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THE BEAM-FOIL SPECTRA OF KRYPTON (2 TO 5 MEV)
Item Type text; Dissertation-Reproduction (electronic)
Authors Cardon, Bartley Lowell, 1940-
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/289579
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I I
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77-18,667
CARDON, Bartley Lowell, 1940-THE BEAM-FOIL SPECTRA OF KRYPTON (2
TO 5 MeV).
The University of Arizona, Ph.D., 1977 Physics, atomic
Xerox University Microfilms , Ann Arbor, Michigan 48106
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THE BEAM-FOIL SPECTRA OF KRYPTON (2 TO 5 MeV)
by
Bartley Lowell Cardon
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF PHYSICS
In Partial Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
19 7 7
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THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by Bart lev Lowell Cardon
entitled The Beam-foil Spectra of Krypton ( 2 to 5 MeVl
be accepted as fulfilling the dissertation requirement for
the
degree of Doctor of Philosophy
issertation Director Date
As members of the Final Examination Committee, we certify
that we have read this dissertation and agree that it may be
presented for final defense.
^ft,/7? c—w,
3/29/7;
%/,. / f t / . y /so)?*
Final approval and acceptance of this dissertation is contingent
on the candidate's adequate performance and defense thereof at the
final oral examination.
-
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of
requirements for an advanced degree at The University of Arizona
and is deposited in the University Library to be made available to
borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without
special permission, provided that accurate acknowledgment of source
is made. Requests for permission for extended quotation from or
reproduction of this manuscript in whole or in part may be granted
by the head of the major department or the Dean of the Graduate
College when in his judgment the proposed use of the material is in
the interests of scholarships. In all other instances, however,
permission must be obtained from the author.
djjy t&A-y
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ACKNOWLEDGMENTS
And so, here, the odyssey of ray graduate studies ends. Many
people over many years, beginning with Sumner Davis at Berkeley,
then
Kenneth Andrew and Robert Stanley at Purdue, Henry Hill at
Wesleyan
and The University of Arizona, and finally John Leavitt at The
Univer
sity of Arizona, have contributed to seeing it all brought to a
success
ful conclusion. It was John Leavitt, above all others, whose
calm and
wise guidance, and example, provided me with a supportive and
productive
environment in which to fruitfully pursue my dissertation. His
high
standards are hopefully reflected in this work. Other members of
the
physics faculty who gave freely of their time and energy and to
whom
I express my appreciation are Carl Tomizuka, John Robson, Leon
Blitzer,
J. D. Garcia, Stanley Bashkin, Larry Mclntyre, John Stoner, Bill
Bickel,
Doug Donahue, Dan Dietrich, Bob Kalbach, John Kessler, Bob
Parmenter
Bob Chambers, Bruce Barrett, Mike Scadron, and John McCullen.
Dick Van
Reeth and the Physics Creative Laboratory were very helpful.
Peter
Stoss saw to the well-being of the Van de Graaff Laboratory and
A1
Sheehan and Richard Lamoreaux saw to my electronics and computer
prob
lems. Jackie Fahey, Evelyn Burros, and Lois Couch provided
efficient
and cheerful secretarial aid. John Howe gave the artist's touch.
Hank
Oona assisted me in several phases of the data taking. Ron
Pamachena
resolved some computer mysteries. Marsha Mapes endured the
preparation
iii
-
iv
of the final spectral line list and carefully and diligently
checked
ray calculations. Barbara Otke Bickel was my excellent typist
and I
appreciate her care. Delmar Barker and Ed Middlesworth were
good
companions and thoughtful colleagues.
A special note of appreciation is due my mother and father,
sisters and their husbands, and Marion Meyer. Their constant
support
and devotion helped buoy me up during the darker moments. I
thank them
for their unselfish love.
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TABLE OF CONTENTS
Page-
LIST OF ILLUSTRATIONS vii
LIST OF TABLES ix
ABSTRACT x
1. INTRODUCTION 1
2. EXPERIMENTAL APPARATUS AND PROCEDURE 6
Accelerator and Selector Magnet 6 Excitation Chamber 8 Detector
System 11 Spectrometer 14 Spectrometer Calibration 17 Spectrometer
Refocusing and Intensity Enhancement .... 25
Refocusing 29 Intensity Enhancement 32
Recording and Reduction of Data ' 40
3. DETERMINATION OF CHARGE STATE 54
Charge State Distribution of Krypton 55 Multiple Scattering of
Krypton in Carbon Foil 68 Charge State Identification Via
Electrostatic Deflection . 70
4. THEORY 81
Polarization Model of the Atom 83 Spectral Line Intensities 99
Spectral Analysis Miscellany 103
5. DISCUSSION OF SPECTRA AND CONCLUSIONS 106
Krypton III 107 Krypton IV 108 Krypton V 108 Krypton VI 109
Krypton VII Ill Krypton VIII 115 Krypton IX-XIII 122 Conclusions
122
v
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TABLE OF CONTENTS--Continued
vi
Page
APPENDIX A: GAUS2Z: SPECTRAL LINE FITTING PROGRAM ... 147
APPENDIX B: PROGRAMS LAMSORT AND ORDSORT 150
APPENDIX C: THE KRYPTON SPECTRAL LINE LIST f400 - 6000&) .
154
APPENDIX D: RYDBERG AND LLAMBDA: ENERGY LEVEL AND SPECTRUM
GENERATING PROGRAMS 186
REFERENCES 189
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LIST OF ILLUSTRATIONS
Figure • Page
1. Krypton beam deflected in an electrostatic field 3
2. Side and top views of the experimental apparatus from the Van
de Graaff accelerator to the McPherson monochromator 7
3. Diagram of the photon counting detection system showing the
photomultiplier tube, pre-amp, multiscaler, and digital-analogue
output 12
4. Diagram of the Fabry-Perot filter used to determine the
periodic error in the spectrometer calibration 20
5. Top view of monochromator with incident beam passing through
foil and into Faraday cup 22
6. Spectral line FWHM as a function of wavelength for the
several refocused conditions of the spectrometer .... 31
7. Focus wavelength X versus energy E of K̂r* beam for IE lenses
2 through 8 34
8. Focus wavelength X versus energy E of 28N2 calibration beam
for IE lenses 2 through 8 35
9. Focus wavelength X versus IE lens diameter D 38
10. Detector and grating combinations used to record Kr and N2
spectral scans 41
11. Intensity enhanced spectra of 2 MeV krypton in the region
3375 - 3455& 43
12. Intensity enhanced spectra of 5 MeV krypton in the region
2959 - 2985X . . . ' 44
13. Histogramg of the number of observed kryptog wavelengths per
100A interval in the region 400 - 6000A 53
14. Electrostatic deflection chamber for the determination of
charge state distributions in krypton 57
vii
-
viii
LIST OF ILLUSTRATIONS—Continued
Figure Page
15. Charge state fractions as a function of incident beam energy
60
16. Equilibrium charge state distribution for 1 and 2 MeV
krypton in carbon foil 6 ugm/cm2) 62
17. Mean charge q versus incident beam energy E 65
18. Charge state distribution width d versus incident beam
energy E 66
19. The charge state electrostatic deflection apparatus ....
72
20. Screening parameters versus orbital angular momenta for
outer electron n = 4 - 10 in Kr IX 87
21. Dipole polarizability of krypton ions versus core charge ?
92
22. Relative intensities for An = 1,2,3 Rydberg supermultiplets
102
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LIST OF TABLES
Table Page
1. Particle densities and numbers for nitrogen (1.67 MeV) and
krypton (2,5 MeV) beams 11
2. Properties of the McPherson 225 gratings 15
3. Line widths of krypton and nitrogen beam-foil spectral lines
28
4. Characteristics of the intensity enhancement lenses ....
36
5. Spectrometer calibration parameters for the McPherson ,225 .
48
6. Equilibrium charge-state fractions for 1 and 2 MeV krypton in
carbon foil 64
7. Mean charge and distribution width for 2,3,4, and 5 MeV
krypton in carbon foil charge-state distributions .... 68
8. Multiple scattering angles for 1, 2, and 5 MeV krypton in
carbon foil 69
9. Charge state analyzed krypton spectral lines 78
10. Ground state electron configurations for Kr III - XIII ...
82
11. Summary of krypton ion electron polarizability results . .
97
12. Wavelengths and fine structure splittings for 4s4p 3P -4s4d
D and 4s4p 3P - 4p2 3P of Kr VII 113
13. Observed Rydberg transitions in Kr VII 114
14. Observed and predicted Rydberg transitions in Kr VIII . . .
116
15. Observed and predicted Rydberg transitions in Kr IX . . . .
123
16. Observed and predicted Rydberg transitions in Kr X ....
128
17. Observed and predicted Rydberg transitions in Kr XI . . . .
132
18. Observed and predicted Rydberg transitions in Kr XII . . .
136
19. Observed and predicted Rydberg transitions in Kr XIII . . .
141
ix
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ABSTRACT
We evaluated the usefulness of the beam-foil source for pro
ducing high quality spectral data and extended our knowledge of
the
spectra in the fourth period of the periodic table by recording
the
beam-foil spectra of krypton between 400 - 6000X. The Doppler
broadening
was reduced by refocusing and lens imaging techniques. The
spectra were
recorded with a McPherson 225 one-meter scanning monochromator.
Special
attention was given to determining the calibration of the
spectrometer
with the krypton spectra interposed with calibration scans of
known
nitrogen lines recorded under similar conditions. The incident
krypton
beam energies were 2, 3, 4, and 5 MeV. The photoelectric scans
(inten
sity versus wavelength) were fitted by hand and with a Gaussian
curve
fitting program on the CDC 6400 computer. Approximately 650
nitrogen
profiles established the spectrometer calibration to within an
average
uncertainty of ± 0.3&. The approximately 2400 krypton line
profiles
were analyzed to produce a list of 965 calibrated vacuum
wavelengths.
We determined the equilibrium charge state distribution of 1 and
2 MeV
krypton in carbon foil and extrapolated our results to 5 MeV. We
mea
sured the multiple scattering of krypton in carbon foil at 1 and
2 MeV
and extrapolated our results to 5 MeV. The charge state
distributions
of krypton in carbon foil and the intensity variation in our
spectra at
2, 3, 4, and 5 MeV were used to deduce charge states. We
investigated
a direct method for determining charge states of specific
line/
x
-
xi
line-complexes by deflecting the post-foil beam in an
electrostatic
field. We determined the charge states of 24 line/line-complexes
and
comment on the limitations of our method.
A simple core polarization modification of the
Bohr-Sommerfeld
model of the atom is considered. We use this model to obtain
values of
the electronic dipolar polarizability for Kr VIII - XIII from
our spec
tral data. We find a quadrupolar polarizability for Kr XI and
XII.
These polarizabilities are used to predict other An = 1,2,3 (and
4, in
the case of Kr IX) transitions in these ions. Relative line
intensities
among Rydberg supermultiplets are discussed and a recipe for
obtaining
intensity centers-of-gravity for close lying transitions is
presented.
A method for extrapolating values of the dipolar polarizability
along
an isoelectronic sequence is explained and used to predict the
polariza
bilities for Kr VI and VII. Features of Kr III-VIII, identified
in our
line list from the previous work of other authors, are
discussed. Of
the 956 spectral lines observed, and tabulated in our
appendices, 434
possess some kind of identification, 324 of which were
previously
unreported. Five hundred thirty-one (531) krypton wavelengths
have yet
to be identified. We conclude that the beam-foil source is
capable,
with care, of providing spectroscopic data accurate to about ±
O.lA and
that future effort might reduce this to ± 0.03A.
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CHAPTER 1
INTRODUCTION
The field of beam-foil spectroscopy can properly be said to
have begun with the pioneering researches of Kay (1963) and
Bashkin and
Meinel (1964). In the short span to 1977 this field has grown
and
developed enormously such that at least some part of it has been
the
basis of investigation at practically all major physics
laboratories
in the world. This has prompted four international conferences
to be
held over a period of nine years devoted to its various aspects.
The
published proceedings of these conferences (Bashkin 1968;
Martinson,
Bromander, and Berry 1970; Bashkin 1973; Sellin and Pegg 1976)
chronicle
the brief history and follow the increasingly sophisticated
development
of beam-foil spectroscopy. Indeed, the scope and character has
so
altered from its original notion of purely spectroscopic study
that
Martinson (Martinson and Gaupp 1974) has suggested that it might
be
more accurately described as atomic physics with ion
accelerators.
To appreciate some of the capabilities of beam-foil
spectroscopy
in the study of atomic processes, let us examine, in simplified
terms,
the beam-foil source. We project, by means of a particle
accelerator,
an incident ion beam on a thin foil target (typically carbon).
As a
result of this encounter, which results in the capture and loss
exchange
of electrons between the beam and the foil material, the beam
emerges on
1
-
2
the other side as a charge distribution of ions, the mean ionic
charge
higher, the greater the incident energy. On the back surface of
the
foil, or in the electron rich environment immediately adjacent,
the ions
recombine with electrons and begin radiating and continue to do
so as
they move downstream. In figure 1 we have a photograph of a
krypton
beam emerging from a carbon foil and partially separated into
its ion
components by means of a perpendicular electric field. The
entire exci
tation process occurs in a time period of the order of 10~15
seconds or
less. We now have a coherent light source (by virtue of the
abrupt
excitation of the atomic states in the ions) which emits
radiation from
a distribution of typically highly ionized atoms, for which the
observed
decrease in light intensity as a function of distance downstream
is
related to the decay time of the atomic states participating
(the time
scale t is t = x/v where x is the distance downstream and v is
the beam
velocity).
The coherence of the radiation and its anisotropy have been
exploited to study fine and hyperfine structures, g factors, and
Lamb
shifts. The variation in intensity with distance downstream,
which pro
vides a direct measurement to the lifetime of the atomic states,
has
provided a wealth of lifetime data which had heretofore been
very diffi
cult or impossible to obtain by other spectroscopic sources.
Recently,
Andra (1976) used the beam-foil source in conjunction with laser
excita
tion to obtain cascade free lifetime measurements accurate to ±
0.15%,
a remarkable achievement. Despite these fruitful applications of
the
beam-foil source, however, the question remains of how useful it
can be
for providing spectral results and be in some way competitive
with other
-
3
Figure 1. Krypton beam deflected in an electrostatic field.
A h. vA, 2 MeV krypton beam emerges after colliding with a
carbon foil at left and is deflected upwards by a 24 KV/cm electric
field. The bottom field plate is positive and is strongly
fluorescing due to electron bombardment. The lower edge of the
upper plate, 1 cm away, is barely visible. The photograph is a
Cibachrome print of a Kodachrome 64 slide taken at f/3.5 for 12
minutes with a 50 mm lens. Scale is 1:1.
-
4
spectroscopic sources, e.g., the sliding spark and theta-pinch
light
sources, which also produce high stages of ionization (albeit
not as
readily or easily as the beam-foil source), but with narrower
line
widths. It was early recognized that the price one paid for high
stages
of ionization in the beam-foil source was large Doppler
broadening as a
consequence of the large beam velocities used. This broadening
was
sufficient to obscure all but the grossest features in the
visible part
of the beam-foil produced spectrum. In addition, as the
techniques of
beam-foil spectroscopy have nevertheless yielded valuable
lifetime and
spectral information concerning the lighter elements, where
there exists
ample data from earlier work with other sources to act as a
guide, it
has become desirous to extend spectral analyses to the higher
stages of
ionization of heavier elements where there is much less
supportive infor
mation from other studies. Furthermore, as a result of the
efforts now
being put into controlled thermonuclear fusion, there is a
demand for
spectroscopic information concerning wall materials and
diagnostic gases
which are highly ionized.
To evaluate the degree to which the beam-foil source would
be
useful in providing such information and to assess the accuracy
attain
able in a beam-foil spectroscopic study, we decided to undertake
an
extensive and thorough analysis of the beam-foil spectra of an
element
incorporating recent advances in the reduction of spectral line
width
from fast-ion sources with special attention paid to obtaining
the best
calibration of the spectrometer consistent with its
capabilities. The
resulting spectra would then be used to test the suitability of
a simple
atomic model for determining electric dipole polarizabilities of
the
-
5
electron cores and screening parameters. These quantities and
their
extrapolation along isoelectronic sequences have been valuable
in system
atizing the hyrogen-like transitions in the lighter elements and
it
remains to be seen how useful they will be in elucidating the
beam-foil
spectra of the heavier elements.
The element of study was krypton, isotope A = 84 (56.9% abun
dant), which comments itself by being monatomic, chemically
inert, and
easy to use in the particle accelerator. Its atomic structure
places
it near the middle of the naturally occurring members of the
periodic
table. Preliminary calculations of the anticipated spectral
features,
using a simple modified Bohr atomic model, indicated fine
structures
which would be resolvable and would therefore reveal something
about
the details of the ions responsible. The well known atomic
spectra of
nitrogen, produced under conditions identical to that of
krypton, were
chosen for internal calibration.
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CHAPTER 2
EXPERIMENTAL APPARATUS AND PROCEDURE
The equipment used to produce and record the krypton spectra
and
attendant nitrogen calibration spectra consisted of four basic
elements
(see figure 2): the particle beam accelerator and selector
magnet, the
excitation chamber wherein the beam-foil interaction occurred
and spectra
were produced, the spectrometer which analyzed the spectra, and
the detec
tor system which photoelectrically recorded the spectrometer
output and
generated analogue and digital records of intensity versus
wavelength.
Each of these elements will be described, with special emphasis
on the
spectrometer, as it was this instrument which determined the
final
quality and reliability of the spectral data obtained.
Accelerator and Selector Magnet
The particle accelerator is a model CN Van de Graaff with a
utilizable accelerator voltage range of 1-5.5 MV. The
accelerator is
mounted vertically. The accelerated beam, upon exit, passes
through a
90° bending magnet which directs the ion beam horizontally to
the exci
tation chamber. The 90° bending magnet can be operated at
sustained
fields of more than the 13,200 gauss required to deflect a 5 MeV
84Kr+
beam. The 90° deflection angle insures excellent selection of a
specific
q/m, thereby isolating a beam free of contaminants from nearby
q/m values.
6
-
foil wheel viewing (Translatable •«•») port Model CN
Van de Graaff Accelerator
Faraday Cup
p7>—photo-detector ^4 housing
excitation chamber
grating
McPherson 225
Monochromator 90° analyzing / magnet
quadrupole
focusing magnet
side view top view
Figure 2. Side and top views of the experimental apparatus from
the Van de Graaff accelerator to the McPherson monochromator.
The side and top view scales are not the same.
-
8
This is substantiated by the complete absence of any noticeable
impurity
lines in the krypton spectra.
Excitation Chamber
This is a stainless-steel box which fits over the entrance
slit
housing of the spectrometer and is evacuated by both an oil
diffusion
and Ti getter pump, the latter pump possessing a low pumping
efficiency
for the noble gases. These pumps maintain a high vacuum
environment
(1 - 2 x 10"6 torr) and consequent low background gas pressure
for the
incident ion beam. At the downstream end of the chamber the ion
beam
terminates in a large aperture (2" diam.) Faraday cup with
electron
suppressor ring (battery biased at -180 V). The current from the
Fara
day cup permits the amount of the incident ion beam to be
continuously
monitored. A quartz window port-hole opposite the entrance slit
enables
observation of the ion beam as well as the introduction of light
into
the spectrometer from external stationary sources. The foil
wheel is
mounted in the upstream side of the chamber. It is a
stainless-steel
notched wheel mounted on a horizontal shaft and capable of
holding 24
foil holders, each holder containing two foils over 3/16" holes.
This
horizontal shaft may be translated along the beam axis
permitting the
distance from foil to spectrometer optic axis to be varied for
lifetime
measurements. A linkage between the horizontal shaft and the
outside of
the chamber allows any of the 48 possible foil positions to be
rotated
into the beam path. A typical time interval of one hour was
required to
bring the excitation chamber and spectrometer up to atmospheric
pressure,
-
9
remove the foil wheel, change foils, replace the foil wheel, and
pump
back down.
The foils used throughout the experiment were made of
spectro-
scopically pure carbon. They were fabricated in this laboratory
and
their thicknesses, selected to be between 4-8 ugm/cm2, were
determined
according to the method described by Stoner (1969).
Approximately
2000 carbon foils were used in the execution of this beam-foil
study.
The lifetimes of the carbon foils dictated the amount of
current
selected for the incident ion beam. For the 1.67 MeV N2 incident
beam
used for producing the calibration spectra, a typical foil
lifetime was
nominally 10 minutes for beam currents of 6 - 8 uamps. For the
incident
krypton ion beams the following average behavior was observed:
two min
ute foil lifetime for a 2 namp, 2 MeV, Kr+ beam and a five
minute foil
lifetime for a 5 pamp, 5 MeV, Kr+ beam. To maintain foil
lifetime and
prevent wandering of the beam position, it was essential that
the beam
be broadly focussed, i.e., that it have a diameter at least the
size of
the foil or 3/16".
For the above beam parameters we can calculate the
approximate
number of radiating atoms within the acceptance angle of the
spectrom
eter. Let the krypton beam have a velocity v. Then,
v = gc = c v/2E7931A , (2.1)
where E is the beam energy in MeV, A the atomic number of the
beam ion
(A = 84 for the krypton isotope used throughout the experiment),
and
c the celerity of light. Let the ion beam current be i.
Then,
-
10
i = n q e v a , (2.2)
where n is the beam particle density, q the beam mean charge
(determined
from the charge state distribution of the post-foil beam), e the
charge
of the electron, and a the cross-sectional area of the beam. The
number
of particles which pass through the foil per unit time is
N/t = nva , (2.3)
where N is the number of particles contained in the defining
cylinder of
the beam (assuming no divergence) which radiate within that part
of the
beam intercepted by the acceptance angle of the spectrometer.
This
cylinder is ad long and a particle takes time t = ad/v to
traverse this
distance. Hence,
n = /931A/2E (2.4) qeca
and
N = naad . (2.5)
The acceptance angle a is 1/10 rad., the perpendicular distance
of the
beam from the entrance slit is d = 6.6 cm, and the beam diameter
is 4.8
mm, from which we construct table 1. Note that the background
gas at
a pressure of 5 x 10~6 torr and 300°K has a particle density
of
̂2 x 1011 particles/cm3.
-
11
Table 1. Particle densities and numbers for nitrogen (1.67 MeV)
and krypton (2,5 MeV) beams.
A E (MeV) i (pamp) q n (part./cm3) N (part.)
28 1.67 7 2.0 3.5 x 105 4.1 x 10̂
84 2.0 2 5.6 5.6 x 10̂ 6.6 x 103
84 5.0 5 8.9 5.6 x 10̂ 6.6 x 103
Detector System
The photon counting detector system consists of a
photomulti-
plier with power supply, battery operated preamplifier, 4000
channel
multiscaler, analog strip-chart recorder, and high-speed digital
printer.
A diagram of the detector system is shown in figure 3. To cover
the
O spectral range 400 - 6000A accessible with the spectrometer,
three
photodetectors were employed. These detectors and their
operating
parameters are summarized below:
(1) Bendix 4219 EIC Spiraltron Electron Multiplier -
windowless.
O Operated at room temperature; range of use 400 - 1600A (1% of
peak sensi
tivity at 1500X); cathode is grounded with collector at
+2200V;
wavelengths observed above 1500A are of second or higher
order.
(2) EMR 541F-08-10 - selected ultraviolet LiF window.
Operated
at room temperature; range of use 1050 - 3000A (abrupt lower
cut-off at
1050A); cathode is at -3800V; wavelengths observed above
2100& can be
second or higher order.
(3) RCA 1P28 - Corning #9741 UV transmitting glass window.
Operated at LN2 cooled temperature; range of use 2500 - 6000A;
cathode
-
disc, level
discriminator ireamp counter memory o-
Intertechnique Multiscaler
x>
Q. CD
Figure 3. Diagram of the photon counting detection system
showing the photomultiplier tube, pre-amp, multiscaler, and
digital-analogue output.
A representative photon pulse is shown, amplified,
discriminated, and shaped for the pulse counter. •-•
-
is at -800 V; (1% of peak sensitivity at 1700 - 1800A);
wavelengths
O observed above * 3400A can be second or higher order.
An important feature of these detectors is the cut-off wave
lengths for their different regions of response. This greatly
facili
tated culling out second and third order lines in the final
reduction
of the spectral line list. All the detectors performed in a
predictable
and trouble-free manner.
The preamplifier is an in-house designed and fabricated
(Sheehan
and Lamoreaux 1974) battery-operated circuit employing an MC
1552 mono
lithic video amplifier chip. This preamp has a bandwidth of
about 10
MHz and gain of 50-100. Its operation was plagued from time to
time
by pickup. This was eventually eliminated by isolation from any
nearby
power supply cables and insuring that both preamp and preamp
housing
were properly grounded.
The output from the preamp was fed into a DIDAC
Intertechnique
4000 channel multiscaler where it was further amplified and the
pulse
height discriminated to reduce noise, and finally counted. The
onset of
the counting process was activated by a pulse from the
spectrometer
drive, enabling us to begin the photon counting process at a
known and
reproducible setting of the spectrometer. The duration of the
photon
counting for one channel, the channel integration time, was
flexible and
could be set in the multiscaler. When the counting for one
channel was
terminated, the results were stored in the memory of the
Intertechnique
and the counting process was automatically advanced to the next
channel.
The number of channels, up to 4000, was flexible and could be
set in the
multiscaler. Upon completion of the photon counting for the
number of
-
14
channels chosen, the counting process either terminated or
automatically
restarted. The results of each cycle or scan was displayed on an
oscillo
scope. From the memory, four bins which retained the channel
contents
of four different scans, the number of counts per channel for
each scan
can be retrieved and can be either plotted on a Heath model
EU-20B servo-
recorder (analogue output) or printed out in digital form on
adding
machine paper by a Franklin Printer (Mohawk model 1200 Digital
Strip
Printer). It was typical that both analogue and digital records
of the
spectral scans were generated, the plots providing useful visual
evi
dence of the scans, the digital print-out of photon counts
versus chan
nel number being ultimately transferred entirely to IBM punch
cards for
computer analysis.
For all the spectral scans in this experiment the integration
or
dwell time per channel was 0.6 seconds, a value chosen so as to
make the
channel duration correspond to convenient intervals of
wavelength. For
O O example, if 50A are to be scanned at a spectrometer scan
rate of 5 A/min.,
it will take 10 minutes to perform the scan. For a 0.6 second
dwell
time per channel we will require 1000 channels. Each channel in
turn
will correspond to 0.05A in wavelength.
Spectrometer
The spectrometer used to obtain the spectral data in this
experiment was a McPherson Model 22S normal incidence one-meter
vacuum
UV scanning monochromator. Two gratings enabled wavelength
coverage of
O 400 - 6000A. The properties of these gratings are listed in
table 2.
-
15
Table 2. Properties of the McPherson 225 gratings.
Grating 1 Grating 2
rulings 600 Jl/mm same
size 96 mm x 56 mm 90 mm x 50 mm
radius of curvature 995.4 mm 998.8 mm
coating A1 with MgF2 overcoat same
blaze wavelength 1500A 5000&
construction tripartite monopartite
manufacturer Bausch § Lomb same
SSF: ent. slit gap 2.2 mm 2.2 mm
exit slit gap 2.9 mm 9.0 mm
micrometer setting 0.360" 0.285"
The final three rows of table 2 are the optimum settings for
stationary source focus of the spectrometer. They refer to the
gaps
between the entrance and exit slit housing and the tube
extensions of
the spectrometer body and the respective settings of the grating
microm
eter inside the spectrometer.
XB The useful range for high efficiency of a blazed grating is ±
-y
about the blaze wavelength (Davis 1970, pp. 9-12). For grating 1
this
O would mean a range of 750 - 2250A. In practice we found these
limits
could be stretched and the useful range extended from 400 -
3000X. With
grating 2 the useful range is 2500 - 6000A, the upper wavelength
repre
senting the mechanical limit of the spectrometer drive. All data
taken
-
with this grating were within the interval 2500 - 6000X. The
plate fac
tor for both gratings, with the spectrometer at stationary
source focus,
is 16.6 A/mm.
A six inch oil diffision pump immediately beneath the
spectrom
eter body provided a vacuum of 1 - 5 x 10"6 torr when the
spectrometer
was evacuated. In practice it was essential that the
spectrometer be
evacuated for all the beam-foil studies, ijr calibration work
with
stationary sources and when changing foils in the excitation
chamber,
the spectrometer was filled with dry nitrogen. A high vacuum
(< 1 x 10~5
torr) was mandatory for the proper operation of the windowless
Bendix
spiraltron photodetector.
As mentioned earlier, the spectrometer provided a starting
pulse
for the multiscaler. This was facilitated by a 3-3/4 inch
notched wheel
attached, by sprocket-chain-idler wheel with a 5:1 reduction, to
the
spectrometer drive shaft near the wavelength odometer
(displaying wave-'
lengths to the nearest Angstrom). These four notches, 90° apart,
stroke
a microswitch in a 4.5 V battery powered circuit which is
normally open
but can be closed momentarily by a pressure switch activated
from the
side of the spectrometer body. Each turn of the master screw
corre-
O sponds to a wavelength change of 50A which, with a 5:1
reduction, means
O the notched wheel turns through 10A per revolution making
available a
starting pulse every 2.5A. It was crucial to the reproducibility
of all
the spectral scans taken, especially in the case of multiple
scans over
the same spectral region, that the starting pulses be reliably
dupli
cated. The starting pulses were therefore continuously checked
during
the initial (about six months) calibration period of the
spectrometer.
-
17
These checks were most readily made by scanning many times over
the same
stationary source spectral line or line complex and observing
the shift
in line center and change in line width. In this way, aside from
the
thermal drift in the spectrometer to be discussed shortly, the
starting
pulses were found to be reproducible to ± 0.05A, a value below
the un
certainty in the wavelength calibration of the spectrometer.
Of the twelve synchronous reversible scanning speeds
available
from the drive mechanism, only four speeds were used to perform
actual
scans (although the screw drive was slewed to starting points at
200 or
500 A/min). These were 50 A/min, 20 A/min, 10 A/min, and 5
A/min, producing scans of 0.5 A/chan., 0.2 A/chan., 0.1 A/chan.,
and 0.05 A/chan.
O The rapid scans of 0.5 A/chan. were called survey scans, the
others,
slower, resolution scans. Most of the krypton spectral scans
were taken
O at 0.1 and 0.2 A/chan.
Spectrometer Calibration
The prior use history of our spectrometer was not accurately
known except that previous studies (Stoner and Leavitt 1971b;
the
difference between the observed and handbook value of the
nitrogen
fine structure separation at X = 3482A reported therein is 0.4A)
had
indicated an anomalous behavior in the wavelength calibration.
As it
was the consuming goal of this spectral study to obtain the
highest
quality data heretofore accessible with a beam-foil source, in
coopera
tion with optimization of the spectral line width possible with
refocus-
sing of the spectrometer, thereby producing spectral lines
measurable to
O ± 0.05 - 0.10A, it was essential to eliminate any
peculiarities in the
-
spectrometer calibration and determine accurately and
reproducibly the
wavelength calibration. In a straightforward, although time
consuming,
way the general performance and reproducibility of the
wavelength deter
mination with the spectrometer were systematically checked. This
was
accomplished in four stages. In stage one the entrance and exit
slits
were calibrated and found to be within ± 3p of the slit
micrometer
settings. Relative separations between a large number of
stationary
source wavelengths generated by a Hg penlite source and He, Ar,
and Ne
filled Geissler tubes were measured. It was readily apparent
that the
calibration anomaly had a periodicity of 5oX corresponding to
one revo
lution of the grating drive master screw. A careful inspection
was made
of all mechanical aspects of the drive mechanism seeing to it
that all
set screws in the gear train were properly seated and tight. The
master
and slave screws, as well as the motor and drive bearings, were
carefully
lubricated. No binding or damage to any of the gears could be
found.
It was during this period that a long-period and unpredictable
drift in
the peak location and line width of strong Hg calibration lines
lead us
to suspect that changes in the ambient temperature at the
spectrometer
were also influencing wavelength calibration. Daily records were
kept
of the temperature with a mercury-in-glass thermometer situated
atop
the spectrometer body (2 meters above the floor).
In stage two a Fabry-Perot etalon was used as a wavelength
filter (Tolansky 1970) to produce calibration wavelengths at
controlled
and regular spaced wave number intervals for the wavelength
interval
3400 - 5400X. For a Fabry-Perot etalon of spacing t there is a
trans
mission peak for wavelength X at angle 0 with respect to the
optic axis
-
19
if 2t cos 9. = pX where p is the order of interference.
Restricting
o b s e r v a t i o n o f t h e i n t e r f e r e n c e p a t t
e r n t o n e a r t h e o p t i c a x i s , 0 ^ 0 ,
and 2t = pX. We let a = 1/X so 2ta = p. If two transmission
peaks
of wavenumber a and a + ACT differ by one in order of
interference,
then Aa = l/2t. (Act is called the free-spectral-range of the
etalon.)
Wavelengths which differ from a by multiples of Aa are therefore
trans
mitted. If a continuum light source illuminates the etalon and
the
resulting central region of the interference pattern is
projected onto
the entrance slit of the spectrometer, a series of discrete
wavelength
peaks are produced which are equally spaced by wavenumber ACT =
l/2t and
whose range is limited only by the continuum light source and
the reflec
tivity of the etalon coatings. Figure 4 is a diagram of the
Fabry-Perot
arrangement which produced the calibration fringes used to check
for
periodic error in the spectrometer drive. An air-cooled tungsten
halo
gen lamp and Leitz projector provided sufficient intensity to
produce
O calibration peaks in the range 3400 - 5400 A. The etalon
spacer was
comprised of three tungsten carbide balls, 120° apart, either
1/32" or
1/64" in diameter producing a free spectral range of 6.2 or 12.5
cm"1
O ° (1.0 or 2.OA at 4000A). The measured overall finesse (the
ratio of the
free spectral range to the FWHM of the transmission profile) of
the
etalon was 3.8. The transmission peaks of the etalon were
scanned by
the spectrometer and the resulting peak centers determined. A
least
squares fitting program from the IBM Scientific Subroutine
Package
(IBM 1968) was modified to fit the peak number versus wavenumber
to a
first or second order polynomial. If the calibration of the
spectrom
eter was free of error; then the first order fit should have
zero
-
^ 20.5 cm, ^ „ 30.5 cm . ^
front surface mirror
f 19 cm
i fWs ESSS
port window (quartz)
_ j ) ^16 dia. stop !
Fabry-Perot etalon
ground glass plate
|ens
i
% entrance slit (30/x)
continuum light source
laser (to check alignment)
Figure 4. Diagram of the Fabry-Perot filter used to determine
the periodic error in the spectrometer calibration.
-
21
residuals between the observed wavenumber and the calculated
wavenumber.
Any periodic error in the calibration or systematic drift would
show up
in wavenumber residuals. Hence, the residuals were determined
and dis
played by plotting the residual wavenumbers, converted to
wavelength,
versus wavelength. These results convincingly demonstrated the
presence O
of a periodic error per screw revolution of magnitude ± 0.5A.
Fitting
of this data to a second order polynomial did not change the
conclusions
except to indicate that there might be long term variations in
the spec
trometer calibration or long term thermal drift in the
Fabry-Perot
etalon.
In stage three we assumed that the spectrometer calibration
had
two sources of error: a periodic error lodged somewhere in the
motor-
drive,slave screw,and master screw train, and a long term
mechanical
distortion of the spectrometer body due to thermal drift. By
observing,
with a cathetometer, the rate of passage past a cross-hair, the
teeth
in particular bevel gears on the drive shafts leading to the
master
screw, as well as the rate of turning of the drive-box selector
dial,
we determined that the error in the drive up to the master screw
was
accurate to ± 0.1&. One revolution of the master screw
corresponded
to 50&. With the spectrometer drive set at 2 A/min, a
periodic error
O of ± 0.1A would show up in the field of view as the early or
late arrival
by ± 3 seconds of the final tooth in the bevel gear, a time
interval
measurable with a stopwatch. The master screw was further
checked by
placing a depth gauge against the end of the grating table arm
resting
against the master screw nut block (see figure 5). The observed
depth
gauge reading was compared with the expected reading as the
screw
-
VDG BEAM
TOP VIEW:
FOIL
CUP GRATING
SCREW DRIVE^
GRATING MIC-""^*^ CAM
PHOTOTUBE
Figure 5. Top view of monochromator with incident beam passing
through foil and into Faraday cup.
Light passes through the entrance slit, reflects off the grating
seated on a base attached to a spring loaded arm which, riding
along the adjustable cam, is driven by the master screw, and
through the exit slit to the phototube.
N) N>
-
23
turned through one revolution, the fractions of a revolution
noted by
the passage past a cross-hair of a tooth in a bevel gear (25
teeth)
observed with a telescope. The pitch of the master screw was
previously
O determined to be 0.6983 mils/A. A ± 5 mil feeler gauge rested
against
the top of the nut block to watch for screw and bearing
wobble
(Ingalls 1952a,b,c). Although no noticeable wobble was measured,
the
O master screw was found to have a ± 0.5A error per revolution.
We
decided that the most dependable remedy to this problem was to
replace
the entire master screw assembly with a new one from McPherson.
When
the new master screw assembly was installed, the grating table
was
completely dismantled, cleaned, and reassembled. During
reassembly of
the table, ball bearings upon which the table rides were
repositioned
so as to avoid noticeable wear spots in the kinematic grooves.
The
entire master screw and drive were again thoroughly lubricated,
a ritual
that was followed at regular intervals during the nine months
the spec
tral data were recorded.
In stage four, the new master screw was checked for periodic
error and wobble. The improvement was dramatic. The detectable
period
ic error did not exceed ± 0.1&, a value we felt to be
consistent with
the ultimate capability of the instrument. We then determined
the spec-
O trometer wavelength calibration in the region 2500 - 6000A
using wave
lengths from stationary sources of Hg, Ne, and He. The resulting
curve,
a plot of wavelength correction versus McPherson wavelength,
showed a
smooth, monotonic change with the measured points scattered
within
± O.lA above and below this curve. However, it remained obvious
that
remedying the errors in the master screw did not remove all
errors in
-
the calibration. There remained unexplained day to day shifts in
the
location of the peak centers of calibration wavelengths
indicating
potential systematic errors of greater than ± O.lX. for data not
recorded
close together in time. The greatest source of these errors was
corre
lated with changes in the temperature gradient top and bottom of
the
spectrometer body which resulted from changes in the heating of
the
bottom of the spectrometer when the drive motor was turned on
and off.
It, therefore, became a mandatory procedure to turn the drive
motor on
at least one-half hour before taking data and to leave it on for
the
duration of the data taking day. In addition to the thermometer
atop
the spectrometer, a second thermometer was placed in close
proximity to
the motor and spectrometer base. Readings from both thermometers
were
recorded continuously during all data taking. A fan was
installed to
continually flush fresh air under the spectrometer and thereby
prevent
stagnation of heated air under the spectrometer from nearby
pumps and
motors. We attempted to relate the ambient room temperature and
temper
ature differential top and bottom of the spectrometer to
observed
wavelength .shifts and changes, in line width, but our efforts
were incon
clusive and not pursued. Enclosing the entire spectrometer in a
temper
ature controlled environment was considered impractical. The
temperature
sensitivity of the spectrometer was accepted as an inevitable
source of
error in the wavelength calibration and was ultimately the
limiting
factor in the quality of our wavelength determination.
It might be concluded from our experience above that the
McPherson 225 is not the instrument to use for these high
quality spec
tral studies; nevertheless, it was the instrument available and
our
-
25
calibration tests and remedies enabled us to thoroughly and
confidently
understand its characteristics.
Spectrometer Refocusing and Intensity Enhancement
The limitation on the quality of the data that can be
obtained
from a beam-foil source is governed by the line width of the
spectral
lines. Poor line width leads to loss of resolution, washing out
of
spectral details, and the poor determination of line centers.
This,
in turn, leads to poor calibration curves and subsequent poor
wavelength
determinations. In the preceding sections the spectrometer
calibration
limits were discussed. In this section attention is given to the
mini
mization of spectral line widths produced by the beam-foil
source.
From the consideration of the relationship of spectrometer
reso
lution to through-put luminosity CJacquinot 1954), it is clear
that
narrowing the line width alone does not improve the spectrometer
perform
ance. Reducing the line width to increase the resolution
decreases the
spectrometer through-put, and increases the detection time. In
practice,
one strives for a balance between narrow line width and high
luminosity.
This is especially important for beam-foil sources where there
is low
inherent luminosity and limited foil lifetime. It is not useful
here to
discuss the theory of the grating spectrometer (Stroke 1967,
Davis 1970)
or the origins of line width in fast ion-beam sources (Stoner
and Leavitt
1973). We merely review here the salient features of grating
spectrom
eters and spectral line width as they pertain to the McPherson
225 and
this experiment.
-
26
The optimum position settings of the entrance and exit slits
on the Rowland circle for stationary source focus (SSF) of the
McPherson
225 is provided by the manufacturer. These settings are achieved
by
two adjustments: the positioning of the slit housings in their
respec
tive tube extensions in the spectrometer body, a positioning
that
affords a coarse focus setting, and moving the grating table
precisely
by means of a micrometer screw (see figure 5). With the entrance
and
exit slits equal and set at approximately the optimum slit
width
(Sawyer 1963), we observed the change in line width as a
function of
the micrometer setting for a stationary source wavelength
(typically
Hg 5461A, 3650A, or 2537A). The minimum in the plot of line
width
versus micrometer setting established the optimum focus setting.
We
thereby confirmed the SSF settings for the two gratings used in
this
experiment. The values of the body-tube separations for the
entrance
and exit slits and micrometer settings are listed in table 2.
The
cammed arm against which the grating table arm rides assures
that once
the spectrometer is optimally focussed for one wavelength it is
focussed
for all wavelengths. The instrumental line width is governed by
the
dispersion of the spectrometer and, for both gratings used in
this
experiment, was 16.6 A/mm. For 50 p slits this yields a line
width of AXj = 0.8A.
The actual observed line width, however, depends not only on
the instrumental line width, but the source line width as well.
The
actual line width properly involves the convolution of the
natural line
width (normally neglected as it is typically less than O.OIOA),
line
broadening effects in the source, and the instrumental width.
The line
-
broadening effects from the source are the Doppler broadening
due to
the velocity of the ion-beam and finite acceptance angle a of
the spec
trometer, and multiple scattering of the ion-beam in the foil.
The
nonrelativistic (valid for the energies encountered in this
exerpiment)
Doppler broadening due to finite acceptance angle is given
by
AAq = 2XQg sin a/2 . (2.5)
For small values of a, equation 2.5 becomes
AXn = X g a (2.6) Do v
where Xq is the rest frame wavelength, g = v/c with v the beam
velocity,
and a the acceptance angle of the spectrometer. For example,
consider
a 5 MeV 0t*Kr+ beam so that 3 = 0.0113, and let a = 1/10. Then
AX̂ =
1.1A for X = lOOoA and AX_. = 6.8A for X = 6000A. We can reduce
the o Do
Doppler width for a given Xq and g by decreasing a through
masking the
grating with, however, a resultant decrease in through-put for
the
spectrometer.
The angular spread in the beam due to multiple scattering in
the foil produces a resulting line width described by
AX = H JuTTo1 . (2.7) so '
This result is similar to the Doppler width with the acceptance
angle
replaced by /£n 2 • 0. Here 0 is the r.m.s. multiple scattering
angle
(see discussion of table 8, page 69) Again for a 5 MeV 81fKr+
beam
0 = 2.3 x 10 2 rads., and AXg = 0.2A at 1000A and 1.3A at 6000A.
For
a 2 MeV K̂r beam these values are multiplied by 1.6.
-
28
If we assume that the line profiles due to instrumental
effects,
Doppler broadening, and multiple scattering can all be described
by
Gaussians, the resultant total line width is a simple sum of
quadra
tics, namely,
AX2 = AX2 + AX2 + AX2 . (2.8) T I D S
Values of AX̂ , for 50 u slits are listed in table 3. It is
evident
from the above discussion that the ability to do any medium
resolution
(X/AX ̂ 10,000) spectroscopy with a beam-foil source is severely
limited
by the Doppler broadening. Recent investigations, however, by
Stoner and
Leavitt (1971a,b), Leavitt and Stoner (1972), and Leavitt,
Robson, and
Stoner (1973) have shown that the Doppler broadening can be
significant
ly reduced without simultaneously severely reducing the
spectrometer
through-put. Indeed, in the instance of using a lens imaging
technique,
aptly named "intensity enhancement," the available intensity
was
Table 3. Line widths of krypton and nitrogen beam-foil spectral
lines.
Ion-Beam X (X) A^-f(^) O T
5 MeV 8lfKr+ 1000 1.4
6000 7.0
2 MeV 8ItKr+ 1000 1.1
6000 4.9
1.67 MeV 28N2 1000 1.4
6000 6.9
-
o improved while providing line widths of 1 - 2A. We discuss
below the
two techniques, refocusing the spectrometer and intensity
enhancement,
which we employed to reduce the Doppler broadening in our
beam-foil
spectral source.
Refocusing
The theory behind refocusing of a concave grating
spectrometer
has been thoroughly discussed by Leavitt, Robson, and Stoner
(1973).
By moving the exit plane back a distance
D = XQg/K (2.9)
where K is the plate factor (reciprocal linear dispersion) for
the
spectrometer, the exit slit is placed at the convergence point
of the
Doppler shifted rays coming from the fast-ion beam. For the
McPherson
225, the exit slit is not typically moved. Rather, by means of
the
micrometer adjustment, the cam akd grating table are moved back
a
distance D/2. Refocusing, in this fashion, for a particular Aq
insures
the spectrometer will be refocused for ail Xq, as was also true
for the
SSF, for the particular beam velocity v.
In practice we refocused the spectrometer beginning at the
SSF.
The position of the entrance slit was left undisturbed. We
selected a
particular XQ and beam energy of interest from which D was then
deter
mined. We next determined the distance along the cam (figure 5)
at
which the grating table arm was located from the zeroeth order
position
for the X under consideration. This enabled us to calculate what
o
fraction f this position is to the position of the arm at
6000A
-
30
(the grating arm moves a distance 0.12"/1000X along the cam).
When the
cam micrometer is displaced a distance x, the grating table and
grating
are moved back a distance fx. This in turn is equivalent to
moving the
exit slit a distance 2fx off the Rowland circle. For a refocus
distance
D, we want, therefore, to move the micrometer a distance x =
D/2f.
Often, however, the beam velocity is so large that the
micrometer travel
is not sufficient to refocus for the entire distance D. Under
these
circumstances the exit slit must be moved as well. For the
energies
used in this experiment, all refocusing was accomplished with
the cam
micrometer, the exit slit remaining at its position for SSF.
Starting
with the SSF values in table 2, the calculated micrometer
settings used
for 5 MeV ahKr and 1.67 MeV 28N2 were 0.243" for the 1500&
blaze
grating and 0.168" for the 5000X blaze grating. The actual
values
used in this experiment were 0.248" and 0.200" respectively.
Hence,
for the 1500$. blaze grating the spectrometer was refocused for
5 MeV
01tKr+. The resulting line width for 2 MeV 8lfKr was found to be
essen
tially the same as for 5 MeV 8ltKr+ permitting us to perform our
spectral
scan at different energies with one refocus setting. The
refocus
O setting of the 5000A blaze grating represents a compromise
setting
between 2 and 5 MeV 8lfKr. The line width as a function of
wavelength
is displayed in figure 6.
Data which were ultimately to be analyzed were taken with
the
spectrometer refocused and equal slit widths of 50 y or 100 y
(except
for one scan performed with 75 y slits). The 100 y slits were
typically
used in regions with weaker lines. Both choices of slit
settings
-
2.0
1.8
°S
2 X $ li.
JZ +-
-g 5 a> c:
1.6
i:o
© - 2 MeV Kr, 1500 A blaze, refocus
® - 5 MeV Kr. 1500 A blaze, refocus
© - average of 2-5 MeV Kr. 5000 A blaze, refocus
1.4 -
©
1.2 -
1000 2000 3000 4000 5000 6000
wavelength (&)
Figure 6. Spectral line FWHM as a function of wavelength for the
several refocused conditions of the spectrometer. w
-
32
intentionally exceed ws0pt and ŵ 0pt discussed by Leavitt,
Robson, and
Stoner (1973) because of the low intensity available in the
krypton
beam-foil source. The consequent line widths are therefore
slightly
larger than the optimum line width discussed in the above
paper.
Intensity Enhancement
For a spectrometer set at SSF, Stoner and Leavitt (1971a)
and
Bergkvist (1976) have shown that a suitably placed cylindrical
lens on
the optic axis between the fast-ion beam and the entrance slit
will
obtain narrow line widths with attendant large entrance slit
widths.
The lens permits an increase in through-put of the spectrometer
because
of increased entrance slit width while maintaining narrow line
width
through partial compensation of the Doppler broadening. In this
experi
ment, the average observed increase in peak intensity was 5.8
fold over
results taken under the same conditions with the spectrometer
refocused.
This increase in intensity by use of a cylindrical lens is
called Inten
sity Enhancement and the lens, Intensity Enhancement Lens (or IE
Lens).
O The resultant decrease in the total line width at 6000A was a
factor of
three compared to results obtainable with the spectrometer
viewing a
fast-ion beam at SSF.
The results of Stoner and Leavitt (1971 a) show that the
focal
length f of the cylindrical lens is related to the beam velocity
v, the
rest frame wavelength XQ, the spectrometer plate factor K, the
grating
angles of incidence i and diffraction r, the grating focal
length fg,
and the lens-grating distance p by
-
33
W V*WO J. I jj~x __ p UVO X I -1-
cK cos il f r cos il f V. ./ v. s ./ s (2.10)
where is the refocus distance of equation 2.9. Effectively this
lens
produces an image of the fast-ion beam, collected over a larger
accept
ance angle than that of the spectrometer, at the entrance slit
where the
Doppler shifted wavelengths across the image are compensated for
by the
linear dispersion of the spectrometer. For the IE lenses used in
this
experiment (six in all), (p-f)/fg = 1 to within 0.5% and cos
r/cos i =
1.01 at 1000A and 1.05 at 6000A. Hence f - D̂ . The cylindrical
lens
is placed approximately a distance f (Berqkvist 1976) from the
entrance
slit. From equation 2.10 it is seen that a particular f is
optimum only
for a particular Xq. The selection of lenses to enable study of
an
extended spectral region, therefore, represents a compromise.
These
choices are best made by recasting equation 2.10 in a different
form.
We replaced the focal length of the cylindrical lens with f =
D/2[n(X)-l]
where D is the diameter of the lens and n is the wavelength
dependent
index of refraction of the lens material (Jenkins and White
1957).
Expressing the beam velocity in terms of its energy E, we
find
In figures 7 and 8 are plotted X versus E for the IE lenses used
in this
experiment (the IE lens number along with its diameter is
tabulated in
table 4) for a 8l*Kr and a 28N2 beam. The lens material is fused
quartz
and its index of refraction has been tabulated for various
wavelengths
(Handbook of Chemistry and Physics 1971). By drawing a vertical
line
X •O • SCXFT
(2.11)
-
34
6000
5500
5000
4500
o<
*< 4000
DC I— o z UJ 3500
UI
1 ̂3000
2500
931A
2000
1500 0 2 3 7 4 5 6
ENERGY E (MeV)
Figure 7. Focus wavelength X versus energy E of 8tfKr+ beam for
IE lenses 2 through 8.
-
35
6000
DK (n-l)
5500 • 931A
5000-•
4500- -
©<
^ 4000- -
X H* O z UJ _1
3500- -
UJ
p 3000--
2500- -
2000 -
1500
0 2 7 3 5 4 6
ENERGY E (MeV)
Figure 8. Focus wavelength X versus energy E of 28N* calibration
beam for IE lenses 2 through 8.
-
Table 4. Characteristics of the intensity enhancement
lenses.
a - Wavelength at which minimum linewidth occurs, b - Minimum
linewidth observed. c - Useful wavelength range.
IE 2 MeV &tKr 5 MeV 84 Kr Lens No. D(mm)
ent. CM)
exit CM) Aa(A)
h ° AX°(A)
C O 6 X (A)
ent. CM)
exit CM)
Q O AaCA)
b ° AX CA)
c o 6X (A)
2 1.37 ± 0.03 450 50 3010 1.3 2750-3950 350 (some 0 1000)
50 2800 1.6 1550-2800
3 2.03 ± 0.03 450 50 4150 1.7 3800-5350 450 50 2400 1.4
2200-3900
4 2.45 ± 0.03 450 50 6000 1.7 5200-6000 450 50 3700 1.8
3400-4100
5 3.00 ± 0.03 - - - - - 45051000 50 5300 2.2 4100-4925
6 3.56 ± 0.03 - - - - - 1000 50 5100 2.2 5800-5600
8 4.00 ± 0.07 - - - - - 1000 50 5810 2.5 5400-6000
w ON
-
for the beam energies of interest through this family of curves,
we
selected the appropriate lens to use for a particular wavelength
and
wavelength range. It is important to realize, however, that
this
2 family of curves is sensitive to the value of [(DK/2)
(931A/2)] and,
therefore, to errors in D and K. For example, if the value of
the
above expression is changed by 10%, the resulting curves are
shifted
along the energy axis about 1/3 their respective spacings. The
errors
which arise from neglecting the factor
rc£sr) fefl COS X I f ̂' S
are easily incorporated into an error in D. To account for
errors in
the constants of equation 2.11 and for changes in the value of E
due to
energy loss in the foil we found it useful to plot Xq versus D
for the
values of E (figure 9) encountered in this experiment. Hence
D = 8̂E/951A Xq . (2.13)
The values of E chosen are for 2 MeV and 5 MeV 81tKr incident on
a
6 Mg/cm2 carbon foil. The energy loss in the foil for 1.67 MeV
28N2
and 5 MeV 8lfKr+ are negligibly different so that their g's are
the same
and one curve describes both beams. We can now see (figure 9)
what
influence errors in our parameters, all lumped into D, have on
our
choice of optimum wavelength and wavelength interval when using
IE
lenses to produced our observed spectra. In table 4 we summarize
the
relevant IE lens parameters used in this spectral study. We
determined
the optimum slit width by examining with increasing slit widths
the
change in line width to peak intensity.for a particular spectral
line.
-
38
6000
5500
5000
4500
o<
X h O z Ui -J
3500 •
> $ 3000 •
2500 •
n= — /8E. U K V 93| a
2000 •
1500 0 2 3 4
I E Lens Diameter 0 (mm)
Figure 9, Focus wavelength, \ versus IE lens diameter D.
Curve A is for 2 MeV K̂r"*" incident on a 6 ygm/cm2 carbon foil.
Curve B is for 1.67 MeV anc* 5 MeV K̂r4" incident on a 6 ugm/cm2
carbon foil.
-
We selected that slit width which, if increased further, would
have pro
duced a larger line width with no significant improvement in
intensity.
Table 4 also lists the minimum observed line width in each
wavelength
interval accessible to the various IE lenses. Because of the
increased
viewing angle of the IE lens, the foil wheel was moved upstream
to per
mit an unocculted view of the beam.
It was not an expressed objective of this spectral study to
per
form a detailed analysis of the intensity enhancement technique.
Never
theless, several problems were evident, suggesting future
investigations.
The derivation of the focal length relation (equation 2.10) is
intui
tively convincing, but no thorough treatment after the fashion
of
Leavitt, Robson, and Stoner (1973) of the beam-lens-spectrometer
system
has been accomplished. Bergkvist (1976) has treated the case of
a beam
with zero cross-section, but ignores the more realistic finite
beam size
case. In addition, there is no theory of how line width should
vary with
wavelength. The observed behavior is that the line width goes
through
a minimum near a particular wavelength for a given IE lens. This
needs
to be explained, as well as the apparent disagreement between
the
observed wavelength with minimum line width and the calculated
wave
length. A more reasonable agreement between these two
wavelengths was
obtained by decreasing the product DK by 7-8%, part of this
decrease
accountable if one includes the neglected geometric factors
(equation
2.12). Indeed, it is by no means obvious what effect spherical
aberra
tion, surface defects, and diffraction by the cylindrical lens
will have
upon the resultant fast-ion beam image. Finally, we do not know
what
influence variation of the downstream intensity due to decay of
atomic
-
states will have upon the resultant spectral profiles,
observed and computer-fitted line profiles of isolated
with IE lenses were all symmetrical.
although the
lines recorded
Recording and Reduction of Data
In figure 10 we show the spectral region 400 - 6000& and
the
particular combinations of photodetectors and gratings chosen to
record
the 2-5 MeV 8£fKr+ and 1.67 MeV 28N* Calibration) beam-foil
spectra.
We oriented ourselves to the strongest lines available in the
krypton
and nitrogen calibration spectra by performing survey scans from
400 -
6 6000A with the spectrometer refocused, 300 y slits, and at a
rate of
O 50A/min. The incident krypton beam energies were 2, 3.6, and 5
MeV.
Using these scans as our guide, we made multiple scans of the
strongest
krypton spectral features, spectrometer refocused, using smaller
slit
widths and slower scan speeds. As stated earlier, almost all of
these
scans were recorded at 0.1 or 0.2 A/chan with 50 or 100 p slits.
The
number of multiple scans taken for each spectral feature was
arbitrary
and so chosen as to assure a signal to noise ratio of about
10:1. We
recorded the entire region from 400 - 1600A using 100 p slits at
0.2
X/chan. These scans insured that we obtained all the weaker
spectral
features in this region as well. The spectrometer was then
adjusted
for SSF and the IE lenses installed. Krypton spectra for a 5
MeV
incident beam were then recorded from 1600 - 3000A at
0.2&/chan. No
spectra were recorded in this region at 2 MeV incident krypton
beam
energy because of a lack of the appropriate IE lenses. From
3000- 6000A
the entire krypton spectra for both 2 and 5 MeV incident beam
energies
-
©©-Short Scans (541 F)
X
-4219 EIC-
IP28-541 F-
-4-1000 2000
•1500 A blaze-
4- -4- X 3000 4000 5000 6000
5000 & blaze-
Photodetectors
Gratings
Figure 10. Detector and grating combinations used to record Kr
and N2 spectral scans.
Horizontal scale is wavelength range (X) • •f*.
-
42
were recorded at 0.2 A/chan using IE lenses. Strong, individual
features Q
were also multiply scanned at 0.1 A/chan. Selected, complex,
spectral
features were recorded at incident beam energies of 3 and 4 MeV
to provide
additional intensity information as an aid to unravelling their
origins.
Interspersed among these krypton scans were the 1.67 MeV Ng
calibration scans taken with the spectrometer under the same
conditions
and typically preceding and following a particular sequence of
krypton
scans. With the spectrometer refocused, the nitrogen scans were
of the
O strongest observed lines and recorded at 0.05 A/chan with 50 y
slits.
O In the region 2900 - 6000A, the nitrogen spectra were recorded
entirely
using intensity enhancement at 0.2 A/chan with scans over
selected
strong lines at 0.1 A/chan.
The record of each multiple scan consisted of intensity
versus
multiscaler channel number, starting point of the spectrometer,
scan
scale in Angstroms per channel, number of repetitions of each
scan and
observed beam current. For scans of such duration that foil
changes
were necessary during the course of a scan, the wavelengths at
which the
changes were made were noted. Temperatures top and bottom of the
spec
trometer were always recorded.
The results of the krypton and nitrogen scans were printed
out
on strip charts and the digital information on paper tape. The
charts
became an indispensible visual record, greatly aiding the
computer
fitting of all the spectral data. In figures 11 and 12 are
sample scans
of parts of the krypton spectra.
During the data reduction, these charts were displayed en
masse
on 4' x 8' celotex sheets to permit rapid visual comparison
between scans
-
CSA KrSC CSA Kr EL
3380 3390 3400 3410 3420
WAVELENGTH (X)
3430
2 MeV KRYPTON ON C FOIL (~6fiq /cm4)
entrance slit > 450fi, exil slit 50u
2.2/xAMP beam, 4 scans
Intensity enhancement lens used
Kr 21 ?
- - 1.40 A w 100
3440 3450
Figure 11. Intensity enhanced spectra of 2 MeV krypton in the
region 3375 - 3455X.
Seen here in second order. 4̂ C/l
-
Kr3Zm (8-7) (2—order)
400
5 MeV KRYPTON ON C FOIL (~6/xg/cm2)
entrance slit: lOOO/i, exit slit: 50fj.
3.5ft AMP beam , 5 scans
Intensity enhancement lens used KrX (12—10)(2—order)
a a> u> Q 300 to s Kr 3ZHT (8-7) (2— order)
- 1.67 A to 200 z UJ
100
5970 5960 5940
WAVELENGTH (A)
5920 5930 5950
O Figure 12. Intensity enhanced spectra of 5 MeV krypton in the
region 2959 - 2985A.
Seen here in second order.
-
over the same spectral region at different energies and other
spectral
regions at the same energy. These displays become in large scale
what
photographic plates are to the classical spectroscopist. The
digital
results were transferred manually to IBM cards for later
computer analy
sis. For quick orientation in locating a particular scan, a
"road-map",
divided according to grating used and incident beam energy, was
drawn
O showing the location of each scan in the region 400 -
6000A.
All the krypton and nitrogen spectral scans were analyzed
either
by hand or computer fitting of the intensity profiles. If, by
visual
inspection, the signal to noise ratio of weak spectral features
was so
poor that computer fitting was of doubtful advantage, a profile
was hand
drawn over the spectral feature and the peak center determined
from the
profile center at full-width-half-maximum CFWHM). The channel
number,
determined in this way, was decreased by one to strike agreement
with
the channel numbers assigned from the computer fitting
program.
We computer fitted the spectral data with program GAUS2Z
(see
Appendix A). To accomplish this task it was essential that we
first
determine the line width as a function of wavelength for the
various
conditions of the spectrometer under which our data were
recorded. To
this end we fitted selected strong single lines with GAUS2Z
allowing the
program to determine the best line width. The resulting line
widths
versus wavelength were then plotted and a smooth curve was drawn
through
the data. These curves established the line width used as an
input
parameter for fitting the remaining spectral features.
The results of each computer fitting provided the x2 of the
fit,
peak location (in channel number), uncertainty in the peak
location,
-
peak height and its uncertainty, FWHM and its uncertainty, and
the
calculated area under each peak. When the x2 and visual
appearance of
the fit were deemed satisfactory, we stopped the fitting process
and
converted the peak channel number to observed wavelength. In
this
straightforward, albeit tedious, manner the observed wavelengths
of
approximately 2500 krypton and 750 nitrogen lines were
determined.
These wavelengths, to facilitate further treatment, were punched
onto
IBM cards, each card containing a wavelength, its uncertainty,
intensity,
scan identification, and brief comments about the fit.
From the observed nitrogen calibration wavelengths we
proceeded
to construct calibration correction graphs. As all data had been
taken
in vacuum, we decided to calibrate all our results in terms of
vacuum
O values, including observed wavelengths above 2000A. This
involved con-
verting the tabulated nitrogen calibration wavelengths used
above 2000A
to vacuum values. This was accomplished directly by programming
the
NBS Wavenumber Tables (Coleman, Bozman, and Meggers 1960) into
the
HP-65 calculator (Cardon 1975). The lines in the observed
nitrogen
spectra were identified from Striganov and Sventitskii (1968).
Because
2%2 has a q/m ratio of 28, C0+, Si+, Fe++, A1H+, and MgH* were
poten
tial contaminants in the incident beam and wavelengths from
these ele
ments were considered possible intruders in the nitrogen
calibration
scans. However, in the final analysis, the 652 lines used to
establish
the calibration graphs were mostly nitrogen with the remainder
being
oxygen and carbon lines. The values of AX = X „„ - X , were corr
vac HB obs
plotted versus We then least-squares fitted a straight line
to
the plotted data obtaining the best values for slope and
intercept.
-
47
In this way we established calibration for the 5 MeV 8lfKr+
data. The
beam velocity for 2, 3, and 4 MeV 8tfKr+ was different, however,
from the
1.67 MeV Nj> data. For the IE data taken at 2 and 5 MeV, we
compared
prominent lines at both energies and established the calibration
of the
2 MeV results based on the 5 MeV results. For the refocused data
taken
o below 1600A, there was no noticeable shift of the 2 MeV
spectra with
respect to the 5 MeV spectra. The same calibration was used for
both
energies. For the data taken with the spectrometer refocused and
the
5000A blaze grating, a systematic correction to the 5 MeV
calibration
was applied to the 2, 3, and 4 MeV 8I*Kr+ results. This
correction was
necessary to account for the relativistic transverse Doppler
shift (Jack
son 1962, p. 364). This red shift AX of the rest frame
wavelength Xq is
X 2 ax = ~t $ (-2a4)
for the velocities v encountered in this experiment. The
correction
applied to the wavelengths obtained at 2, 3, and 4 MeV, after
determining
their vacuum wavelengths with reference to the 1.67 MeV
calibration,
was X (5-E)
AX = 78204- C2-15)
o where E is the beam energy in MeV. At 5000A, for example, the
correc
tion to the 2 MeV data accountable to the transverse Doppler
effect is
0.19&. We summarize the parameters used to establish the
calibration
of the spectrometer for the diverse conditions encountered in
this
experiment in table 5. A program LAMSORT (see Appendix B) was
written
that read the cards containing the observed krypton wavelengths
and
-
48
Table 5. Spectrometer calibration parameters for the McPherson
225.
AX — AX , + B ,. X corr obs vac
X , + AX . obs corr
Energy Grating Arrangement (MeV) A B
1500A Refocus 2,5 0.000038 12.11A
ISOOK IE lens 2 5 0.00084 11.70&
1500& IE lens 3 5 0.00084 12.00A
5000& Refocus (before Sept. 18, 1973)
2,3,4,5 -0.000109 -3.56A
5000X Refocus (after Sept. 18, 1973)
2,3,4,5 -0.000109 2.49A
5000A IE Lens 2 2 0.000307 4.15&
5000A IE lens 3 4,5 0.000186 2.2lX
5000A IE lens 3 2,3 0.00000946 2.40A
5000& IE lens 4 2 -0.000223 5.17&
5000A IE. lens 4 5 0.00017 3.79X
5000A IE lens 5 5 -0.000075 3.05A
5000X IE lens 6 5 -0.000173 3.59A
5000A IE lens 8 5 -0.000727 4.62A
-
converted them to calibrated vacuum wavelengths using the
parameters A
and B in table 5. The result of this reduction of the data taken
with
the thirteen different calibrations of the spectrometer, and
accounting
for the transverse Doppler effect, was a listing of 2392
calibrated wave
length measurements. From this list, multiple measurements of
the
same spectral line were reduced to unweighted averages. For
isolated
single lines this was straightforward. In the case of line
complexes
and blends it was often difficult to decide which measurements
belonged
together, as the spread in the observed wavelengths for a
particular
line often overlapped the wavelengths of nearby lines. For each
of
these cases it was necessary to study the individual scans and
make
judicious guesses. With the averaging process, the line list was
re
duced to 1187 lines. A search was next made by hand, wavelength
by
wavelength, for second and,possibly, third order lines. The
wavelength
o response of the photodetectors and the lower wavelength O
1600A)
transmission cutoff of the IE lenses greatly facilitated
isolating
those regions where higher orders were likely interlopers. The
possi-
o bility of second order lines appearing in the region 400 -
800A from the
o first order lines in the region 200 - 400A was carefully
examined although
acknowledged unlikely because of the response of the grating
coating in
this spectral region (Samson 1967) and our extreme displacement
from the
grating blaze. Data were obtained for 5 MeV krypton in the
region 100 -
400A with a grazing incidence VUV spectrometer (Mclntyre and
Bernstein
1976) which showed no strong krypton features that would likely
pass to
the second order with the McPherson 225. We also checked, to no
avail,
for second order wavelengths of transitions seen in a krypton
seeded theta
-
o pinch light source observed between 209 - 319A (Englemann,
Thomson, and
Monaghan 1976). We concluded that the 1500X blaze grating in
the
McPherson 225 is not responsive to wavelengths below
approximately 400X.
When a second or third order line was identified (there were
o only 12 third order lines with the 1500A blaze grating and two
third
o order lines with the 5000A blaze grating), it was averaged
with the
first order results, the wavelengths weighted according to their
order
(1 for first order, 2 for second order, etc.)- If a line could
not be
clearly identified as to its order it was assumed to be a first
order
line. A histogram was plotted of the difference between the
first order
wavelengths and the average wavelength for all orders, where
possible.
The histogram was symmetric about and peaked at the zero
wavelength
difference, indicating no systematic errors in calibration.
Confidence
in the spectrometer was further gleaned from the observed small
scatter
among the multiple measurements of particular wavelengths taken
with the
spectrometer under the diverse calibration conditions. Indeed,
it was
from the standard deviation
I ZX* - nX2
' = V • * C2'16)
where is a particular measurement, X the wavelength average, and
n
the number of measurements (n > 3) that the wavelength
uncertainty for
three or more measurements was established. The were rounded
off
o to the nearest 0.05A and became the accepted uncertainties. If
there
was only one measurement for a particular wavelength, the
assigned un
certainty was two channels for the scan rate at which the
measurement
was taken and for two measurements it was the deviation of the
values
-
51
o from the average rounded to the nearest 0.05A. Furthermore,
any
uncertainties greater than 0.6& resulted in the wavelength
being
deleted from the final list. We plotted a histogram of the
uncertain
ties in our final wavelength list (see Appendix C). The plot
was
o symmetric about the peak uncertainty of ± 0.35A; the observed
uncer
tainties extending from ± 0.1-0.6A. Although our observed
wavelengths
are uncertain to order O.lA, they are tabulated to the nearest
0.01A
so as to preserve and display behavior in this least significant
digit.
o We compared our wavelength list below 1200A with results
tabu
lated in Kelly and Palumbo (1973). These wavelengths are so
identified
in Appendix C. The agreement between our results and those
previously
tabulated and assembled in Kelly and Palumbo is often well
within the
uncertainties assigned our observations. Thus, we further
supported
the validity of our calibration and method of establishing
uncertainties.
No attempt was made to determine the spectral, response of
the
o spectrometer between 400 - 6000A. The intensity or intensities
listed
for each wavelength in Appendix C must therefore be acknowledged
as
approximate count rates for a spectrometer under similar
conditions.
Because the spectral lines were recorded under greatly differing
condi
tions, leading to variations in recorded intensity, all the
intensity
values, realizing that the spectral response was being ignored,
were
normalized to a common beam current, slit settings, and
multiscaler
dwell time. Intensities recorded with the spectrometer refocused
were
all normalized in units
-
52
v-umiua + ~ 50 y slits • 0.6 sec dwell time • 10 yamp beam
current
Similarly, intensities recorded using intensity enhancement were
norma
lized in units
counts ,2 450 y ent - 50 y exit slits • 0.6 dwell time • 10 yamp
beam current
Because the intensities recorded with intensity enhancement are
depen
dent upon transition lifetimes and the consequent post-foil
light
distribution whereas the refocus intensities are taken near the
foil and
from a well-defined portion of the beam, the refocus intensities
were
considered the more reliable. Where both refocus and IE
intensity
values existed for the same spectral line, the ratio of IE
intensity
to refocus intensity was calculated. These ratios were plotted
in a
histogram from which a conversion factor, refocus to IE
intensity, was
determined. This factor, an average of the results for 2 MeV and
5 MeV
krypton, was 5.8. We thereby reduced all intensities to refocus
values
and expressed the results in the units of equation 2.17. Note
that
this unit can also be written as [counts/C50yslits • 6 yC)]
although
the dwell time is now concealed.
The krypton spectra line list (Appendix C) extends from
417.44-
o 5595.96A and consists of 965 lines. Of these, 110 have been
previously
observed and/or identified by other authors. We discuss in
Chapter 5
these previous observations in addition to new identifications
which
follow as a result of this investiation. In figure 13 we plot a
histo
gram of the number of our observed krypton wavelengths in this
study.
-
53
50-
CO
f 40-c _a> a
-o a> > a> in £X