THE BEAM-FOIL SPECTRA OF KRYPTON (2 TO 5 MEV)

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Authors Cardon, Bartley Lowell, 1940-

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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

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

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

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.

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

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

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

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

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.

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.

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

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-o a> > a> in £X