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“‘3

lIBRARY
Michigan State
University

This is to certify that the

dissertation entitled

Low-Lying Dipole Strength in 200

presented by

Erik J. Tryggestad

has been accepted towards fulfillment
of the requirements for

Ph.D Physics

 

 

degree in

MAML/

Major professor

Date lo/fl/H

MS U i! an Affirmative Action/Equal Opportunity Institution

 

 

 

 

 

 

PLACE IN RETURN Box to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

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6/01 c-JCIRCIDateDuepss-pts

LOW-LYING DIPOLE STRENGTH IN 200

By

Erik J. Tryggestad

A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2001

ABSTRACT
LOW-LYING DIPOLE STRENGTH IN 200
By

Erik J. Tryggestad

Theoretical calculations suggest that a significant fraction of dipole (E 1) strength is
shifted towards lower excitation energies in neutron-rich nuclei. The availability of fast
radioactive beams allows the possibility for probing the E 1 strength function in un-
stable nuclei via Coulomb excitation. Therefore, we have performed two experiments
at the NSCL at Michigan State University to investigate low-lying E1 strength in
both 180 and 200 via virtual photon scattering. 100 MeV/u beams of 18*‘ZOO impinged
on a 30 mg/cm2 enriched 208Pb target. De-excitation “Hays were detected with the
large ORNL—TAMU-MSU BaF2 array placed at forward angles. The 7-ray energies
were Doppler-corrected and a nearest neighbor add-back was performed, improving
the response of the array. The 7—ray energy was correlated with projectile energy-
loss measured with the S800 spectrograph. y-rays having (projectile-frame) energies
between 1 and 8 MeV were collected for both 18O and 20O.

Monte Carlo simulations which have utilized the radiation detection code GEANT
while incorporating known information for 18O and theoretical predictions for 200
were used to make direct comparisons with the experimental results. The analysis
reveals that the observed excitation function for 200 is dominated by transitions re-
sulting from E 1 excitations, while that for 18O is dominated by decays following E2
excitations. We have established the existence of two previously unmeasured 2OO 1‘
levels at 5.35 and 6.85 MeV. The 7-decay branching from these states has been approx-
imately determined, while B(E 1) information has also been extracted. Specifically,

B(E1; 0.00 —> 5.35) T 2 0.062 62 fn12, while B(E1; 0.00 —> 6.85) T 2 0.035 e2 fm2.

To Grandpa

iii

ACKNOWLEDGMENTS

Alas, it has recently been discovered that the experience of finishing a Ph.D. is rather
anticlimactic. From time to time I have had visions of what it would be like being a
“Dr.” - so far I have to say that it is not all it’s cracked up to be. The achievement
of this esteemed title, while not intensely thrilling, has, nevertheless, been personally
rewarding. I am indebted to so many for their support over the years, both academic
and personal.

First and foremost I would like to acknowledge my advisor, Dr. Michael Thoen-
nessen. Thanks, Mike, for taking me on as a student. Perhaps it was good that you
weren’t aware of what you were getting yourself into at the time! Thanks also for
your patient guidance all throughout my naive experimental and data—analysis jour-
neys. Your relatively relaxed approach to mentoring is one which has been ideal for
my personality and also for my problem-solving development. A warm thanks to my
experimental collaborators, from here, ORNL, and abroad. I hope I’ll have the op-
portunity to work with you again soon! Thanks also to my pre—advisor, Dr. Aaron
Galonsky, who first introduced me to the world of nuclear physics when I came to the
lab as an R.E.U. intern. I had a wonderful time that summer of ’95 working with you,
your students and with your neutron-wall collaborators from Hungary and Japan. It
was indeed a worldly experience. I would also like to thank Dr. Thomas Baumann,
for his always-enthusiastic help with so many of my recent struggles, especially thesis
formating questions. Thomas, thanks for putting up with me — you are a god of PAW
and MEX.

I owe a special thank-you to the NSCL computer department and support staff.
The great work you guys do every day is what makes this place run smoothly. From
day-1 I was impressed with the open atmosphere at the lab. People here are always

willing to help solve your problem, which provides for a very friendly and professional

iv

environment. I must also acknowledge the financial support for this study which came
from the NSF.

I would also like to thank certain physics professors at M.S.U., namely Dr. Stump,
Dr. Repko, Dr. Mahanti and (especially) Dr. Zelevinsky for their lecturing abilities
and teaching philosophies which allowed for stimulating courses at a time in my life
when I was most-exhausted mentally! Thank you for sharing your talents!

I owe a wealth of gratitude to the graduate students at the NSCL who, daily,
provide a wonderful, friendly and stimulating environment that is a joy to be a part
of. Thanks (in order of their graduation) to old-timers Jack Caggiano, Heiko Scheit,
Jon Kruse, Don Anthony, Valentina Maddalena, Barry Davids and Marcus Chromik.
Together you represent the old-school breed which the newer generations here strive
to emulate! Thank you, Jon, for being my first friend here, and introducing me to
everything I had to know to get by. For example, Jon, you introduced me to the
Peanut Barrel, to the Beastie Boys (re-introduction), to Spartan sorry-football, to
silicon detectors and oscilloscope etiquette, to Bells Oberon (Black Label too), to fly
fishing, to espresso, to peanut-butter chili...need I go on?? Thanks for convincing me
to come to M.S.U. Thanks also for having me usher at your wedding to Jodi, despite
my bad haircut at the time. You two are one of the coolest couples that I know — I
hope to stay in touch. Jon, Jack, Heiko, Valentina and Barry, especially Barry, thanks
for putting up with my incessant pestering regarding questions of physics. Without
folks like you around I wouldn’t be where I am today. On a more personal note,
Barry, thanks, also, for introducing me to the superiority of pressed coffee, and for
sharing my undying enthusiasm for the International Bread Company. Cheers to the
Bumstead! Don, once god-father of the laboratory, thanks for your conversation, for
your witty attitude, your advice, for your love of beer and food, and for marrying
Poala! I aspire to fix up an old house and throw dinner parties of the caliber that you

and your wife have established. Don, beware of the screen! Marcus, fellow “big-ugly,”

thanks for all the fun times we’ve had over the years. Thanks for helping me with my
thesis experiment. I was lucky to be able to take part in your thesis experiment here,
from which I gained invaluable experience such as how to align a beam pipe properly
by making use of a 2x4. Thanks for looking sad enough to get us free court-side
seats to the 1999 season, big-ten basketball closer against Wisconsin (A-J-Grangerl).
Thanks for participating in ENAM and Euroschool with me, these were fun times.
I promise I will share any royalties, 50-50, that are received from the “Big Ugly’s
Chicken Experience” which will soon be an enticing contribution to the sandwich
entourage at the Peanut Barrel.

And as for the current graduate posse here at the lab, consisting of honorable folks
such as Joann Prisciandaro, Daniel Groh, Ben Perry, Jeremy Seitz, Mark Wallace,
Declan Mulhall, Ryan Clement, Chris Freigang, Paul Heckman, Pat Lofy and Katie
Miller — thanks for being the delightful people that you are! Special thanks to my
office mates Paul, Dan, and Ben for putting up with me. Ben, I’m sorry I called
you “Benjamin,” and I dig that blond hair. Huge thanks also to my group-mate
Paul for all of the left—wing conversations, for helping me with my painful analysis
(I hope I have provided you with some help also), and for loaning me the golf clubs!
Thanks to Mark Wallace for his interest and ability in the sport of volleyball. (No,
I’m not available on Monday to sub.) And finally, thanks to Pat for his enthusiasm,
his perpetual high-and-tight hair cut, and his impromptu D.J.-ing abilities. Pat, it
wasn’t the same without you at our last party...”oh yeah, that’s the spot!” Thanks
for organizing all the softball over the years, it’s been an honor to proudly display

”

the name “Art’s on my chest with the bold “00” on my back.
Thanks so much to my family, who have always been so supportive of me in my
academic pursuits. While you, Mom and Dad, Spren and Maia, may not have always

understood my love of physics, nor felt like you could communicate with me about

the details of my studies, you have always acknowledged me by way of your love and

vi

by your pride, both vocal and demonstrated. Mom and Dad, you have taught me
how to think and how to set goals for myself. Now you have to listen to me complain
about not knowing what to do with the rest of my life!

Finally, I must also thank the newest, most—important addition to my life, my
dearest Angela! While you may not think that you have contributed, you’ve said as
much just yesterday in fact, this is most assuredly not the case. Just being able to
come home to you at the end of every day, to sit with you and vent-away the stress
from hours spent sitting in front of this very computer terminal, both in conversation
and in silence, has made me a very lucky person. You are there for me every day, all
the time. My new life with you has helped me to put all other goals into a humbled
perspective. Because of you, my days on this earth are taken for granted much less-
often, and this gets right down to the meaning of life. My love, I am so looking forward

to our future ventures together.

vii

Contents

1 Introduction 1
1.1 Experimental motivation ......................... 2
1.2 Coulomb excitation ............................ 5
1.3 Accessible states in 18O .......................... 8
1.4 208Pb contributions ............................ 10
1.5 Status of 20O spectrosc0py and shell model predictions ........ 11

2 Experimental details 13
2.1 The 8800 spectrometer .......................... 15

2.1.1 Position-sensitive CRDC detectors ............... 17
2.1.2 Ionization chamber and scintillation detectors ......... 19
2.1.3 S800 electronics .......................... 19
2.2 The ORNL-TAMU-MSU BaF2 Array .................. 21
2.2.1 Detector construction ....................... 22
2.2.2 BaFg properties .......................... 23
2.2.3 BaF2 electronics .......................... 23

3 Experimental data analysis 27

3.1 Projectile analysis with the S800 .................... 27
3.1.1 18O and 20O identification .................... 27
3.1.2 CRDC mask calibration ..................... 30
3.1.3 Corrections to S800 parameters ................. 31
3.1.4 Effects of the beam blocker on 0“ ................ 35

3.2 y-ray analysis with the ORNL-TAMU-MSU BaF2 Array ....... 36
3.2.1 Energy calibration ........................ 36
3.2.2 Background suppression ..................... 39
3.2.3 Shower reconstruction ...................... 43
3.2.4 Doppler correction ........................ 46

3.3 Beam rate monitoring with the MCP detectors ............. 48

3.4 Experimental results ........................... 49
3.4.1 Random background removal .................. 49
3.4.2 S800—BaF2 energy correlation .................. 49
3.4.3 18O and 2"O strength distributions ............... 51
3.4.4 180 and 2"O angular distributions ................ 53

viii

4 Interpretation of experimental results
4.1 The simulation ..............................
4.1.1 Selection of the excitation channel ................
4.1.2 Selection of the de-excitation path ................
4.1.3 Projectile scattering .......................
4.1.4 y-ray decay ............................
4.1.5 Simulating BaF2 detector response ...............
4.1.6 Simulating S800 response .....................
4.1.7 Limitations of the simulation and related comments ......
4.2 18O results .................................
4.2.1 Projectile energy-loss vs. total 7-ray energy ..........
4.2.2 18O strength distributions ....................
4.2.3 Angular distributions .......................
4.3 Extension to 20O .............................
4.3.1 Initial interpretations .......................
4.3.2 7-decay branching estimates ...................
4.3.3 2"O strength distribution and results ..............

5 Closing remarks
5.1 Experimental conclusions .........................
5.2 Future virtual photon scattering studies with 20O at the NSCL . . . .

A Reaction kinematics
A] Review of Lorentz transformations ...................
A.2 Two—body collision dynamics .......................

B Intermediate-energy Coulomb excitation
B.1 The excitation cross section .......................
B.2 Quantum mechanical corrections ....................
B.3 Differential cross section functions ....................
Bibliography ...................................

ix

List of Figures

1.1

1.2
1.3
1.4

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

3.1
3.2

3.3
3.4

3.5

3.6
3.7
3.8
3.9
3.10

3.11
3.12
3.13
3.14
3.15

Comparison of the total photoneutron excitation function for the stable

oxygen isotopes, 1"'lmgO .......................... 4
Summary of states in 180 which could be populated. ......... 9
Summary of states in 208Pb which could contribute as background. . . 10

Known 2OO spectroscopic information along with theoretical predictions. 12

Schematic of the 2"O experimental setup ................. l4
Schematic of the S800 Spectrometer. .................. 15
Schematic of the S800 focal plane ..................... 16
Simplified diagram of the S800 electronics ................ 20
The front face of the forward BaF2 array ................. 21
Perspective drawing of one BaF2 detector. ............... 22
Diagram of the ORN L trigger box, TB8000. .............. 24
Simplified diagram of the electronics for the Ban arrays ........ 25
Example of the first step in the 18O identification process. ...... 28
2—D histogram of RF_E1_TAC vs. E1-GEO-MEAN used for 180 iden-

tification. ................................. 28

2-D histogram of E1_DOWN vs. ELUP also used for 18O identification. 29
2-D histogram of RF_El.TAC vs. S801_CEN_F IT which illustrates the

final step in the 20O identification process. ............... 30
Calibrated mask spectra from CRDCl along with a template of the
mask. ................................... 31

Mean 18300 raw parameter RF .ELTAC vs. experimental run number. 32
Mean 18300 CRDC drift time parameter vs. experimental run number. 33

Uncorrected 20O 0t and (at distributions for runs 91—95. ........ 34
Simplified picture to illustrate the effect of the beam blocker ...... 35
Comparison of 18O dispersive angular distributions gated on projectile

energy-loss. ................................ 36
Examples of raw 88Y and PuBe calibration data for one Ban detector. 37
Calibration fits for BaF2 detectors 135 and 202. ............ 38
Sample 88Y and PuBe calibration spectra for detectors 135 and 202. . 38
18O Ban time spectra for selected detectors ............... 39
Comparison of the calculated T.O.F.(Rp_Amy) parameter for 18O against

that for 20O ................................. 41

3.16
3.17

3.18
3.19

3.20
3.21

3.22
3.23

3.24
3.25
3.26

4.1

4.2
4.3

4.4
4.5
4.6
4.7
4.8

4.9

4.10
4.11
4.12

4.13
4.14

4.15

4.16

Comparison of a fast vs. slow 2-D histogram generated for a particular
BaF2 forward detector using data from the 18O against the 2"O equivalent. 42
A gate placed a 2-D plot of calibrated BaF2 energy vs. T.O.F.(Rp_mmy)

constrains a 18O fast vs. slow histogram. ................ 43
Cluster multiplicity as a function of incident 7-ray energy. ...... 45
Sample PuBe calibration data showing the improvement of the array
response when shower reconstruction is employed. ........... 45
Representation which describes how the 'y-ray emission angle was de-
termined. ................................. 47
T.O.F. vs. energy for 18O data showing the prompt Tray gate along
with the shifted gate ............................ 49
Shows the final event selection criterion for the 180 and 2”0 studies. . 50
Projection of events included within energy gates shown in Fig. 3.22
onto the Doppler-corrected axis for lBO and 200 ............. 51
Doppler-corrected, experimental strength distributions for 1’30 and 2"O. 52
18O and 20O angular distributions ..................... 53
Comparison of Doppler-corrected strength distributions obtained after
gating on specific d), regions for 18O and 2DO ............... 54
Schematic representation of the selection of a particular step in the
decay sequence. .............................. 58
Sample input file for the 18O simulation. ................ 59

Comparison of Monte Carlo-generated 18O angular distributions with
the corresponding differential cross section functions generated using

MATHEMATICA ............................... 60
The geometrical setup of this experiment defined within GEANT. . . . 65
GEANT particle tracks resulting from twenty 18O excitations ...... 66
Ban resolution fit for a determination of the constants in Eq. 4.16. . 66
Comparison of simulated against actual calibration data. ....... 68
Doppler-corrected, 18O BaF2 energy spectra for two extreme examples

of calibration drifting. .......................... 69
The observed (6,, at) acceptance “window” for ISO. .......... 70
Simplified illustration which defines the parameters in Eq. 4.18. . . . 71
Elastically scattered beam (blocker out) energy distributions for 180

and 2"O projectiles as measured by the S800 ................ 73
Sample data from the CRDCl mask calibration which has been gated

on the central region of CRDC2 to select straight-line trajectories. . . 75

Angular distributions for elastically scattered 1BO and 20O projectiles. 77
Projectile energy-loss vs. total, forward, reconstructed, Doppler-corrected

'y-ray energy for 18O. ........................... 79
Projectile energy-loss vs. forward, reconstructed, Doppler-corrected y-
ray energy for simulated 18O data ..................... 81
Projectile energy-loss for 18O events in which the forward array recorded
between 4.48 and 5.52 MeV. ....................... 82

xi

4.17

4.18

4.19

4.20

4.21

4.22

4.23

4.24
4.25

4.26

4.27

4.28

5.1
5.2

A.1
A2

B1

B2

Comparison of simulated 18O strength distribution generated using
known B(E/\) and branching information with the experimental re-
sult. .................................... 84
Comparison of simulated 180 strength distribution generated using
slightly adjusted B(E)\) and branching information with the experi-

mental result. ............................... 85
Changes that were made to previously established 18O experimental
quantities in generating Fig. 4.18. .................... 85
Final 180 6t and (15‘ experimental angular distributions shown against
the results obtained from the improved simulation. .......... 86

Comparison of the simulated 18O strength function from Fig. 4.18 with
that obtained after increasing the area of the acceptance “window” by

a factor of two. .............................. 87
Projectile energy-loss vs. total, forward, reconstructed, Doppler-corrected
7-ray energy for 2"O. ........................... 88
Projections of “decay gates” 1 and 2 from Fig. 4.22 onto the 7-ray
energy axis. ................................ 90
Simulated 2OO strength distribution shown with experimental data. . 92
Simulated projectile energy-loss vs. forward, reconstructed, Doppler-
corrected y-ray energy for 2DO ....................... 93
Improved 200 simulated strength distribution shown with experimental

data ..................................... 96
The simulated strength curves resulting from excitations to the two 1’
states. ................................... 98
The final 20O 6, and a, experimental angular distributions shown against

the results obtained from the simulation. ................ 99
2"O E 1 strength prediction from Ref. 27. ................ 102
Predictions for intensities of 7-rays between 8 and 20 MeV ....... 103
Scattering of two particles in the laboratory frame. .......... 106
Scattering of two particles in the center-of-mass frame. ........ 111

Coulomb excitation of the projectile as it scatters from the Coulomb

field of the target .............................. 115
Approximate and exact differential cross section functions, deA(l9, é) /dQ,

for E 1, E2, and E3 excitations, shown for different values of the adia-
baticity parameter, 6 ............................ 121

xii

List of Tables

1.1

1.2

2.1
3.1
4.1

4.2

4.3

4.4
4.5

4.6

5.1
B.1

The result of total Coulomb excitation cross section calculations for
excitations to discrete 1‘, 2+ and 3‘ states in 1SO assuming an angular
acceptance of 20 mrad ........................... 9
The result of total Coulomb excitation cross section calculations for
excitations to discrete 2+ and 3‘ states in 208Pb assuming an angular

acceptance of 20 mrad. .......................... 11
Relevant experimental quantities .................... 14
The beam’s dispersive and non-dispersive angular offsets ........ 34

Angular widths used to modify the incoming and outgoing projectile

distributions in the simulation. All values are in mrad. ........ 77
E 1 branching from the first two excited 1‘ states calculated from the
predicted level scheme presented in Fig. 1.4. .............. 90
The projectile and target level schemes utilized in the production of
the simulated results presented in Fig. 4.24. .............. 94

All 20O branching used for the simulated results presented in Fig. 4.24. 94
The projectile and target level schemes utilized in the production of

the improved 200 simulated results presented in Fig. 4.26. ...... 97
1‘ branching used for the improved simulated results presented in

Fig. 4.26. ................................. 97
20O shell model predictions for 1" levels ................ 101

The factors by which the curves in Fig. 82 should be multiplied . . . 122

xiii

Chapter 1

Introduction

The structure of the atomic nucleus, which is made up of N neutrons and Z protons
(N + Z = A total nucleons) bound together by an attractive force known as the
nuclear strong force, is, in general, extremely complex. Stable nuclear species, or
those which are more readily found in nature, have been studied exhaustively. Over
the last fifty years, useful theoretical tools have been developed which have described
various observable aspects of these nuclear systems with a varying degree of success.
The so—called nuclear shell model, which has stood out as the most successful of
these tools, emerged out of an attempt to describe the observed “magic” numbers of
nucleons Z, N = 2,8, 28, 50, 82, 126 (as in 4He, 1"O, etc.), which are linked to strong
nuclear binding. Formally speaking, the shell model is a microscopic theory, in that it
deals with the individual nucleons; a simplified description of the problem which the
shell model attempts to solve is that of independent protons and neutrons moving
within an average nuclear potential, or mean field, while simultaneously interacting
with one another. Indeed, within this context, the mean field itself is a manifestation
of the collection of nuclei, and is therefore a macroscopic feature.

As alluded to, the shell model, when applied to stable nuclear systems, is impres-

sive in its ability to explain nuclear magicity and, for example, predict observable

features such as nuclear mass (nuclear binding) or energies and quantum numbers
for excited levels. The natural progression of scientific technology in the realm of nu-
clear research facilities and their instrumentation has allowed for new experimental
techniques, thereby Opening the door for exciting studies of 6 and nucleon-unstable
nuclei. In an effort to better understand the structure of these radioactive nuclei, e.g.,
to further challenge and extend the shell model and other working models of nuclear
structure, modern nuclear science has undertaken the difficult task of the systematic
investigation of short-lived species. One intriguing feature that has come to light in
this new environment, for example, is new proton and neutron magicity, i.e., remark-
able stability has appeared on the nuclear (Z ,N ) landscape in places where it was
not predicted to exist from studies of the stable nuclei. (In this sense, modern nuclear
science has witnessed the break-down of the traditional nuclear shell model.) Neutron
or proton halos and skins, which are further examples of interesting features observed
in unstable nuclei, are directly attributed to more extreme asymmetry in the neutron-
to—proton ratio of the nucleus. Halos (typically 1 neutron or proton loosely bound to a
stable core) result in large RMS nuclear radii and small binding energies, while skins
(a small number of neutrons or protons bound to a stable core) are responsible for
interesting collective effects such as the “Pigmy” resonance (e.g., Refs. 15 and 27).
These and other phenomena have provided the impetus for ground-breaking exper-
imental work which complements an increasingly complex nuclear theory, and vice

versa.

1.1 Experimental motivation

Collective modes, which, in general, are excitations or resonances which can be de-
scribed within the context of c00perative motion of the individual nucleons comprising

the nucleus, are important probes of nuclear structure. The Isovector Giant Dipole

Resonance (IVGDR) is one such collective excitation which can be thought of as the
motion of a neutron sphere or fluid against that of the protons. In heavy, spherical
nuclei, the average excitation energy of this single-peaked resonance, Econ, varies
rather smoothly with the number of nucleons, A. Specifically, EGDR or A’1/3, the
constant of proportionality being approximately 79 MeV from a fit to experimental
results. It should be mentioned that this A“1/3 dependence is not an analytic result,
but rather, can be derived from simple assumptions (see, e.g., Ref. 15). In lighter
nuclei, A S 50, the GDR resonance energies are seen to deviate from this simple re-
lation, favoring lower values. Additionally, the GDR excitation (or strength) function
for lighter systems tends to display multiple peaks, which is a feature resulting from
the growing importance of the individual nucleon (or single particle) sub-structure.

While the GDR has been studied extensively for stable nuclei, very little exper-
imental information exists for unstable nuclear configurations. Recently there has
been a great deal of theoretical speculation surrounding the question of how collec-
tive strength evolves as one progresses towards greater neutron excess. For example,
the excitation function for the GDR mode is expected to fragment substantially, fa-
voring, in particular, the onset of increasing strength at lower excitation energies
(see Refs. 12, 14, 27 and references therein). The low-energy, or soft, portion of the
strength distribution in neutron-rich nuclei is often ascribed to a so—called Pigmy
resonance. Mentioned above, this excitation can be thought of as oscillation of the
neutrons which comprise the neutron skin against the residual nuclear core.

Indeed, the evolution of the GDR in the stable oxygen isotopes sheds favorable
light on the theoretical predictions. Shown in Fig. 1.1 is experimental (total) pho-
toneutron cross section data which has been collected (for example) by way of quasi-
monochromatic annihilation photon scattering [17]. The experimental motivation for
the current studies which will be described within this thesis came from the neces-

sity to extend this picture further to 20O. Photon-induced reactions using short-lived

nuclei (such as 200), however, require more sophisticated experimental strategies, as
the system under study is not a target but instead is a relativistic projectile.

Two complementary methods for these types of experiments exist. Both methods
rely on the virtual excitation of the projectile, i.e., Coulomb excitation, whereby the
projectile is excited as it passes through the Coulomb field of a high-Z target. The so-
called “virtual photon absorption” method takes advantage of particle decay modes
following excitations to the projectile continuum, specifically, the (7,1772) channels.
This method has been proven viable, having been employed with a great deal of
success, for example, by the LAND (Large Area Neutron Detector) collaboration at
GSI. In fact, an experiment to measure the dipole strength function in the oxygen
isotopes, specifically 1820220, has been performed at GSI and the results have recently

4 - 9 .‘?-‘§l°121.29.3?-3§-4°

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Figure 1.1: Comparison of the total photoneutron (GDR) excitation function for the
stable oxygen isotopes, 16'17’180, taken from Ref. 17. Low-lying strength emerges with
the addition of neutrons to the doubly-magic core.

been published [5,21]. The second method, known as “virtual photon scattering”,
relies on real projectile y-ray decay following virtual excitation [6, 24]. As compared
with the absorption technique, this method suffers from a large suppression factor
(between roughly 10“2 and 10‘3) related to the relatively low probability of the
(7,7’) decay channel. However, the scattering method is advantageous with regard to
its dipole (E 1) selectivity, since the absorption method is inclusive of contamination
from other virtual photon multipolarities. Additionally, the scattering method has
the ability to probe the strength function below the neutron separation energy (5"),
which is ideal.

Out of a need to establish the viability of this alternate method for GDR stud-
ies of radioactive systems, we chose to perform successive virtual photon scattering
experiments with beams of 18O and 2"O. The projectiles collided with a lead target,
providing the virtual photon field. Given the fact that 180 is stable and its strength
function established (e.g., Fig 1.1c), this experiment was carried out first to serve as
the control for the more difficult radioactive beam experiment which followed. Un-
fortunately, due to the small cross section for GDR virtual photon scattering events,
essentially no 'y-ray statistics were collected above Sn for either experiment. The ex-
perimental analysis, which will be the subject of all discussion to follow, was therefore
dedicated to the discrete region of these nuclei. Specifically, the analysis sought to
further establish the level structure of 2(’O, as its discrete, 1‘, states had not been
previously explored. Possessing this information, conclusions could then be drawn

regarding discrete E1 strength in 20O as compared with 18O.

1 .2 Coulomb excitation

Coulomb excitation, mentioned above, is a well-understood process which occurs dur-

ing interactions of a projectile (Z A) with a target (23) whereby one of the participat-

ing nuclei is excited as is passes through the electromagnetic field of the other. The
process can therefore be thought of as the absorption of a virtual photon by either
the target or the projectile. Because, in pure Coulomb excitation, the participating
nuclei stay outside the range of the nuclear strong force, the excitation cross section
can be expressed in terms of the same multipole matrix elements that characterize
excited-state 7-ray decay. Hence, Coulomb excitation amplitudes are strongly cou-
pled with valuable nuclear structure information. This fact is illuminated when one
examines an expression for the differential Coulomb cross section for the projectile

which has been taken from state [1) to state If) [1]:

2 ,.
) a‘2’\+2B(E/\,I, —+ If)£1[§§91§’ (1.1)

 

(iOEA— ZBG
(IQ — ho

where, as given in Appendix B, a is half the distance of closest approach, g is the
adiabaticity parameter, 1) is the incoming velocity of the projectile, and i9 is the
scattering angle of the projectile in the center-of—mass.

The important B(E)\, I,- —> I 1) factor appearing in Eq. 1.1 is the reduced (electric)
transition probability, which is proportional to the electric multipole matrix element.

Specifically,

I
2I,+1

 

B(EA, 12‘ ‘9 I!) = W!“ MlEA) llIi>l2° (1-2)

This matrix element, which depends directly on the wave functions of the involved
states, [1.) and [If), is a measure of collectivity in the nuclear transition and is
therefore linked to structural features such as nuclear rotation or vibration. Indeed,
transitions which couple states II.) and IIf) that are comprised mostly of single
particle motion (which cannot give rise to collective phenomenon) will be marked
by small matrix elements, (1,“ M(7r/\) ||I,). Therefore, Coulomb excitation tends to

probe collective configurations in nuclei.

The derivation of Eq. 1.1 involves a semi-classical approach. The trajectory of the
projectile is treated classically, assuming a Rutherford scattering distribution, while
the interaction which causes the nuclear transition in the projectile or target is found

using first-order perturbation theory, i.e.,

do do
— = _ Pi—t a 1
(“2 (do) Ruth. f ( 3)

where the probability, P,_,f, is given by the square of amplitude of the nuclear exci-

tation process:

1 0° .
Piaf : laz'—>.fl2 i (ii—>1 : 52/ (fl V(1'(t)) ll) 81(Ef—E’Vh dt : (1'4)

Since a more-detailed description of the cross section derivation can be found in
Appendix B, it is sufficient for the current discussion to present the final expressions.
For the experimental analysis it was necessary to include only electric contributions
to the virtual excitation spectrum, namely from E1, E2, and E3 (justification is
provided below in Sec. 1.3.) Substitution of the differential cross section functions,

deA/dQ, for these specific cases (given by Eq. B.20) into Eq. 1.1 allows the following:

 

 

 

d (:0 Z (E1,I,«—) I .
am a = (1%“ .83)” 311.4(2) ” [1¥_.<o.g)+1f.w,a]
doE2(19 5) _ l) ZBCY)2B( (E2 I '7 If)
— ‘ (25 ( a2sin"(%) x

3 1

[(g) {[22_ 2( 29 6 )+ 1222(29,)£)}+ (3)1220(0«€)]

(1053919 6)— 71’ 230 (E3, Ii —) If)

:_9)(T )2B( a4sin (g) x

l———"| A
A A
SIC”

) {134025) + lama} + Q) {13-.(0.§>+ 13mm] ,

(1.5)

where 1’3 is the incoming velocity of the projectile and the substitution e2/hc —+ a
has been utilized. It is assumed that the reduced transition probability is expressed
in units of e2 - fm”.

The 11,419, 5) functions in Eq. 1.5 are defined in Ref. 1 as the Coulomb excitation
functions and are given by Eq. BM in complicated integral form. However, the fact
that the projectiles detected in this study were limited to small forward angles ensures
that the approximate expression for the I ”(29,0 functions, Eq. B.13, is valid (see
Fig. B.2). It should be mentioned that Eq. 1.5 has been derived assuming projectile
excitation. To convert these expressions to relations which are valid for excitation of

the target, one need only exchange ZB for Z A.

1.3 Accessible states in 18O

Given the relatively small probability for Ml virtual photons, and the fact that no
(unnatural parity) 1+ states exist in the region below the neutron binding energy
[35], it was sufficient to restrict the analysis to electric excitations. The existence of
states with spin and parity of 1“, 2+ and 3‘, in principle, allows for excitations with
/\ = 1 —-> 3. Shown in Fig. 1.2 is the low-lying level structure of 18O which is relevant
to the current study. The B(EA) strengths given in Fig. 1.2a are known experimental
values [31,35]. (The upper limit for the 11“ state comes from an electron scattering
study [22].) The complicated radiative decay scheme for these excited configurations,
included as Fig. 1.2b, demonstrates that excitations to only a few levels will, in
general, produce rather convoluted results.

To gain some perspective regarding the relative importance of these excitation
channels for the 18O study, note the total cross section values in Table 1.1 that have
been calculated (using the formalism introduced in Sec. 1.2) assuming an overall pro-

jectile angular acceptance of 20 mrad in the center-of—mass. Based on these B(E/\)

a) b)
Possible Excitations Radiative Decays
Ex some (e’fmz‘) 1'
S

Excitation Energy (MeV)

 

180 180

Figure 1.2: Summary of states in 18O which were accessible. 3.) Experimentally deter—
mined B (E A) information for excitations from the ground state [22,31,35]. b) Possible
radiative decays resulting from the excitations in (a). Images in this dissertation are
presented in color.

Table 1.1: The result of total Coulomb excitation cross section calculations for exci-
tations to discrete 1‘, 2+ and 3‘ states in 180 assuming an angular acceptance of 20
mrad.

 

 

 

 

 

Coulomb excitation predictions for 18O
,7: Energy (MeV) B(E/\) (e2 fmm) 0 (11b)
11— 4.456 <4E-06 <3E—01
1; 6.198 1.9E—03 4.1E+01
13‘ 7.619 6.1E-04 5.2E+00
2? 1.982 4.65E+01 2.35E+03
2;" 3.920 2.0E+01 6.9E+02
2; 5.255 2.98E+01 6.76E+02
31' 5.098 1.120E+03 9.860E+00

 

 

 

 

 

 

 

Target
Exckaflons ]

 

 

 

 

 

 

 

; Ex 3(Ezt)i(e’rm") J“
o
2 4.085 2.9E+03 2’
v 4 -
> \°
9 E)
a: S
.5 3~ .
: 2.6.15 6.11E4OS 3
.9
U
.2 2- «
U
X .5
l“ “c.-
O
1- .. <
o 0’
zoapb

Figure 1.3: Summary of states in 208Pb which could contribute as background. Known
B (E )1) values are given for excitations from the ground state [23,26]. Both states decay
directly back to the ground state configuration.

values, the calculations predict that quadrupole (E2) excitations will completely dom-

inate over dipole (E1) and octupole (E3) excitations. The largest, non-E2, contribu-

tion comes from the second-excited 1" state.

1.4 208Pb contributions

Background resulting from excitations in the target was a significant experimental
obstacle. Fig. 1.3 shows the pertinent 208Pb level scheme, which includes 2 states,
namely the first-excited 3’ and 2+ configurations. Included in this figure are known
values for the reduced transition probability for excitations of these states [23,26]. A
prediction for the relative importance of target contributions follows from comparisons
of Coulomb cross section calculations for 208Pb, shown in Table 1.2, with the results
obtained for the projectile, 180 (Table 1.1). For example, from these calculations, one

would expect that the target should account for ~20% of the total E2 cross section

10

Table 1.2: The result of total Coulomb excitation cross section calculations for exci-
tations to discrete 2+ and 3" states in 208Pb assuming an angular acceptance of 20
mrad.

 

Coulomb excitation predictions for 208Pb

 

 

 

 

 

J; Energy (MeV) B(EA) (e2 fm”) 0 (ab)
2:: 4.085 2.9E+03 9.1E+02
31— 2.615 6.11E+05 5.30E+01

 

 

 

 

in the 18O experiment.

1.5 Status of 20O spectroscopy and shell model
predictions

From the Coulomb excitation cross section calculations for 18O presented above in
Sec. 1.3, along with 18300 systematics, it is reasonable to assume that an analysis
which includes E 1, E2, and E3 virtual excitations is also required for the 20O study.
The fact that limited 200 experimental spectroscopic information exists, however, de-
mands that we look to theoretical predictions for guidance. The left panel of Fig. 1.4
summarizes the pertinent status of 20O spectroscopy [26, 34]. Aside from our knowl-
edge of the B(E2) for the 2? and the branching from the 2;, only the energies and
spin-parity of observed 20O levels have been established. Notice, especially, that apart
from the tentative 3‘ assignment of the 5.614 MeV state, no experimental information
regarding the 20O negative-parity, discrete structure exists. Meanwhile, the theoreti-
cal picture for 2"O, illustrated by the right panel of Fig. 1.4, is interesting. Comparing
the B(E2) T predictions from EA. Brown [9] with measured B(E2) T values for the
analogous excited 2+ configurations in 18O (see Fig. 1.2a) we see a marked suppres-
sion of E2 strength. Contrasting this is the trend which unfolds from a comparison
of the 20O B(E 1) T predictions with the measured 18O values for the first three 1‘

states. As mentioned in Sec. 1.1, a relative increase in low-lying dipole strength in

11

 

 

 

 

 

   
 
  

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10
Experimental Theoretical
Information Predictions

Ex 3(5).» (e’fm’*) J“ 2 2, K -

8 7.608 5.. r Ex B(Em (e fm ) J

A _ _
> 5.614 (3) 7.2 1.45 03 1
° s;
E 51234 2' 7 6.2 1.7E-03 1‘
> 5~5-992 ,.- ' ~ 5.3 7015-04 2‘ -
a, 4...-.0 5.1 245-03 1‘
L Ru 0
a) E-..
c ............................................................ . .....
u.1 - 4% , ? 5.0 1.6E+O3
g 4 4.072 2 ........ 4-2 7-85+00 2’ _
45 3.570 2
.4:
g s s
u.1 :3 PI
[_ q 2.0 2.9e+01 2:
2 1.674 2.se+01 2° , .......
0 0 o
20° 200

Figure 1.4: Known 20O spectrosc0pic information [26, 34](1eft) along with sd shell
model predictions from EA. Brown [9] (right). Included on the left are all states
~ below the neutron separation energy which have determined spin and parity (with
the exception of a 5‘ state at 7.252 MeV). Only the B(E2) T value for the 21+ has
been measured, and decay-branching is known only for the 2;. The predicted 1’
states have not yet been observed experimentally.

neutron-heavier 20O is expected. While the cross section calculations in Sec. 1.3 show
that 1" states are not expected to be strongly-excited in the 18O experiment, theory

clearly predicts that this will not be the case with 20O.

12

Chapter 2

Experimental details

In October of 1998, two successive experiments with the goal of investigating virtual
photon scattering in 18O and 20O were performed at the National Superconducting
Cyclotron Laboratory (NSCL). For the first experiment, 180, having been accelerated
in the K1200 superconducting cyclotron to an energy of 100 MeV/u, was delivered
directly to our experimental hall. The second study required a radioactive beam. 22Ne
primary was accelerated in the K1200 to an energy of 120 MeV/ u. This beam impinged
on a thick 9Be production target. Fragments produced via projectile fragmentation
were then analyzed with the A1200 Fragment Separator [29]. Using a combination of
two magnetic bends along with a wedge degrader and momentum slits, this device
selected 20O at 100 MeV/ u with a momentum spread (Ap/ p) of 0.5%.

After being produced and transported to the S800 experimental hall, the 132200
beams were guided through the S800 analysis line (described in Sec. 2.1) to a target
pot, where they impinged on a 30 mg/cm2 208Pb (99.09% enrichment) reaction target.
Reaction products were then analyzed using the S800 spectrograph. Being primary
beam, the intensity of the 180 beam was constrained by the capabilities of the S800
focal plane detectors, which can count up to ~104 frag. /second. The 20O intensity,

limited by production, was ~5x105 particles/second. Table 2.1 summarizes some

13

Table 2.1: Relevant experimental quantities

 

Beam Energy (MeV/u) Intensity (part. /sec.) Impurity Run Time (hrs.)
18O 100 limited by 8800 — 13
200 100 ~5x105 <20% 17N 117

 

 

 

 

 

 

 

 

relevant experimental quantities.

The set-up specific to the 20O experiment is represented in Fig. 2.1. Two BaF2
arrays were used to measure y-ray decays which came in coincidence with the detected
reaction fragments. It was anticipated that projectile-correlated BaF2 timing would
be critical for y-ray selection in the BaF2 arrays. Because an inherent momentum
spread in the secondary beam necessarily results in the spreading of the prompt-7-
ray BaF2 time peak, two Multi-Channel Plate (MCP) detectors, designed and built
at ORNL, were included into the 20O set-up to improve BaF2 timing. For the primary
beam study with 18O, timing was not of concern. Therefore, the MCP detectors were
employed only for the 200 experiment. (Incidently, The MCP detectors additionally
allowed for a determination of the 20O beam intensity.)

9Be
Production Target

‘ Timin Detectors
MCP MCPZ lb i

30 mg/cm

   
  

 

         

  

 

     

‘ A1200 1 -"—z 3 m 5800
K1200 / / n—43'4—mu y 45.1 cm
ZINe 200 \/
120 MeV/u 100 MeV/u

BaF2 Arrays
Figure 2.1: A schematic (not to scale) of the 200 experimental setup. The Multichan-

nel Plate (MCP) timing detectors, developed by ORNL, were used to improve BaFg
timing.

14

2.1 The 8800 spectrometer

As has been mentioned, projectiles and reaction fragments were analyzed using the
S800 spectrometer, operated at 0°. As shown in Fig. 2.2, the S800 spectrometer [10]
consists of a fragment analysis line and a large magnetic spectrograph. The analysis
line itself is comprised of four bending dipoles, one quadrupole doublet, five quadru-
pole triplets and four sextupoles. The standard S800 target chamber is located at
the dispersive image of the analysis line. For the present study it was necessary to
remove the target chamber in order that there be sufficient space for the large BaF2
array. Thus, the 208Pb target was repositioned 85 cm upstream from the usual target
position.

The magnetic spectrograph bends nuclear species of appropriate rigidity to its
focal plane (enlarged in Fig. 2.3). Two dipole magnets, D1 and D2, each with a
bending radius of 2.8 m and maximum central field of 1.6 T, provide an overall
bending power of 4 Tm. Quadrupoles Q1 and Q2, located immediately downstream

from the target chamber, focus fragments in the dispersive (2:) and non-dispersive (y)

Focal Plane
Detector

   
 

 

 

Doublet
/’ - Sextu pole DZ Dipole
! "-5-. ,E -
I — ‘/ V~§ Intermediate
\/ \\ Image
\‘; 01 Dipole
5800 Production ’3’ \
Target (Not Used) % Dipole Reaction
‘ /§ I. Tariget
\‘AI‘ =.:. ‘_,:'
~l —. no..- 1. "f?! R
/
Triplet—/ 8an

Array Q1 Q2

Figure 2.2: Schematic of the S800 Spectrometer. It consists of an analysis line and a
large, 4 Tm magnetic spectrograph.

15

 

El,E2,EB Sclntlllators

 

 

 

 

 

 

 

 

 

Figure 2.3: Schematic of the S800 focal plane. Fragments are focused onto CRDCl,
the first of two position-sensitive detectors. The CRDC detectors, together, provide
fragment trajectory information, while the IC, E1, E2 and E3 provide AE, E and
timing.

directions thereby Optimizing the angular acceptance of the device.

Operated with the target at its designed location, the S800 has an angular accep-
tance of 7° and 10° in the dispersive and non-dispersive directions, respectively [37].
With the target repositioned, from simple geometric arguments, approximately half of
this acceptance is lost. The design of the position-sensitive elements of the focal plane
detector (to be discussed in Sec. 2.1.1) allows for an angular resolution of 2 mrad.
The energy resolution of the device is improved by operating in dispersion-matched,
energy-loss mode. Running in this mode, the device compensates for intrinsic beam
momentum spreading in the dispersive direction, which ideally results in a zero-width

image at the focal plane. For every ~10 cm at the dispersive image (reaction target),

the S800 is capable of correcting for 1% in Ap/ p.

16

2.1.1 Position-sensitive CRDC detectors

T wo cathode readout drift chamber detectors (CRDCl and CRDC2) are the position
sensitive elements of the S800 focal plane. Each CRDC detector has an active area
of 30 cm x 59 cm and is filled with a mixture of 80% CF4 and 20% C4H10 gases to a
pressure of 140 Torr.

Charged particles traveling through the detector ionize molecules in the gas. Elec-
trons produced during this process then drift through a region of constant electric
field until they reach a grounded F risch grid. Passng through this grid, the electrons
are accelerated towards an anode wire. The radial geometry of the electric field in
this region is such that charge amplification, which results from an electron avalanche,
takes place near the anode. 224 cathode pads, staggered on either side of the anode
wire with a spacing of 2.54 mm (over the 59 cm dispersive dimension of the detector)
measure induced charges from electron showers collected at the anode. Because no
avalanching occurs in the region of constant electric field, the Frisch grid insures that
the integration over all pad signals will be independent of the charged fragment’s
interaction distance from the anode.

A Gaussian fit over non-zero pad signals determines the incident fragment’s dis-
persive (17) position within the detector. The incident fragment’s non-dispersive (2;)
position within the detector is found by measuring the drift time of the electrons from
the point of interaction to the anode. Typical drift times of electrons in the CRDC
detectors are $20 as, which directly limits the counting rate to ~10" frag. /second.
Achievable position resolution in these detectors is designed to be better than 0.48 mm
in either direction.

Information collected from the CRDC detectors completely determines the trajec—
tory of fragments reaching the focal plane, parameterized as (:1: f, 6f, yf, of). 6, and
of are angles of the trajectory taken in the 23—2. and y—z planes, respectively, while

the subscripts, f, denote that these quantities are measured at the focus. Because

17

the magnetic fields present within the spectrograph have been mapped (this process
is described in detail in Ref. 10), it is possible to reconstruct, analytically, the tra-
jectory of fragments of known magnetic rigidity through the S800. In practice, from
knowledge of (2,, 6f, yf, 45;) one is able to calculate (approximately) quantities which
describe the motion of the fragments as they left the target (6,, yt, (£51., 6,), where (it is
related to the fragment’s kinetic energy. Specifically, 6, = (E -— Ec)/Ec, where EC is
the kinetic energy of projectiles traveling along the central axis of the spectrometer,

determined by

C \/2mEC
Bpggoo = I); = . (2.1)

q

 

Here Bpsgoo is the magnetic rigidity setting of the device and m and q are the mass
and charge, respectively, of the fragment.

The matrix equation which relates the target quantities to those at the focus is

(9t) (1‘!)

yt . 9]

(Pt 3!!

K52} KM

where R, known as the inverse matrix, is calculated by the code COSY INFINITY [7],

 

 

 

 

which analytically inverts the direct expression, given by

(55A (92\

9
’ =s 3” . (2.3)

451

KM K52}

For Eqs. 2.2 and 2.3 the dispersive object beam spot-size at the target (which is not

 

 

 

 

18

the same as the beam spot-size due to intrinsic momentum dispersion) is assumed

negligible.

2.1.2 Ionization chamber and scintillation detectors

After passing through the CRDC detectors, fragments enter the S800 Ionization
Chamber (IC). The IC is filled with P10 gas (90% argon and 10% methane) to a
pressure of 300 Torr. As with the CRDC detectors, molecules of the gas are ion-
ized by the charged fragments. Segmented into 16 individual chambers, each with a
1 in. anode oriented perpendicular to the fragment’s path, the IC chamber samples a
fragment’s energy-loss multiple times, thus reducing noise and providing an accurate
energy-loss (AE) signal.

Fragments are then stopped in a series of three large plastic scintillator detectors,
E1, E2, and E3, which, in the standard arrangement, are 5, 10 and 20 cm thick, respec-
tively. (The charged particles of interest for this study did not penetrate beyond E2.)
Photons produced by charged-particle interactions within these scintillators travel to
either end of the detector where they are collected and converted into an electronic
signal by photomultiplier (PMT) tubes (2 per detector). The signals produced in these
detectors provide timing as well as AE and total energy information. Thus E1, E2,
and E3 information, combined with the signal from the IC, allow standard AE vs. E

and time—of—flight (T.O.F.) vs. E fragment identification techniques to be employed.

2.1.3 3800 electronics

Diagrammed in Fig. 2.4 are the S800 electronics which were used for the present
study. Data readout in the S800 was triggered by a simultaneous signal in both the
PMTs which sense light output from the E1 scintillator. Specifically, the S800 master
gate was created by the logical AND of constant fraction discriminator (CFD) signals

from both E1 scintillator PMTs. This master gate was then directed to the trigger

19

 

> @ BaF, Trigger Box

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TBBOOO
El Up cro
p @ m 000000....
E1 Down CFD
( tart
x 2 TAC ADC $800_TAC
CRDC Anode 1 CPD 11—41— Stop

 

 

 

 

 

   

X 2 x 224
CRDC Cathode Pad

 

5800 Pad

W

 

 

 

Figure 2.4: Diagram of the S800 electronics. For simplification, only one anode channel
and one CRDC pad channel is shown. The triangular symbols represent shaping
and/or amplification of the signal. (Adapted from Ref. 10.)

box of the BaF2 array, which controlled the computer acquisition for this experiment.
(BaFg electronics will be discussed in detail in Sec. 2.2.3.) The S800 master gate
was also piped as the START input to each CRDC time-to-analog converter (TAC),
the stop coming from the individual CRDC anodes. Additionally, the 8800 master
gate was the start for a TAC which measured time relative to the cyclotron RF.
The analog signal coming from these TACs was then integrated and digitized by a
12-bit analog-to-digital converter (ADC), thus creating the electron drift-time and
S800 T.O.F. parameters. Finally, the master gate, AND-ed with the CRDC anode,
became the start for the fast encoding and readout ADCs (FERAs), which integrated

the charge collected from the individual, amplified CRDC pad channels.

20

 

85 cm

 

 

Figure 2.5: The front face of the forward array which consisted of 144 individual
hexagonal crystals. The center of the array was placed directly on the beam axis.

2.2 The ORNL-TAMU-MSU BaFg Array

'y-rays coming from both projectile and target de-excitations were captured and ana-
lyzed using two arrays of Ban detectors. The larger, forward array was placed 45 cm
downstream from the target, covering angles between 11° and 48° in the laboratory
frame. The forward array consisted of 144 individual hexagonal detectors, packed
tightly in hexagonal geometry around the beam pipe, as shown in Fig. 2.5. From
the center of the array moving outward, the detectors were positioned systematically
closer to the target (in steps of 1 cm). This packing design allowed for an improvement
in total solid angle coverage. Those detectors owned by Oak Ridge National Labora-
tory (ORNL) and Texas A&M University (TAMU), which together represent a large
fraction of the forward array’s detectors, are essentially identical, having crystals with
inscribed diameters of 6.5 cm and lengths of 19.5 cm. The Michigan State Univer-
sity (MSU) crystals, however, have inscribed diameters of only 6 cm and lengths of

24.5 cm. Thus, the placement of the MSU detectors within the array was strategic so

21

Tension Strap
and Assembly

   
 
 
  

B-Field Shielding
(PMT and Base Inside)

BaF2 Crystal

Figure 2.6: Perspective drawing of one BaF2 detector. The crystal is coupled to the
PMT using an optical grease. A tension strap adds stability to the detector.
as not to destroy the tight symmetry (e.g. they were placed mostly at the top of the
array).

A smaller, 7-element (backward) BaF2 array was placed behind the target, ~28°
off the beam axis, to monitor target contributions within the forward array. The
hexagonal crystals which comprised this array were larger — 8.7 cm inscribed diameter

and 20 cm in length.

2.2.1 Detector construction

Fig. 2.6 is a representation of an individual BaF2 detector. The crystal is coupled
to the quartz window of the PMT with VISC-600M (General Electric Corp.) optical
grease. This grease is chosen because it is transparent to the deep UV (fast) component
of light produced by interactions within the crystal lattice [18.28]. (Properties of Ban
crystals will be discussed in Sec. 2.2.2.) In order to insure maximum light collection,
the crystals are wrapped in Teflon tape, which has good reflective properties, and
aluminum foil. The coupled crystal and base are then tightly wrapped in electrical
tape to mask all ambient light. A magnetic shielding is placed over the PMT and its

base. Stability is added to the coupling joint by tightening a tension strap which is

22

anchored at the end of the shielding. The hexagonal aluminum rings of the tension
assembly, machined to the same dimensions as the crystal, support the weight of the

PMT and shield when the detector is lying on its side as in a typical experiment.

2.2.2 BaF2 properties

Inorganic scintillators emit UV light when fast electrons, resulting from interactions
with 7-rays, neutrons, 0 particles, or other heavy species, displace electrons from the
crystal lattice. BaF2 is one type of inorganic scintillator which has relatively good ef-
ficiency and excellent timing properties. Its timing capabilities are directly attributed
to the emission of a fast UV (210 nm) burst of light which has a characteristic de-
cay time of 0.6 ns [20]. This fast light is emitted when electrons are displaced from
the outer core band of the ionic crystal and a valence electron drops to fill the va-
cancy [19]. A slow component of light with a longer, 620 ns characteristic decay time
is also emitted at slightly longer wavelengths (320 nm). This is the component of the
emission which is a result of de—excitations in excited activator atoms. (Free electrons
are captured to excited activator orbitals.)

Because of its light emission properties, BaF2 is also capable of pulse-shape dis—
crimination (PSD). PSD is based on the principle that different particles interact dif-
ferently within the crystal. PSD between 7-rays, and neutrons (or charged-particles)
is achieved with BaF2 by comparing the amount of fast to slow light emitted by the

detector during an event. (Examples of PSD will follow in Sec. 3.2.2.)

2.2.3 BaF2 electronics

The BaF2 array used for this study is a relatively mobile device, and as such, its
basic operational principle from experiment to experiment changes very little. As
depicted in Fig. 2.7, the array’s trigger box, TBSOOO, controlled the type of events

which were recorded at run time. Two standard BaFg trigger levels exist, hi-7 and

23

Input Trigger Examples

   
 
    
   

TBBOOO

  
    
 
 
 

  

Busy
AND

Lo-y

   
 
  
 

Master Event

Tri er
Hi-y gg

  

5800 Master

Figure 2.7: Diagram of the ORNL trigger box, TB8000, which controlled the computer
acquisition for these experiments. The trigger box accepts multiple trigger inputs,
provides down-scaling, and also checks for a system inhibit. (Adapted from Ref. 28)

10-7. Hi-y is true when one element of the array records a signal above Th, the high
threshold setting (between approximately 2 and 4 MeV). It follows that 10-7 is true if
one detector fires above T1, the low threshold setting (below 1 MeV). In either case,
only the signals from those detectors which fire above T; are charge-integrated.

The hi-7 and 10-7 logic signals are fed to TB8000, as well as any logic signals
which are specific to the experimenter’s setup — in this case the S800 master gate. For
the present study, two other trigger levels were important, namely 8800 singles and
3800+hi-7 coincidences. In general the 10-7 trigger was used for taking calibration
data, while 8800 singles and 8800+hi-7 coincidences were used to investigate the
physics of interest. A trigger is accepted into the data stream with the flip of a toggle
switch on the trigger box, which makes for smooth transitions between different types
of runs. TB8000 has the capability to reject any input triggers due to a system inhibit
(acquisition busy). Optionally, the inputs to T B8000 can be down-scaled. Comparison
of the scaler output to the reduced scaler output allowed for a determination of system
dead-time.

Because of the type of electronics which were used to readout BaF2 events, the

array was logically subdivided into 16-channel banks. One channel in each bank was

24

 

 

— In Out

LED

X10
T» 0. El @

Common Start

Master Event
Trigger

 

 

     

 

 

 

TDC .—’ BaF2 Time

 

 

 

 

 

Rotary
Logic Path Atten.
X 0 l 7 1 O

 

 

 

 

 

 

 

 

 

Linear Path

   

 

)(1n

 

 

: BaF, Fast Energy

 

Atten.
Splitter
x 0 l ~1500 ns

I FERA
ln om—bBaFz Slow Energy

Figure 2.8: Simplified diagram of the electronics for the BaFg arrays. The detectors
were subdivided into “banks” of 16 for a total of 10 banks. (Adapted from Ref. 28)

 

 

 

 

 

 

 

 

 

 

 

reserved as a spare. In all, 10 banks of electronics were therefore required. Fig. 2.8 is
a simplified schematic of the electronics set-up for the array.

The signals coming from each detector followed two paths. Tracing the logic path,
the individual signals were first attenuated to insure that the T, and Th thresholds
applied using the leading—edge discriminators (LEDs) were consistent in energy. This
was necessary because the LEDs are sensitive to the fast light, while, in general,
the ratio of fast to slow light emitted for a given detector is highly dependent on
the quality of its crystal-to—PMT coupling. Following attenuation, the NIM signals
for each bank were split and converted to 16-channel ribbon cable with a NIM—ECL
converter. The ribbon cables carrying the attenuated signals for each bank became
inputs for the LEDs. The OR output of the Th LED from each bank, OR—ed, provided
the hi-7 trigger. In addition to providing the 10-7 trigger, the OR output of the

T; LED from each bank, OR—ed, was used to generate the fast (~50 ns) and slow

25

(~1500 ns) FERA gates. The individual T1 LED signals, meanwhile, provided the
individual FASTBUS T DC stops.

The linear path was less complicated. The N IM signals for each bank were sent to
a splitter/attenuator/delay box which was designed at built at ORNL. This module
splits the signals, the outputs being 16-channel ribbon cable format. One ribbon cable

provided the input for the fast FERA, while the other was sent to the slow FERA.

26

Chapter 3

Experimental data analysis

The experimental data analysis for both experiments was performed in a consistent
fashion. Fragments produced via interactions of the beam projectiles with the 208Pb
target were swept to the focal plane of the 8800 Spectrometer, where identification
could take place. Except when used to monitor the 8800 set-up, elastically scattered
beam fragments were not of interest. to this study. To eliminate these background
events from the data stream, a beam blocker was strategically placed in front of
CRDCl. After selecting only those S800+7 coincident events where a beam projectile
was detected at the focus, the projectile’s measured energy loss was compared with

the total decay ‘y—ray energy captured in the BaF2 array.

3.1 Projectile analysis with the 8800

3.1.1 180 and 20O identification

As mentioned, being able to select those events where a beam projectile scattered
inelastically from the target was the first step in the analysis of these experiments.
In order to achieve this, the AE, E and T.O.F. information gathered at the focal

plane was utilized. Specifically, particle identification (PID) for the 18O experiment

27

8 s
snwm:ss35¥§
I.I.II U.-

IC__SUM (a.u.)

8 8

  
    

p
c
.

 

8

nil
I

E_TOT (a.u.)

 
   

Figure 3.1: The first step in the 18O identification process. A gate is placed on a 2-D
histogram of IC_SUM vs. E_TOT.

(a.u.)

‘ §
-sa.a:;u:a5
III-III...
C (a.u.)
asu.mm:ssss
III-Ill..-

Q
g

I

RF_E1 TAC
§ §

RF_E1 TA
a s

 

 

 

l

 

150 l h: V 250 1 0‘ ‘‘‘‘‘‘ 150 IIIIII 2150‘ llllllll so:
E1_GEO_MEAN(aJL) E1_GEO_MEAN(aJL)

Figure 3.2: 2-D histogram of RF_E1_TAC vs. E1-GEO.MEAN before (a) and after
(b) the application of PID gate 1. On b) the next PID gate is defined.

involved a three-step gating process. First, a gate was placed on a 2-dimensional (2—D)
histogram of the fragment’s energy loss in the Ionization Chamber (IC_SUM) vs. its
total energy as measured in scintillators E1 and E2 (E_TOT). An example is given
in Fig. 3.1.

For an ideal S800 experiment, this gate would be very effective in suppressing con-
taminants. Unfortunately, one of scintillator E2’s photo-multiplier tubes was sponta—
neously jumping between two gain settings, the higher of which resulted in signals
from beam projectiles being off-scale. Therefore, only one PMT from E2 was utilized
for PID. An attempt was made to correct this lone E2 signal for position sensitivity.
E_TOT is a parameter which includes these corrections.

The next step in the 18O identification process involved applying a condition

28

 

 

      

197 51
us. 34-
,. i3: ,3" 'b) Gated on 1&2 f2:
. 1’4 . 'Jfg 11
3 1" 7|
. 9- 3.3.». “v-. 5.
m 5' m , 3-
v SI V 2-
:I 1-
g» 1' 2250- 1-
O O
a" 0'1““
H H
LU " m1“-
.Lrnlu. .lurmuimururuiluu.

 

 

 

a!)

E1_UP (a.u.) E1_UP (a.u.)

Figure 3.3: A 2-D histogram of ELDOWN vs. ELUP before (a) and after (b) the
application of PID gates 1 and 2. Note the appearance of lighter-mass bands below
the 180 band in a). The final PID constraint is shown in b).

on T.O.F. and AE parameters. As discussed in Sec. 2.1.3, the T.O.F. parameter,
RF_E1_TAC, is measured between the S800 master (the E1 signals) and the cyclotron
RF. The AE parameter used in this step is the geometric mean of the signals from

scintillator E1, defined as,

E1_GEO_MEAN = VELUP x E1_DOWN .

The advantage of defining El’s AE parameter in this way is that the detector’s
position sensitivity has been effectively removed. Fig. 3.2b shows an example of this
PID gate.

The final, arguably redundent, step in 1BO identification is shown in Fig. 3.3b. A
constraint was placed on the individual PMT signals E1_UP and E1_DOWN. Fig. 3.3a
is an example of a 2-D histogram of these parameters before any gating has been
applied. Note the appearance of lower-mass contours below the uppermost band, 180.
Application of the gates 1 and 2 has removed all contaminants from this upper-band.

Particle identification for 200 followed in a similar fashion. As was the case for 18O,
the first condition was applied to the AE and E parameters IC_SUM and E_TOT. (For
200 scintillator El’s contribution to E_TOT was ignored.) Scintillator E1 was then

constrained with the application of a gate similar to step three in the 18O PID. These

29

 

 

a
a

It
a) fig: 500,, _b) —Projedlon
25:- of cut
' 4000
“’
in
3 j-
8,.

 

"4 J K

M l .............. mgr”

‘ 50 2:!)
RF_E1_TAC (a.u.)

 

 

 

 

 

 

Figure 3.4: a) A 2—D histogram of RF_E1.TAC vs. SSOl_CEN_FIT which illustrates
the final step in the 20O identification process. The contaminant appears as the upper
band. b) A projection of the dot-dashed cut in a) onto the T.O.F. axis along with
the projection of the final 200 gate. The contaminant is removed.

two conditions, applied together, were successful in the suppression of all reaction
fragments. However, the beam contaminant which was mentioned in Chapter 2, 17N,
was not fully removed by the application of the first two gates. Therefore, a final

constraint was applied to the parameters representing T.O.F. and raw dispersive

position at the focus, S801_CEN_FIT (see Fig. 3.4).

3.1.2 CRDC mask calibration

Trajectory reconstruction for the 18"200 beam particles depends on their positions
and angles at the focus. Deducing this trajectory information required a calibration
of each CRDC detector. To accomplish this, a de—focused beam was sent through the
S800 which then illuminated a “mask” positioned in front of each CRDC. A pattern
emerged in the resulting :1: and y data from each detector which mirrored that of
the strategically-spaced holes in the mask. The known spacing between the holes
of the mask was then used to calibrate each detector. It should be mentioned that
because the spacing between cathode pads in the CRDCs is known, and their positions
fixed, these detectors are, in a sense, self-calibrated in the dispersive direction. The

dispersive mask calibration is therefore redundant, but a nice verification nonetheless.

30

 

2
.PW

§
I'I'UIIIIII
a~.amaaa§£§

ll'llll'l

.a.‘ 0

§

§
llll'lllllll

 

Slit

 

y, + 512 (0.4 mm/ch)
5

"Itlllllll l I ll

§
I

L?

a

. N 3--

an
n
3

500 :— U 7' ' ' /
E Center Hole (0,0) .
450 :— O

 

 

 

 

 

 

Wag—“WilllllllwlllLllllfillllllll
Xf + 512 (0.4 mm/ch)

Figure 3.5: Calibrated mask spectra from CRDCl along with a template of the mask.

3.1.3 Corrections to 8800 parameters
TAC corrections

The raw S800 timing parameters displayed shifts, or drifts, over the course of the
experiments. To quantitatively monitor these problems, data was grouped in blocks
according to run number; in general, one inelastic scattering run encompassed about
an hour of uninterrupted acquisition. The mean parameter value over each run was
recorded and, in general, treated as an offset for subsequent analysis.

For example, RF_El_TAC, the raw S800 T.O.F. parameter, deviated by ~200
channels or ~2.4 ns over the 18O runs and by ~250 channels or ~3.0 us over the
200 runs (See Fig. 3.6). A slow drift in the RF signal from the K1200 was suspected
as the cause for this problem, as evidenced by a similar problem with MCP timing

which is also measured against the cyclotron’s RF. As will be explained in Sec. 3.2.2,

31

 

 

   

 

 

 

 

 

 

3200 r l I l r I I r 1700
’2‘ a) ’7
s mm .=.
V b d v
v 0 1600
.3. a 2
in 3100 m
> A " > 1500
2 2
PI 3050 PI
3 H 1400
| 3000 “J.
11. IL
I! a: ..
s 2950 . . g 1300
o o
2 2
m l 1 J L l l L l 1200 ‘ ‘ 1 l l
36 4° 44 48 52 56 5° 64 100 120 140 160 180
Run Number Run Number

Figure 3.6: The mean value of the S800 raw parameter RF_El-TAC for 180 (a) and
20O (b) plotted as a function of the run number. The scale on the y-axis is 12.15 ps/ch.
The fits are included merely to accentuate the trend.

S800 T.O.F. was subtracted from the raw BaF2 times to arrive at a parameter which
represented y-ray T.O.F.. Because the flight path for y—rays from the target to the
array was only ~05 m, a 2—3 ns drift in S800 T.O.F. was significant, and therefore
required a correction.

Also significant was a systematic shift in the raw electron drift-time parameter
from CRDC2, 8802_TAC, shown as the open squares in Fig. 3.7. This problem, which
has been observed in previous studies using the 8800 (e.g., Ref. 10), can be attributed
to a slow improvement of the CRDC fill—gas. Over the course of the experiment, im-
purities in the CF4—C4Hlo mix are removed, resulting in a shorter electron drift-time.
Run-to—run fluctuations were also observed in both CRDCs, especially between in-
terruptions in inelastic data—taking (the observable gaps in Fig. 3.7), which typically
arose from technical problems with beam-delivery or the 8800. These fluctuations
likely resulted from the magnetic optics of the beam-line or S800 being slightly per-
turbed after each technical failure, causing the beam’s average position and trajectory
to deviate.

As explained earlier, these raw TAC values directly determine the fragment tra-
jectory parameters y; and (23,. With a gain on the raw CRDC TAC parameters of

~1 mm/ 20 channels, the systematic drift of CRDC2 was a significant, >1 cm effect,

32

3800

 

 

 

 

 

 

 

I I I I I
CRUD 323‘
,7 3600 — ”'5th 1%- :15
.r: “@713
3 3400 f “Layman,“ mm C, -
2 .v
'- 3200 " -i
O 8801 CRDC1
8 a $802 icaoczij
a: 3000 - .
U
C
m 2800 - .
g .-. ................
9- ‘--..__... 1.. ......
2600 l- a
2400 1 1 1 L 4
100 120 140 160 180

Run Number

Figure 3.7: The mean value of the raw CRDC drift time parameters plotted as a
function of the 20O run number. A systematic shift is observed in CRDC2. Also
observed are small fluctuations from run-to—run in both detectors.

while the run-to-run fluctuations in both detectors were on the order of 1 mm. There-
fore, the raw TAC parameters from both CRDCs were modified. The mean value over
the run was subtracted, so that each CRDC TAC distribution was centered around

y=0.

Angular corrections

After removing effects related to fluctuations or drifts in raw time parameters, the
8800 reconstruction, as explained in Sec. 2.1.1, produced reliable results. Parameters
9, and (151, which represented the angular trajectory of the inelastically-scattered pro-
jectile as it left the target, were calculated from parameters measured at the focus. Of
importance, however, was the fact that the beam, in general, impinged on the target
at an angle which slightly deviated from the z-axis (against which the angles 6, and
d», were measured). Therefore, a calculation of the polar scattering angle, 6,, from
the dispersive and non-dispersive angles 6, and 05,, introduced undesirable systematic

error. Because knowledge of O, was important for comparisons with the simulation

33

Table 3.1: The beam’s dispersive and non-dispersive angular offsets.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

180 200
Runs 9, (mrad) c5, (mrad) Runs 9: (mrad) qb, (mrad)
33—38 -3.8 — 91—95 5.5 -5.6
43—54 -13.6 — 100—112 5.3 -5.7
61—65 -15.1 — 119—125 5.3 -5.8
127—136 5.3 -5.8
138—154 5.3 -5.5
156—160 5.1 -5.7
175—181 5.1 -5.7
191-195 4.9 -5.5
3.5 10‘ , 3.5 10‘ ,
‘5 . :52"... ‘3'?" °"" - a) ‘5 . :f'niff'fzc‘fil“?;' 331.91.”) b)
g 310 L {2333: :Lig'cfsétflsggfiggs?) 'l E 3 10 - inelastic Cdlgc. (Runs 91-95)
‘9 2.5 10‘ L °°.
O D
g 2 10‘ L g
8 1.5 10‘ . 3
3 1 10‘ L E
O 0
E 5000 . E
2 5
o .

   

Figure 3.8: Uncorrected 20O 9, (a) and 9% (b) distributions for runs 91-95, shown with
elastic distributions which were recorded immediately before. Notice that the 8800
singles events can also be used to monitor the beam. (Normalization is arbitrary.)
(to be described in detail in Chapter 4), a correction was implemented which related
91 and 03, to the true beam axis.

Table 3.1 lists the dispersive and non-dispersive beam offsets over all inelastic
scattering runs for both experiments. For the 1SO study, the position of the beam
in 91 and 45, for the elastic scattering runs, recorded before each subset of inelastic
scattering runs, was used to determine the offsets. For the case of 200, however, elastic
scattering was monitored less frequently. Thus, the beam offsets for 2"O inelastic runs
were monitored using 8800 singles events, which had distributions that were quite
similar to those for elastic scattering. This fact is evidenced by Fig. 3.8, which shows

uncorrected dispersive and non-dispersive angular distributions for the subset of 2OO

34

$800 CRDC1\

Acceptance
A

x E2=E

blocker-

L
7

Energy- Loss

 

 

 

 

    

 

Blocker/
E1 = Eblocker

Figure 3.9: A simplified picture to illustrate the effect of the blocker on projectiles
reaching the focus. The football-shaped objects represent the envelopes of trajectories
in the dispersive plane for the projectiles with energy E1 and E2 which are within
the S800 acceptance. The blocker cuts into the dispersive trajectory distributions at
different angles, 61 and 62

runs recorded closest to an elastic scattering run.

3.1.4 Effects of the beam blocker on 9N

Though vital for the success of the experiment, the presence of the beam blocker in
the focal plane nonetheless complicated the resulting angular information obtained.
While, in principle, the presence of the blocker should not introduce asymmetry to
the non-dispersive angular distributions, 0’)”, the same cannot be said for dispersive
angular distributions, 0” (e.g., see Fig. 3.8a). Fig. 3.9 naively illustrates the effect
of the blocker. From this representation it follows that for the envelope of projectile
trajectories which have the same energy-loss, E, at which the blocker is positioned,
half of the dispersive angular distribution, or all 6 < 61, will be blocked from reaching
the focus. Additionally, for trajectories of less-energetic projectiles, represented by
the E2 envelope, the blocker removes less of the distribution.

To minimize non-dispersive asymmetry attributed to use of the blocker, the mag-

netic field of the S800 was slightly perturbed in an effort to move its focus slightly

35

 

 

 

N

O

8
I
m
i
in
to
N
3
0
<

 

 

H
U!
0
O
I

     
 

Normalized to Area
r Above 0.0 mrad.

500

Normalized Counts/1.6 mrad.
8
8

 

 

 

o l ‘ ‘ w.“ 1 4A
-80 -60 -40 -20 0 20 4O 60 80
0t (mrad.)

Figure 3.10: 18O dispersive angular distributions, binned by projectile energy-loss. In
general, the blocker removes roughly half of the distributions. However, notice the
slight increase in counts below 0 mrad. for increasing energy-loss.

upstream so that it coincided with the plane containing the blocker. As can be ver-
ified by redrawing Fig. 3.9 with a shifted focus, assuming a blocker of infinitesimal
thickness, this process, ideally, would have the effect of completely eliminating the
6m asymmetry. Likely due to a combination of finite blocker thickness and imperfect
refocusing, however, asymmetry in the non-dispersive angular distributions persisted.
In fact, Fig. 3.10, which shows 180 dispersive angular distributions binned by pro—
jectile energy-loss and normalized to the region of positive 6;, would tend to indicate
that the effect demonstrated in Fig. 3.9 is experimentally observed — notice that there

are relatively more counts below 0 mrad. for increasing energy-loss.

3.2 y-ray analysis with the ORNL-TAMU-MSU
BaF2 Array

3.2.1 Energy calibration

For the experiments, the detectors had been approximately gain-matched by their
applied voltages so that they would be capable of digitizing signals from y-rays up

to an energy of ~40 MeV. To make reasonable conclusions from the data, the arrays

36

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a. - a) [Raw “Y Calibration Data] b) IRaw PuBe Calibration Data]
, 250
.- r‘l .,......-ji ”533-”;
300 - ‘ft‘0898 MeV 200 Escaperl-P JV” p
3 250 _ Photo-peak :3 rm ‘)1/
c » 1.836 MeV———4> i: ,5. de J]
8 2°" - Photo-peak [‘0 3 ,,\ _ ‘
U 150 H [I U Single- [I]
— JJ 1‘ 1‘” Escape l:
‘°° k f L 5.
50 WMEQW L, —
0 1111111111111111 Illllllllllllllllllllllllllllllf! 111111 llllllllllllTT‘r-d 0 llllllhfilill Illllllllt‘ 111111 1.1}:
I 40 50 60 70 00 93' m.‘ 18) 200 220 260
QDC Channel QDC Channel

Figure 3.11: Examples of raw 88Y (a) and PuBe (b) calibration data for the same
detector. After fitting the spectra in the regions shown, assuming Gaussian-like photo-
peaks on top of linear backgrounds, the photo-peak positions are recorded. Note the
appearance of the single and double-escape peaks in (b).

had to be more-precisely calibrated in energy. For reasons that will become evident in
Sec.3.4.3, it was sufficient to rely on source calibrations using 88Y, which provided two
7-rays with energies of 0.898 and 1.836 MeV, and PuBe, which emits a 4.438 MeV
'y—ray.

Examples of raw calibration spectra for a detector which displays particularly good
resolution are shown in Fig. 3.11, along with Gaussian photo-peak fits that have been
generated assuming linear backgrounds in the regions shown. Two “escape peaks” are
visible in Fig. 3.11b because the process of pair-production, (to be discussed in more
detail in Sec. 3.2.3), competes with the photo-electric effect in the Ban crystal.

While only one PuBe calibration was performed at the end of the experiments,
many 88Y calibrations were performed at regular intervals to monitor time-dependent
gain fluctuations in the individual detectors. With the assumption that the relation-
ship between the 4.438 MeV signal-height and that for both 88Y y-rays be preserved,
it was possible to simply extrapolate the 4.438 MeV photo-peak position from the
associated 8’E‘Y calibration data. A linear regression fit using the two 88Y calibration
points and the extrapolated PuBe value then established the precise gain and offset
for each detector, as in Fig. 3.12. The general rule for analyzing the S800+7-ray co-

incidence data, then, was to calibrate the arrays with 88Y data gathered nearest in

37

 

 

 

 

 

 

 

5 I I r I l

4 - _
A
5
E: 3 — _
V
3
b 2 ' ‘
C
LU

1 L _

Energy (135) s 013862 + 0.01907SxChJ
— Energy (202) I 0.074596 4» 0.016632“)!
0 1 l l l
0 50 10 150 200 250 300

o
QDC Channel

Figure 3.12: Sample calibration fits for detectors 135 and 202. Notice the linear re-
sponse of the detectors in this energy region.

 

 

r If I l l I 320 I I I I I I —

4oo - a) —Dct. 135 - 13) —o.r. 135
“Y 2202 W _o:.. -
240 . , -
300 - _ L ’ W
200 - , -
160 . , _

100 L g 80

 

Counts
Counts

     

 

 

 

 

 

0 0:4 0:8 1:2 1:6 ‘ 2.4 0 3:2
Energy (MeV)

 

i 43 5.2
Energy (MeV)

Figure 3.13: 88Y (a) and PuBe (b) calibration data taken simultaneously for detec—
tors 135 and 202, which shows the difference between a detector with good energy
resolution and one with poorer resolution.

time to the current inelastic run.

The energy resolution of the detectors in the arrays varied substantially detector-
to—detector, as depicted in Fig. 3.13. Detector 135, which has particularly good res-
olution of ~7.3% FWHM at 4.44 MeV, is shown with data taken simultaneously for
detector 202, which displays much poorer resolution. Notice that the escape peaks

visible for detector 135 in Fig. 3.13b are not resolved for detector 202.

38

 

150 i r #

 

— FL» (inner
— FW outer
Bw

l_ Cyclotron g
RF 5

m H-

Counts/0.1 ns

 

 

 

200 250

10 150
Calibrated Time (ns)

Figure 3.14: 18O Ban time spectra for selected detectors. The peak at 100 ns results
from the projectile-correlated events of interest. Overlay-ed on top of this time corre-
lated time peak is a background which displays the periodicity of the cyclotron RF.
The detector in the backward (BW D) array sees very little background as compared
with the inner detector in the forward (FWD) array.

3.2.2 Background suppression

The individual BaF2 TDC coincidence gates were such that, on average, peaks from
four consecutive beam bursts were visible in the 8800+y-ray time data. One of these
peaks, the most intense, contained the events of interest, namely the projectile-
correlated y—ray events, while the others were the result of neutrons or low-energy
y-rays detected in the array in coincidence with uncorrelated, or random, projectiles
arriving at the S800 focus. Because these random projectiles could come from the
same or other beam bursts with equal probability, the random feature of the indi-
vidual time spectra was of periodic structure, mirroring that of the cyclotron’s RF.
Some sample time spectra are shown in Fig. 3.14 from strategically selected detec-
tors. Notice the inner detector (closer to the beam pipe) of the forward (FWD) array
has counted many more background events than either the outer FWD detector or
the detector from the backward (BWD) array. Moreover, the periodic structure of
the background for the BWD detector has almost disappeared. This is evidence that
neutrons were the dominant background contribution, since they would tend to be

emitted at forward angles.

39

T.O.F. analysis

F light-time constraints could be used to minimize contributions from these random
events in the array. A calibration of the individual BaF2 spectra which made use of
the periodic feature of the random background was first performed. The calibration
offsets were adjusted to line up the individual projectile-correlated time peaks. As
was explained in Sec. 2.2.3, BaF2 times were measured between 8800 master gate,
which served as a common start for all detectors, and the individual detector’s thresh-
old trigger. Therefore, the raw BaF2 times were dependent on the projectile’s flight
time through the S800. Higher-resolution T.O.F. parameters could be constructed
by subtracting this S800 flight time from the individual BaF2 calibrated time pa-
rameters. Specifically, an event’s RF-to-array flight time, T.O.F.(RF_A,,ay), could be

reconstructed using the following:
T-O-F~(RF—Array) = CBAFT — a X RF_E1_TAC + b .

Here CBAFT is the calibrated BaFg time parameter, a is a gain—matching constant,
and b is some arbitrary offset.

Since the momentum spread of the beam in the case of the 180 study was nar-
row, the beam’s flight from the K1200 to the target introduced very little additional
spreading. Therefore, for the 180 experiment, the calculated T.O.F.(Rp_Ar,ay) essen-
tially differed from the T.O.F.(Ta,g_-mray) by only a constant, i.e.,

180 180
T'O'F'(RF~Array) 2 T'O°F'(Targ.~Array) + COHSt.

A comparison of the resulting T.O.F.(Rp_m,ay) data for 180 and 200, as in Fig. 3.15,
verifies the expected result that the prompt, pro jectile-correlated 'y-ray peak is better—

resolved in the primary beam experiment with 180. Recall, however, that the multi-

40

7000 i I I i

 

 

 

5000 - DO: FWHM =26 n5] . —100 -
' 2"O (norm)

~ L200: FWHMY=3.1 ns]

 

 

5000 -

 

4ns

bE,=4.8-9.6 MeV

I-

Counts/0
‘6
8

  

 

 

 

 

2000 r-
1000 l-
o 1 1
160 1810 O F 200 220 240 260
I O I "S
(RF-Array) ( )

Figure 3.15: A comparison of the calculated T.O.F.(RF_Array) parameter for 18O with
that for 2"O, summed over contributions from all detectors. The 2"O data has been
normalized to the 180 such that the area under the prompt-y peaks is roughly equiv-
alent. A y-ray energy constraint was implemented to minimize the spreading due to
LED walk. Notice that the projectile-correlated cy-rays are better resolved in the 18O
data.

channel plate timing detectors were introduced into the 2OO set-up for precisely this
reason.
Better resolved flight-time parameters, T.O.F.(Mcpl,2_Al-ray) are, in principle, at-

tained by using the relation,

T-O-F-(MCPlg—Array) = CBAFT — T-MCP1,2 + b ,

since T-MCP1,2, the individual multi-channel plate timing signal, is measured in ref-
erence to the S800 master gate. These parameters measure flight-time that is directly
tagged with the beam projectile at the position of the MCP detector. The approxi-

mate relation,

T202F-(MCP1‘2—Array) 2’ T-O-F-(Targ.—Array) + CODSt. ,

is therefore restored. The closer the individual multi-channel plate detector is located

to the target, the better this approximation, since, in reality, the constant which

41

equates the two T.O.F. parameters is dependent on the individual beam-particle’s
velocity.

In practice, however, it was difficult improve, resolution-wise, on the T .O.F.(RF_ Amy)
results obtained for the 200 study. Efliciency losses of ~52% and ~88% in MCPl and
MCP2, respectively, resulted in much poorer statistics for the individual MCP T.O.F.
measurements, introducing more inherent error in the prompt-7 alignment process.
For reasons that will become clear in Sec. 3.4.3, constraints placed on T.O.F.(RF_An-ay)
were found to be sufficient. Being no longer dependent on the multi-channel plate de-

tectors, a ~100% increase in overall 20O counts was regained, which was beneficial.

Fast vs. slow gating

Use of “Fast vs. slow gating,” which takes advantage of Barium F louride’s PSD ca-
pabilities (described in Sec. 2.2.2), was also useful for background suppression. y-rays
were separated from neutrons (charged-particles) when detector’s fast QDC signal was
plotted against the calibrated slow QDC signal, as shown in Fig. 3.16. The y-rays ap-
pear as the streak found just above that of the neutrons which becomes visible near
10 MeV. It is worthwhile to mention that the neutrons which are discernible have ac-

tually undergone collisions with protons in the BaF2 crystal; it is the moving protons

 

 

     
 

 

    

321
18 I.” I 20 ~ I
0120 - . 57 I 0120 - 143 a
c . . .' _ ' - n n .
cm - .‘ _ _. ' .' . 1,3: g 3:
‘ , . '2 u" r.” 1m -
m ' ' i. ’. -_ ..‘ 0 S I m 0 I
5 . -. .: «. aria g: c g:
. _ ’ . .2. . _.-‘.' ‘- .. 2 6"
U '° . : , -_ .- 32*: sax-«€21 1 . U 9° - 1 .
o m ' f t I ' a. .-.'.-'.:).'.': " A' O 50
o2 2 * o2 .
u 0 f 2 ' 45-3 40
a ‘ s I
m m i m 20 z.

 

 

n O : 50 ll I 100 150 I 50 ' ‘ 100 a 150
Slow Energy (160 keV/ch) Slow Energy (160 keV/ch)
Figure 3.16: A comparison of a fast vs. slow 2-D histograms generated for a particular
BaFg forward detector using data from the 18O (a) and 20O (b) study. Neutrons appear

below the 'y-rays on these plots. A relative increase in neutrons is observed for the
case of 20O.

42

 

 

arssw'ififir

2
III... II.

b) 180: Gated On T-O-F'mF-Array)

   
   

33
aunnel
8 5:

8
wwwwmu533ty2

’é
9

Cal. En. (160 keV/ch.)
3: §
8

    

Fast QDC Ch

8

 

.10 250 am $50 ’2' -
T.O.F.,,._,,,,,,,(0.8 ns/ch.) Slovsii Energyw(160 kesil/ch) 2“

Figure 3.17: A gate placed a 2-D plot of calibrated Ban energy vs.T.O.F.(Rp_Ar,ay)
(a) is used to constrain the 180 fast vs. slow histogram from Fig. 3.16, which appears
as (b) here. It’s apparent that the random background is made of mostly neutrons
and lower—energy y-rays.

which interact, creating light pulses. A comparison of a fast vs. slow 2—D histogram
generated with 180 data against that generated with 200 demonstrates, as expected,
that more neutrons were present for the secondary beam experiment.

The claim that neutrons and low—energy 'y-rays dominated the random background
is verified by a comparison of Fig. 3.16a with Fig. 3.17b. The T.O.F.(RF_Amy) gate
shown in Fig. 3.17a, placed just to the right of the prompt y-ray peak, has been used
as a constraint in generating the fast vs. slow plot in Fig. 3.17b. The streak resulting
from neutrons has been enhanced relative to the y-ray band by application of this

gate, while, on average, the 'y-rays are of lower energies.

3.2.3 Shower reconstruction

y-ray events, having been selected by use of T.O.F.-gating in tandem with the ap—
plication of fast vs. slow gating, were analyzed using shower reconstruction, which
is the summing of energy that is simultaneously deposited in neighboring Ban de-
tectors. In general, the process of converting photons to fast electrons, which are
ultimately responsible for light production in the BaF2 crystals, is complex. Essen—

tially three types of interactions compete to produce these fast electrons, namely the

43

photo-electric effect, Compton scattering, and electron-positron pair production [19].

The photo-electric effect, which typically dominates for photon energies under ~1
MeV, is the process by which the photon is absorbed in an atom of the crystal and then
replaced by an energetic electron which has been displaced from the atom’s K shell.
The electron, therefore, carries away the photon’s energy minus the K shell binding
energy (~10 keV) in the form of kinetic energy. Compton scattering dominates in
the region of ~1—10 MeV. This process can be thought of as the scattering of the
incident photon from an atomic (essentially free) electron, which then recoils, carrying
away a portion of the original photon’s energy. The Compton scattering process is

represented by

E7

— 1+;%(1—cos€)’

E;

 

(3.1)

where E, and El, are the energies of the incident and outgoing photon, respectively,
m0 is the electron rest energy (0.511 MeV), and 6 is the angle of the outgoing photon
with respect to the incident photon’s direction. Notice that at maximum electron
recoil, which occurs at 6=7r, the photon retains a portion of it’s initial energy.

The last of the competing processes, pair-production, dominates for higher-energy
y-rays. The incident photon is replaced by an electron-positron pair such that total
momentum and energy is conserved. For this to be energetically possible, the incident
photon must have an energy of at least 1.02 MeV, or twice the electron rest mass.
The positron eventually slows in the crystal and then annihilates with an electron,
causing the emission of back-to-back 0.511 MeV photons. Pair production is therefore
responsible for “escaped” 0.511 MeV photons, when one or both of these annihilation
photons leaves the boundary of the absorbing crystal and is lost. This was the cause
of the escape peaks which were visible in Fig. 3.13.

For a given photon which was incident on the array, then, the competition from

44

 

 

 

 

   

10s I 02 Mev Ave mm: 1.03
I 2-4 MeV Ave Mult: 1.16
I 4—6 MeV Ave mm: 1.25
. I 6-8 Mev Ave Molt: 1.31
1° I 8-10 MeV Ave mm: 1 36
l
a 1000
In
I:
0
U
5 100

1 2 3 4 5 6
Detector Multlpllcity Within Cluster

Figure 3.18: The number of detectors participating, or the cluster multiplicity, binned
by incident y-ray energy in steps of 2 MeV for photons provided by the 20O experi-
ment. The data from energy bins above 2 MeV has been normalized to the 0—2 MeV
bin for multiplicity=1 events. Average cluster multiplicity increases with incident
photon energy.

these photon—to-electron conversion processes caused energy to be deposited in more
than one detector simultaneously. A single incident photon, therefore, could result
in a cluster, or shower, of neighboring “hits” over which the photon’s energy was
distributed. On average, as expected, the number of participating detectors increased

with photon energy. This trend is evident in Fig. 3.18, which shows detector multi-

plicity binned as a function of incident photon energy for sample 200 data.

 

  
        
     

 

2.510‘ . ...., . .
_ N0 Rm‘uucflon PhC'tO'Peak
2 1°. —WIth Reconstruction ‘
> i
3 ‘ Single-Escape
O 1.5 10 — : 4‘
N i
\ i
19 Double-Escape i
C 1 10“ l .
3 i !
a 2
5000 — 3 1
o ... I1. .1L....f1 ...1....1. ..
2.5 3 3.5 4 4.5 5 5.5

 

 

 

Energy (MeV)
Figure 3.19: Sample PuBe calibration data showing the improvement of the array

response when shower reconstruction is employed. Notice that counts have been ef-
fectively “put back” into the photo-peak.

45

Shower reconstruction, on an event-by-event basis, therefore vastly improved the
response of the BaF2 arrays. Its importance is visually demonstrated by Fig. 3.19
which shows sample PuBe energy calibration data that has been expanded in the
region near the 4.438 MeV photo-peak and the neighboring escape peaks for data

taken with and without multiple-hit energy reconstruction.

3.2.4 Doppler correction

Also important to y-ray energy reconstruction for these experiments was Doppler
correction. Photons which originated from 18O and 200 nuclear de—excitations were
emitted in reference frames which were moving at relativistic velocities (fl 2 0.4) with
respect to the laboratory coordinate system. The well known Doppler shift equation
(e.g., Ref. 16) describes the relationship between the jl-ray energy in the rest (E57)

and laboratory (E7) frames:

E; = 7E,(1 — 1’3 cos 0) . (3.2)

Above, 9 is the angle of the emitted photon with respect the rest-frame’s direction in

the laboratory frame, and

1
=———. 3.3
7 1—5‘2 ( )

The inherent segmentation of the array allowed for a determination of the angle
6. For example, the detector within an event cluster recording the largest energy
signal, labeled as the “primary” detector, could be taken as the detector in which
the incident photon interaction occurred. To a first approximation, the position of
the center of the face of the primary detector then gives the interaction point of the
incident photon. An assumption is then made that all projectiles initially travel along

the beam axis. In principle, improvement on the angle determination is achieved by

46

Energy (a.u.)

 

Detector x,y-Position

 

 

t—-Average

Simulated y-Ray ‘
Interaction-Position
Distribution for the ‘
Primary Detector ‘

  

Counts (a.u.)

Vij’ .

 

 

 

 

 

y-Ray z-‘Position

Figure 3.20: A representation which describes how the y-ray emission angle, 0, was
determined event-by-event.

considering the energy distribution for participating detectors within a cluster. As
depicted in Fig. 3.20, for the experiments, the interaction position of the incident
7—ray in the plane transverse to the beam-line was actually determined by energy-
weighting over participating detectors. As a further improvement, the interaction
position along the beam-line was found using the statistical average for the primary
detector which had been determined with help from simulation. (The simulation,
which was performed using a GEANT [3] environment, will be described in detail in
Chapter 4.) Likely due to the low average cluster multiplicity which was observed in
these studies (as given in Fig. 3.18), these B-determination improvements had barely-

measurable effects on the resulting Doppler-corrected data.

47

3.3 Beam rate monitoring with the MCP detec-
tors

Aside from aspects related to pro jectile-correlated y-ray timing, an additional impetus
for the inclusion of the multi-channel plate (MCP) timing detectors into the 200
experimental set-up was the desire to count the incoming beam projectiles. This
information is especially useful for converting experimental y-ray yields into units of
photon scattering cross section, which are more informative in the sense that they
are universal. The extraction of a true 20O counting rate from either MCP detector,

NMCp, in principle, involves the determination of its counting efficiency, 6, since

, P - D - n, ,
NMCP = 6 “CF 9 (3.4)

 

where nMcp is the raw MCP counting rate, P is the purity of the secondary beam and
D is the inverse of any down-scaling factor that applies. For this experiment, 6 could
be determined by comparing the S800 (CRDC) counting rate with that of the MCP
for target-in, blocker-out sets of data. Unfortunately, only one such target-out (elastic
scattering) run was recorded on tape at the beginning of the 2OO experiment, thereby
allowing for only one determination of the MCP efficiencies. After calculating the
run-by-run integrated number of beam particles for each detector, using the method
prescribed above, it became immediately obvious that the MCP detectors displayed
some unpredictable behavior. Specifically, a comparison of the run totals from each
detector, run-by-run, revealed inconsistencies that could only have been caused by
large counting efficiency fluctuations in both detectors, unfortunately deeming any

counting information from these detectors unreliable.

48

 

 

       

1302
’7 Random 3%:
5111‘ Contribution ‘ 1;; -
§ \ . 37 -
CU um I. ......... } '. 1g:
x . ‘3'i1l'.TO.F. . . 3:
O 90 Cate ' 1 I
m .
3 EU 2,_ ..: l' ., . -:’V i ‘1er. -"
a 40 4’ .
L
g :12 1
Lu 1, __ c. .
400 500 600 00
T.O.F.(RF.A,,,,, (0.4 ns/ch.)

Figure 3.21: T.O.F. vs. energy for 180 data showing the prompt 'y—ray gate along with
the shifted gate which samples the background.

3.4 Experimental results

3.4.1 Random background removal

As was explained in Sec. 3.2.2, high-resolution T.O.F. parameters were constructed
for prompt 'y-ray selection, therefore minimizing the random contribution to sub-
sequent BaF2 analysis. However, by virtue of the BaF2 coincidence window-length
which included several beam bursts, resulting in the periodic structure for the ran-
dom events, it was possible to sample the random contribution within the prompt-y
gate by simply shifting the T.O.F. gate by one RF period. As an example, Fig. 3.21

shows the placement of the prompt and shifted gates on 18O T.O.F. vs. energy data.

3.4.2 S800—BaF2 energy correlation

Appropriately, final event selection involved placing simultaneous energy constraints
on the 8800 and Ban results. It was required that projectile energy-loss, as measured
with the 8800, be correlated with reconstructed, lab—frame, 'y-ray energy. Examples of
this selection process are given in Fig. 3.22, which shows data from both the 18O and
200 study (plots (a) and (c), respectively). Projectile energy loss is on the vertical

axis while 'y-ray energy captured in the forward array is plotted on the horizon-

49

 

 

     
    

.-

250 ‘_ 2"o . Prompt-y .- .

256.250 Prompt-y "
. :33

Hun-8
numwuuwcnw

IIIIII ‘III
M.-

unwu-mmuumm
IIIIII‘III

-\

"V

yawn-m

IIIIII‘III
a”

Hwnwhwwmnww

IIIIII“III

Hwb—PJP47J

 

Projectile Energy-Loss (80 keV/ch.)
Projectile Energy-Loss (80 keV/ch.)

 

I H ' so A 00 150 200
Recon. Lab. y Energy (80 keV/ch.)

.10). I 150 200‘
nergy (80 keV/ch.)

.‘.'
.4.

50
Recon. Lab. 7 E

 

 

 

Figure 3.22: Shows the final event selection for the 18O (a) and 20O (b) studies. A
gate is drawn on a projectile energy—loss vs. reconstructed, forward, laboratory-frame,
y—ray energy histogram. The same gate is placed on equivalent histograms generated
with the shifted time gates, (c) and (d).

tal. Note the enhancement of events appearing along the diagonal, which represents
cases where projectile energy-loss is fully-recovered in the array. This final energy
constraint was inclusive of events falling left of the diagonal, which resulted specif-
ically from cascade decays whereby the projectile’s de-excitation process proceeded
through an intermediate state; one (or more) of the resulting 'y—rays was not detected.
Also included in Fig. 3.22 (plots (0) and (d)) are equivalent spectra which have been
generated with shifted T.O.F. gates. These histograms therefore represent the back-
ground which has been unavoidably included in (a) and (b). All data included within
these energy gates was then projected onto the Doppler-corrected BaFg energy axis.
Examples are given in Fig. 3.23, plotted on a logarithmic scale. A subtraction of the
random-gated spectrum from the prompt-y—gated spectrum produced the final results

for these experiments.

50

1000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1000 .
——Prompt T.O.F.
-— Random T.O.F.

g 100 3 100 -

x x

O O

N N

a

:I 10 g 10 - -

8 u

, , e l . l 1
0 2 4 6 8 1o 12 o 2 4 6 a 10 12
FWD Recon. Doppler-Crctd. 1 En. (MeV) FWD Recon. Doppler-Crctd. 1 En. (MeV)

Figure 3.23: Projection of events included within energy gates shown in Fig. 3.22 onto
the Doppler-corrected axis for the 18O (a) and 20O (b) experiments.

3.4.3 180 and 20O strength distributions

The effectiveness of this background removal technique is demonstrated by comparing
the final background-subtracted strength distributions with equivalent data generated
using less constraining background suppression. Fig. 3.24 shows the final, Doppler-
corrected, experimental results for both studies (black) along with data generated
entirely without the use of fast vs. slow gating (red) and also with data generated
using widened T .O.F. gates (blue). More specifically, the T.O.F. gates used for these
blue curves were expanded to encompass the width of the an entire beam burst.
Impressive is the fact that no difference in the final result is observed when the
background suppression techniques are relaxed. This allowed, for example, greater
timing flexibility with the 200 experiment, which justified the decision not to rely on
the multi-channel plate detectors for higher-resolution timing.

Note the appearance of the pronounced peaks at ~2 and ~1.7 MeV in the 18O and
20O strength functions, respectively. These peaks resulted from de—excitations from
the first-excited 2+ states, which produce y-rays of 1.98 MeV for 18O and 1.67 MeV
for 2"O [34, 35]. Observation of these peaks at the proper location in energy is ex-
perimental verification of the Doppler-correction process and of proper identification

of the projectiles. Broader structures were observed at energies above the sharp 2+

51

 

 

     
     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

II + I T I I I I I I
> O 21 —Norrnal > 1000 t — | -
o 1000 _ - MeV — Norml (No Dower cm) 0 — Normal (No Doppler Crctn)
8 — No Fast vs. Slow Gating ‘ x — No Fast vs. Slow Gating
a — Widened T.O.F. Gates :3 — Widener! T.O.F. Gates
E 13 g 2
c a) 0 c 100 b) ”o .
a 100 L a a
8 c
U
E: 10 . :16 10
o E
z 2
1 P 1 1_
0 2 6 8 1o 12 o 2 4 6 s 10 12
FWD Recon. 1 Energy (MeV) FWD Recon. 7 Energy (MeV)

Figure 3.24: Shown in black are the final, Doppler-corrected, experimental strength
distributions for 18O (a) and 20O (b), respectively. For comparison, the same results
are obtained with no fast vs. slow gating (red) and with widened T.O.F. gates (blue).
states but below the neutron separation energies, 8,. (8.044 and 7.608 MeV for 18O
and 200, respectively). These wider peaks were the result of contributions from sev-
eral, higher-lying, discrete projectile levels in addition to a background contribution
from excitations of the first-excited 2+ in the 208Pb target (4.085 MeV) [23]. The tar-
get contribution becomes more evident when looking at the green curves of Fig. 3.24,
which are the non-Doppler—corrected distributions, since the target can be considered
at rest in the laboratory.

As alluded to in Sec. 1.1, evident in Fig. 3.24 is the fact that essentially no appre-
ciable statistics were gathered for 'y-rays of energy greater than 3,, for either study.
This was the direct result of the cross-section for GDR Virtual Photon Scattering
being too low given the available beam currents and energies. In addition, at the time
the experiment was proposed, the acceptance of the S800 had been overestimated.
(An analysis pertaining to this topic will be the subject of Sec. 5.2). To interpret the
experimental results, draw conclusions, and ultimately make comparisons regarding
dipole strength in these two nuclei, it was necessary to focus on the region in en-
ergy of the discrete transitions, where other virtual excitation-photon multipolarities

were contributing. To this end, a Monte Carlo simulation was utilized which included

52

 

 

 

 

 

 

 

      

      

 

 

 

 

 

 

 

 

 

‘ I f T I : I T I I I . I I T
— '00:“ 200:“
«5 1200 - 1 1'5 1200 - .
e E
E E
a an
. 800 _ 0 « 2 800 - 9 4
° A ia 2 ‘
B ccep nce :3 Acceptance
C :I
3 400 L - 8 400 - -
U
o k 4 ‘— 0 l I I j
-60 -60 -4o -20 0 20 40 60 so -80 -60 -40 -20 0 20 40 60 80
Scattering Angle (mrad.) Scattering Angle (mrad.)

Figure 3.25: Final 180 (a) and 20O (b) angular distributions. The a), distributions,
as expected, are relatively symmetric, while the blocker distorts the 9: distributions.
Approximate acceptance cuts are visible in the 9: distributions.

Coulomb excitation formalism into the useful environment provided by GEANT [3],
which could simulate BaF2 detector response.

Important information stood to be gained from a more detailed analysis, as the
the level structure of 20O has not been well explored. As was mentioned in Chap—
ter 1, with the exception of that for transitions from the first-excited state in 200, no
reduced transition probability (B (E A)) values, which are critical for Coulomb excita-
tion calculations, have been measured previously [26]. Additionally, knowledge of the
level scheme for negative-parity states in 2"O is incomplete. Results from the analysis,
therefore, emerged after making appropriate adjustments to theoretical predictions
for specific states in 200. Important B(EA) information was obtained for 200, along
with the observation of previously unmeasured 1' states. All important details of the
analysis involving the Monte Carlo simulation of these experiments will be explained

in Chapter 4.

3.4.4 180 and 20O angular distributions

The final experimental angular distributions are shown in Fig. 3.25. The 6t data

shows S800 acceptance cuts at approximately 20 mrad which is ~2 / 3 of the expected

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) 180 b) 200
.\ 0,>0.0
> >100 "
3 g ‘ ‘ i ‘ . ’7‘
i . | l' ' 2
S g 10 . L
3
8 — “1' < 5 mrad. .‘ 8 — |a| < S mrad.
—Smrad.<|¢‘|<15mrad. . f —-5mrad. <|¢|<15mrad. ]l
— 15 mrad. < "J < 25 mrad. gi . —— 15 mrad < ioi < 25 mrad.
1 l . 1 1" 1 1
1 2 3 4 5 6 7 1 3 4
FWD Recon. Doppler-Crctd. 1 En. (MeV) FWD Recon. Doppler-Crctd. 7 En. 6(MeV)7

Figure 3.26: Comparison of Doppler-corrected strength distributions obtained after
gating on the specified regions in cf), for 180 (a) and 20O (b). The constraint, 6, > 0.0,
was used in generating these histograms. The curves shown in red and green have
been normalized to the data represented in blue.

value. The more-limited acceptance observed in the Q5, distributions, meanwhile, is a
result of the angular constraint from the momentum slits. It should be noted that the
non-dispersive distributions, as anticipated, are reasonably symmetric. Unexpected,
however, are the differences between these qfit distributions for the two experiments.
Specifically, the 180 o, distribution is single-peaked, while that for 2"O exhibits the
expected double—peak. (Double-peaking is expected because the differential Coulomb
excitation cross sections for all projectile and target states are zero at 19 = 0.) As
will become evident in Chapter 4, the difference can be explained when the overall
shape of the 8800+blocker acceptance as observed in (6;, 4),) space is considered. This
2-dimensional acceptance contour for the case of 20O is more symmetric about (I); = 0
than it is for the 180 study.

Fig 3.26 shows final strength distributions generated after gating on different
regions of the non-dispersive angular distribution for both 180 and 20O. The slight
differences which are noticeable (especially for 20O) are due to the differing shapes
of the angular distributions for the discrete excitations which are contributing. For
example, excitations occurring via absorption of E1, E2 and E3 photons are each

described by characteristic angular distributions.

54

Chapter 4

Interpretation of experimental

results

To gain a better understanding of the experimental results for this study, and ulti-
mately extract information regarding dipole strength in the discrete region of 20O,
a Monte Carlo simulation was developed and employed. The simulation made use
of the intermediate-energy Coulomb excitation formalism discussed in Chapter 1 to
incorporate the inelastic excitation processes which occurred in both the projectile
and the target. This treatment was adequate since inelastic nuclear processes are neg-
ligible given the small acceptance for these experiments (~1° in the lab-frame). ’y—ray
analysis was performed by the realistic radiation detection code GEANT [3], which
was developed at CERN (Geneva, Switzerland). GEANT’s capabilities are such that
the y-ray detection materials and geometries which were specific to the current study
could be defined rather conveniently. S800 resolution constraints were applied to out-
going projectile angles and energies so that appropriate energy gates and angular
acceptance cuts could be placed on the simulated events.

Because all quantities which are relevant to Coulomb excitation and subsequent

y-ray decay (such as spin and energy of states, B(EA) information, and y ray de-

55

cay branching) are known for 18O, appropriate adjustments could be made to the
simulation upon comparison with the actual 18O experimental results. A confident
extension of the simulation to the 20O case, with help from theoretical predictions,
could then follow. Using a comparative analysis of simulated against experimental

data, quantitative interpretations of the 200 results were possible.

4.1 The simulation

4.1.1 Selection of the excitation channel

As was made evident by the comparison of total excitation cross section information
in Sections 1.3 and 1.4, it was essential that target excitations be included into the
analysis. The process of assigning an excitation channel in either the projectile (A)
or the target (B), event by event, was consistent with the relative probabilities, P:

and PE, calculated from total cross section information.

A 03,

P3 = '2 ; P3 = '2 . (4.1)
Zn 0;? + Zn’ 02’ Zn 0': + Zn’ Ur?’

 

 

Defined in such a way, the probabilities given above have the convenient property,

ZPf+ZP3=r (4.2)

In Eq. 4.1 0;? (02.) represents the total Coulomb excitation cross section for the 72‘“

”h) excited state in the projectile (target) obtained by an integration over 29 of

(n
the corresponding differential cross section expression, dag/c119 (dag/d0), to some
(C.M.-frame) maximum angle, '93,...” (922,771....) This maximum center-of-mass angle

was calculated from a corresponding laboratory-frame angle, which was chosen to be

well-beyond the experimental acceptance. In general, the relationship between the

56

scattering angle in the two frames contains a dependency on the excitation energy
(see Appendix A) so that, for example,

19A :05 E.“ 9’“ ‘2‘ :02.“ 1529'“

innax iJnar( :1 rnax) Té'djanax JJnaI( ]’ 1n01)'

However, the fact that the excitation energies for the states in this study were small
in comparison with the kinetic energy of the projectile allows

19A 2 17A

innax JJnar ‘

Therefore, in practice, the integration limits which went into the determination of the
total cross section were the same for all states in the projectile and the target.
The differential cross section expressions, dafi/dfl and dog, /di9, themselves were

calculated from the expressions provided by Eq. 1.5 since

d d

35 = 2.. sin .9 fi . (4.3)
Computational efficiency was improved by simplifying these calculations so that they
were evaluated only for discrete values of 19, in steps of 0.1 mrad. Specifically, using

the example of projectile excitations, for any given stepwise value of 19, the differential

Coulomb cross section was calculated by

A
do,“

(it?

 

—_— C(A, n) B(EA, o —> n) F(o,g(n),1) , (4.4)

where the quantity, F, defined through

F(i9,€(n), A) = sin 19 de,\(;9§,2€(n)) , (4.5)

 

had been tabulated beforehand using MATHEMATICA [36]. Explicit forms for the dif-

57

0.0 RNDM ] 1.0

Figure 4.1: Schematic representation of the selection of a particular step in the decay
sequence. A random number has been used to select the transition whereby the pro-
jectile goes from the 6th to the 2nd excited configurations. This process is repeated
until the nucleus reaches the ground state.

ferential cross section functions, deA(i9, £(n))/d9, appearing in Eq. 4.5 can be found

in Appendix B. Meanwhile, direct comparison with, for example, Eq. 1.1 provides the

definition for the multiplying factors:

C(xn)==ar(§%9)2aen—”+2. (46)

For target excitation, one need only replace ZB with Z A in the above expression.

4.1.2 Selection of the de-excitation path

The simulation included known or estimated 'y-decay branching information for the
contributing states in the projectile and the target. Specifically, for the selection of
the decay from state it to a particular, less-energetic state m (m < n), a random
number was first selected on the limit 0 to 1. This random number was compared
against the branching probabilities from this excited configuration, denoted here for

the projectile as PA in a way that is schematically represented by Fig. 4.1. Of

n—imi

course, the branching probabilities themselves are defined such that

3
|
._.

—l
A __ . B _
RHm—l. E fiqW—l.
0 171:0

a
ll

This process was repeated at each intermediate decay step until the excited-nuclei’s

specific path back to its ground state was determined.

58

DO NOT MODIFY THE FORMAT OF THIS FILE!

if.tifiitfitiitfifiifiitfifiiiflfififiitfiitifiti*fiififiiiflitfiii

 

 

 

 

 

"'EXCITATION‘*' ‘ 018_GSTATES.DATA E.J.T. 1.12.01 '
SI E_ex L del dist. file B(EL) * This file contains the information that GEANT '
(MeV) (18 chars) e‘2‘fm‘(2L) * will need to determine prob.'s and branching *
itiififitittttifiifititIItittittitfititIIIIIIIIIII‘IIfi.
1 1.98 2 olB_deZ_1.98.data 4.650005+01
2 3.92 2 olS_de2_3.92.data 2.00000£+01
3 4.46 1 olB_del_4.46.data 4.00000E—06
4 5.10 3 018_de3_5.10.data 1.120008+03
5 5.25 2 018_df32_5.25.da:a 2.98000E+01
6 6.20 1 018_del_6.20.data 1.90000E-C3
"'DECAY/BRANCHING"’ ORIGINAL ESTIMATES FROM REF: D.R. Tilley (NPA 1995)
CI 54 E_ex tot Br. Prob.to# Br. Prob.tot Br. Prob.tot Br. Prob.tot Br. Prob.to# Br. Prob.
(MeV) (l=100%) (l=100%) (1=100%) (1=100%) (1=100%) (1=100%)
1 0 0.00 0 0 000 0 0 000 .0 0 000 0 0.000 0 0.000 0 0.000
2 1 1.98 1 1 000 0 0 000 0 0.000 0 0 000 0 0.000 0 0.000
3 0 3.55 2 1 000 0 O 000 0 0 000 0 0.000 0 0.000 0 0.000
4 0 3.63 2 0 997 1 0 003 0 0 000 0 0 000 0 0.000 0 0.000
5 2 3.92 2 0 876 1 0 124 0 0 000 0 0 000 0 0.000 0 0.000
6 3 4.46 4 0 704 2 0 271 5 O 025 0 0.000 0 0.000 0 0.000
7 4 5.10 2 O 761 5 0 176 3 0 063 0 0 000 O 0.000 0 0.000
8 5 5.25 2 0 559 1 0 303 5 0 087 6 0 030 3 0.011 4 0.010
9 0 5.34 2 0 580 6 0 420 0 0 000 0 0.000 0 0.000 0 0.000
10 6 6.20 1 0 887 6 0 041 8 0 036 4 O 025 9 0.011 0 0.000

 

'ADDITIONAL COMMENTS MAY BE ADDED HERE‘

Figure 4.2: Sample input file for the 180 simulation which gives all relevant excitation
and decay information for the projectile. A similar file serves as input to the code for
target excitations.

The information which the simulation code used to select both the excitation
channel and de—excitation path was incorporated into two input files, one containing
information for the projectile, and the other giving target information. A sample input
file is included in Fig. 4.2 which shows the ease with which necessary changes could

be made to any excitation or de-excitation input field.

4.1.3 Projectile scattering

On an event-by—event basis, after selecting the excitation channel based on total exci-
tation cross section information and the de-excitation cascade using y-decay branch-
ing information, it was necessary to assign the projectile center-of-mass scattering an-
gles, i9 = HMO", and ¢A’,cm° Since the differential cross section expressions are indepen-
dent of the azimuth, ¢A'.cm1 this angle was chosen randomly over the range (0 —> 2 ii).

For the selection of 19, the so—called Monte Carlo rejection method was utilized, which

59

 

 

 

 

 

   

 

 

 

 

 

 

 

 

   

   
  
    

 

 

2 u I 40 I r 10 r r
a) 1'2 @ 6.20 MeV 0) 2’2 @ 3.92 MeV C) 3'l @ 5.10 MeV
35 '-
E 1 E2 8 r- E3
1.5 r- 30 [- ~
2‘ e .
25 r - E — Mathematica
u— .
b V “C, 6 — Monte Carlo l
3 . 5 5 (277K Events)
CD 1 — Mathematica ‘ % 20 f q q;
E" — Monte Carlo \ .3
m (290K Events) ~15 . . E4 " ‘
b b b
”u '3 '3
0.5 b -4 10 e .
— Mathematica 2 . .
— Monte Carlo
5 ‘ (333K Events) ‘
o l I 0 l L o l l
0 0.025 0.05 0.075 0 0.025 0.05 0.075 0 0.025 0.05 0.075
G (rad.) 8 (rad.) 9 (rad.)
an an cm

Figure 4.3: Comparison of normalized Monte Carlo-generated 18O angular distribu-
tion with the corresponding differential cross section function, daEA(19, E ) / c119, as gen-
erated using MATHEMATICA for the: a) 12‘ state b) 2'; state c) 31‘ state.

involved a simple prescription. Two random numbers were chosen: The first repre-
sented the abscissa, mm", which falls somewhere in the domain, 27min 5 17m. 5 mm”,
over which the probability function being generated, P (at) (in this case the differential
cross section), was defined. The second random number ymn took on values between 0
and gm, where ym is the maximum value of the probability function over its limits.
A simple comparison of gm, against P(.’Emn) followed. The event, characterized by
the physical observable xmn, was generated if and only if gm, 3 P(:r,.a,,).

Possessing limited knowledge of the differential cross section for a given excitation
channel, as it was tabulated only at discrete values of 29, it was necessary to use a

cubic spline interpolation to evaluate, approximately, the cross section distributions

A

B
n,ma:c 2 19

for any random value of 19 from O to 19 "an,”

= 19",”. This interpolation
method, by design, created approximate differential cross section functions within
the intervals which were smooth in the first derivative and continuous in the second

derivative. Details on the subject of spline interpolation formalism can be found in

Ref. 25. Particular examples of generated angular distributions are shown in Fig. 4.3

60

for three particular states in 180. For comparison, the actual differential cross section
functions generated with MATHEMATICA also appear in this figure.

Having determined the spherical scattering angles for the projectile in the center-
of-mass, a straightforward application of equation Eq. A.15 allowed for a calculation
of 6N)”. Meanwhile, oAtjab was found with greater ease — because the azimuthal angle
is determined by projectile motion which is transverse to the direction of the C.M.

motion, it follows that

¢A’,cm = ¢A',zab -

4.1.4 y-ray decay
Finding the lab-frame momenta for emitted y-rays

For simplification, the assumption that the process of 'y-ray decay was isotropic in the
spherical emission angles 6., and (25., was adopted for both projectile and target de-
excitations. (In reality, each y-ray decay is associated with its own multipole-specific
angular distribution — see, e.g., Ref. 1.) For each decay, this was facilitated using a

set of random numbers, 0 g RAN.)2 g 1, such that
d), = 2 7r RAN; ; 6., = arccos (2 RAN?2 — 1) . (4.7)

For the specific case of projectile y-ray decay, an isotropic treatment demanded that
these angles be chosen in the frame where the projectile was at rest. Justified by
the assumption that the target was stationary, the emission angles for target decay,
meanwhile, were measured directly in the laboratory coordinate system.

Because GEANT event-generation required knowledge of the momenta of the emit-
ted 7-rays in the laboratory frame, target decay events needed no further analysis.

However, the case of projectile decay was more complex since the emission occurred

61

 

from a moving frame. It was necessary to first relate the chosen emission angles in
the projectile rest frame, Own”; and (1).,”on to the corresponding angles in the non-
moving frame, 9;“, and 925;.lab' For 6 this was accomplished using Eq. A.15 with the

subscript substitutions, A’ —> ‘y and cm —> p7‘0j., and using the fact, 57.,»01. = 1,

which allows

. 6 r0'
tan(93,z.b) 2 sm( mp J.) (48)

'7 (cos(6,,proj,) + x3) '

 

Meanwhile, the azimuthal relation is simply
at... = mm. . (4.9)

The remaining factor 5 (and 'y) in Eq. 4.8 refers to the velocity of the outgoing
projectile in the lab, BAIJab, which can, for example, be calculated using an adapted

form of the last expression given in Eq. A.14,

7A’Jab = 7cm [3cm COS(6A’,cm)\/ 7,150". — 1 + 7A’,cm] . (4-10)

along with

r _ —2
fiA’Jab -— V 1 _ 7N)“ -

In Eq. 4.10, [3cm refers to the velocity of the target+projectile CM. frame in the
laboratory, which is given by Eq. A.10. The relativistic factor appearing in Eq. 4.10,
mum, is calculated from knowledge of the excitation energy in both the projectile
and target (See Eq. A.17).

The fact that the projectile itself moves in the laboratory with a momentum that is

not oriented purely along the the beam (2) axis means that. the y-ray emission angles

62

given by Eqs. 4.8 and 4.9, 61”,“, and Cymlab’ are not the same as the emission angles with
respect to the lab axes, defined here as 67M, and $7,101,. A rotation, R, which utilized

knowledge of QAIjab and oAIjab was required to find the direction, (67,101,, (25,101,).

R = A2I(I£)Ay(a) ; a = 2 7r — 9A'Jab; h‘ = 2 7r — cp'Aijab. (4.11)

Specifically, we have (e.g., Ref. 4)

cosa- O —sina
Ma): 0 1 0 . (4-12)

sina 0 cos a

and
cos K. sin K. 0
Ax“) = — sin Ii cos K 0 - (4.13)
O 0 1
Hence,
x” :1: cos H.(.rcosa — zsina) + ysinh:
y” = R y = — sin h:(:r cosa — zsin a) + ycosn: - (4-14)
4” z (:1: sin a + 2 cos 0)

Above, the unprimed (Cartesian) unit vector refers to the (spherical) direction, (61710»

(153.1%), while the double-primed unit vector points in the desired direction, (67,105,

63

$7,100) i‘e'a

:1: :r
y —> ( 3,101,. 451,101,) ; y” —> (97.1111), (157.1111)) .
3 Z”

Projectile recoil

As will be verifiedin a later discussion involving the simulation of 8800 response
(Sec. 4.2.1), the inclusion of projectile recoil was critical for the reproduction of certain
aspects of the experimental results. For each decay, the projectile’s laboratory-frame
momentum was adjusted by the laboratory-frame momentum of the emitted 7—ray,
57,1111). (found using the previously-described analysis) such that total momentum and

energy was conserved during the process, e.g.,

q, -¢ -o . I _ *
pA’Jab = pA’Jab — Pmlab , mA' — mA’ — E7 ' (4-15)

Above, E; is the excitation energy lost due to emission of the 7-ray. Neglecting a very
small difference due to 4-momentum conservation, this excitation energy is equivalent

to the energy of the y-ray in the projectile rest frame, i.e.,

t
E7,proj. 2 E,y a

4.1.5 Simulating BaF2 detector response

GEANT uses well-known information about y-ray interactions in matter to determine
energy deposition in active volumes, which, for this simulation, were hexagonal BaF2
crystals. Using a hierarchal structure of volumes, both active and inactive (detector
supports, beam-pipe structures, etc.), the pertinent geometrical setup was defined

with GEANT’s convenient initialization routines. For simplification, the center of the

64

   

Forward
Array

 

 

Figure 4.4: The geometrical setup of this experiment drawn using GEANT. It was
sufficient to define only a portion of the existing support structures.

mother (laboratory) volume, in which all subordinate volumes were positioned, coin-
cided exactly with the target position. Fig. 4.4 shows the geometrical setup for the
simulation as drawn by GEANT. As can be seen in this figure, only a portion of the
beam-pipe structures were actually included, as it was discovered that their presence
had negligible effects on the simulated results. As an illustration of GEANT capabili-
ties, simulated particle tracks are shown in Fig. 4.5 which have resulted from twenty

180 nuclear excitations as seen upstream from the target (the backward array has

been hidden).

Creating realistic energy signals

In order to emulate realistic BaF2 detector response, it was necessary to fold the total
energy deposition information which GEANT provided for each simulated detector,
event by event, with the experimental BaF2 resolution, characterized by (FWHM)

width, AFWHM, which has the approximate functional dependence:

B
AFWHM(E‘dep.) 2 Edep. A + — - (416)
Edep.

65

 

 

y Tracks

Multiple

-
\ Iv—Compton

 

 

 

Event

Figure 4.5: Sample events generated from twenty 18O excitations as shown by the
resulting particle trajectories. 'y-ray tracks, for example, appear as dotted blue lines.
Secondary processes have occurred.

Above, A and B are constants which were determined from a fit to experimental

data. Fig. 4.6 shows such a fit for data points provided by sample 88Y and the PuBe

calibration sets. The AFWHM information was obtained by fitting the photo—peaks

from the calibration spectra which were generated by summing contributions from all

detectors.

AWN/Energy

.°
p
U!

9
p

 

 

 

 

 

 

 

 

 

0.05

 

V 5 WWW-ammo) I
Vulul EM):
1111 0 016943 ,
m2 0 12343
Ohio 0 00027279 81’
R 0 95439 7 m2 1
CNN

 

 

 

 

 

 

i 5
Energy (MeV)

Figure 4.6: BaFg resolution fit for a determination of the constants in Eq. 4.16.

66

Application of energy thresholds

Another consideration for the simulation was the application of energy threshold
constraints to simulated BaF2 signals. As discussed in Sec. 2.2.3, only those events
where at least one detector recorded a signal larger than Th (the high threshold)
were accepted by the acquisition. Additionally, for a given detector within an event,
charge integration only occurred for signals larger than T), the low threshold. Including
threshold effects into the simulation involved “setting” a unique set of threshold
values for each detector, such that the average of these threshold values over all
detectors were free parameters, Tf‘ve' and vae', which were adjusted upon comparison
with experimental data. The width of the distribution of low threshold values was
also an adjustable parameter. The width of the Th distribution, however, was scaled
proportionately with the low threshold distribution, as the choice of the low threshold
for a given detector, Tl", automatically determined its T ,? setting. Specifically, it was

assumed that for a given detector the two threshold cuts should be related by,
n TAve. 72
Th : (nave) Tl '

This relationship is justified by the fact that the fast-light response (or gain) is lin-
ear with incident 7-ray energy. Recall, it was the detector’s fast component which
triggered the discriminators.

A comparison of simulated versus actual calibration data is presented in Fig 4.7
for 88Y (a) and PuBe (b), which includes the summed contributions from individual
detectors of the forward array. For both plots, the simulated data has been normalized
to the area under the most energetic photo-peak of the actual data. The background
included in the simulated data in all cases is linear. As was standard for recording all
calibration data, the high threshold was set to the same value as the low threshold.

Notice the discrepancy of the simulated data at low energies if threshold settings of

67

 

3.5 10“ . . r . . r T 3 10‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,_. I
, a) ”Y . .. Sim.+8kgmd. (Norm) b) PuBe rwo Demon
3 1° " ,, 0 Sim.+Bkgrnd. (Norm) ‘ 2 5 104 _ .
Data '
B 2-5 1°‘ " FWD Dem ‘ a 2 1°. _
g 2 1°, _ 13?: 100 keV . x
N FWHM“: 0.7T‘V" °
\ "h "" Q 1 s 10‘
~ -(
1g 1.5 10‘ 12 . . 1.5;“: 650 kev‘ * 12
3 «A. we.
8 ‘ ”C FWHMth 0.7T”, 3 1 10‘ _ 0 Sim.+8k9rnd. (Norm) -(
1 1o - r 8 Data
.00. ,
5°00 .. - 5000 *- . #3293 650 keV"| ’
FWHMIQ‘LC" 0.7TLBC.
l 1 J l l l L l l
00.6 0.8 1 1.2 1.4 1.6 1.3 2 2.2 0 3_5 f
Energy (MeV) Energy (MeV)

Figure 4.7: A comparison of simulated against actual calibration data for 88Y (a)
and PuBe (b). The background included with the simulated results is linear. a) The
simulation using 100 keV threshold values is not consistent with experimental results

at low energies. Better overall agreement is achieved using threshold settings of 650
keV.

100 keV are used. Much better agreement was achieved with average threshold values
of 650 keV.

Preliminary comparisons of simulated results with experimental 18'200 data re-
vealed that the inclusion of an additional energy-smearing effect was necessary for
reproduction of the BaF2 response. This was especially true for the 180 comparison.
As was explained in Sec. 3.2.1, the analysis of the experimental BaF2 data involved a
dynamic energy calibration whereby the set of calibration coefficients used for a given
detector depended on the run number for the data set being analyzed. The fact that
photo-multiplier tube gains were drifting continuously throughout the experiment
(due to temperature fluctuations, for example) rather than “jumping” abruptly from
one calibration to the next effectively resulted in degradation .of the experimental
BaF2 energy resolution when making comparisons of simulated against experimental
data.

The importance of this effect could be established quantitatively for a subset of
the detectors (which had sufficiently low Th settings) by observing the position of
the peak resulting from de-excitations from the first-excited 2+ state. For 180 data,

this investigation showed that the energy calibration for the (subset of the) detectors

68

20

 

All 1"0 Events —Io=216
l ‘\ —-ID-222

2’,@1.98 MeV

 

 

.

 

d

Counts/20 keV
8 G
__ _

 

U'I

 

 

0
0.5 1 1.5 2 2.5

3 3.5
Doppler-Corrected Energy (MeV)

Figure 4.8: Doppler-corrected, l80 BaF2 energy spectra for two extreme examples
of calibration drifting. The 2:“ peak is off by over 9% in both cases. A calibration
correction was performed to remove this drifting in detectors which displayed this
2?“ peak. To account for the remaining detectors which could not be corrected, an
additional energy-smearing factor was folded into the simulated BaFg response.
displayed an overall spread (a) of ~4.5%, while the same investigation for 200 revealed
a less dramatic drift of ~1.5%. This difference is explained when one considers that
only one BaF2 energy calibration was performed at the end of the 180 experiment
while five subsequent energy calibrations were taken throughout the course of the 2"0
experiment. It is not surprising that significant gain-drifting occurred during those
first ~13 hours of the 130 study.

Fig. 4.8 illustrates this calibration drifting for two particularly extreme 180 cases.
The proper position of the 2;“ peak is marked by the dotted black line. The calibration
in both cases is off by over 9%. It was possible to improve the experimental BaF2
response by adjusting the calibration coefficients for detectors which displayed this
problem. However, given the fact that most detectors had high threshold settings
which suppressed detection of 7—rays of this energy, these calibration corrections were
performed for only ~35% and ~44% of the detectors for the 180 and 200 experiment,
respectively. Hence, for the simulation it was assumed that the remaining detectors
of the array behaved in a similar fashion as the subset which had been sampled and

corrected.

69

4.1.6 Simulating 8800 response

A simplified approach was taken to account for the 8800 response within the sim-
ulation. Possessing experimental knowledge of relevant projectile observables at the
target position, it was not necessary to propagate the simulated projectiles through
the S800 using the direct map (as in the reconstruction formalism mentioned in
Sec. 2.1.1). Working within a dispersive and non-dispersive fragment trajectory de-
scription, measured S800 resolution and acceptance limitations were therefore applied

directly to the corresponding simulated projectile parameters.

8800+blocker acceptance

 

Inclusion of the blocker was essential for later comparisons with simulated results.
Its introduction was facilitated by first applying an energy cut to simulated events.
Specifically, only those projectiles which recorded an energy-loss, AEA, which was

greater than some cutoff, EBlckm were accepted as events for further analysis, i.e.,

AEA = EA,lab — EA’,lab Z EBlckr. - (4-17)

Because the blocker also affected the angular distributions (see Sec. 3.1.4), includ-

 

    

A‘w 15
15 All "0 Events 13:
U 9 I
\_ 350 a
'o 17;:
E 3.. 3:
E 3:
V: 250

8

to 200

In Acceptance

E: 150 “Window”

.9“

 

 

6,4256 (0.4 mrad/ch.)

Figure 4.9: The observed acceptance “window” for 18O, as shown in (6,,45.) space.
The gate shown here was used to constrain simulated 180 events, assuming 100%
transmission for events falling inside.

70

 

 

 

 

 

 

 

 

Figure 4.10: A simplified illustration which defines the parameters relevant to
Eq. 4.18. For a projectile with a given interaction position, as, from the central axis of
the S800, the angular acceptance is effectively changed from 00 to 03. The difference
between these two angles scales as x/lefld where leg, is the effective distance from the
target to the aperture.

ing only this energy constraint on the simulated data was inadequate. Reproduction
of the observed angular distributions required that the acceptance of the entire appa-
ratus (S800+blocker) be somehow included. Rather than attempt to understand and
then incorporate each complicated facet of the acceptance (e.g., projectile scattering
from the entrance slits and/or within the 8800, blocker effects), the overall experi-
mental acceptance for each study was, instead, mapped by drawing a free-form gate
on a 2-D histogram of Bt vs. (I), data, as shown in Fig. 4.9. For the simulation, the as—
sumption was made that projectile transmission for events meeting this simultaneous
9: and <15; criterion was 100%.

Assuming that the gate shown in Fig 4.9 defines a pseudo S800 entrance window
or aperture, the experimental beam spot size was incorporated into the simulation by
slightly perturbing the position of this acceptance window in 6, and 45;, event-by-event
(while keeping its area constant). Fig. 4.10 shows (naively) the effect that finite spot
size has on the S800 acceptance. The parameter which scales the importance of this

perturbation is the effective distance from the target to the entrance aperture, leg,

since

 

(4.18)

71

Eq. 4.18 is derived directly from the relation,

 

 

.. d
tan6$= T+ 219$,
lefl.
along with,
d
tan 6,, = 2 90 ,
lefl.

where the small angle approximation has been utilized. The beam spot size, ~5 mm
FWHM, was estimated by observing 180 and 2"O yt distributions for elastic scatter-
ing runs. Assuming an effective target to aperture length of approximately 300 cm,
the acceptance perturbation is on the order of 2 mrad. In reality the geometry of
the so—called acceptance window was also dependent on projectile kinetic energy, as
the refocusing of the projectiles onto the blocker was not completely successful (see
Sec.3.l.4). However, given the small energy-loss for projectiles in this study, it was
sufficient to assume that only the projectile’s position at the target modified the S800

acceptance event-by-event.

Energy resolution

The energy spreading for experimentally observed projectiles was the result of three
contributing factors, namely, intrinsic dispersion in the beam, energy straggling in
the 208Pb target, and finite resolving power of the focal plane detectors. For the sim-
ulation, it was adequate to assume that the incoming projectiles were mono—energetic
and then account for these energy-smearing effects by modifying the outgoing pro—
jectile energies accordingly. To quantify the spreading experimentally, the elastically
scattered (beam) energy distribution was analyzed, as shown in Fig 4.11. As expected,

due to a greater intrinsic energy spread of incoming beam particles, the distribution

for 200 had a larger width (0) than that for 180.

 

 

80 I I .0 I I I

a

T 1 i r f

1": ° «an 70 b)’°o:Run87 . ° °Data .
h a) 0 Run 60 f: —Fif(o=0.282 Mevi l 3...: Fit(o=0.715 MeV)

§

  

 

 

 

 

 

 

 

.. _. 6° ’- 0 . 0 o "
> zoo ; - , .
0 x
X 250 )- -‘ o
a N
\ 200 - 'l E
13 c
3 150 - - 3
3 u
100 F .1
so I- -1
a!
:4
0-3 -2 -1 o 1 2 3 -3 - -1 o 1 z 3
Projectile Energy-Loss (MeV) Projectlle Energy-Loss (MeV)

Figure 4.11: Elastically scattered beam (blocker out) energy distribution for 18O (a)
and 2“O (b) projectiles as measured by the S800. Intrinsic energy dispersion, target
straggling, and finite detector resolution all contribute to the spreading which is
observed. 200, as expected, has a wider intrinsic energy spread than primary beam,

18 O.
Angular resolution

The final angular distributions for projectiles were similarly affected by intrinsic mo-
mentum dispersion, angular straggling in the target, and CRDC resolution. To real-
istically incorporate these factors into the simulation, an angular spread (09,“, ow")
which was consistent experimentally with combined contributions from the intrinsic
beam spread and angular straggling in the target was included for incoming pro-
jectiles. Spreading due to finite detector resolution, labeled 00,,“ and 0W“ for the
dispersive and non-dispersive angles, was used to modify outgoing projectile distri-
butions.

The determination of the spreading widths 09,," and 0am: like the determination
of the energy spreading width (Fig 4.11) involved observing the elastic dispersive and
non-dispersive, target-position angular distributions. Unfortunately, folded into these

elastic distributions was the spreading width due to CRDC detectors themselves:

 

 

_ 2 2 . _ 2 2
00,131 _ 00,111 + 00,113 ’ 0¢.€l “ \/O¢,in + Comes ‘ (419)

73

 

Fortunately, the two contributions to elastic spreading could be separately determined
by making use of target-out mask calibrations.

For the dispersive direction, we have

(119 2 d6 2
00,res—¢(d—Il'0.r1) +(E012) a (4.20)

where an and r2 are the dispersive coordinates as measured in CRDCl and CRDC2.

 

The scaling factors in Eq. 4.20, dB/dcrl and dG/dzrg, are found directly from the

expression which determines the scattering angle:

 

9 = arctan ($2 I131) , (4.21)

where l is the distance between the CRDC detectors, or 1073 mm. Therefore,

£13_ (10

(1172 _dTl = [1(1 + tan2 9)]‘1 2 [l (1 + 02)]71, (4.22)

where the small angle approximation has been used in the last step. The analysis was

simplified by assuming that CRDCl and CRDC2 have similar resolving power, i.e.,
or, 2 01.,

Hence,

\/§ 0..

00,res(9 = 0) 2 l

(4.23)

The uncertainty in the dispersive position, 01,, was itself determined from the
experimental mask calibration. Specifically, a gate was placed on the central portion
of CRDC2 to select straight-line fragment trajectories through CRDCl, over which

the mask had been placed. The observed spot size (of width 0m.ask,;rl) in the resulting

 

CRDCl position spectrum was the result of intrinsic detector resolution folded with

the size of the aperture (Uhozel- Hence,

0mask,xl : V 032;, + 0,210“. , (4.24)

which, rewritten, becomes

2 2 2

0:131 : amask,.rl _ ahole ' (425)

Realistically, the contribution from the hole is that of a step function which spans
the hole-diameter, Ax (A2: = 1.57 mm). Comparing a Gaussian to a step function of
the same area, it can be found that the width, ohm, is related to the hole diameter

by

ohoze 2 0.39112: .

 

 

50 f I I I I I I
o Mask Calib. Data
0 -— Fit (0:0.861 mm)
40 » -
E
”I 30 f .
2
lg 20 . .
3
0
U
10 e .
O
O O 1 1 -1;

 

 

 

o v 1 1 v V
-60 -59 -58 -57 ~56 -55 -54 -53
x-Position (mm)

Figure 4.12: Sample data from the CRDCl mask calibration which has been gated
on the central region of CRDC2 to select straight-line trajectories. The fit for this
particular mask hole gives Omsk,“ = 0.861 mm.

75

‘ L.
*3-1'

 

'2.“

I

Thus, Eq. 4.25 simplifies to

2 2
011 2 0171ask,.r1 — (

0.39A1‘)2 . (4.26)

Fig. 4.12 shows an example of the fitting process using data from the CRDCI mask
calibration. The plot shown has been expanded about a peak which results from one
of the 1.57 mm holes in the mask. Several of these peak widths were averaged to find

that Umaskm = 0.83 mm. Inserting this result into Eq. 4.26 gives the experimental

I
1

dispersive position resolution, 01,1 2 or, = 0.56 mm, which is consistent with the
designed value for these detectors. The corresponding dispersive angular resolution

of the S800, 09,8, (given by Eq. 4.23), was therefore 2 0.74 mrad.

 

Exactly the same formalism can be applied for finding the non-dispersive width,
045,“. A more simplified approach, however, which was sufficient for the simulation,
came from comparing the average width from the dispersive mask calibration (e.g.,
Fig. 4.12) with that from the non—dispersive mask calibration; the resolution of the
8800 in the non-dispersive direction was found directly from a simple scaling argu-

ment:

0,, a (M) 0,, .
Omsk-,1.

From the non-dispersive CRDCl calibration, it was determined that 0mask,yl = 0.47 mm.
From the expression above, again assuming that the resolving power of the CRDCs
was roughly equivalent, we have 0y, 2 0y, 2 0.32 mm. Hence, the experimental
uncertainty in the non-dispersive angular determination, U¢>,res, was 2 0.42 mrad.

Fig 4.13 shows dispersive and non-dispersive scattering angle distributions from
elastically scattered beam projectiles for both studies. A Gaussian fit to these distri-

butions gave the widths, 09,61 and 0¢,el- Use of Eq. 4.19, possessing knowledge of 09”,

and 0W“, allowed for the determination of the incoming beam angular spreads, 09,,"

76

 

 

 

 

 

 

   

 

 

I 1 I 64 ,. I r . 0 I .
zoo - a) 180: Run 60 _° 9, b) 2"0: Run 87 -Flt (3-335 mrad.)
' -F1t (o=1.61 mrad.) 56 - . , . 1
. 2. . 41. . ;. -Fit (0:33.22 mrad.)
1': s.- - Fit (0:2.07 mrad.) 1: 48 ~ ' , : -
E 150 _ . . B
E E
2. a
3.100 g
c ‘2
3 a
u 50 8
o « ‘ o .
~10 -s o 5 10 -1o -5 o 5
Projectile Scattering Angle (mrad.) Projectile Scattering Angle (mrad.)

Figure 4.13: Angular distributions for elastically scattered (blocker out) 180 (a) and
20O (b) projectiles as measured by the 8800. The fits give the widths, 09.6) and am),
which can be used in Eq. 4.19 to determine 09,,” and 04,)".

Table 4.1: Angular widths used to modify the incoming and outgoing projectile dis-
tributions in the simulation. All values are in mrad.

 

Beam 00,111 Join 00,1'es comes
8o 1.43 2.03 0.74 0.42
200 3.27 3.19 0.74 0.42

 

 

 

 

 

 

 

 

and 04),“, which were used to modify the incoming projectile angles in the simulation.
Table 4.1 summarizes the pertinent angular information which was utilized for the

simulation.

4.1.7 Limitations of the simulation and related comments

The limitations of the simulation come not from its inherent design, but are instead
attributed to an experimental limitation. It was not possible to incorporate raw ex-
perimental cross section (and therefore B(EA)) information for discrete transitions
into the simulation. Obviously critical for these cross section determinations is a quan-
titative comparison of the appropriate experimental 7-ray yield to the total number
of incoming projectiles. Unfortunately, for these studies, no incoming beam monitor
existed. A beam rate estimate based on the S800 singles rate, for example, was not

possible due to the presence of the beam blocker. For the 200 study, the capability for

77

beam rate monitoring would have existed had it not been for the efficiency instability
of the multi-channel plate timing detectors (recall the discussion in Sec. 3.3).

As the reader can verify from a review of, for example, Eq. 4.4, it is the B(EA)
value for a particular discrete excitation which ultimately determines the excitation
probability for this state within the simulation. For the case of 18O, the simulation was
constrained in the sense that all pertinent B(EA) information has been previously
measured. Therefore, essentially two free parameters were left for 18O simulations,
namely the average high-threshold (Th) setting and the blocker positioning. (The
average low-threshold setting, T), had been approximately established from the simu-
lations of 7-ray source data presented earlier.) The best achievable strength function
agreement was found by first adjusting only these two simulation fields. Because the
overall normalization of the simulated 1’30 strength curve was fairly well established
by the collection of known B (E A) information, it was expected that slightly adjusted
B(EA) and branching information could be extracted from subsequent simulations
which had attempted to improve the overall strength function agreement.

The situation was rather different for the case of 200. As has been mentioned,
only the B(E2) strength for its first excited state has been measured. Because this
state is found at 1.67 MeV (~25 MeV in the lab), contributions from this state
were dramatically affected by both blocker positioning and the average Th setting.
In this sense, the overall simulated strength function normalization was inherently
more ambiguous. However, as will become more evident in Sec. 4.3.3, it was the
target background which facilitated the extraction of B(EA) information from the
2"0 experimental results. Specifically, contributions from the target 2? level, being
unaffected by blocker positioning, and much less affected by the high-threshold setting
than the 2? state in 200, provided the overall normalization, effectively constraining

the B(EA) strengths for higher-lying projectile levels.

 

 
 
 
  
 
 
 
    
 

:18!

1:0 '7 .' r..-

m_-..

par-b-

._.
wummmom-r-

80-:" .. _:.
n

60‘"

 

 

 

I I V 'l | l 1 1
10 30 10 so so 7n en

FWD, Recon., 11c. 7 En. (so keV/ch.)

Proj. En.-Loss (80 keV/ch.)

Figure 4.14: A plot of projectile energy-loss vs. total, forward, reconstructed, Doppler-
corrected 'y-ray energy for 180. Notice the pronounced off-diagonal enhancement
which appears at a 'y-ray energy of ~3.2 MeV.

4.2 180 results

4.2.1 Projectile energy-loss vs. total y-ray energy

The simulation proved to be an invaluable asset with regard to understanding the
more elusive aspects of the experimental results. Especially complicated, for exam-
ple, were the 2—D histograms generated by plotting a projectile’s energy loss against
the total reconstructed, Doppler-corrected (or lab-frame) 'y-ray energy captured si-
multaneously in the forward BaFg array. Such a plot with 180 experimental results
is shown in Fig. 4.14. As explained earlier in Sec. 3.4.2 the pronounced diagonal
enhancement appearing in this figure results from events whereby the projectile’s ex-
citation energy has been recovered as 'y-ray radiation in the forward array. (For this
particular example, the diagonal enhancement has a slope which is greater than one
since Doppler-corrected energy, not lab-frame energy, is plotted on the :r-axis.) Any-
thing falling below and to the right of this diagonal is energetically forbidden, while
events above and to the left result from multi-step 'y-decays in which one (or more)
of the 'y—rays was not detected. This correct interpretation opened more challenging
questions, though; the physics which is manifested in the sub—structure observed in

Fig. 4.14 is less trivial.

79

For example, notice the pronounced ofl-dz’agonal enhancement which is highlighted
in Fig. 4.14. Projected onto the Doppler—corrected, 'y-ray energy axis, these events
are found near 3.2 MeV. One could deduce from the large relative cross section for
transitions to the 5.255 MeV (see Sec. 1.3) along with the strong decay branch from
this state through the first-excited state at 1.98 MeV (~56%) that one should see
an abundance of 'y-rays at ~3.2 MeV. What was not expected a priori, however, was
the fact that this enhancement was not characterized by the same projectile energy-
loss as those events which recorded a total y-ray energy of ~5.2 MeV. Resolution to
this apparent contradiction, which was first revealed by the simulation, comes after
considering the systematic bias introduced by the 'y-ray detection setup. Because of its
solid angle coverage, the forward BaF2 array was relatively less eflicient in its ability to
detect 7—rays which had been emitted at backward angles in the projectile rest-frame;
for these events, the projectile receives an energetic “kick” from its recoil against
the 'y-ray. Specifically, the (off-diagonal) enhancement found at a 'y-ray energy of
~32 MeV was correlated with a smaller projectile—energy loss than the (on-diagonal)
structure at ~5.2 MeV because it resulted from a missing 1.98 MeV y-ray — all else
being equal, the array had a detection deficiency for projectiles receiving an energetic
(positive-z) boost from that missing 7-ray.

Fig. 4.15, which plots the same quantities shown in Fig. 4.14, strategically illus-
trates an evolution in the simulation’s level of sophistication. For simplification, the
blocker has not been incorporated. Fig. 4.15a has been generated without including
projectile-y-ray recoil. Furthermore, perfect detector resolving power has been as—
sumed. Notice the horizontal lines which result from excitations to each particular
level in 180 that have been highlighted by orange dotted lines. Sub-structures ob—
served within these horizontal enhancements result from multi-step decay events for
which at least one 'y-ray has eluded detection. Enhancements resulting from the two

contributing target states are also shown — an indication that the physics is simply

80

 

1o r.rfi.»rrfiw vf. 4+, .fiir riY—rr
a) -“Perfect" Energy Resolution 18
- No Projectile Recoillng O?

 

' - No Blocker
28 .L
> i
u . . .
5 ----- u-* - :r. ‘- :..a=vm@a—s.193(vm1.i 10
in , ‘, ’ _ . .‘ -
m 1 .
.3 6 r' ' r W565 1M1.) -
> i
E’
8
w 4 «wt—3 .920 (Proj.)
é’ 1 ass (big ) 1
g 2 615 51mg) 1
t 2 1 9132(ij) ‘

l
1

_ kEnergy Correlation
0 __‘_7 Diagonal :in Sim. Egcltations jlo.

 

     

 

 

 

 

 

 

 

 

 

180 animal)
’3 p - _'.-'.: g .2. j
s 255 p
3 ( m ) 10
5
In
8
+6”’
>~
E‘ 1
g I
in . - .085 (Tara)
I) ‘ E— - ' ’1 1
= ‘. ' i
g ‘. 1.982 (Proj.)
2 i.
a 3‘. 2 615 Tara.)
2
D) -‘Perfe ct” Energy Resolu ion
— "at. 7‘. wheat-.1 Recoiling
- No Bocker I j 10‘
0 ~ leb" Sim 7

 

 

 

 

 

 

 

 

’>‘
I)
5 .
ti . 1’
3 6 -
$. 1
E
[u
2 ‘ ‘
' c)- Experimental Energy Resolution
-w_im Projectile Recoiling _
.. - No Blolcker -
o ' 1 2x10‘ Sim 7,
o 10

FWD, Recon., D.C. 1 Energy (MeV)

Figure 4.15: An evolution plot of projectile energy-loss vs. total reconstructed,
Doppler-corrected 'y-ray energy for simulated 180 data, generated with an increas-
ing level of sophistication. a) The recoil of the projectile from the emitted 'y-rays has
been neglected. Ideal detector resolution has also been assumed for both the 8800
and the Ban arrays. b) Projectile recoil has been included. c) Projectile recoil and
experimental detector resolution have been included. The blocker has been placed at
0.0 MeV projectile energy-loss in all cases.

81

wrong for this case is that the target states do not fall on the energy correlation
diagonal, shown as the dotted blue line. Fig. 4.15b shows the equivalent histogram
generated after the inclusion of projectile recoil from emitted 7-rays into the simu-
lation. A diagonalz'zation of the multi-step decay lines is observed when comparing
Fig. 4.15b with Fig. 4.15a. Additionally, the slope of the energy correlation diagonal
is seen to increase, and it now properly encompasses the target states. Fig. 4.150
incorporates the experimental detector resolution for both the 8800 and the BaF2
detectors.

Direct comparison of Fig. 4.150 with the experimental equivalent (Fig. 4.14) pro-
vides confidence, though an 8800 energy resolution discrepancy remains. Specifically,
the experimental 8800 projectile energy-loss measurement is plagued with signifi-
cantly poorer resolution than that of the simulation. It is assumed that this observed
difference is a manifestation of the S800 reconstruction process. This is logically jus-
tified by the fact that the simulation, by construction, has included no additional

smearing due to trajectory reconstruction; any discrepancy observed must therefore

0!
O
O

 

 

 

 

 

 

 

T I l r T I l

“'0 a
a — Exp. (o.< 15 mrad.)
-¥ 400 - — Exp. (0315 mrad.)
8 For Events Having —Slmulatlon (All 0.)
E DepOSIted Between
: 300 - 4.48 and 5.52 -
8 MeV in the o—lelO‘ Simulated
U Forward Array Excltations
‘D 200
0
5
'5
g 100
O
2

0

 

0 2 12 14 16

4 6 8 1o
Projectile Energy-Loss (MeV)

Figure 4.16: Projectile energy-loss for 180 events in which the forward array has
recorded between 4.48 and 5.52 MeV, which selects essentially only excitations of the
2;”. The experimental data has been subdivided with a constraint on the projectile’s
spherical scattering angle, 9,. Note that the experimental S800 energy resolution
is worse for larger scattering angles. The simulation, shown in black, includes no
smearing effects due to the reconstruction process, causing the resolution discrepancy
observed here.

82

be attributed to this process.

For the present discussion it is constructive to examine Fig. 4.16, which shows
experimentally-measured projectile energy-loss distributions gated on (spherical) scat-
tering angle, 6,, for events having deposited between 4.48 and 5.52 MeV (Doppler-
corrected) in the forward array. This energy constraint essentially selects only those
events whereby the 5.25 MeV projectile state has been excited. Also included in
this figure is the simulated result, which, by comparison, reveals that the projectile
energy resolution discrepancy is more dramatic for larger projectile scattering an-
gles. Due to imperfections in the magnetic field mapping, the 8800 reconstruction
precision is known to suffer for more-extreme projectile trajectories [7]. In principle
the experimental energy resolution could be modestly improved by performing the
8800 reconstruction calculations to higher order (>2). Still, with the current study,
obtaining higher-precision 8800 energy measurements would in no way improve the

experimental results, as they are derived from complimentary BaFg information.

4.2.2 180 strength distributions

Shown in Fig. 4.17a is the final experimental 18O strength distribution (red data
points) along with simulated data (black solid line) which was generated using known
B (E A) and branching information as input [22,31,35]. The experimental results have
been normalized to the simulated data in the region where the target 4.085 MeV state
is the dominant contribution (between 2.5 and 2.9 MeV). The simulation reproduces
the experimental data reasonably well, though there exist discrepancies which seem to
be tied to excitations to the third-excited 2+ state at 5.255 MeV. For example, a small
decrease in the B(E2) T value for the 5.255 MeV combined with an increase in the
branching ratio from this state to the first-excited 2+ configuration at 1.982 MeV will
improve the comparison. For additional improvement, the B(E2) T to the second-

excited 2’“ at 3.920 MeV might also be increased. Fig. 4.17b shows the individual

83

 

 

 

 

I I I T I I I I

 

 

 

 

s —
a) 1.5x1o' Simulated Sim. Total 1° b) 1.5x10' Simulated fl'fg-Efix
_ '- Excitations ° Norm. Exp. Excitations E1 Total
. , q 10‘ _ — £2 Total
Exp. Data Normalized _ 53 7°“

 

    

,. a... to Sim. Data Between .
2.5 and 2.9 MeV

:- ‘ ‘ -
or. .
‘0 o
. . :45

o a
5'.
b ‘ d
O

 

 

 

 

 

Normalized Counts/20 keV
H N u 8 U! V
. § § g 2 g E § §
Counts/20 keV

l l l l 1

2 3 4 5 6
FWD, Recon., D.C. Energy (MeV)

2 3 4 5 6
FWD, Recon., D.C. Energy (MeV)

Figure 4.17: a) Final experimental 18O strength distribution (data points) shown with
simulated data (solid line) generated using known B(EA) and branching information
as input [22,31,35]. The experimental data has been normalized to the simulated re-
sults in the region where target contributions dominate (between 2.5 and 2.9 MeV). b)
The individual components which contribute to the total simulated strength distribu-
tion. Notice that E2 excitations completely dominate over the other multipolarities.
The target background is significant.

components which contribute to the total simulated strength distribution. This his-
togram demonstrates the fact that E2 excitations completely dominate the excitation
function for 18O in this energy region. The target background is clearly not a negligi—
ble component. As an illustration of the capabilities of the simulation, in light of the
above discussion regarding better agreement with experimental data, Fig. 4.18a shows
a simulated 180 strength distribution generated using slightly adjusted B(EA) and
branching information as input. Fig. 4.19 outlines the specific changes that were made
to previously established quantities. While better agreement in the targeted regions
has been established, a discrepancy at 'y-ray energies of ~4.3 MeV lingers. An adjust-
ment which would fill-in the simulated spectrum in this energy region involves, for
example, increasing the B(E 1) T value for the first-excited 1‘ state at 4.456 MeV by
approximately three orders of magnitude above the upper limit established in Ref. 22
(see Fig. 1.2). Alternatively, one could introduce a previously unobserved [35] decay

branch from the second-excited 1‘ state at 6.198 MeV to the first-excited 2+ state at

1.982 MeV. Unfortunately, due to the ambiguities that are associated with the simu-

84

 

 

    

 

 

 

 

 

 

 

 

8000 l I I I I 105 I I l 5' T t I
> 7000 _ a) . 1.5x10' Simulated — Sim. To“. . b) 1.5x10' Simulated _ “Ti fog,
g - Excitations - Norm. Exp. ‘ Excitations _ El Total

1° F — 52 Total
O 6000 ~ -
Q ' . > — E3 Total
3 5000 - . Exp. Data Normalized _ a)
g - to Sim. Data Between :1000
84000 ,_ . 2.5 and 2.9 MeV _, Q
'0 B 100
.. - C
g 3000 , . ‘r, . 3
“’ 2000 - . "it” . U
E “ 10
o
z 1000 — 4
o J l l I 1
1 2 3 4 5 6 7 1 2 3 4 5 6
FWD, Recon., D.C. Energy (MeV) FWD, Recon., D.C. Energy (MeV)

Figure 4.18: a) Final experimental 18O strength distribution (data points) shown with
simulated data (solid line) generated using slightly adjusted B(EA) and branching
information as input (see Fig. 4.19). As with the previous comparison, the experi-
mental data has been normalized to the simulated results in the region where target
contributions dominate. An improvement in overall agreement between simulated and
experimental data is obtained. b) The individual components which contribute to the
total simulated strength distribution.

 

 

    
 

10
Changes Made for
Improved Simulation
8 ” I Adopted ‘
9 I Used
in
E
‘; egezme‘rm‘) _
Bi 2.98(./.o.17)e+01
a: 2.9os+01 2‘
c s a“
“J 2 z
c 2.0(+/-0.3)E+01
2 4 . E+ 1 2.:
U
(D
9:
U
X
Lu
2 ._2_.
o o

 

 

 

 

180
Figure 4.19: The specific changes that were made to previously established 1"30 ex-

perimental quantities in generating Fig. 4.18. Known values are given in dark blue
while changed values appear in red.

85

lated blocker position and high—threshold setting, no recommendations regarding the
accuracy or status of 180 information can be confidently offered. What is important
to take from these comparisons is the fact that every feature of the experimental 18O
strength distributions has been reproduced, i.e., all the individual components have

been accounted for.

4.2.3 Angular distributions

The 180 dispersive (6t) and non-dispersive (cit) angular distributions obtained from
the “improved” version of the simulation (Fig. 4.18) are displayed as the solid lines
in Fig. 4.20 along with the final experimental distributions which appear as the data
points. While the agreement observed in this comparison is less than ideal due to
the complex nature of the S800 acceptance, further inspection reveals that exact
acceptance reproduction is unimportant insofar as the results of this comparative
analysis are concerned. Indeed, Fig. 4.21 shows a simulated 18O strength distribution
which was obtained after increasing the area of the acceptance “window” in (0,, 4),)
(see Sec. 4.1.6) by a factor of 2. Also included in this figure, for comparison, are the

simulated results from Fig. 4.18. The data, as before, has been normalized to the

 

 

 

 

 

 

 

 

 

 

 

 

       

 
  

 

 

 

 

 

 

2510‘ r T r . . . a _ 210‘ . . . T a r
E 0 Norm. Exp. 0 Norm. Exp.
E 2 10‘ - ‘ E 5 104 7 J
:9 . , 1.5x10' Simulated “2 1' ’ ..\ ,
o 0.- Excitations ° .4". '. 1.5x10' Simulatedl
g 1 5 10‘ .. g «e ’. Excitation:
3 3 1 10‘ -
g 1 10‘ ~ .8
.5 .5
— a 5000 -
E 5°°° ‘ E
O
o Q 0 O.
2 °\ 2 o.
o ‘ 1 1 L 1 o 4 l l I l l
-20 -10 0 10 20 30 40 50 60 40 -30 -20 -10 0 10 20 30 40
0t (mrad.) a! (mrad.)

Figure 4.20: The final 180 0, (a) and d), (b) experimental angular distributions (data
points) shown against the results obtained from the “improved” simulation (solid
lines). The experimental data has been normalized to the simulated results. Due to
the complexity of the S800 acceptance, the agreement observed is less than ideal.

86

 

 

 

 

 

' I I T T
g 1.4 10‘ L Exp. Acceptance .
x , — Exp. Acceptance x 2
4
g 1.2 10 . l
\ .
. Normalized between
13 1 1° r 2.5 and 2.9 MeV i
3
8 8000 - 1.5x10' Simulated -
1: Excitations
O 6000 . .
.5
E 4000 . .
O
z 2000 _ ..
o 1 1 1 1 1

 

 

 

2 3 4 s 6
FWD., Recon., D.C. Energy (MeV)

Figure 4.21: A comparison of the simulated 18O strength function from Fig. 4.18 with
that obtained after increasing the area of the acceptance “window” by a factor of
two. The former data set has been normalized to the newer in the region between 2.5
and 2.9 MeV. Notice that only slight differences can be seen.

region between 2.5 and 2.9 MeV. Notice that only a small change is perceivable in

the overall strength distribution.

4.3 Extension to 200

4.3.1 Initial interpretations

Recall the 200 experimental strength distribution presented in Chapter 3, which dis-
played two broad peaks between 5 and 7 MeV. The enhancements which are respon-
sible for these peaks are highlighted in Fig. 4.22, which is a familiar plot of projectile
energy-loss against total 7-ray energy. We interpret these structures as resulting from
E 1 projectile excitations. Specifically, two 2"0 1" states are observed at ~ 5.2 and
~ 6.7 MeV. The fact that these structures fall directly on the energy correlation di-
agonal is irrefutable evidence that these configurations were excited directly. Indeed,
the interpretation that these excitations are 1' states is the only conclusion which is
consistent with the theoretical shell model predictions. For instance, virtual excitation

of the known 2+ state at 5.234 MeV (see Fig. 1.4) with a strength that is consistent

87

pnnbmwagt‘dS:

 

   

   

i
.4 iii“ l’ .11. ~
E Energy Carrelatlon
rd «anonal :-
J11 l.‘ r" -|»_

FWD, Recon., D.C. 7 En. (so keV/c.)

 

    
  
 

Proj. En.-Loss (80 keV/ch.)

 

Figure 4.22: Projectile energy-loss vs. total, forward, reconstructed, Doppler-corrected
'y-ray energy for 200. Two projectile states at 5.2 and 6.7 MeV are observed. Gates
which have been drawn along the multi-step decay paths are highlighted.

with the results of this study would require that the predicted B(E2) be over four
orders of magnitude too low. The same logic applies to excitations of the (tentatively
assigned) 3‘ state at 5.614 MeV; in this case the theoretical B(E3) would have to be

increased by roughly two orders of magnitude.

4.3.2 'y—decay branching estimates

As discussed in Chapter 1, with the exception of decays from the second—excited
2+ state, no *y-decay branching has previously been established. It was entirely use-
ful, therefore, to extract any of this information which was warranted by the cur-
rent results. This goal established, first approximations for 'y-decay branchings were
taken from complementary information in 18O and/or from mean lifetime (7') esti-
mates based on theoretical B (EA) information. This information was then scrutinized
against any experimental evidence which was available.

The current discussion will, of course, benefit from particular examples. In light
of the interpretations in the previous section, of particular interest for the analysis
was decay information for these new 1‘ states. An investigation of analogous levels in
180 reveals that the 11‘ state decays via two significant channels, namely the 2? state

(~30%) and the 0? state (~70%), while the 12' state decays with high probability

88

(~90%) directly to the ground state [35] — i.e., decays which proceed via the emission
of E 1 photons dominate, as expected. For the extension to the unknown case 200,
mean lifetime calculations, assuming pure E1 decay for these 1‘ states, performed
using theoretical predictions for the B(E 1) i values, are undoubtedly useful.

Before proceeding, a short digression for a review of nuclear decay formalism as
it applies to this particular case is beneficial. The decay probability per unit time for
a particular nuclear configuration through decay channel n, denoted 7", is inversely

related to the mean lifetime, 7,, [15]. i.e.,
7,, = — . (4.27)

Assuming the decay probabilities for every possible channel are determined, the ab-

solute branching ratios, Br.", likewise are known, since

# chnls
Br." — 7" , with, 7,0,. = Z 7". (4.28)
n=1

7tot.

 

For the case of E 1 7-ray decay, the mean lifetimes are determined from the energy of
the emitted photon, Em, and the reduced transition probability, B(E 1; n) i, which

contains the nuclear information for the involved states. Specifically,

0.629

E3... B(E1;n) i ’ (4'29)

 

7“,, [fsec.] 2

where, above, the reduced transition probability has been expressed in units of 62-fm2
and E7," in MeV.

Table 4.2 summarizes E1 decay branching for the first two excited 1‘ states calcu-
lated with the formalism described above from the theoretical level scheme presented
in Fig. 1.4. For each decay path, the energy and spin-parity of the final state along

with the B (E 1) i value for the transition are specified, along with the resulting mean

89

Table 4.2: E1 branching from the first two excited 1‘ states calculated from the
predicted level scheme presented in Fig. 1.4.

 

 

 

E,- J;;, E, ,1, E, B(El) i 1 Br.
(MeV) (MeV) (MeV) (e2 fm2) (fsec.) (‘70)
5.1 1; 0.0 0; 5.1 1.4303 3.3E+00 77
5.1 1; 5.0 0; 0.1 2.1303 2.93+05 ~0
5.1 1; 2.0 2; 3.1 2.0303 1.1E+01 23
5.1 1; 4.2 2; 0.9 1.2303 7.2E+02 ~0
6.2 1; 0.0 0; 6.2 1.0303 2.6E+00 66
6.2 1; 5.0 0; 1.2 2.5303 1.5E+02 1
6.2 1; 2.0 2; 4.2 1.3303 6.5E+OO 26
6.2 1; 4.2 2'; 2.0 3.2E-04 2.5E+01 7

 

 

 

 

 

 

 

 

 

 

lifetime. This calculated branching information can serve as a guide when interpreting
the experimental evidence obtained after application of the free-form gates (“decay
gates” 1 and 2) which are defined on Fig. 4.22. The projections of these gates onto the
7—ray energy axis are shown in Fig. 4.23. Unfortunately, with the experimental 8800
resolution obtained, these cuts not mutually exclusive, e.g., some strength resulting
from excitations to the 11‘ state is inadvertently included in the decay cut for 12'
excitations.

An examination of Fig. 4.23a arguably reveals the signature of each of the expected

700 500 i l I I 1

13)

 

 

I

1,‘ Decay Cut

  
  

   

I

.1

i

400
500 a
a a
x x 300 j
o 400 ‘ O
3 e
c 300 .l g 200 "
8 3
u 200 a
100 ..
100 -

 

 

 

 

 

 

 

 

FWD., Recon., D.C. Energy (MeV) FWD., Recon., D.C. Energy (MeV)

Figure 4.23: a) Projection of “decay gate 1” from Fig. 4.22 onto the 'y-ray energy axis.
Included mostly within this cut is strength which results from excitation of the 11‘
state. b) The same for “decay gate 2,” therefore selecting excitation of the 12" state.
Evidence for various decay modes is highlighted for both excitation channels.

90

decay branches for the first-excited 1‘ state. For instance, the peak at ~ 3.7 MeV
likely contains components from both the 2;“ (4.072 MeV) and decays through the 2?“
(~ 3.6 MeV). Evidence also exists for decays via the first-excited 0+ at 4.456 MeV.
Decays which proceed through this state generally involve the emission of three simul-
taneous 7-rays, as, in most cases, the 0? state itself will decay sequentially through
the first-excited 2+ configuration. Assuming the 11‘ state exists at 5.2 MeV we have
the following for the energies of these three photons: 0.74, 2.79, and 1.67 MeV ——
the energy of the first photon in this set is adjustable in the sense that it depends
on the actual energy of the 11‘ state. Including the small but observable peaks at
roughly 900 keV and 2.8 MeV, evidence exists for all three of the 7-rays for decays
through the 0?. Additionally, the appearance of a 900 keV low-energy photon (rather
than 740 keV) is a first indication that the 11' state might actually be located above
5.3 MeV.

Moving on to a similar investigation of Fig. 4.23b, again, strong evidence of decays
proceeding through both of the first two excited 2+ states is visible. The fact that the
peak near 2.4 MeV (22* —> 21+ remnant) is sharper in this case suggests that decays
through the 2'; might be more important for this excitation channel. Assuming the
1; state is found at roughly 6.7 MeV, decays through the 0}“ state would necessarily
emit a ~ 2.24 MeV photon, which, in this case, is at an energy above the average
Th setting. Given the absence of an intense peak in this energy region, no decisive
evidence exists for decays through the Of“. This conclusion is consistent with the
evidence provided by analogous 180 states, as only its 11' state decays through the
0}” state with significant probability.

What has not been mentioned in the analysis of either spectrum in Fig. 4.23 is the
unmistakable structure at ~ 1.35 MeV. The analysis has revealed that this bump is
actually an escape peak for 1.674 MeV transitions. It appears at about 320 keV below
the 1.674 MeV peak, rather than 511 keV below, because this is a Doppler-corrected

91

spectrum. The fact that an escape peak is visible in this case and not for 2? decays in
18O is a manifestation of the Th settings, which, on average, were significantly higher

for the 180 experiment.

4.3.3 200 strength distribution and results

A comparison of the 200 experimental strength distribution with a simulated equiva-
lent is presented in Fig. 4.24a. With this comparison rather impressive agreement has
been established in the region above 3 MeV. To facilitate this, the first two excited 1‘
states were positioned at 5.35 and 6.85 MeV, which places them slightly higher than
the initial prediction from Sec. 4.3.1. The positioning of the If, indeed, is entirely con-
sistent with the interpretation based on the branching analysis in the previous section
which placed the state above 5.3 MeV from the observation of low-energy 7—rays at
~900 keV. Shown in Fig. 4.24b, meanwhile, on a logarithmic scale, are the individual
components which contribute to the simulated strength distribution. Most significant

is the fact that E 1 excitations, as expected, are dominating, which is especially true

 

 

 

    

 

 

 

 

6
1 10s , , r T , . 1o , , g 1
3 4 ‘ Norm EX 10’ - acmmns — £1 Total
8 10 1.5x10‘ Simulated - -— £2 Total
3 Excitations > ‘ — 153 Total
B 3 10
c 6 10‘ . o
5 Exp. Data Normalized N 1000 .
to Sim. Data Between E
‘8 4 10‘ 4.5 and 8.0 MeV .l g
.5 o 100 -
E U
2 10‘ .
o 10
z
o 1

 

 

 

 

 

 

 

4

2 3 4 s 6 7 2 3 s ' 6 7
FWD, Recon., D.C. Energy (MeV) FWD, Recon., D.C. Energy (MeV)

Figure 4.24: a) Final experimental 20O strength distribution (data points) shown with
simulated data (solid line) generated using estimated branching information along
with appropriately adjusted B(EA) values. The experimental data has been normal-
ized to the simulated results in the region between 4.5 and 8 MeV. b) The individual
components which contribute to the total simulated strength distribution. Notice that
E1 excitations are now the dominant contribution.

92

1 10'
i

. 220.0?
i

6.85 (Proj.) ,’

H
O

on

, 5.35 (Proj.) ‘7 10

.h

   

 

N

L .: 2x10“ Simulated Excitations J
12

l
1 ‘
o 'L' I

o 2 2 4 6 8 1o
FWD., Recon., D.C. 7 Energy (MeV)

 

 

Figure 4.25: Projectile energy-loss vs. forward, reconstructed, Doppler-corrected "y-
ray energy for simulated 2°C events. Comparison with the experimental equivalent,
Fig. 4.22, provides confidence that the results of the 200 experiment have been prop-
erly interpreted.

above 4 MeV. A comparison of Fig. 4.22 with Fig 4.25, which is the simulated version
of projectile energy-loss vs. total, forward, Doppler-corrected 'y-ray energy, further
emphasizes that the simulation has achieved remarkable agreement. Moreover, it is
apparent from this comparison that nothing significant has been overlooked in the
interpretation of the experimental results.

The production of this simulated result presented in Fig. 4.24 has utilized the
200 level scheme which is given in Table 4.3 along with the branching presented in
Table 4.4. The measured value of the B(E2) for the 2? state has been used, while
the B(E2) for the 2; is consistent with the theoretical prediction for this state of
7.8 82 fm“. Notice that the simulation has incorporated a 3’ level at 5.0 MeV. Re—
call, the experimental 200 level scheme includes two states with undetermined and
unconfirmed spin-parity at 5.002 and 5.614 MeV, respectively. For the simulation, it

was simply assumed that the 5.002 MeV is the 3‘ state which corresponds to the

93

Table 4.3: The projectile and target level schemes utilized in the production of the
simulated results presented in Fig. 4.24. The known experimental value of the B(E2)
for the 21* state in 200 has been used [26], along with that of the B(E3) for the 31’
state in 208Pb [31]. The B(E2) value for the 21+ state in 208Pb has been adjusted

within the reported experimental limit [26].

Projectile: 200

 

 

 

E; (MeV) J}: B(EA) T022511”)
1.67 2; 2.80E+01
4.07 2; 9.00E+00
5.00 3; 1.60E+03
5.23 2; 7.001304
5.35 1; 1.351302
6.85 1; 1.10E-02

 

 

 

Target: 208Pb

E1 (MeV) J]: B(EA) T (82 fm”)
2.61 3; 6.11E+05 L
4.09 2; 2.60E+03

 

 

 

 

 

 

 

 

Table 4.4: All 200 branching used for the simulated results presented in Fig. 4.24.
Only the branching from the 25; state has been previously established [34].

 

 

 

 

 

 

 

 

 

E,(MeV) J3, E,(MeV) 5;, E,(MeV) Br.(%)
1.67 2; 0.00 0; 1.67 100
3.57 4; 1.67 2; 1.90 100
4.07 2; 1.67 2; 2.40 74
4.07 2; 0.00 0; 4.07 26
4.46 0; 1.67 2; 2.79 100
5.00 3; 4.07 2; 0.93 18
5.00 3; 3.57 4; 1.43 6
5.00 3; 1.67 2; 3.33 76
5.23 2; 4.07 2; 1.16 10
5.23 2; 1.67 2; 3.56 60
5.23 2; 0.00 0; 5.23 30
5.35 1; 4.46 0; 0.89 22
5.35 1; 4.07 2; 1.28 10
5.35 1; 1.67 2; 3.68 38
5.35 1; 0.00 0; 5.35 30
6.85 1; 4.07 2; 2.78 28
6.85 1; 1.67 2; 5.18 40
6.85 1; 0.00 0; 6.85 32

 

 

 

 

 

 

 

 

94

 

predicted level at 5.0 MeV, though no experimental evidence exists for this assign-
ment. Given the expected insignificance of E3 excitations from the predicted B(E3)
value for the theoretical 3‘ state, the specific placement of this level essentially has
no effect on the results. Hence, this ambiguity is of no concern.

What has not yet been discussed concerning Fig. 4.24 is a significant discrepancy
between the simulation and the experimental results from roughly 2 to 3 MeV. For
the simulation (as can be seen in Fig. 4.24b), this is the region where 'y-rays from the
first-excited 2+ state in the target and the 2'; level in the projectile are the dominant
contributions. Reproduction of the escape-peak at ~1.35 MeV along with a 1.67 MeV
peak intensity which remains consistent with the measured B(E2) for 2? requires
that the average T h setting used in the 200 simulation be lowered substantially from
3.8 MeV (the value used for 180 simulations) to roughly 1.5 MeV. It is precisely this
lowering of the average Th settings, however, which facilitates the emergence of the
observed discrepancy. Keeping the average Th threshold at a low setting, much better
agreement between 2 and 3 MeV can be established by simultaneously increasing the
B(E 1) values for the 1‘ projectile levels while decreasing their 2'; decay branching,
effectively reducing the relative intensity of the discrepancy.

An illustration of this point is provided by Fig 4.26, which is a familiar plot of
simulated data which has been generated using precisely this strategy. The reader
can verify that much better agreement with the experimental result in the targeted
region has been established. Table 4.5 specifies the B (EA) information which has been
incorporated into the simulation to produce these results. Note, especially, that the
B(E 1) strength for the 1‘ states has been increased substantially. For example, the
B(E 1) for the 1; has been boosted by a factor of more than 14 over B. A. Brown’s
prediction. Two new discrepancies have emerged in this process, namely, the simula-
tion now under-produces 'y-rays from de—excitations of the 21* and 2; levels. Out of an

attempt to resolve the latter issue, the B(E2) for the 2; was increased by a factor of

95

 

 

10‘ I t —T I

 

 

r j r ' r ' —Slm. Total

_ a). Sim Tom ‘ b) 1.5x10‘ Simulated H mg Tm,
‘° . ' 105 L Excitations ._ E1 Total
1.5x10‘ Simulated : ' I p. -— £2 Total

 

    

 

 

Excltatlons — E3 Total

3.

 

Exp. Data Normalized
to Sim. Data Between
4.5 and 8.0 MeV

u. .. 3 ...
3. 2‘2. 8.. 3..
Counts/20 keV
§ §

 

 

Normallzed Counts/20 keV

 

 

 

 

1.. 1 1 1 , 1 | 1 1 1
o 2 3 4 s 6 7 s 1 3 4
FWD, Recon., D.C. Energy (MeV)

 

 

2 s 6 7
FWD., Recon., D.C. Energy (MeV)

Figure 4.26: a) Final experimental 20O strength distribution (data points) shown
with simulated data (solid line) generated using, for example, substantially increased
B (E 1) values for each of the 1’ states. The experimental data has been normalized to
the simulated results in the region between 4.5 and 8 MeV. Much better agreement
has been established in the targeted region. b) The individual components which
contribute to the total simulated strength distribution.

nearly four, to 30 62 fm“. Further improvement of the discrepancy at ~4 MeV could
be gained by additional increases of the B(E2) for the 23L state. However, this would
come at the expense of an increased overabundance of 2.4 MeV 7-rays — recall, the 2';
configuration decays with high probability through the 2:" state. The only strategy
for simultaneously improving both of these new discrepancies involves lowering the
B(E2) strength for the 2; closer to its predicted value while further-increasing the
B(E 1) values for the 1— states. A relative boost of 2? and 2‘; 7—decays could then
be provided by funneling more of the 1— decay probability through each of these 2+
levels, at the expense of the direct ground state decay channel.

Given this, the B(E 1) strengths presented in Table 4.5 can be interpreted as
experimental lower limits. While these B(E 1) strengths are, in general, higher than
the shell model predictions for levels below 6.9 MeV, they are not unreasonable.
For example, calculations performed by H. Sagawa and T. Suzuki (using the WBlO
residual interaction) predict the existence of two 1‘ levels between 6.7 and 7.5 MeV

with B(El) strengths of 0.014 and 0.024 e2 fm2 [32]; alternatively, an integration of

their calculated dipole strength curve (which is presented as Fig. 5.1 in Chapter 5)

96

Table 4.5: The projectile and target level schemes utilized in the production of the
improved 200 simulated results presented in Fig. 4.26. The B(E2) strength for the
2? state in 20O has been increased within the established limit [26], while that of the
22+ state is a factor of nearly four above the prediction. Note, the B(E 1) strength has
been substantially increased.

 

Projectile: 200

 

 

Ex (MeV) J],r B(EA) T (e2 fm”)
1.67 2; 3.0013+01
4.07 2; 3.00E+01
5.00 3; 1.60E+03
5.23 2; 7.00E-04
5.35 1; 6.20E-02
6.85 12- 3.50E-02

 

 

 

Target: 208Pb
E; (MeV) J; B(EA) T (e2 1m”)
2.61 3; 6.11E+05
4.09 2; 2.60E+03

 

 

 

 

 

 

 

Table 4.6: 200 1‘ branching used for the improved simulated results presented in
Fig. 4.26. Branching for all other states is the same as presented in Table 4.4.

 

 

 

E,-(MeV) J51, E,(MeV) g], E,(MeV) Br.(%)
5.35 1; 4.46 0; 0.89 19
5.35 1; 4.07 2; 1.28 5
5.35 1; 1.67 2; 3.68 46
5.35 1; 0.00 0; 5.35 30
6.85 1; 4.07 2; 2.78 10
6.85 1; 1.67 2; 5.18 39
6.85 1; 0.00 0; 6.85 51

 

 

 

 

 

 

 

 

from 4 to 8 MeV, the region that encompasses the two established 1‘ states, results
in ~0.09 e2 fm2. Also, complementary WBP shell model calculations by B. A. Brown
(which have been the basis for previous comparisons within this thesis) predict the
existence of a ~7.7 MeV state with a larger B(E 1) strength of 0.075 62 fm2 [9].

The specific 1‘ 7-decay branching which was incorporated into the simulation to
produce the results presented in Fig. 4.26 is given in Table 4.6. All other branching
used for this improved simulation is identical to that presented in Table 4.4. As has

been mentioned, the decay ratios for the 2; state are the only ones which have been

97

 

 

Simulated 1,’ Excltatlons

Simulated 1,” Excitations

-

Counts/20 keV

 

 

 

 

 

 

                

l l l l 1 .L

 

 

 

 

1 2 3 4 s 6 2 o i 2 3 4 s 6 7
FWD., Recon., D.C. Energy (MeV) FWD., Recon., D.C. Energy (MeV)

Figure 4.27: The simulated strength curves resulting from excitations to the If (a)
and 12‘ (b) states. Peaks resulting from various decay paths are highlighted. Note the
similarities with Fig. 4.23.

previously established [34]. For both the improved 200 simulation, and the former
presented as Fig. 4.24, educated guesses have been made for the branching from 0?,
31’, and 2'; states based mostly on comparison with the known 180 level structure [35].
Again, given the fact that excitations to the 31‘ and 2; states are unimportant, how-
ever, the uncertainty associated with this guessing bears no weight on the results. As
has been demonstrated in previous discussion, the branching for the two 1‘ states was
established from theoretical predictions, 180 information, and from “trial and error”
comparison against experimental evidence, the latter method ultimately bearing the
most weight. Precisely because of this method by which the 1“ branching has been
determined, it is extremely difficult to establish the associated uncertainty. A conser-
vative estimate, though, can come out of a comparison of the 1‘ branching presented
in Table 4.4 with that in Table 4.6, e.g., no individual decay branch differs by more
than 20 (in units of absolute percentage).

Confidence in the obtained 1‘ branching information is gained from a comparison
of Fig. 4.27, which shows the (improved) simulated strength curves resulting from
excitations to the 11’ (a) and 1; (b) states, against the experimental equivalent pre—
sented earlier (Fig. 4.23). Unlike the experimental 1‘ decay spectra (which contained

contamination due to inadequate S800 energy resolution) the simulated spectra are

98

 

 

3 10s 1 r T T u r r 2.5 105

 

 

 

 

 

 

 

 

 
   
   

  

 

 

 

 

 

 

o I I I T T l l
E a) —-Slm. cm 6 b) Sim. Data
E 2_5 105 _ . Norm, Exp. Data _ g 2 05 . Norm. Exp. Dan
1 " an -4
q Q ‘ “ ’44. I
o 2 105 ~ 1.5x10' Simulated . O- A 1.5x10 Simulated
E Excitations E 1 S 105 _ Excatatlons
C
:1 1.5 10’ ~ - g
8 8 .
3 1 10‘ - 1 3 1 10 h '
E .5
E 5 10‘ ~ . “‘ 5 10‘ ~ -
o E
z .. o
A” J ‘F‘ ' Z 0 ‘4" 1 1 1 1 1 1
-30 -20 -10 0 10 2° 30 4° 50 —4o -30 -2o -10 o 10 20 30 40
0t (mrad.) 1’: (mrad.)

Figure 4.28: The final 200 6; (a) and (b; (b) experimental angular distributions (data
points) shown against the results obtained from the improved simulation (solid lines).
The experimental data has been normalized to the simulated results.

generated with a software out which excludes contributions from all other excitations.
The differences observed between Fig. 4.27 and Fig. 4.23 can therefore be attributed
to a combination of y-decay branching uncertainty and contamination in the experi-
mental curves. The important conclusion from this comparison is that no transitions
(peaks) in the experimental decay spectra are unaccounted for, i.e., all important 1"
decay branches have been incorporated into the simulation.

For completeness it is necessary to show the angular distributions obtained with
the simulation against those which were experimentally observed. As was the case with
the 180 comparison, Fig. 4.28 demonstrates that while the microscopic agreement is
not so impressive, the overall acceptance has been adequately reproduced. Moreover,
the simulation has reproduced the double-peak structure observed in the experimental
a, data. As was first explained in Chapter 3, the distribution is double-peaked for
the case of 200, rather than single-peaked as in the 180 experiment, because of the

differences in the shape of the acceptance “window.”

99

Chapter 5

Closing remarks

5.1 Experimental conclusions

Two successive Coulomb excitation experiments were performed at the NSCL in order
to investigate low-lying isovector GDR strength in 18O and 200. While no conclusions
could be reached regarding E 1 strength above the neutron separation energy for ei-
ther nucleus, it was possible to analyze the 'y-ray transitions resulting from excitation
of the discrete states. Monte Carlo simulations written within 3 GRANT environment,
used for direct comparisons with the experimental results, were invaluable with re-
gard to interpreting the experimental data. The analysis showed that E2 excitations
dominated the observed strength function for 180 while E1 excitations became more
important for the case of 200, as predicted by theory.

Two previously unmeasured 200 1‘ states were observed at 5.35 and 6.85 MeV.
These energies are in good agreement with, for example, B. A. Brown’s shell model
predictions that place excited 1’ levels at 5.1, 6.2 and 7.2 MeV [9] (see Table 5.1). '7-
decay branching from these 1‘ states has been established to within ~20%. Along with
direct ground state branches, both 1‘ states decay through the 2;“ state. Evidence

also exists for 1‘ *y-decays through the 2‘; configuration, this branch probably being

100

Table 5.1: 200 shell model predictions for 1’ levels from B. A. Brown [9] and also
from H. Sagawa and T. Suzuki [27, 32].

 

 

 

 

2OO shell model predictions

B.A. Brown (WBP) H. Sagawa and T. Suzuki (WBlO)

J],r E (MeV) B(El) T (e2 fm2) J}: E (MeV) B(El) T (e2 me)
11‘ 5.1 4.3E—03 11‘ 4.1 3713—04
12’ 6.2 3.1E-03 12‘ 5.5 2.5E—03
1; 7.2 2.6E-03 13‘ 6.1 8.9E-03
14' 7.7 7613-02 14’ 6.8 1.4E-02
1;; 7.5 2.4E—02

 

 

 

 

 

 

 

 

more important for the 6.85 MeV state. Specific to the 1‘ state at 6.85 MeV was the
observation of a decay branch through the 0+ level at 4.456 MeV. In addition to having
established the energies and approximate 7-decay branchings from these two excited
1‘ configurations, approximate B(E 1) T lower limits have been extracted from the
results. Specifically, B(E1;0.00 —> 5.35) T 2 0.062 e2 fm2, while B(E1;0.00 —) 6.85) T
2 0.035 82 fm2. As can be verified from a comparison with Table 5.1, these values are,
in general, somewhat higher than predictions for 1‘ levels.

To investigate the mechanism which results in larger B(E 1) values for these 1‘
levels in 200 it may be useful to compare 180 strengths and the current 200 results (in
Weisskopf units) with known B (E 1) strengths for discrete levels in complementary 2
and 4-valence-neutron systems such as 42"“Ca and/or 58"50M. Unfortunately, due to
the experimental challenges associated with much higher level densities in this mass
region, not much experimental information is currently available for these nuclei. For
example, only one 1' level has been established in 42Ca (3.885 MeV) [30] while none
are established in 44Ca [11]. No B(El) information is currently known for either
calcium isotope. 1‘ levels have been established in 58Ni (at 5.903 and 6.024 MeV,
having B(El) strengths of 0.0070 and 0.0015 W.u.) from (e,e’) and ('y, 7’) studies [8].
Unfortunately, no such information currently exists for the more relevent 4-neutron

skin configuration, 60Ni [2].

101

5 .2 Future virtual photon scattering studies with
200 at the NSCL

Shown in Fig. 5.1 is an 200 dipole strength prediction which has been calculated as-
suming lflw excitations in the (0p-180d—1p0f) shell model space with a WB10 residual
interaction. While the current study has been unable to verify these predictions re-
garding strength above the neutron binding threshold, the results summarized in
Sec. 5.1 provide confidence that a follow-up study using a similar experimental set-up
will be successful. For example, the measured intensity of de-excitations from the
6.85 MeV level in the current study allows for a reliable estimation of counting rates
for higher-energy 'y-rays. Fig. 5.2a) plots expected 'y-ray intensities per 1 MeV bin,
normalized to the intensity of 6.85 MeV de-excitations. This figure has been generated
from Coulomb excitation calculations which have utilized the B(E 1) information in
Fig. 5.1 along with the shell model prediction for the B(E 1) T value for the second-
excited 1‘ state (0.0031 e2 fm2) [9], assuming, conservatively, that neutron decays
are 1000 times more probable than 7—ray decays above Sn. Separate intensity curves
have been generated for total laboratory frame acceptances of 20, 40, and 60 mrad.

It should be mentioned that the incorporation of the current experimental findings,

 

A 2°o 1'
> Mabel
(D —T.-2
Z ----- 1,.3 WB10
\
~ 0.2

E :‘-
H— ,I.
v :..

3 E‘ 1
2 =' .
«or i :i '.
tr. "="1
x. 5 ' i.
to ,i \
'O .'

0.0

 

 

 

2 6 10 14 184222 26 30 3738 42
2°O Excitation Energy (MeV)

Figure 5.1: 200 E1 excitation function, dB(E1) /dw, calculated with lhw excitations
in the (0p-180d-1p0f) model space using a WB10 interaction (taken from Ref. 27).

102

 

1 I I I I I

 

 

 

 

  

 

   
 

 

 

 

 

 

 

 

 

0‘1 I I I I I Mai 20 d
. --o--e 2 m .
> .- 6.72 come/hr. 56;. a
g 0,3 _ . . ""'9Lab“° mrad. ..
o' 5 Ma .
0 01 - . 4 \ '4' ~,. --0--6La;=60 mrad.
.A t . 5. Q .
.4" , : - i 0.6 ~ .
:7 * in . o p- a , ,.
\ v I \
0—0 0.001 '- - U ‘ ‘
1: I ‘ 4
g 0 0.4 _ ‘\‘ \. "
g *eflfggzo mrad. g 4.18 coinc./hr. . 0
0.0001 ~ -e—e[‘§§e40mna. 4 .g 02 _ 1--“ u.“ , ‘ .
-*— Snag-60 mrad. U ‘ ‘ ‘ F r ..
1.42 colnc./hr. “‘..
10's 1 1 1 1 L 0 l l 1‘--.'Lfi"’-l-Qg-4
8 10 12 14 16 18 20 8 10 12 14 16 18 20
rRay Energy (MeV) y-Ray Energy (MeV)

Figure 5.2: Predictions for intensities of 'y-rays between 8 and 20 MeV based on
Coulomb excitation calculations which have used theoretical information presented
as Fig. 5.1 along with the B(El) prediction for the 12' state. Curves have been
generated for laboratory-frame acceptances of 20, 40, and 60 mrad. a) The y-axis has
been normalized to the intensity of y-rays resulting from de-excitation of the 6.85 MeV
level. b) The experimental counting rate for 6.85 MeV excitations has been used to
re—express the intensity calculations in more informative units. — these intensities are
valid for a 200 beam intensity of ~ 5 x 105.

namely that the B (E 1) for this 1‘ level is likely a factor of ~10 above the prediction
of 0.0031 e2 fmz, would shift the intensity predictions in Fig. 5.2a) a corresponding
factor of 10 downwards. This factor is regained, however, if we assume that neutron
decays are 100 (rather than 1000) times more likely.

Based on the experimental observation of approximately 7500 6.85 MeV decays
within a total run time of ~120 hours, with the assumption that the counting efficiency
of the array is flat in the energy region shown, one can translate the y-axis of Fig. 5.2a)
to units of coincidences per hour per 7-ray MeV. (The energy of the emitted, rather
than detected, 7-ray is what is specified by this conversion). The result of this re-
scaling process is given in Fig. 5.2b). The total integrated count rates per hour are
~1.4, 4.2, and 6.7 for the 20, 40 and 60 mrad acceptance curves, respectively. The
reader may recall from the 200 angular distributions (e.g., Fig. 4.28) that the achieved

S800 acceptance was ~20 mrad. This acceptance value, however, does not incorporate

the fact that the blocker removed approximately half of the 6; distribution which

103

eliminated ~25% of the projectile scattering cone, effectively reducing the count rate
by ~25%. Hence, the integrated count rate for y-rays between 8 and 20 MeV which
is predicted by Fig. 5.2b) for the current study becomes approximately 1 per hour,
which provides an explanation as to why the experiment was not successful at probing
the strength function in this energy region.

As one can see clearly from the relationship between the curves in Fig. 5.2, a
modest improvement in the experimental acceptance would markedly improve the
counting rates for 7-rays from the targeted energy region. This is a direct manifesta-
tion of the fact that the E1 Coulomb excitation probability distribution (as a function
of laboratory-frame scattering angle) peaks between roughly 20 and 60 mrad. For a
follow-up study using essentially the same set-up (with the re-positioned target) the
GDR-region coincidence counting rate would likely benefit from operating the S800
at, say, 1.7°. In addition to reducing the counting / acceptance losses due to the blocker,
this spectrometer placement would strategically sample the peak (rather than the in-
cline) of E 1 probability distribution function. These strides made in the counting rate
due to S800 positioning are meek, however, when compared with the improvement in
200 beam intensity which has been made available by the recent coupled cyclotron
upgrade at the NSCL. For example, according to the CCF/A1900 production rate
code LISE [33], the predicted beam intensity for 100 MeV/u 200 (assuming a 22Ne
primary beam on a 9Be production target) is ~ 1 x 107 which is an impressive factor
of 20 times that which was available for the current study. These combined improve-
ments boost the expected counting rate for y-rays between 8 and 20 MeV to ~100

per hour, which is indeed an exciting prospect.

104

Appendix A

Reaction kinematics

This appendix will delve into the realm of relativistic two-body kinematics. Relations
which are pertinent to the current study will be derived from standard momentum and
energy conservation principles. For simplification of all expressions, the replacement
0 ——> 1 will be made, or, equivalently, we will work in a scheme with implied units
for momentum and mass, [p] and [m], of [E] /c and [E] /c2, respectively. The physical
process we will examine involves a collision in the laboratory of particle A, with mass
mA and momentum pA, with particle B, of mass m3, which is initially at rest, as
represented in Fig. A.1. As is typically the case, symbols referring to quantities after
the collision will be denoted with a prime. The particles are scattered in the reaction
plane to laboratory angles 6A: and 63: with respect to the direction of [7}. Particles A’
and B’ carry away momenta 13A: and 53:, respectively. The possibility for an inelastic

process occurring is introduced by the simple substitutions,

mAr —-+ mA + ER.

7123: -> 7723 + EB’ , (A.1)

where E‘. and E", are the excitation energies of the particles after the collision.

105

(.L 5
>

Figure A.1: Scattering of particles A and B in the laboratory frame. Particle B is at

rest initially.

A.1 Review of Lorentz transformations

Before proceeding further into the dynamics of the collision using a relativistic treat-

ment, it will be useful to review the basics of Lorentz transformations. Formally, we

will work in Minkowski space, in which a particle’s 4-momentum is represented as

(Pl)

P2

 

 

W

(A.2)

This discussion will benefit from a particular example, where we relate a particle’s

4-momentum in a moving frame, denoted p’, to that in a frame which is at rest, p.

For simplicity we will assume that the motion of the primed frame is along the z-axis

of the stationary frame. The relationship is:

106

where A, the Lorentz transformation matrix, has the form [13]

(10 0 0 )

0 1 0 0

O
O

7 Mfi
-Mfi 7}

 

 

f
O
CD

To apply this for a simple case, assume the particle is at rest in the moving frame,

i.e.,

(o)

0
0

Kim)

The 4-momentum of this particle in the stationary frame can be calculated using the

 

 

inverse relationship

p=A*#. (Am

where the inverse transformation, A", is related to the direct transformation by

A-1==A52_,.

107

 

 

Therefore,
{1 0 0 0 \
0 1 0 0
A”: (A6)
0 0 ’l 4776’
(0 0 m3 7 }
Hence,

(0)

0

76m
KW}
But, on the other hand, since the particle is at rest in the boosted frame, this implies

(0)

0

 

 

 

\iE/

since the motion of the boosted frame is entirely along the z-axis.

 

 

Equating the two 4-vector expressions for p we find

I? = 75m

E = 7m , (A.7)

which are the well known relations for a particle of mass m which moves with velocity

3- Lorentz invariance demands that the contraction of the 4-momentum in any frame

108

be equivalent, so that

p-p=p2-E2=p’-p’=-m2.

Which gives us the famous relation,

E2 = p2 + m2 . (A.8)

A.2 Two-body collision dynamics

Of specific interest to this study is the derivation of an expression which will relate
the center-of-mass scattering angle, 6,156,", to that in the laboratory frame 6Arjab.
This is necessary since one of the tasks which the simulation needed to perform was
a calculation of BMW, given 9mm... EMab, and the excitation energy (energies) of
particle(s) A’ (and B’). A derivation of a useful expression for the total energy in the
center-of-mass is first required. Taking advantage of Lorentz invariance of the inner

product of the total 4-momentum before the collision in each frame we have

pcm ' pcm : plab ° plab °

Since the total momentum in the CM. system is by definition zero, the above relation

becomes
2 _ 2 2
Ecm _ Elab — plab '
But,

Elab = EAJab + EB,lab ; EB,lab = mg -

109

Hence,

2 _ '2 2 2
Ecm _ EA,lab + 2EAJGb m'B + 7’28 — plab ‘

Substituting
P1255 2 1921.165 = E21725 — mi 1
we come to the useful result,
Efm = 2EAJab mg + 7712), + 171% . (A.9)

Equation A.9 will be utilized at a later stage in the derivations. Of immediate
importance is knowledge of the velocity of the center-of—mass frame in the laboratory,

13cm —> 6. The Lorentz transformation gives it directly, since

p3,cm = 0 = A33 D3165 + A34 134,165 = 70371155 - 513mb) .

Rearranging, with E10,, 2 ENG], + m3, we find

pAJab
2 30m = —-—'— . A.10
B i EA,lab + m3 ( )

We will now work with quantities after the collision to derive the useful relationship
between the scattering angles of particle A’ in the laboratory and center-of—mass

frames. The 4-momentum of particle A’ can be expressed as

110

 

 

 

Figure A.2: Scattering of particles A and B as viewed in the center-of-mass frame.

(plumb Sin(9A',iab)

0
pA’.lab =
pA’,lab COS(6A',lab)

K iEA'Jab

 

in the laboratory frame, and as

(p... sin(9~,cm)

0
pA’,cm :

 

\ iEA’,cm

)

 

J

\

plum COS(6A’,cm)

 

}

(A.11)

 

(.412)

in the center-of—mass frame. The two are related by a Lorentz transformation, e.g.,

_ —1
pA’,lab — A PA',cm -

111

 

Thus,

{ pA’,cm Sin(6A’,cm) \

0
P713155 = . (A.13)

7{pA’,cm C03(6A’,cm) + IBEA’xm}
KiA/{B pA’,cm COS(6A’,cm) + EA’,cm})

 

 

Comparison of Eq. A.11 and Eq. A.13 provides three useful relations, namely,

pA’Jab Sin(9A'.iabl = PA'.cm. Sin(9A',cm)
19.1,,sz COS(6A’,lab) = 702.95.. 604011.55.) + BExlm}

EA',lab = ’7{5PA',cm 008(9A',cm) + EA’,cm} - (A-14)

Division of the first two yields

 

 

 

sin 6 ’cm
tan(6A',,ab) = ( A, 398..., ’
’7 (COS(6AI,cm) + 7477f?)
or,
. 6 [cm
tan(9Aijab) = Sln( A ’2 ) [3 . (A.15)
7 (cos(6A,,cm) + 13.9....)

This nice result is dependent on 6,156,,“ the velocity of particle A’ in the CM.
frame, which is a quantity that we would like to express in terms of those we already
know. We expect a priori that 5,0,0", has no angular dependence since total momentum
in this frame is always zero. We will begin by writing down an expression for the total

momentum in the center-of—mass after the collision:

 

_ _ 2 2
Ecm - EA’,cm + EB',cm - 7A’,cm mA’ + \/pBi,Cm + mB’ .

112

 

 

But since pg. m = 12%. cm, this becomes,

 

_ . . .‘2 2
Ecm — "I’A’xm 77’A’ + \/pA’.cm + 7”B’

 

: 7A’,cm 7nA’ + \/A”r2\’,cm 771fo — 772%, + 17228,

 

_ , , 2 A2 2
_ 7A,.C771171A’ + V772-AI( [IAI‘C1n — 1) + 77pr a (‘A.16)

This result, which is quadratic in “mm, can be easily solved for "mam. The solution
is

mi. - 77123, + E2

, (A.1?)

 

A __
IA’ ,cm —

2771A: ECm

which directly gives 13,156", since,

fiA’xm : V 1 — 7X30"; - (A.18)

From Eq. A.17 it becomes clear why Eq. A.9, which was derived from quanti-
ties before the collision, is particularly useful. Substitution of the solution for BMW
into the expression for 6A7)“, Eq. A.15, provides us with the desired relationship
which depends only on 6,156,,“ E Mob, and the excitation energies of the participating

particles.

113

Appendix B

Intermediate-energy Coulomb

excitation

This appendix will provide some useful mathematical formalism which is applicable
to the process of intermediate energy Coulomb excitation. “Intermediate” refers to
projectile kinetic energies of tens to a few hundred MeV/ u. The approach which will
be outlined here is semi-classical since a classical Rutherford trajectory is assumed
for the projectile, while the interaction between the projectile and target is treated

quantum-mechanically using first-order perturbation theory.

B.1 The excitation cross section
The differential cross section for Coulomb excitation can be expressed as [1]

d0 d0
— = — i—> 9 Bl
d0 (d5) ) Ruth. P f ( )

where the classical Rutherford cross section relation is given by

do a2
— = ———.- . B2
(d9) Ruth. 45in4 (2) ( )

2

114

 

 

 

Figure B.1: Coulomb excitation of the projectile (A) as it scatters from the Coulomb
field of the target (B), depicted in the center-of-mass frame. A virtual photon has
been absorbed in the process.

In Eq. B.2 the angle 19 is the projectile scattering angle in the center-of—mass, i9 =

6A,,cm, while a is defined as half the distance of closest approach:

a_b_ZAZBe2
’_2_ [1122 °

 

(13.3)

Above, Z A and 2;; are the atomic numbers for the projectile and target, respectively,
while 1) is the relative velocity of the projectile and target. (Since the target is at
rest initially, v = 12A.) The parameter n represents the reduced mass of the projec-
tile + target system, ll E mAmB/(mA + m3). It should be mentioned that excitation
of the projectile or the target is dealt with in an equivalent manner. For the remain-
der of this discussion, however, we will assume projectile excitation; all expressions
to follow are valid for target excitation with a simple exchange, Z A H 23.

The excitation process is understood as resulting from interactions of the pro-
jectile with the time-dependent electromagetic field, V(r(t)), which sweeps over the

projectile as it passes the target. From first-order perturbation theory we have

1 °° .
PH, = |a,-_,f|2 , where a,-_.f = fi/ (fl V(r(t)) Ii) e'lEf‘E‘V" dt (B.4)
—CXD

115

is the amplitude of the process which takes the projectile from state 2' into state f.
The electromagnetic interaction, V(r(t)), includes contributions from both electric
and magnetic multipoles. For this study it was sufficient to consider only electric
contributions (A = 1 — 3). As outlined in Ref. 1, the electric amplitude can be written

as

471'236 1
1;, = —,-—-' —-—— Lilli EA, 1 ‘1 f S . B.
a f m 1,. 2A+1< |M( MIN 1) Exp ( 5)
Defined in such a way, the nuclear properties enter the amplitude only through the

electric multipole matrix elements, (IiMil M(EA, p) [Ifo)‘, while the kinematics of

the collision are contained solely in the orbital integrals, S EM“ which are given by

 

Sm = / Kim’fim] e‘lEf‘Eil‘mdt. (8.6)

.. r<t>i+1

To further isolate the nuclear properties, the multiple matrix elements themselves
are expressed as a product of a Wigner 3—j symbol, which is the contribution from

angular momentum geometry, and a reduced matrix element, e.g.,

1,- 1 I,
—1’II,' [1 Mf

<11M.'|M(E/\,#)|11Mr>=(-1)""”‘ <1.“ M(E/\) Ill/l - (B7)

The complex orbital integrals, SEA,“ can be re-expressed as

__1_().-—1)! /2A+1 .
SEW—645914»! 77 R’V‘w’f) (8'8)

where 5 is defined as the adiabaticity parameter:

 

_a.Ef—E,-

6 2) h

116

 

Qualitatively speaking, the adiabaticity parameter can be thought of as the ratio of
the collision time (or amount of time the projectile spends within the target field)
and the characteristic nuclear period associated with the small change in energy,
E; —> E). This quantity must be comparable or less than unity for the transition
[2) —> | f) to occur - for larger values of 5 the nucleus will follow the perturbation due
to the potential adiabatically [1]. Given an incident beam energy, 6 therefore provides
an upper limit on the energy which the participating nuclei can absorb during any
virtual excitation process.

The form of the new orbital integrals, R1,,(i9, 6), which appear in Eq. B8 is intro-

duced through the relation:

123010 = 2 (121386) '2

 

[I z

u

The I ”(6,5) functions appearing in Eq. B.10 are defined in Ref. 1 as the Coulomb

excitation functions, which have the form

 

°° e+coshw+z'\/e2 —1sinhw ” . . ,
[Ap(l9,€) : / ( ) ez£(esmhu+w) dw ’

—oo (1 +ecosh w)’\+# (13.11)

where /\ and u are integer values, with A Z 0. The variable 5 used above represents
the eccentricity of the hyperbolic orbit, which is purely a function of the scattering

angle 19.

 

(13.12)

It is worthy to note that, defined as such, the I 1,,(19, 5 ) functions are real, i.e.,

14141915) = 13109.6)-

117

 

As will be discussed in Section 8.3, the I ”(19,5 ) functions can be calculated nu-
merically using MATHEMATICA [36] for all values of i9 and 5. Such numerical solutions

are rather computationally intensive. The approximation

-1 (Hi/2 ”‘1”? —).+ +1 _
1099.5) 2 (——)€—— (25) F (—2—”—) e “5/2W_%_;(2€e). (B.13)

which holds for small scattering angles, 19, was especially useful for the current
study since the scattering angles of 18"ZOO were limited to a small forward cone.
The W_%_% (265) quantities in Eq. B.13 are Whittaker functions, which are related

to confluent hypergeometric functions, U(a, c; z) [4]. Specifically,
W,m(1:) = e"“’/2r"’+1/2 U(m — l + 1/2, 2m + 1; :r) . (B.14)

Rewriting the expression for the differential Coulomb excitation cross section
(Eq. B.1) while making use of the definitions in Equations B.8, B10, and 8.11, along
with the expression for the contribution from nuclear properties, Eq. B.7, we have

deAWaE)
d9 .

 

B.1

—h_v

Z 2
dUEA < Be) a-2A+2B(E/\,Ii _) If)

Above, we have used the definition for the so—called differential cross section functions,

2

W Rims) sin‘4<

d9

(1— 1)!

(2A +1)!! ” (13°16)

lols‘o

=47rl

 

along with the expression for the reduced transition probability:

1
21f+1
1

= 21.- + 1|<1;IIM(EA) ||1.>|" . (13.17)

B(EAJi -> 1;) = |<1z‘||J\/1(E/\)||1;>|2

 

 

118

 

B.2 Quantum mechanical corrections

Up to this point the classical portion of this Coulomb excitation treatment has ne-
glected projectile energy—loss due to inelastic processes. One might expect that better
solutions for the Coulomb cross section might be found by replacing v with some
average velocity of the projectile over its trajectory. In fact, following the logic intro-
duced in Ref. 1, which makes use of quantum mechanical symmetry arguments, it is
realized that an improvement to this semi-classical approach is achieved if one uses
“symmetrized” expressions for a and 6. By these arguments, the (relative) velocity,
v, in the expressions for a and 5 (Equations B.3 and B9, respectively) should be
replaced by the average velocity of the projectile before and after the collision, i.e.,

v ——> vsym = (11A + vAr)/2, so that

ZAZB 62
uvém
_ ZAZB 82

— #UAUA'
as m E —E2
6 _> {sym :( y ) f h

vsym

= ——Z"ZBe2 (i — i) . (13.18)

fl '0 A’ U A

 

Hence, we arrive at the corrected version of the Coulomb excitation cross section,

 

 

 

£10151 dUEA Z138 2 _2,\+2 de,\(19.€sym)
, __ _ B E [i .5 1 ~ , B,
d9 ( d9 )sy ( hv ) 03y... ( A’ ’) d9 ( 19)

B.3 Differential cross section functions

As mentioned in Sec. 8.1, of specific importance to this study were contributions to the
virtual photon flux from three electric multipoles, namely E 1, E2, and E3. Therefore,

discussion for the remainder of this appendix will focus on a more detailed derivation

119

of the differential cross section functions, de),('l9, €)/d§2, for the three pertinent values
of x\. Notice that the arguments of the spherical harmonics (13,,(6, d))) appearing in
Eq. B.10 are constants. Specifically, 6 = 7r/2 and ab = 0. Given the property of
these functions that the product of p and the argument ¢ determines the complex

contribution, with all a5 = 0, we have the special situation where

_ #

i.e., all Y», coefficients in Eq. B.10 are real. Therefore, given the reflection properties

of the spherical harmonics, this implies

 

m =<—1)~Y;,1 =(—1>HYM. Ll '
Hence,
Yip 2 Y3“ .

Meanwhile, the fact that the argument 6 takes on the value 7r / 2 for all (A, it) gives us

YIO = Y2i1= 330 = Y3i2 =0.

Using the specific values for the remaining YA“ coefficients, along with the fact
that all I ”(19,5 ) are real, we arrive at the following expressions for the differential

cross section functions:

120

 

 

 

W = (517) 31:12; ( 7r;"_){1 l,(29 g) )f+1 09,0}
S’fE—jfn'fl = (fi) £77237 [(31.35— ) {13 2( (29 as) + 122209 £)}+ (1%)1300m]
deawlél : 1 4772
do (343) sin4(g) X
[(69%) {1; 309 a) + 1:309 a} + (Til ) {13-1010 + 1mm] -

(13.20)

MATHEMATICA [36] was used to generate both the exact versions of Eq. 8.20 (solid
curves), which were calculated using numerical solutions for the 1A,,(19, é) functions

(given by Eq. 8.11), and the (small-angle) approximate curves (dashed), which used

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70 r T I I I 3's I I I l I I 1.5 I If I I I '
A l 52' c) E3
II 60 :5
R l
( I
<9 .'

1; 50 1- 5
H :
3 40 :'
u U
o
.5
a 30
g 0.5- -
c 20 -
v
3 10 _
‘ir
o o l l l l l 1
00.511.522.53 00.511.522.53 00.511.522.53
0, (rad.) 0, (rad.) e, (rad.)
Am A,au A,cm

Figure B.2: Differential cross section functions, deA(i9,£)/dfl for El (a), E2 (b),
and E3 (c) excitations, shown for different values of the adiabaticity parameter, 5.
The solid curves were generated using numerical solutions for the exact expressions,
IM(19,§) (Eq. B.11), while the dashed curves were generated using the small-angle
approximate solutions for 1A,,(19, é) (Eq. B.13). The functions deA(19, £)/dQ have been
normalized such that the exact curves are unity at 0A:,c,n=7r. Table 8.1 gives the
appropriate multiplication factors.

121

Table B.1: The factors by which the curves in Fig

. B.2 should be multiplied

 

 

 

 

 

 

 

 

 

5:01 5:02 5:0.5

del(0,g)/d52 9.19 E -1 5.62 E —1 1.12 E -1
dfmw, g)/dn 4.97 E —2 3.89 E -2 1.32 E -2
de3(0,g)/dn 4.32 E —3 3.76 E -3 1.76 E -3

 

Eq. B.13 to generate the I,\#(19, 0’s. Some examples are given in Fig. B.2 for different
values of adiabaticity (€=0.1,0.2,0.5) and virtual photon multipolarity. For reference,
the adiabaticity parameter for the 200 study was ~0.018. The curves in Fig. B.2 have
been normalized such that the exact solutions, shown as the solid lines, are unity at
6A:,m=7r. The factors by which the curves in Fig. B.2 should be multiplied are given
in Table. 8.1.

As evidenced by Fig. B.2, the approximate solutions for the differential cross sec-
tion functions are accurate up to 19 2 0.5 radians, which is a region which extends
well beyond the angular acceptance for these experiments. Moreover, the approximate
solution is better for lower multipolarity. Indeed, for the specific case of E1 excita-
tions, the approximate solution for small adiabaticity is seemingly valid for all 19.
The approximate solutions, which were much less computationally demanding, were
therefore used for all Coulomb cross section calculations that went into the Monte

Carlo simulation, the details of which are included in Chapter 4.

122

Bibliography

[1] K. Alder and A. W inther. Electromagnetic excitation: theory of Coulomb exci-
tation with heavy ions. North-Holland Publishing Company, lst edition, 1975.

[‘2] P. Andersson, L. P. Ekstrom, and J. Lyttkens. Nuclear data sheets for A260.
Nucl. Data Sheets, 48:251—344, 1986.

[3] Application Software Group, Computing and Networks Division, CERN, Geneva
Switzerland. GEANT —— detector description and simulation tool, 1993.

[4] G. Arfken. Mathematical methods for physicists. Academic Press, Inc., 3rd
edition, 1985.

[5] T. Aumann, A. Leistenschneider, K. Boretzky, D. Cortina, J. Cub, W. Dostal,
B. Eberlein, T. W. Elze, H. Geissel, A. GriinschloB, M. Hellstrom, J. Holeczek,
R. Holzmann, S. Ilievski, N. Iwasa, M. Kaspar, A. Kleinbohl, J. Kratz, R. Kulessa,
Y. Leifels, E. Lubkiewicz, G. Miinzenberg, P. Reiter, M. Rejmund, C. Scheiden-
berger, C. Schlegel, H. Simon, J. Stroth, K. Siimmerer, E. Wajda, W. Walus, and
S. Wan. Giant resonances in unstable oxygen isotopes. Nucl. Phys. A, 649:2970-
304C, 1999. Proceedings of the Giant Resonance 98 conference, Varenna, Italy,
1998.

[6] C. A. Bertulani and A. M. Nathan. Excitation and photon decay of giant res-
onances from high-energy collisions of heavy ions. Nucl. Phys. A, 554:158—172,
1993.

[7] M. Berz, K. Joh, J. A. Nolen, B. M. Sherrill, and A. F. Zeller. Reconstructive
correction of abberrations in particle spectrographs. Phys. Rev. C, 47 :537—544,
1993.

[8] M. R. Bhat. Nuclear data sheets for A=58. Nucl. Data Sheets, 80:789—893, 1997.
[9] B. A. Brown. Private communications.

[10] J. A. Caggiano. Spectroscopy of exotic nuclei with the S800 spectrograph. PhD
thesis, Michigan State University, 1999.

[11] J. A. Cameron and B. Singh. Nuclear data sheets for A244. Nucl. Data Sheets,
88:299-416, 1999.

123

[12] F. Catara, E. G. Lanza, M. A. Nagarajan, and A. Vitturi. Effect of large neutron
excess on the dipole response in the region of the giant dipole resonance. Nucl.
Phys. A, 624:449—458, 1997.

[13] H. Goldstein. Classical mechanics. Addison-Wesley, 2nd edition, 1980.

[14] I. Hamamoto and H. Sagawa. Low energy strength in low-multipole response
function of nuclei near the neutron drip line. Phys. Rev. C, 532R1493-R1496,
1996.

[15] K. Heyde. Basic Ideas and Concepts in Nuclear Physics. Institute of Physics
Publishing, 2nd edition, 1999.

[16] J. D. Jackson. Classical electrodynamics. John Wiley & Sons, Inc., 2nd edition,
1975.

[17] J. W. Jury, B. L. Berman, D. D. Faul, P. Meyer, and J. G. Woodworth. Pho-
toneutron cross sections for 1"'0. Phys. Rev. C, 21:503—511, 1980.

[18] W. Klamra, T. Lindblad, M. Moszynski, and L. O. Norlin. Properties of optical
greases for BaF2 scintillators. Nucl. Instr. and Meth. A, 254:85-87, 1987.

[19] G. F. Knoll. Radiation detection and measurement. John Wiley & Sons, Inc.,
3rd edition, 2000.

[20] M. Laval, M. Moszyr’lski, R. Allemand, E. Cormoreche, P. Guinet, R. Odru, and
J. Vacher. Barium flouride — inorganic scintillator for subnanosecond timing.
Nucl. Instr. and Meth., 206:169—176, 1983.

[21] A. Leistenschneider, T. Aumann, K. Boretzky, D. Cortina, J. Cub, U. D. Pra-
manik, W. Dostal, T. W. Elze, H. Emling, H. Geissel, A. GriinschloB, M. Hell-
stréim, R. Holzmann, S. Ilievski, N. Iwasa, M. Kaspar, A. Kleinbéhl, J. Kratz,
R. Kulessa, Y. Leifels, E. Lubkiewicz, G. Miinzenberg, P. Reiter, M. Rejmund,
C. Scheidenberger, C. Schlegel, H. Simon, J. Stroth, K. Siimmerer, E. Wajda,
W. Walus, and S. Wan. Photoneutron cross sections for unstable neutron-rich
oxygen isotopes. Phys. Rev. Lett., 86:5442-5445, 2001.

[22] D. M. Manley, B. L. Berman, W. Bertozzi, T. N. Buti, J. M. Finn, F. W. Hers-
man, C. E. Hyde-Wright, M. V. Hynes, J. J. Kelly, M. A. Kovash, S. Kowalski,
R. W. Lourie, B. Murdock, B. E. Norum, B. Pugh, C. P. Sargent, and D. J. Mil-
lener. Electroexcitation of negative-parity states in 180. Phys. Rev. C, 4322147-
2161, 1991.

[23] M. J. Martin. Nuclear data sheets for A2208. Nucl. Data Sheets, 47:797—964,
1986.

[24] A. M. Nathan. Statistical and nonstatistical photon emission from giant reso-
nances. Phys. Rev. C, 43:R2479—R2482, 1991.

124

 

[25] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical
Recipes in FORTRAN: the Art of Scientific Computing. Cabridge University Press,
2nd edition, 1992.

[26] S. Raman, C. W. N. Jr., S. Kahane, and K. H. Bhatt. Predictions of B(E2) T
values. At. Data and Nucl. Data Tables, 42:1-54, 1989.

[27] H. Sagawa and T. Suzuki. Pigmy and giant dipole states in oxygen isotopes.
Phys. Rev. C, 59:3116—3119, 1999.

[28] N. P. Shaw. High energy 'y-rays from highly excited thorium, californium, and
meitnerium. PhD thesis, State University of New York at Stony Brook, 1999.

[29] B. M. Sherrill, D. J. Morrissey, J. A. N. Jr., N. Orr, and J. A. Winger. Initial
operating experience with the a1200 fragment. separator. Nucl. Instr. and Meth.
B, 70:298—303, 1992.

[30] B. Singh and J. A. Cameron. Nuclear data sheets for A242. Nucl. Data Sheets,
92:1—146, 2001.

[31] R. H. Spear. B(E3) T to the First 3‘ State. At. Data and Nucl. Data Tables,
42255-104, 1989.

[32] T. Suzuki and H. Sagawa. Private communications.

[33] O. Tarasov and D. Bazin, Aug. 2001. Documentation on program LISE is avail-
able online at: http://www.nscl.msu.edu/"tarasov/lise/lise.html.

[34] D. R. Tilley, C. M. Cheves, J. H. Kelley, S. Raman, and R. H. Weller. Energy
levels of light nuclei A220. Nucl. Phys. A, 636:249—364, 1998.

[35] D. R. Tilley, H. R. Weller, C. M. Cheves, and R. M. Chasteler. Energy levels of
light nuclei A218—19. Nucl. Phys. A, 59521—170, 1995.

[36] S. Wolfram. The MATHEMATICA book. Cambridge University Press and Wolfram
Media, 4th edition, 1999.

[37] J. Yurkon, D. Bazin, W. Benenson, D. J. Morrissey, B. M. Sherrill, D. Swan,
and R. Swanson. Focal plane detector for the 8800 high-resolution spectrometer.
Nucl. Instr. and Meth. A, 422:291—295, 1999.

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