21 respectively.
Ei
Ai0
Ai1
Ai2 E2 E1
E0
Figure 2.4: Level scheme of the radiative decay of the level i. The total radiative transition probability is the sum of all decay channels.
τi = P
26
1 k Aik
(2.5)
3. Selection Rules
For radiative transitions between dierent energy states certain selection rules concerning the angular momenta J and L, the parity change, and the spin have to be obeyed. The spin angular momentum magnitude for an electron, |s|, is given by
|s| =
q
s(s + 1)¯ h
(3.1)
where s = 12 is the spin quantum number. The orbital angular momentum magnitude, |l|, is given by
|l| =
q
l(l + 1)¯ h
(3.2)
where l is the azimuthal quantum number (l = 0, 1, ..., n − 1) and n is the principle quantum number. In most light systems (Z60
14.5 / 12.2 h
Te−
5p5 2 P3/2
0.42 ± 0.05
0.45
Table 19.1:
♠
- Fine structure levels not resolved
93
Part VI: Author’s contribution A summary of my contribution to the experiments. I have participated in the experimental work i all papers presented in this thesis, but I have not been involved in the theoretical work.
Paper I
Responsible for electronic and laser setup. Responsible for data recording and data analysis.
Paper II
Responsible for electronic and laser setup. Responsible for data recording and data analysis.
Paper III
Suggested atomic system for investigation. Responsible for electronic and laser setup. Responsible for data recording and data analysis. Written the paper.
Paper IV
Participated in electronic and laser setup and data recording. Involved in the data analysis.
Paper V
Responsible for electronic and laser setup and data recording. Involved in the data analysis.
Paper VI
Participated only in the titanium experiment. Responsible for electronic and laser setup. Responsible for data recording. Involved in the data analysis for the Ti II experiment.
Paper VII
Responsible for electronic and laser setup. Responsible for data recording. Involved in the data analysis.
Paper VIII
Responsible for electronic and laser setup. Responsible for data recording. Involved in the data analysis.
Paper IX
Responsible for electronic and laser setup. Responsible for data recording. Involved in development of new method for data analysis.
Paper X
Responsible for electronic and laser setup. Responsible for data recording and data analysis. Written the paper.
Paper XI
Responsible for electronic and laser setup. Responsible for data recording. Involved in the data analysis.
Paper XII
Responsible for electronic and laser setup. Responsible for data recording.
Paper XIII
Responsible for electronic and laser setup. Responsible for data recording.
96
Part VII: Acknowledgements This part of a thesis is usually the most read so hopefully I won't disappoint to many of you. I can't mention all of you here but you can be sure of that I wont forget all support, laughs, discussions and help you have given me during these years. To start with I would like to thank my excellent supervisor Prof. Sven Mannervik who gave me the opportunity to work within this fun, exciting and, sometimes, frustrating area. I don't really now what more to say to you but you have truly been a SUPERvisor. Thank you! Peder Royen - your kindness and expertise regarding everything has been invaluable. Is it something you don't know about physics? I actually don't think so, but I do know that you wouldn't admit it. Lars-Olov Norlin aka LON - the master of electronics, signals, detectors and jazz. Your knowledge together with your northern coolness has really been a source of inspiration and fruitful discussions. My former colleague Peter Schäf - without you I would not be here. For this I'm very grateful. On top of this we shared a lot of fun during the years so thank you and take care dude! My present (soon former) roommate Jonas Gurell - a genius in grammar, well-read, kind and funny. I can't think of a better roommate and colleague. Thank you and good luck!
The sta at MSI - kind people all of you. You gave me many ions over the years (I always wanted more though) and we had some great results together. Thanks!
Finally my family and friends - without you this would have been impossible. You have supported me in 'nöd och lust' throughout these years (I know I've been absent now and then!) so thank you. I truly love you.
And now, the end is near And so I face the nal curtain. My friend, I'll say it clear, I'll state my case, of which I'm certain. - P.Anka
98
Bibliography
[1] C. Bailey, The Greek Atomist and Epicurus (Oxford, 1928). [2] J. Burnet, Early Greek Philosophy (Kessinger Publisher, 2003). [3] J. Dalton, A New System of Chemical Philiosophy (Norman Library of Science, 1808-1827). [4] J. Thomson, Philosophical Magazine
44, 269 (1897).
[5] J. Thomson, Philosophical Magazine
7, 237 (1904).
[6] E. Rutherford, Philosophical Magazine [7] N. Bohr, Philosophical Magazine
21, 669 (1911).
26, 1 (1913).
[8] I. Newton, Optics 4th ed. (1730). [9] G. Kirchho and R. Bunsen, Ann. Phys.
110, 160 (1860).
[10] C. Oates, K. Vogel, and J. Hall, Phys. Rev. Lett.
76, 2866 (1996).
[11] S. Bashkin, Beam-Foil Spectroscopy (Springer, 1976). [12] P. Dumont, Y. Baudinet-Robinet, H. Garnir, E. Biémont, and N. Grevesse, Phys. Rev. A 20, 1347 (1979). [13] A. Schawlow and C. Townes, Phys. Rev.
112, 1940 (1958).
[14] Z. Zhang, A. Persson, Z. Li, S. Svanberg, and Z. Jiang, Eur. Phys. J. D 13, 301 (2001). [15] E. Biémont, H. Garnir, P. Quinet, S. Svanberg, and Z. Zhang, Phys. Rev. A 65, 052502 (2002). [16] S. Snyder and A. LeRoux, Plasma Science [17] M. Kono, Chemical physics
25, 824 (1997).
282, 101 (2002).
[18] H. Andrä, A. Gaupp, and W. Wittmann, Phys. Rev. Lett. 31, 501 (1973). [19] P. Barton, C. Donald, D. Lucas, D. Stevens, A. Steane, and D. Stacey, Phys. Rev. A 62, 032503 (2000).
99
[20] M. Knoop, C. Champenois, G. Hagel, M. Hossein, C. Lisowski, and F. Vedel, The European Physical Journal D 29, 163171 (2004). [21] W. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. Lett. (1986). [22] N. Yu, W. Nagourney, and H. Dehmelt, Phys. Rev. Lett.
56, 2797
78, 26 (1997).
[23] S. Møller, in Conference Record of the 1991 IEEE Particle Accelerator Conference, K. Berkner, ed., (1991), p. 2811. [24] E. Jaeschke et al., IPAC (1988), Vol. 1, p. 365. [25] K. Abrahamsson et al., Nucl. Instr. Meth. Phys. Res. B
79, 268 (1993).
[26] M. Jensen, U. Pedersen, and L. Andersen, Phys. Rev. Lett. (2000). [27] S. Møller, Nucl. Instr. Meth. Phys. Res. A
84,
1128
394, 281 (1997).
[28] E. Träbert, A. Wolf, E. Pinnington, J. Linkemann, E. Knystautas, A. Curtis, N. Bhattacharya, and H. Berry, Phys. Rev. A 58, 44494452 (1998). [29] J. Lidberg, A. Al-Khalili, L.-O. Norlin, P. Royen, X. Tordoir, and S. Mannervik, Nucl. Instr. Meth. Phys. Res. B 152, 157 (1999). [30] J. Lidberg, Ph.D. thesis, Department of Physics, Stockholm University, 1999. [31] G. Woodgate, Elementary Atomic Structure, 2:nd ed. (Oxford Science Publications, 1974). [32] M. Bautista, T. Gull, K. Ishibashi, H. Hartman, and K. Davidson, Mon. Not. R. Astron. Soc. 331, 875879 (2002). [33] H. Hartman, T. Gull, S. Johansson, N. Smith, and H. E. C. T. P. Team, A&A 419, 215 (2004). [34] H. Hartman, J. Gurell, P. Lundin, P. Schef, A. Hibbert, H. Lundberg, S. Mannervik, L.-O. Norlin, and P. Royen, A&A 480, 575580 (2008). [35] S. Kaufman, Optics Communication
17, 309 (1976).
[36] A. Paal, A. Simonsson, A. Källberg, J. Dietrich, and I. Mohos, DIPAC in
6th European Workshop on Beam Diagnostic and Instrumentation for Particle Accelerators (2003).
[37] S. Mannervik, Physica Scripta
T105, 6775 (2003).
[38] W. Demtröder, Laser Spectroscopy, Basic Concepts and Instrumentation, 2:nd ed. (Springer, 1998).
100
[39] S. Mannervik, J. Lidberg, L.-O. Norlin, and P. Royen, Phys. Rev. A R1075 (1997).
56,
[40] S. Mannervik, A. Ellmann, P. Lundin, L.-O. Norlin, D. Rostohar, P. Royen, and P. Schef, Physica Scripta T119, 4954 (2005). [41] A. Ellmann, Ph.D. thesis, Department of Physics, Stockholm University, 2003. [42] D. Hanstorp, Nucl. Instr. Meth. Phys. Res. B
100, 165 (1995).
[43] R. Cowan, private communication with S. Mannervik . [44] R. Cowan, The Theory of Atomic Structure and Spectra (University of Califonia Press Berkley CA, 1981). [45] S. Mannervik, L. Broström, J. Lidberg, L.-O. Norlin, and P. Royen, Phys. Rev. Lett. 76, 3675 (1996). [46] H. Danared et al., DESIREE - A double electrostatic storage ring for merged-beam experiments, AIP Conf. Proc. 821, 465472 (2006). [47] http://www.atom.physto.se/Cederquist/desiree.html, . [48] L. Löfgren et al., DESIREE - A double electrostatic storage ring, EPAC Conf. Proc. p. 252 (2006). [49] K. Rensfelt et al., DESIREE - A double electrostatic storage ring, EPAC Conf. Proc. 12, 14251427 (2004). [50] P. Schef, A. Derkatch, P. Lundin, S. Mannervik, L.-O. Norlin, D. Rostohar, P. Royen, and E. Biémont, Eur. Phys. J. D 29, 195199 (2004). [51] E. Biémont and P. Quinet, Phys. Rev. Lett.
81, 3345 (1998).
[52] M. Roberts, P. Taylor, G. Barwood, P. Hill, H. Klein, and W. Rowley, Phys. Rev. Lett. 78, 1876 (1997). [53] D. Marger and H. Schmoranzer, Phys. Rev. Lett.
146, 502 (1990).
[54] C. Sikström, M. Schultz-Johanning, M. Kock, Z.-S. Li, H. Nilsson, S. Johansson, H. Lundberg, and A. Raasen, J. Phys. B: At. Mol. Opt. Phys 32, 5687 (1999). [55] S. Johansson et al., Physica Scripta
T100, 71 (2002).
[56] D. Rostohar, A. Derkatch, H. Hartman, S. Johansson, H. Lundberg, S. Mannervik, L.-O. Norlin, P. Royen, and A. Schmitt, Phys. Rev. Lett. 86, 14661169 (2001).
101
[57] H. Hartman et al., A&A
397, 11431149 (2003).
[58] P. Quinet, M. L. Dourneuf, and C. Zeippen, A&A
120, 361 (1996).
[59] S. Mannervik, J. Lidberg, L.-O. Norlin, P. R. A. Schmitt, W. Shi, and X. Tordoir, Phys. Rev. A 83, 698701 (1999). [60] T. Zethson, T. Gull, H. Hartman, S. Johansson, K. Davidson, and K. Ishibashi, Astron. J 122, 322 (2001). [61] R. Garstang, J. Res. Natl. Bur. Stand. Sect. A
68, 61 (1964).
[62] F. Plumelle, M. Desaintfuscien, J. Duchene, and C. Audoin, Opt. Commun. 34, 71 (1980). [63] B. Warner, Mon. Not. R. Astron. Soc. [64] A. Gallagher, Phys. Rev.
139, 115 (1968).
157, 24 (1967).
[65] H. Winter and M. Gaillard, Z. Phys. A [66] C. Guet and W. Johnson, Phys. Rev. A
281, 311 (1977). 76, 039905(E) (2007).
[67] E. Iskrenova-Tchoukova and M. Safronova, Phys. Rev. A p. submitted (2008). [68] C. Sur, R. Chaudhuri, B. Sahoo, B. Das, and D. Mukherjee, J. Phys. B 41, 065001 (2008). [69] B. Warner and R. Kirkpatrick, Mon. Not. R. Astr. Soc
144, 397 (1969).
[70] Y. Ralchenko, F.-C. Jou, D. Kelleher, A. Kramida, A. Musgrove, J. Reader, W. Wiese, and k. Olsen, NIST Atomic Spectra Database p. http://physics.nist.gov/asd3 (ver.3.1.1). [71] H. Hartman, D. Rostohar, A. Derkatch, P. Lundin, P. Schef, S. Johansson, H. Lundberg, S. Mannervik, L.-O. Norlin, and P. Royen, Mon. Not. R. Astron. Soc. 361, 206210 (2005). [72] H. Hartman, P. Schef, P. Lundin, A. Ellmann, S. Johansson, H. Lundberg, S. Mannervik, L.-O. Norlin, D. Rostohar, and P. Royen, Mon. Not. R. Astron. Soc. 361, 206210 (2005). [73] G. Somesfalean, J. Alnis, S. Svanberg, A. Derkatch, S. Mannervik, D. Rostohar, P. Royen, P. Schef, and L.-O. Norlin, Physica Scripta 69, 98 103 (2004).
102
