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LIBRARY
Michigan State
University

 

 

 

This is to certify that the
dissertation entitled

Streamer Chamber Study of Intermediate-Energy
Nuclear Collisions with CCD Cameras

presented by

Silvana Patrizia Angius

has been accepted towards fulfillment
of the requirements for

Ph- D - degree in Ebysi c.s_._._.__

 

flm

r / Major professor /

Date 14 August 1987

 

MS U is an Affirmative Action/ Equal Opportunity Institution 0‘ 12771

 

 

 

 

 

 

MSU

LIBRARIES
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RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. .FINES will
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stamped below.

 

 

 

 

 

STREAMER CHAMBER STUDY OF INTERMEDIATE-ENERGY NUCLEAR COLLISIONS
WITH CCD CAMERAS

BY

Silvana Patrizia Angius

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

1987

ACKNOWLEDGMENTS

I would like to thank my adviser, professor Gary Crawley, for
giving me the opportunity to work on this project and for promptly
reading the manuscript when time was pressing.

Among the members of my group, I especially wish to express my
gratitude to prof. Robert Tickle for his help, encouragement, good humor,
and unfailing optimism.

Richard Au and Ron Fox have provided essential contributions to the
project, designing hardware, writing software, and cheerfully putting in
long hours testing the system. I'd like to thank them for contributing
their professional skills and for doing so in a friendly, good-humored
way.

I wish to express my gratitude to prof. Laszlo Csernai for his help
with the interpretation of the data and for his critical reading of the
manuscript. He has provided much needed advice and direction. Thank you
for caring.

The friendship and companionship of several of my fellow graduate
students have made these years pleasant and have provided moral support.
I especially wish to thank Kedarnath, for a friendship that has made even
the Comprehensive exam tolerable (I); Marcia Torres, for being a

pestiferous, warm, wonderful office-mate and friend; Anna Rosa Lampis,

fellow countrywoman and listening ear; and Dan Fox, for his friendship
and his help during the experiment and with plotting routines.

Erich Ormand has supplied what long-distance help he could (thanks
to BITNET and AT&T, as well!).

A special thank you goes to Ms. Cesarina Belloni, who had
confidence in a shy little girl, and let her know it.

Finally, many heartfelt thanks to my family. To my parents, for

pushing, nagging, and encouraging. To my grandparents, for their

unflinching love. To my sister, for believing in me no matter what.

ABSTRACT

STREAMER CHAMBER STUDY OF INTERMEDIATE-ENERGY NUCLEAR COLLISIONS

WITH CCD CAMERAS

BY
Silvana Patrizia Angius

A system of three charge-coupled device (CCD) cameras has been
designed and built to record nuclear collisions in a streamer chamber.

iniis technical development significantly enhances the usefulness of
streamer chambers as large solid angle (441: sr) detectors for exclusive
measurements in nuclear physics. .

The system has been used in an experiment designed to study nearlyu-
central collisions of Nb+Nb at 100 and 180 MeV/nucleon.

Computer codes have been developed that significantly reduce the

amount of operator intervention in the data analysis.

n' multiplicities are easily extracted by visually scanning the
events. The values obtained are compared to the systematics found for
different systems at higher energies.

Once magnetic rigidities and light intensities are extracted for each

track in each event, the emitted fragments are identified by plotting the

rigidity,intensity point for each ion on a 2-dimensional (I vs. rig)
plot.

One of the most interesting predictions of fluid-dynamical models and
VUU calculations for heavy-ion collisions is the sideward emission of
nuclear matter, due to the high compression created during the collision
[Std 80, M01 85]. The transverse-momentum flow analysis introduced by
Danielewicz and Odyniec [Dan 85] allows to calculate the amount of
sideward momentum carried by the emitted fragments, while minimizing the
distortions caused by finite-multiplicity effects.

This momentum flow analysis has been performed on our 180 MeV/nucleon
data. The slope of the mean transverse momentum per nucleon vs. rapidity
curve at mid-rapidity, or flow, was found to be A7.0zll.3 MeV/c/nucleon.

In order to compare our results to those obtained from other
experiments, scale-invariant transverse momentum, 5", and rapidity, ‘9,

have been introduced [Bal 8A]. The S” vs. § curve extracted from our data
has been compared with the curves obtained for warious systems in
streamer chamber plus photographic film [Dan 85, Ben 8A] and plastic ball

experiments [Dos 85], and the shapes have been found to be very similar.

The scale-invariant flow, E, for 180 MeV/nucleon Nb+Nb is 0.16:0.04.

TABLE OF CONTENTS

page
LIST OF TABLES .................................................
LIST OF FIGURES ................................................
Chapter One- INTRODUCTION
1.1 Review ................................................ 1
1.2 Exclusive Measurements ................................ 9
A n- Multiplicity Measurements ....................... 11
B Collective Flow Measurements: Sphericity
Tensor Analysis .................................... 12
C Collective Flow Measurements: Transverse
Momentum Analysis .................................. 16
Chapter Two- SYSTEM DEVELOPMENT AND DESCRIPTION
2.1 Principles of Operation of the Streamer Chamber ....... 28
2.2 The Streamer Chamber in Heavy-Ion Physics ............. 32
2.3 Charge-Coupled Devices ................................ 3“
2.“ Description of the CCD System ......................... “O
2.5 The LBL Streamer Chamber .............................. “6
2.6 The Experiment ........................................ “9
Chapter Three- DATA REDUCTION AND ANALYSIS
3.1 Introduction .......................................... 52
3.2 Image Enhancement and Track Recognition ............... 53
3.3 Three-View Geometry Program ........................... 58
3.“ Intensity Analysis .................................... 6“
Chapter Four- EXPERIMENTAL RESULTS AND COMPARISON WITH
THEORETICAL MODELS
“.1 Introduction .......................................... 79
“.2 Charged-Particle Multiplicities ....................... 79
“.3 u” Multiplicities ..................................... 85
“.“ Transverse-Momentum Flow Analysis ..................... 89
A Transverse-Momentum Analysis ....................... 91
B Momentum Flow Analysis: Experimental Results ....... 93
“.5 Scaling Behaviour of Transverse Flow Variables ........ 98

vi

vii

Chapter Five- CONCLUSIONS
5.1 Evaluation of the System ..............................
A Electronics and Data Acquisition ...................
B Analysis Software .............................. ....
5.2 Concluding Remarks ....................................

APPENDIX A- PROGRAM CCDSTREAM ...................................
APPENDIX B- SOURCES OF BACKGROUND NOISE IN CCD'S ................

APPENDIX C- STEPS IN THE ANALYSIS OF A CCD-RECORDED NUCLEAR
COLLISION ...........................................

LIST OF REFERENCES ..............................................

108
108
110
110
112

116

120

123

LIST OF TABLES

TABLE PAGE
2.3.1 Characteristics of CCD's in comparison with

photographic film. The values indicated with (*) are

taken from [D10 8“] ...................................... 37
3.“.1 Percentages of various isotopes emitted in a Nb+Nb

collision at 180 MeV/nucleon. The values on the left

are the yields obtained from the experimental data

using the curves shown in figure 3.“.7. Those on the

right are calculated with the code FREESCO ............... 77

“.5.1 Flow F measured from different experiments, and the

corresponding scale-invariant quantity, E (from
[Bon 86]) ................................................ 105

viii

FIGURE

1.

l.

1

LIST OF FIGURES

PAGE

Nuclear equation of state for compressibility K:200 MeV
and K=380 MeV (adapted from [M01 85]) .................... 2

Phase diagram of nuclear matter. Various predicted exotic
phases are shown (from [M01 85]) ......................... 3

Single-particle spectra for the reaction C+C at 50
MeV/nucleon. The solid lines are obtained from a triple
moving source fit (from [Fox 87]) ........................ 6

Density and temperature contours and velocity field
(arrows) obtained for the reaction Ne+U at “00
MeV/nucleon from thermodynamical calculations

(from [Ste 80]) .......................................... 8

Predictions of the intranuclear cascade model and of
hydrodynamics for central and peripheral collisions of

Ne+U at “00 MeV/nucleon (from [Sto 80]) .................. 10

a) n“ multiplicities from Ar+KCl collisions at different
energies. The circles are the results of cascade
calculations. The horizontal arrows give the value of
the compressional energy. b) Ec vs. relative density for

the experimental points in a) and for the nuclear
equation of state with K:250 and K=200 MeV (from
[Sto 82]) ................................................. 13

Experimental flow angle distributions for Ca+Ca and Nb+Nb
and predictions obtained from the cascade model (from
[Gus 8“]) ................................................. 15

Experimental flow angle distributions for two different
multiplicity cuts (histograms) are compared with
hydrodynamical calculations for different impact

parameters (from [Buc 8“]) ................................ 17

a,b) Average transverse momentum per nucleon for data (a)

and Monte Carlo calculations (b) for Ar+KCl at 1.8
GeV/nucleon.

ix

c,d) Differential transverse momentum deposition per unit
rapidity for data (c), and Monte Carlo calculations (d)
(from [Dan 85]) ........................................... 19

a) Flow as a function of multiplicity for Au+Au, Nb+Nb,
and Ca+Ca at “00 MeV/nucleon.
b) Flow as a function of beam energy (from [Dos 86]) ...... 20

Scale-invariant transverse momentum distribution for:

circle, Ar+KCl at 1.8 GeV/nucleon; diamond, La+La at 0.8
GeV/nucleon; square, Nb+Nb at “00 MeV/nucleon. Prom

[Bon 86] .................................................. 23

Contour lines of Rezconstant and cmonstant in the A’Ecm
plane (from [Bon 86]) ..................................... 2“

VUU model predictions of the transverse momentum per
nucleon for Nb+Nb at different energies, for 6:3 fm
(from [M01 85]) ........................................... 26

a) Side view of the streamers produced along the path
of an ionizing particle.

b) End View (along the direction of E) of the streamers... 30

a) Characteristic curve of CCD response to exposure E.
b) Characteristic curve for a photographic film ........... 38

Schematic of the electronics for the CCD camera system.... “1
CCD-to-VAX block diagram .................................. “3

Description of the read/write registers in the CCD
interface ................................................. “5

Main components of the LBL streamer chamber (adapted from
[Sch 79]) ................................................. “7

a) Gaussian-type curve which approximates the intensity

along a cut perpendicular to a track.

b) First derivative of intensity with respect to angle.

c) Second derivative of intensity with respect to angle... 55

Nearly-central collision at 100 MeV/nucleon. Unprocessed
event ..................................................... 56

Event in figure 3.2.2 after image-enhancing processing.... 57

Tracks found for the event in figure 2.3.3 ................ 59

xi

Trajectory of a particle in space and its projections as
seen from two different views. A is the dip angle .........

Bragg peak observed for a proton stopping in the gas of
the streamer chamber ......................................

Experimental distribution of energy losses of 31.5 MeV
proton. The corresponding theoretical Landau distribution
is also shown (taken from [Igo 53]) .......................

Intensity along a track as a function of distance from the
interaction vertex ........................................

Intensity distributions for three different tracks in a
CCD-recorded event ........................................

Intensity along a track as a function of the distance from
the vertex. This illustrates an extreme case of flaring
along the whole length of the track .......................

Intensity histogram for forward-going particles with
rigidity between 1000 and 1“00 MeV/c/Z. Peaks
corresponding to beam—velocity deuterons and a-particles
are indicated ...... . ......................................

2—dimensional plot (intensities are corrected for the dip
angle) for 97 events at 180 MeV/nucleon. The particle-

identification curves shown are calculated from expression
3.1 with X=O.5 ............................................

CCD-recorded image of a peripheral Nb+Nb collision at 100
MeV/nucleon ...............................................

CCD-recorded image of a nearly-central collision at 100
MeV/nucleon ...............................................

Multiplicity distribution for 300 events at 100
MeV/nucleon. The curve is obtained by fitting the
experimental points with a Poisson distribution ...........

Multiplicity distribution for 300 events at 180
MeV/nucleon. The curve is obtained by fitting the points
with a Poisson distribution ...............................

Nb+Nb collision at 180 MeV/nucleon, in which a negative
pion is created. The particle is clearly recognizable
from its curvature in the magnetic field ..................

Negative pion multiplicities obtained from our data are
compared with the values found by Stock et al. from

60

66

68

69

7O

72

7“

76

80

81

83

8“

86

xii

Ar+KCl measurements [Sto 8“] .............................. 88

Scaled negative-pion multiplicities as a function of

incident energy per nucleon for various systems. The

curve is obtained from the analytical formula described

in the text ............................................... 90

a) Distribution of the azimuthal angles between 01 and

611 obtained by Danielewicz and Odyniec [Dan 85] for

Ar+KCl at 1.8 GeV/nucleon.
b) Similar distribution for Monte Carlo generated events,
in which a reaction plane does not exist .................. 9“

Distribution of azimuthal angles between OI and 511 for
180 MeV/nucleon Nb+Nb ..................................... 96

Mean transverse momentum per nucleon, corrected for the
deviation from the true reaction plane, as a function
of rapidity ............................................... 97

Mean transverse momentum per nucleon projected onto the

true reaction plane, as a function of the normalized
center-of-mass rapidity. The solid line is the result of

a least-square fit to the experimental points, and its

slope represents the flow obtained for this experiment.... 99

Scale-invariant transverse momentum vs. scale-invariant
rapidity for Ar+KCl at 1.8 GeV/nucleon (circle) [Dan 85],
La+La at 0.8 GeV/nucleon (diamond) [Ren 8“], Nb+Nb at 0.“
GeV/nucleon (square) [Dos 86 and Rit 85], and Nb+Nb at

180 MeV/nucleon (black triangles). From [Bon 86] .......... 10“

Contour lines in the A,Ecm plane for cmonstant. The

dotted curve represents the prediction for low energies.
The various symbols refer to the experimental values

listed in table “.5.1: for o.u<E<o.325, n for
o.325<§<o.275, for 0.275<E<o.225, e for 0.225<E<

0.175, V for 0.175<§<O.125, A for O.125<§<0.1 [Bon 86].... 106
Dark current vs. temperature .............................. 117

Dark current vs. exposure time for different temperatures. 118

Chapter One

INTRODUCTION

1.1 Review

The two main goals in the study of heavy-ion collisions in the range
from intermediate to very high energies are the determination of the bulk
properties of nuclear matter, or the nuclear equation of state, and the
understanding of the collision processes, which may vary over the large
range of energies available today. These two goals are related, and an
improved insight into one can lead to a better understanding of the
other.

Very little is known about the nuclear equation of state, beside its
ground-state properties. It is well established that Ec(p), the
compressional energy, has a minimum for 0:00 (normal nuclear density,
z0.17 fm-3), where it assumes a value of about -16 MeV ( see figure
1.1.1). But the properties of nuclear matter at higher densities and high
excitation energies are essentially unknown. Conjectures have been made
about the possibility of exotic phases such as pion condensate, density
isomer, and a quark-gluon plasma. At lower temperatures, T<20 MeV, and
p<p,, another critical phenomenon is predicted, namely a liquid-gas phase
transitixni.‘This has been discussed both in terms of a fast mechanical
instability [Ber 83] and a slower chemical instability [(hlr 83]. Eiigure
1.1.2 shows a phase diagram of the various phenomena (exotic states and
phase transitions) that have been predicted.

Knowledge of the properties of compressed or diluted nuclear matter
is important to the understanding of diverse processes like the stability

of neutron stars [Irv 81], the evolution of supernovae [Bet 79], and the

 

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Figure 1.1.1 Nuclear equation of state for compressibility K=200 MeV
and K=380 MeV (adapted from [M01 85]).

 

 

 

 

 

 

 

Figure 1.1.2 Phase diagram of nuclear matter. Various predicted exotic
phases are shown (from [M01 85]).

14
early stages of the universe, after the big bang and during the formation
of stellar systems [Sch 81]. In these phenomena, nuclear densities
ranging from 0.1 to 10 times p, are thought to occur, or have occurred.
Unfortunately, these systems do not easily lend themselves to controlled
experiments.

During the last ten years, an alternative way of producing and
studying high-density, hot nuclear matter has become available with the
development of heavy-ion accelerators. The process of a central, or
nearly-central, collision between two energetic, heavy nuclei brings
about the formation of a compressed and highly excited system, and a wide
range of densities and temperatures are expected to occur. Naturally,
these high densities are obtained for short lengths of time (tz10'22
sec), and global equilibrium cannot be reached [M01 85]. Also,
experimentally one does not measure the macroscopic variables directly
related to the equation of state, such as density or compressibility.
Rather, the momentum, mass, and charge of the individual particles
emitted are measured. Furthermore, what is observed is only the final
state of a reaction, i.e. the situation after the system has undergone
compression, successive expansion, and has broken up into light fragments
after freeze-out. If and how these fragments carry the information about
the reaction dynamics and the characteristics of the short-lived dense
nuclear system is a question which must be addressed if a comparison
between theoretical models and experimental results is to be possible.

The progress made in the study of heavy-ion collisions at energies
from *50 MeV/nucleon to a few GeV/nucleon has resulted from the interplay
between theoretical interest in the properties of dense nuclear matter

and the development of new accelerators and detectors. In the following

5
brief review, some of the results obtained nitnmalast decade will be
described, and an attempt will be made to show how the factors mentioned
above (theoretical models and experimental results) have led to the need
for more sophisticated experimental techniques.

Among the first experiments performed with heavy-ions are the
measurements of single—particle inclusive spectra (e.g. Hes 76). One
example of such double-differential cross sections, obtained for C+C at
50 MeV/nucleon, is shown in figure 1.1.3. One important feature, common
to all these measurements, is that the high-energy tails of the spectra
display an exponential slope characteristic of thermal emission. A
'temperature' of the emitting source is readily deduced from the slope of
the energy distributions, and its velocity can be obtained from a lift of
the spectra at different angles. Several models, from a simple
geometrical description like the fireball model [003 77], to microscopic
approaches such as the intra-nuclear cascade models [Cug 80,81,821, to a
thermodynamical description [Std 81], qualitatively explain various
aspects of the data. But difficulties arise when one tries to verify the
consequences of'the different approaches, as will be described later. It
is therefore apparent that inclusive measurements are not a satisfactory
testing ground for the main differences between the various theories. The
origin of this problem lies in the difficulty of separating the different
reaction mechanisms in inclusive measurements. In other words, an
integration over all impact parameters characterises inclusive data, and
collisions at large impact parameters dominate the results.

If we are to study the response of dense nuclear matter, near-

central collisions must be selected, where the collective phenomena are

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7
expected to take place. More exclusive measurements are therefore needed.
Two-particle correlations are a step towards this objective.

.Several interesting results have been obtained in experiments of
this kind. To mention only a few, measures of large-angle correlations
(see, e.g., Nag 79, Tan 80, P00 85) have confirmed that inclusive
measurements, where peripheral collisions dominate, are strongly
influenced by quasi-elastic nucleon-nucleon scattering [Bab 85].
Temperature measurements based on the population of decaying excited
states have given indications of values lower than those extracted from
the slope of single-particle inclusive data [Poc 85]. An experiment
measuring R, the ratio of in-plane to out-of-plane correlations, for a
heavy system (Ar+Pb) shows that R varies from values <1 for 8<70°, to R>1
at larger angles [Tan 80]. This behaviour cannot be explained in terms of
quasi-elastic nucleon-nucleon scattering. Csernai et al. [Cse 81,82] have
proposed an interpretation which takes hnx>account the momentum
distribution of the protons arising from collective. It appears tnuit the
measurements at intermediate angles, where R<1, correspond to high-energy
protons, while the large-angle particles (R>1), have lower energy. This
result is predicted by a hydrodynamic description of the collision, as is
shown in figure 1.1.“. At large angles, it is likely that a proton
emitted by the projectile will be detected in coincidence with a proton
emitted by the target-like source (low energy, opposite side), while
fast, projectile-like protons will be detected at smaller angles.

While these results have broadened our knowledge of the collision
processes, there are still several deficiencies.Ekn-example, dynamic
correlations between particles which are not detected can modify the

correlation function [Bab 85]. In particular, Cyulassy has suggested that

   

500 HOW n
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/ 0......-
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Figune‘L1.“ Density and temperature contours and velocity field
(arrows) obtained for the reaction Ne+U at “00 MeV/nucleon

from thermodynamical calculations (from [Ste 80]).

9
the existence of a reaction plane can cause a difference in the
absorption of particles in and out of plane [Gyu 82]. To make the
determination of the reaction plane possible, all or at least most of the
emitted particles must be observed and identified. Detectors efficient
over a large solid angle (usually referred to as “u-detectors, because of

their acceptance of nearly “a sr) are necessary for this purpose.

1.2 Exclusive Measurements

In figure 1.2.1 the theoretical pictures of a Ne+U collision at “00
MeV/nucleon, as predicted by two different models, are shown. On the
right, one can see the predictions of the intra-nuclear cascade model, a
ndcroscopu:theory:inhich nuclear collisions are treated as a
superposition of independent two-body nucleon-nucleon collisions in free
space [Cug 85]. According to this picture, transparency effects dominate,
and the emission of particles occurs preferentially in the direction of
the beam. On the left, the predictions of hydrodynamic calculations are
shown. This is a macroscopic theory, which refers directly to
thermodynamical concepts. The equation of state serves as an irunn: into
the Navier-Stokes or Euler equations (see, e.g., Std 82). In this model,
compression effects give rise to a flux of particles in the direction
perpendicular to the beam (side-splash) for central collisions (b:0), and
to a bounce-off of projectile-like fragments away from timeliigh-density
region at larger impact parameters.

Ideally, exclusive measurements in “ii-detectors should give
information equivalent to that obtained from these calculations. If A, Z,
and 5 are known for all the emitted fragments, the reaction plane (HUI be

calculated and an analysis in terms of global variables (e.g. the

10

O A IA |
Shela, Hum-um
MW Earn-400 “own

A. cram. man» W7 ““1th

 

 

 

Figure 1.2.1 Predictions of the intranuclear cascade model and of
hydrodynamics for central and peripheral collisions of Ne+U

at “00 MeV/nucleon (from [Ste 80]).

11
sphericity tensor, defined in section B of this chapter) is possible.
This allows the determination of quantities such as the mean flow angle
and the shape of the momentum distribution. The two models mentioned
above differ radically in the prediction of these variables.

Several types of detectors are available today, which come close to
an acceptance of “n sr, and with a granularity fine enough to make them
well suited to the high- multiplicity events that must be studied.
Electronic-type detectors, ranging from the»Plastic Ball/Plastic Hall
spectrometer [Bad 82] to time-projection chambers have been developed and
used in heavy-ion measurements. Visual-type detectors such as streamer
chambers and nuclear emulsions have been borrowed from high-energy
physics and rather successfully employed in nuclear experiments. A new
technical development, which will be described in this thesis, is the use
of charge-coupled device (CCD) cameras with a streamer chamber. The
introduction of solid-state image sensors in place of photographic film
promises to alleviate two of the most problematic features in streamer
chamber measurements, by expanding the dynamic range of the recording
device and by making the data analysis largely automatic. More will be
said about the characteristics of some of these detectors in chapter 2.2.
Here, we will give a review of some of the experimental results obtained

so far, and of the systematics that can be extracted.

A- n- Multiplicity Measurements.

The final stage of a reaction is strongly influenced by chaotic
thermal effects and by the expansion and break-up which follow
compression. In an attempt to avoid these complications, Stdcker,

Greiner, and Scheid have pr0posed to estimate the stiffness of the

12
nuclear equation of state from measurements of pion multiplicities [Sto
78]. This measure offers the advantages that i) the creation of pions
occurs mostly during the compression phase, and ii) multiplicities are
not strongly influenced by expansion and freeze-out.

A rather extensive investigation of the energy dependence of 11‘
multiplicity is described by Sandoval et al. [San 80]. In this study,
performed at the LBL streamer chamber, central and peripheral collisions
of qur on KCl, at energies between 0.“ and 1.8 GeV/nucleon, were
analysed. In figure 1.2.2a the mean 11' multiplicities are shown as a
function of bombarding energy in the center of mass. The predictions of a
cascade calculation, which lacks compressional effects, does not
reproduce the data well. In figure 1.2.2b the compressional energy per
nucleon, estimated from figure 1.2.2a by taking the difference between
the energy obtained from cascade calculations and the experimental energy
for the same multiplicity, is plotted as a function of the relative
nuclear density. The equation of state plotted in figure 1.2.2b

corresponds to a compressibility of 250 MeV.

B- Collective Flow Measurements: Sphericity-Tensor Analysis.

The sphericity tensor is defined as:

Tij = 5 vai(v) pj(v)

where pi and pJ are two components of the momentum (px, p p2) for the

y,
particle v in a given event, and ”v is a weight factor associated with

each particle. If this tensor is diagonalized, the three eigenvectors

have magnitude f1, f f3 and their orientation is characterized by the

2,

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Euler angles 9, c, w.
Nith this procedure, the distribution of the momenta within an event

is represented by an ellipsoid of semi-axes f f2, and f3, and rotated

1,
by 9, 6, n. Thus, the shape of the momentum distribution can be evaluated
and compared with the predictions of different theoretical models. A
particularly interesting parameter is 0, the mean flow angle, which
measures the collective sideward flow.

In determining this quantity experimentally, large distortions due
to finite-multiplicity effects are introduced. Danielewicz and Gyulassy
have shown that these distortions are mostly contained in the Jacobian of
the transformation which relates the six parameters f1, f2, f3, 0, o, “h

to the six independent elements Tx T 'T T‘ , sz [Dan 83].

yy’ 22’ xy
Therefore, when the flow angle distribution is studied, --aé-- nun“: be

x,

corrected by the proper Jacobian. This introduces a term '§%fi’é , and the

corrected distribution is:

1 dN(9) dN(9)

'Eifi‘ ' "86'" : ""dIEds'é)"

where N is the number of events which give a flow angle of 9, after
diagonalising the tensor Tij'

The flow angle distributions allow an interesting comparison between
the cascade model, which predicts a peak at 0 degrees for all impact
parameters, and hydrodynamics or VUU calculations, which predict a non-
zero flow angle varying with impact parameter, mass of the system, and
incident energy.

Several experiments have been performed to study the flow angle

distributions for various systems at different energies using the Plastic

1.00 MeV! nucleon

‘°Cc+Cc °3Nb+93Nb 93Nb+93Nb
Data Data Cascade

Yr

 

 

Fir“

 

 

ledcosO

A l
qfi

LOSmc<SO BOSmc<L0 205m¢<30 SSm¢<20

O —O p a
m 0 in O
- l 4 l
4/dr/f/
A A L A If)
2

 

 

 

 

 

 

0300003000 0500090
Flow ongle 0 [Degrees]

Figure 1.2.3 Experimental flow angle distributions for Ca+Ca and Nb+Nb

and predictions obtained from the cascade model (from [Gus
811]).

16

Ball spectrometer [Gus 8“, Rit 85]. In figure 1.2.3 the data obtained for
“00 MeV/nucleon Ca+Ca and Nb+Nb are compared with cascade calculations.
The experimental distributions clearly show a sideward flow, especially
for the heavier system, which the cascade model is unable to reproduce.
The predictions of the hydrodynamical model for different impact
parameters are shown in figure 1.2.“, where the experimental data for the
appropriate multiplicity cuts are also plotted. Although the agreement is
not perfect, it is clear that the model reasonably predicts the
experimental distributions and their variations with multiplicity.

An asymmetric system was studied by Renfordt et al. using a 0.772
GeV/nucleon Ar beam on Pb at the LBL streamer chamber [Ren 8“]. They find
a well defined flow angle in semi-central collisions (3:62:55 fm), but a
spherical shape in nearly central collisions. This different behaviour,
due to the non-symmetry of the system, is also qualitatively predicted by

the hydrodynamical model.

C- Collective Flow Measurements: Transverse Momentum Analysis

The results reviewed above show that the direction of flow and the
beam axis define a privileged reaction plane. If an evaluation of this
plane is possible experimentally, then one can study the distribution of
the projected momentum, rather than simply the flow angle.

The main problem with the sphericity analysis is its sensitivity to
statistical fluctuations. Danielewicz and Odyniec have suggested a
different approach which helps eliminate finite-multiplicity distortions
from the evaluation of the reaction plane, and which has proved a more
sensitive and powerful tool in revealing collective-flow effects [Dan

85]. In brief (the details will be given in chapter “), the method

17

 

 

 

 

 

(:) I I
‘ —
1.0 r- I, \93Nb . ”Nb
I: \LOO MeV/u
I \\ 30 S mc S L0
I
‘3 (15 I \\ '1
3 \
.. \
o I \
8 I ‘\\
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‘° 0t) ’ ‘
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1‘ In69250
'1 ---o< b<3fm
I ——0 < b<6fm
0.5 '- 1' -‘
I
I
/ \
00 / l l
0 30 60 90

Figure 1.2.“ Experimental flow angle distributions for two different
multiplicity cuts (histograms) are compared with

hydrodynamical calculations for different impact parameters
(from [Buc 8“]).

18
consists ol‘estimating the reaction plane from the transverse momenta of
the emitted particles, and then rotating each event to its reaction
plane. The distribution of the average transverse momenta of the emitted
particles as a function of rapidity is then studied for evidence of
collective effects.

In the paper mentioned above, Danielewicz and Odyniec have applied
their analysis to the data obtained in an experiment performed at the LBL
streamer chamber for the Ar+KCl reaction at 1.8 GeV/nucleon. The same
experiment had been previously analysed with the sphericity tensor
method, and no conclusive evidence had been found of collective flow [Str
83] . With the transverse momentum analysis a substantial total momentum
transfer was found, as can be seen from the data shown in figure 1.2.5).

The same system was studied by another group [Kea 86], again at the
LBL streamer chamber. A comparison of their experimental transverse
momentum distribution with the predictions of VUU calculations seems to
point towards a "medium" to "stiff" equation of state, witli
compressibility values between 200 and 300 MeV.

Doss et al. have studied the dependence of collective flow on beam
energy, multiplicity, and mass of the system in a series of measurements
performed at the Bevalac with the Plastic Ball detector [Dos 86]. 13a+Ca,
Nb+Nb, and Au+Au collisions were studied at energies between 150 and 1000
MeV/nucleon. To minimize the effects of the detector bias on the
quantitative measure of flow, they calculate the slope of the transverse
momentum distribution at mid-rapidity, which they call "flow". In figure
1.2.6a and b a summary of their results is shown. As predicted by
hydrodynamic calculations, and observed in previous experiments [Rit 85],

the flow increases with the mass of the system. Both the multiplicity

19

 

 

 

 

 

 

 

 

 

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3 00 »III Q. . I” Q
3 .. . + w 5° 3
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V

Figure 1.2.5 a,b) Average transverse momentum per nucleon for data (a)
and Monte Carlo calculations (b) for Ar+KCl at 1.8
GeV/nucleon. c,d) Differential transverse momentum
deposition per unit rapidity for data (c), and Monte Carlo
calculations (d) (from [Dan 85]).

20

200

 

150-

 

Flow MeV/c pet nucleon)

 

 

o 25 so 73 100 126
Percent oi maximum mutiplicny

 

 

 

 

 

 

a zoo 400 too 000 1000 1200
Bum my (MeV/Al

Figure 1.2.6 a) Flow as a function of multiplicity for Au+Au, Nb+Nb, and
Ca+Ca at “00 MeV/nucleon. 6) Flow as a function of beam
energy (from [Dos 86]).

21

dependence and the energy dependence of the "flow" are different from the
behaviour of the flow angles shown in figure 1.2.3. The first
distribution (figure 1.2.6a) shows a maximum at intermediate
multiplicities, and the energy dependence shows a rise in flow up to
about 650 MeV/nucleon, then a slight fall—off. These effects might be
partially due to the detector response, which depends on energy and
multiplicity.

The last experiment to be briefly described here, chiefly because it
involves yet another type of detector, is a series of emulsion
measurements with Au and Xe beams, at energies from 0.5 to 1.2
MeV/nucleon [Cse 86]. The energy of the projectile is determined from its
range in the emulsion, the charge of 222 particles is obtained from
ionization measurements, and A is assumed to be = 22. The only other
measured quantity is the azimuthal angle of the fragments. Therefore, a

quantity called pseudo-transverse momentum, defined as
Pt : tan 0 P
u u u

is introduced. Here, P is the longitudinal momentum per nucleon of the

II
beam. The distribution of mean pseudo-Pt per nucleon projected onto the
reaction plane, Px/A, vs. Pt shows a significant collective flow, and
the values extracted are consistent with those obtained in other
experiments.

A way of comparing the results obtained for different systems at

different energies is suggested by Balazs et al. [Bal 8“]. This method

consists of expressing the data in terms of quantities which, in the

22
hydrodynamic model, are scale-invariant. Any deviation from this scale-
invariant behaviour indicates the possibility of processes causing non-
perfect flow, such as dissipation and phase transitions. Bonasera and
Csernai apply this method to a variety of experimental data [Bon 86]. In
their work, they define a scale-invariant transverse momentum and

rapidity:

~x _ x/ CM
9 p ppmJ
~ _ CM/ CM
y ‘ y prOJ

where px and yCM are the transverse momentum and rapidity obtained from

CM and CM
proJ yproJ

of the projectile in the center of mass. The Ex distributions thus

the data, and p are the momentum and rapidity per nucleon
obtained are shown in figure 1.2.7. The behaviour of the various curves
in this scale-invariant plot is remarkably constant over the wide range
of energies and masses shown. In addition, a scale-invariant flow, F, is
defined as the slope of the experimental BX distributions at mid-rapidity
(the 'flow', as introduced by Doss et al. in Dos 86) divided by the
momentum of the beam in the center of mass. This experimental quantity
can be compared with the behaviour of fig, the Reynolds number, which
characterises viscous flow patterns: Similar patterns have the same
Reynolds number (see Bal 8“ and Bon 87 for a detailed description).

In figure 1.2.8 the curves of constant F in the A,ECM plane are
compared with the Rg:constant lines. The most striking difference appears

at low energies, for E MS60 MeV/nucleon, indicating a drastic change

C

0.3

0.2

0.1

0.0

Px/Pp

—O.1

—O.2

—O.3

Figure 1.2.7

23

 

 

 

 

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L
7 o
. D O
. u 05> oo
[- [3000 900 o
oo 0 .

_ ”on 1
. 00 ,
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L 000 D 4
"0 o D —‘
_ n

o n

. I L . I . ll L l l I . l l . I .
—1 —O.5 O 0.5 1

Y/Yp

Scale-invariant transverse momentum distribution for:
circle, Ar+KCl at 1.8 GeV/nucleon; diamond, La+La at 0.8
GeV/nucleon; square, Nb+Nb at “00 MeV/nucleon. From [Bon
86].

2“

 

werfrv'vv-v'vvvvlw

200 '

150 '

Ecm (MeV)

100

.I....l.

50

 

.... .
vrw—va'vvv

 

 

 

 

 

 

.
.

I I I I ' I I I

...I.... .... L... . .... .... ..-. -...

0 50 100 150 200 50 100 150 200
Mass number

 

Figure 1.2.8 Contour lines of Rezconstant and cmonstant in the A,Ecm
plane (from [Bon 86]).

25

either in the equation of state (e.g. a phase transition),cn~in the
reaction mechanism. It is interesting to observe that in this energy
range the Vlasov-Uehling-Uhlenbech (VUU) model predicts a change in slope
in the transverse momentum distribution, as shown in figure 1.2.9 [M01
85]. Some experimental evidence for 'negative' emission angles has been
found in neutron emission studies for the N+Ho reaction at 25 MeV/nucleon
[Dea 87], and from measurements of the circular polarization of
coincident Y-rays emitted from the residual nucleus in the NsSm reacticni
at 20 and 35 MeV/nucleon [Tsa 86]. This effect is due to the attractive
nuclear force which, at these lower densities, overcomes the repulsive
interaction due to pressure build-up. In this respect, the region of
interest in figure 1.2.8 is that at low energies.

'The work presented in this thesis describes the development of a
three-CCD-camera system, which is very well suited for the investigaticni
of heavy-ion collisions in the low-energy region of figure 1.2.8, where
the charged-particle multiplicities do not exceed 50 or 60. This system
was used in an experiment at the LBL streamer chamberlxlinvestigate
nearly-central collisions of Nb on Nb at 100 and 180 MeV/nucleon.

Chapter 2 describes the principles of operation of a streamer
chamber and compares it with other types of “ii-detectors. The CCD system
is then discussed, and its characteristics compared with that of
photographic film. Finally, there is a description of the electronics
set-up and the software developed to run the system during data
acquisition.

In chapter 3 the details of the data analysis will be given, with a

discussion of the uncertainties in the results.

26

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27

The physical results extracted from the experiment will be presented
in chapter “, with a description of the calculations and models
(transverse-momentum analysis, scaling behaviour of physical observables)
used.

A summary of the results, with an evaluation of the performance of
the system is contained in chapter 5. Possible future improvements will
be discussed as well. Lastly, some ideas for future experiments will be

mentioned.

Chapter Two

SYSTEM DEVELOPMENT AND DESCRIPTION

2.1 Principles of Operation of the Streamer Chamber

When a charged nuclear particle moves through a gas, it undergoes a
series of inelastic Coulomb collisions with the electrons in the gas,
ionizing or exciting the atoms to which it comes sufficiently close. In
the process of radiative recombination or de-excitation which follows,
photons are emitted. As a consequence, if the photons are of the
appropriate wave-length, the trajectory of the particle through the gas
can be displayed. In the case of the streamer chamber, the gas used is
mostly neon. The transitions from the 2p1-2p1O levels to the 232-255
levels cause emission of light in the visible part of the spectrum,
giving the neon discharge its characteristic red color [Ric 7“].

Naturally, for the recording of such an image to be possible, there
must be a sufficiently large number of photons to be detected by a light-
sensitive device. Therefore, before the primary electrons and ions
diffuse away from the initial track, an intense electric pulse is
applied, which causes the electrons to accelerate toward the anode. The
time delay between the occurrence of an event and the application of the
high-voltage pulse should be a few microseconds, and the memory time of
the gas should be made to match this value approximately. By adding a few
parts per million of an electronegative gas, such as SF6, the rather long
recombination time of neon is reduced to the proper value. After being
accelerated, the electrons are likely to gain sufficient energy to cause
further ionization when they collide with a gas atom. More electrons are

thus liberated which, after acceleration, will in turn ionize too. As

28

29
this process continues, an avalanche quickly builds up. This process

grows exponentially, and can be described by

n=e (2.1)

where n is the number of electrons produced by one electron IJIEB length
x, and a is the Townsend first ionization coeffichanh defined as the
number of electrons produced in the path of a single electron travelling
1 cm [Rio 7“].

As the number of electrons in the avalanche grows, space-charge
effects become more important, gradually reducing the applied field
within the avalanche, but enhancing it at the head. In the absence of the
electric field, recombination occurs within the avalanche, causing the
emission of ultraviolet photons. Those photons that are liberated near
the head or tail of the avalanche, where the electric field is very high,
can give rise to secondary avalanches, and these in turn can repeat the
process, always along the direction of the applied field. The process by
which the new and old avalanches merge together is called streamer
formation.

A side view of the streamers produced along the path of an itniizing
particle is shown in figure 2.1.1a. Here, by limiting the duration of the
electric pulse, the streamer growth has been arrested, but the trajectory
of the ion is not well defined. Figure 2.1.1b shows how an end view
(along the direction of the electric field) of the streamers offers a
well defined track, and also makes photography easier, the dots

(projections of the streamers) being brighter. At the LBL streamer

30

(I)

 

H (b)

Figure 2.1.1 a) Side view of the streamers produced along the path of an

ionizing particle. 6) End view (along the direction of E) of
the streamers.

31
chamber, the size of the ribbon seen along the perpendicular to the field
is about 1 cm, and about 1 mm when seen in profile.

As we have mentioned, the light recorded in the streamer chamber is
produced not only by the electrons directly liberated by collisions of
the particle with the gas atoms (primary ionization), but also by those
ejected by successive collisions with the accelerated primary (and
secondary) electrons. A measure of either the primary or the total
ionization (which is what is observed in the streamer regime) can give
information on the specific energy loss of the particle, dE/dx, and,
therefore, on its velocity and charge. A number of properties of the
observed tracks depend on the ionization, among them the number of
streamers per unit length and the streamer brightness. But, while the
primary ionization indicates the actual number of collisions that have
occurred, and is therefore directly proportional to the energy loss of
the particle, by the time streamers develop, this proportionality is to
some extent lost. This is the price one has to pay for brightness. One
possible advantage of using the more sensitive CCD's instead of film is
that a decreased light output is acceptable, and the chamber can be
operated at a slightly lower voltage. In this regime, closer to the
avalanche mode, the proportionality between track brightness and dE/dx
(or 22) should be to some extent retained, and the particle
identification capability of the chamber improved. This point will be
further discussed in chapter 3.

Another advantage of operating at a lower voltage is the reduction
of flares. This phenomenon, visible in many events as very bright areas

which obscure the tracks, is caused by energetic 6-rays emitted in the

32
direction of the electric field, shorting the electrodes and producing

extremely bright sparks.

2.2 The Streamer Chamber in Heavy-Ion Physics

The ideal detector for heavy—ion experiments should meet a number of
requirements suggested by the nature of the reaction processes to be
observed. In this section, these requirements will be discussed and the
streamer chamber performance compared with that of other detectors
currently in use or in construction.

The first characteristic of a detector for exclusive measurements is
that of a nearly “n solid angle. The response of the streamer chamber I13
isotropic over almost the entire space, with the exception of a small
cone of about 1 20° along the direction of the electric field. In this
regltni, the streamers fuse with each other, forming a continuous channel
up to a thousand times brighter than the normal tracks, and the tracks
themselves appear as very short, bright stubs. This bias can be
estimated, however, by observing the particles emitted in the
corresponding cone, at a 90° angle with the E-field.

Due to the high multiplicities observed in heavy-ion collisions, a
good multitrack efficiency and two-track resolution are necessary. Events
with up to 150 charged particles have been observed at the LBL streamer
chamber [Van 82]. An estimate of the two-track resolution must take into
account the characteristics of the recording device (CCD or photographic
film), and will therefore be discussed in detail in section 3 of this
chapter. For the moment, it will suffice to mention that, due to the
chamber's fine granularity, its ability to separate adjacent tracks is

better than that of any electronic-type detector.

33

Another important requirement is the triggerability of the device,
so that particular kinds of events can be selected during the
measurement. The memory time of the chamber, of about 2 usec, is long
enough for a set of plastic scintillators, or other electronic detectors,
to establish that an event of interest has occurred and to trigger the
high-voltage pulse in the chamber.

In addition, one must keep in mind that fragments over a wide range
of masses and momenta, corresponding to a wide range of primary
ionization, can be produced in heavy-ion collisions. Ideally, all these
fragments should be identified (2 and A determination) and their momenta
measured. The first limitation, which prevents the detection of all the
fragments emitted in the streamer chamber, is the necessity for a
particle to travel at least 8-10 cm in the gas to be observed, since the
density of tracks is usually very high near the interaction vertex.
Including energy losses in the target material and in the gas, for a 220
mg/cm2 Nb target, and assuming that the particles are produced at the
front surface of the target, the minimum energy for protons and a-
particles to be observed is about 9 MeV/nucleon. For the particles that
are seen, the curvature of the trajectory in the magnetic field of the
chamber allows the determination of the ion's magnetic rigidity (momentum
divided by the charge, p/Z). Therefore, the identification of the charge
is necessary to derive momenta and, hence, energies, rapidities, and
other physical variables of interest.

The problem of the identification of such a wide range of fragments,
with different charges and energies, has been approached in different
ways. The plastic ball [Bad 82] has been used to detect and identify

relatively light ions (up to a-particles), while the “n array, under

3“

construction at NSCL [Res 85], promises to provide good position, charge,
and time resolution for particles over a wide range of charges. Data
obtained at the LBL streamer chamber, with film as a recording medium,
have been analysed using the integrated intensity per unit length along
the tracks to provide a good separation between p, d, t, and “He in a
limited range of rigidities [Uol 81].lJndtations in the performance of
photographic film, which will be discussed in detail in section 2.3,
prevent the identification of higher-charge fragments. It is hoped that
the introduction of CCD cameras as a recording device will help overcome
these limitations, once the problems encountered during the experiment
and in the analysis described in this thesis are solved.

Of the shortcomings of the streamer chamber, as opposed to
electronic-type detectors, one is the slow event rate imposed by the
pulsed high-voltage supply (a Marx generator), and, in the case of CCD
cameras, by the data-reduction and read-out time of the electronics and
the computer. The rate obtained with the system described in this work
was one event per Bevalac spill. At this rate, over 1000 good events
(clean central collisions) were collected at each beam energy during the
allotted time. The relatively slow analysis is another often-mentioned
problem with this type of experiments. The introduction of CCD's has
improved the speed of the analysis, even though the extent of‘tnua
improvement depends strongly on the multiplicity of the events. This

point, too, will be discussed in more detail in section 3.2.

2.3 Charge-coupled Devices
Charge-coupled devices (CCD's) have been used in optical astronomy

for some years, and "have opened new horizons" in the field [Djo 8“]. To

35
mention only one of their most recent applications, they have been used
for imaging fast variations in the coma and tail of Comet Halley [Bau
86].

The introduction of CCD cameras in nuclear physics is a more recent
development, and the system described in this work is the first of its
kind ever to be developed and used as a recording device in an
experiment. The substitution of CCD's for photographic film to record
events in a streamer chamber represents a significant improvement in the
processes of data acquisition and analysis. To appreciate better the
differences between the two media, a brief description of the CCD
characteristics will be given first, followed by a comparison with the
performance of film.

A CCD is a solid state image sensor composed of a matrix array of
charge-coupled photosites, or pixels (picture elements). Photons
penetrating the silicon produce hole-electron pairs in proportion to the
incident photon rate. The holes combine with free electrons in the
substrate, while the photoelectrons are collected in the potential vualls
created by MOS capacitors,innflJ.read-out. Thermal energy in the silicon
lattice produces free electrons, which are indistinguishable from those
created by photons. The contribution of thermally generated charge is
called dark current and it can be reduced to negligible levels by cooling
the CCD's to about -50° C (see Appendix B).

In principle, the advantages of using a CCD system as a recording
device in streamer chamber experiments are manyfold. First, CCD's have a
large dynamic range, a linear response to light, a high quantum
efficiency, and a good performance in low-light conditions. Second, the

output of a CCD is in digital form, and can be recorded directly on tape“

36
thus avoiding the time-consuming processes of developing the film and
digitizing the images. The events can also be displayed on a graphics
terminal, providing a useful tool for on-line diagnostics both during the
beam tune-up phase and during data-taking. Third, the digitized pichlres
can be processed for image enhancement, and easily lend themselves to
computer-assisted track recognition and intensity scanning.

It is interesting to examine how these characteristics compare with
those of photographic film, the other recording medium commonly used in
streamer chamber experiments. A summary of the following discussion is
given in table 2.3.1.

As was mentioned in sections 2.1 and 2.2, a large dynamic range is
necessary in order to separate the wide variety of fragment charges and
energies which are observed in heavy-ion collisions. The dynamic ranges
of CCD's and photographic emulsions are compared in figure 2.3.1a aunl b.
Figure 2.3.1a shows the typical response curve for a charge-coupled
device digitized to 12 bits. Here E represents the exposure, defined as
EztI, where t is the time during which the medium was exposed to the
light source, and I is the illuminance of the source [Eco 83]. The
exposure can be given in units of incident energy per unit area, or as
photons per unit area. The response curve is linear for CCD's, and the
useful dynamic range, after the subtraction of background noise, is of
about 3000:1. A similar curve is plotted in figure 2.3.1b for film. The
'usable' region of the curve, where the response of the medium is
logarithmic, includes a relative density range between about 1 auni 2.5,
corresponding to a dynamic range of about 300:1.

The quantum efficiency, defined as

37

Table 2.3.1. Characteristics of CCD's in comparison with
photographic film. The values indicated with (*)
are taken from [Djo 8“].

 

 

CCD Photographic film
Pixel size 23 pm 8 um
Resolution 1. 7 mu 0 .2 mm
Two-track resolution 3.7 mm 2.3 mm
Linearity z 0.1 S (*) poor (*)
Dynamic range 35 dB (‘) 20-25 dB (*)
Quantum efficiency z 60% z2$ (F)
Data-acquisition rate 1 ev./beam spill ~3 ev./beam spill

(Bevalac Streamer Ch.)

 

 

 

 

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39

Q E _ number of electrons collected

is about 60% for the Thomson devices used in our system, compared to a
value of about 2% for film. This characteristic makes CCD's essentially
photon-counting devices (for some chips the quantum efficiency is as high
as 80%), and ideal for use in low-light conditions.

Resolution is where film offers some advantage over CCD's. Due to
the smaller grain size and the larger area, the typical resolution for
photographic film is about 0.2 mm. For the Thomson CCD's used in the
system described in this work, the pixel size is 23 um square, and the
dimensions of the sensitive area of the chip are 13.2 mm x 8.8 mm. The
resolution, defined as the "real" size of a line mapped on one pixel, is
about‘L7'mm.'nus value depends on the demagnification necessary to
image the whole chamber on the recording device, and the grain (or pixel)
size of the medium. While these values appear very different, one must
also include in the definition the size of the object to be recorded, the
streamers viewed from the side. A better comparison is therefore given by
the value called two-track resolution, defined as the minimum distance
between streamers which can be identified as belonging to t0m><iifferent

tracks [Ana 82]. This value is given by the expression:

 

2
2 Ax 2 1 1
D: D + - ----- + [ AF(M+1)] + M2 (-- + -- )
J A 52mm? 0? RE

where D

A size of a streamer (1 mm)

Ax half depth of the chamber (20 cm)

“O

F = f-stop (2)

M = demagnification (80 for CCD's, 50 for film)
i = wavelength of the emitted light (6000 A)

R1 = lens resolution (100 line pairs)

Rm = medium resolution (100 lp/mm for film

25 lp/mm for CCD's)

The first term in expression 2.3.1 represents the effect due to tine size
of the streamers, the other terms estimate the distortions due to depth
of field, diffraction and resolution of the lens and CCD or film.
The values one obtains for the two media are DCCD=3.7 mm, and Dfilm:
2.3 mm, showing that the resolution is only slightly worsened by the use:
of CCD's.
One of the main advantages of CCD's over photographic film, namely

the possibility of digital image-enhancement and of computer-assisted

analysis, will be discussed in detail in section 3.2.

2.“ Description of the CCD System

In order to do a three-dimensional reconstruction of the tracks,
more than one view of a given event are necessary. For this reason, the
system described here consists of three CCD cameras, with related read-
out electronics. A schematic of the electronics is shown in figure 2.“.1.

The modules provided by Photometrics, Ltd. with each camera head
include a model PS 830 T.E.C. (thermoelectric cooler) Power Supply, a
model CH 8“ Camera Head Electronics Module, and a model 80A Camera

Controller. A 2“ mm f/2 lens was mounted on each camera.

 

 

 

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Figure 2.“.1 Schematic of the electronics for the CCD camera system.

“2

ThelXchhip is mounted in an evacuated enclosure in the camera
head, which also houses the lens-shutter assembly. A thermoelectric
cooler, soldered to a copper heat sink, is connected to the CCD, anni the
heat produced is removed by circulating a water-antifreeze mixture,
cooled to about 10°C. A thermistor bonded to the cold sink near the CCD
allows the determination of the cold side temperature from a reading of
the current.Ihnfing the operation of the cameras, the temperature was
maintained at around -“5°C.

The camera-head Electronic Module provides shutter control, it
contains the clock drivers for the CCD and the analog processing, and it
houses ADC electronics.

The Camera Controller serves several purposes. It provides all
timing signals for the Camera Head, it receives serial digitised data
from the Camera Head, and produces parallel output. Also, it provides
user interfacing through manual input on the front panel, or digital
control input from the rear panel. The control parameters that can be
sent to the camera are in the form of hexadecimal command codes (O-F),
defining the task to be performed, or which data are being transferred,
plus an eight-bit data word determining read-out parameters, such as the
size and origin of the array to be read out in the CCD, exposure time,
etc.

During an experiment, when an event of interest occurs, the CCD's
must be read out, and the resulting image digitally processed and
transferred to tape. The details of the trigger hardware and the software
will be given in sections 2.5 and 2.6. Here, the electronic system
developed to accomplish the purposes mentioned above will be described. A

detailed CCD-to-VAX block diagram is shown in figure 2.“.2.

“3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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WCR=HORD COUNT REG.
BAR=BEGINNING ADDRESS REG.

Figure 2.“.2 CCD-to-VAX block diagram.

 

b---—---

““

Each of the three CCD systems is run by a dedicated SYS68K/CPU-2F
microcomputer. This is a VMEbus based board, which combines a Motorola
68000 CPU chip and, in our case, 1 Mbyte of RAM. The clock frequency is
10 MHz, corresponding to a cycle time of 0.1 usec.

Each camera controller is interfaced to a CPU board through a CCD-
camera to VME interface. This board, designed and built in-house, aillows
operation of the cameras, through a one-word command input register, and
read-out through a one-word Z-digital output register. The same board
also interfaces the VME crate to the external trigger, using a strobe
(write-only) register, and a status (read-only) register. The first
allows visual control of the status of the process, through an LED panel,
where different color lights indicate the current stage of processing:
green, when the camera is ready and waiting for a trigger; yellow, when
the camera is taking an exposure; red during read-out. TWHe status
register contains the information on FIFO synchronism, and trigger and
camera status. A schematic description of the contents of the four CCD-
interface registers is shown in figure 2.“.3.

Each CPU processes the image from one of the cameras using the 1
Mbyte on-board memory, then transfers the results to a Mass Memory Board
(DVME 351, a commercial board, with 1/2 Mbyte of memory) with dual port
access. This board allows read/write access by the VMEbus master and
read-only access by a Read-Only Controller (ROC).

The ROC's have also been designed and built in-house. They provide
for high-speed parallel transfer of data from the dual-ported memory to
the DR11-W board, which resides in a VAX computer. The events are then
stored on magnetic tape, and they can also be displayed, cur-line, on an

AED screen.

“5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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l5 [ | | DILSB

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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[RESET BIT [RED LIGHT
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LINPUT READY fir W
___ROY CAMERA FIFO OUT FIFO IN
,;_TIP CAMERA TRIGGER BEGIN
STR .____TR|GGER END

 

 

 

Figure 2.“. 3 Description of the read/write registers in the CCD
interface.

l)6
The next sections will deal with the rest of the experimental set-
up, and will describeIthe software used to run the system during data-

taking.

2.5 The LBL Streamer Chamber

The main components of the LBL streamer chamber are shown iJT.figure
2.5.1, in which a schematic view of the chamber, seen from the top, is
given. The Marx generator provides the high-voltage pulse; a main spark
gap and a Blumlein transmission line shape the pulse before it is applied
to the chamber; and the trigger counters with their electronics fixwa the
Marx generator and the cameras when an event of interest occurs. Not
shown in the figure is the dipole magnet in which the chamber is placed.

The streamer chamber has a rectangular shape, Halcmllong, 60 cm
high, and 40 cm deep. Its body is made of polyurethane foam, except for
the back plane, which is made of aluminum, and the transparent mylar
front window, through which the photographs are taken.

'The high-voltage electrode, made of stainless steel wire mesh, is
placed in the center of the chamber, so that the chamber itself is
essentially divided into two 20 cm deep areas.'Nu2fTont electrode is
also made of wire mesh.

The dipole magnet, whichIgenerateS the magnetic field in the
chamber, produces a field of up to 1.32 T, normal to the electrodes.

A two-stage Premarx and a twelve—stage Marx generator provide the
high-voltage pulse, of up to 720 W. The main spark gap controls the
voltage of the pulse applied to the chamber, and a Blumlein line reduces
and controls the duration of the applied field. The length of the pulse

can be varied between 5 and )5 ns [Van 82].

'47

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 2.5.1 Mgin co}n;ponents of the LBL streamer chamber (adapted from
Ch 79 .

#8

A coincidence between a plastic scintillator (S3), located at one of
the focuses of the beam, and a scintillator (R-counter), located inside
the chamber, about 5 cm upstream from the target, defines the beam
signal. The trigger scintillator (P-counter) was placed about 30 cm
downstream from the target and is used in anticoincidence with the signal
from the two beam counters. The S3 counter was 0.22 mm thick, and was
mounted at a lIS° angle with respect to the beam direction. For the R-
counter, a thickness of 0.614 mm was used for the 180 MeV/nucleon beam,
and 0.22 mm at 100 MeV/nucleon. The P-counter was 2 mm thick.

'The plastic scintillators are inserted through the back plane, and
are connected to long light-pipes, so that the phototubes are outside the
chamber.

In order to have a trigger signal for the Marx generator and the
cameras, we required a valid beam signal (S3-R) with a pulse in the P-
counter below a predetermined threshold (trigger : S3-R-5). By varying
the threshold level, it is possible to select events corresponding to
different amounts of energy deposition in the downstream (P) counter,
from an 'Luflaiased' trigger, when the threshold is at beam pulse height,
to central trigger, when the threshold is at about 10% of the beam pulse
height.

The purpose of the experiment described in this work was the study
of central collisions between two Nb nuclei, which, at 100-200
MeV/nucleon, are characterized by the shattering of the target and
projectile into»a.large number of fragments, emitted in different
directions. The central trigger was therefore selected for the

experiment.

A9
2.6 The Experiment

The Bevalac produces a pulsed beam, with spills about one second

long and A seconds apart. As a consequence, the cameras start an exposure .

at the beginning of a beam pulse, and the read-out must begin when an
event of interest occurs, simultaneously with the triggeringIof the Marx
generator. A listing of the assembly-language code that handles the
various signals and operates the cameras is given in Appendix A. What
follows is a description of how the different tasks are executed.

Before a beam burst starts, the cameras are running in the "fast
charge dump" mode, which clears the CCD's continuously, until a new
comand is issued. At the beginning of a beam pulse, the fast clear
instruction is interrupted by sending a set of commands that define the
size and origin of the array to be read out (the entire CCD in our case).
The CCD's are now being exposed. If a valid event signal is sent at any
time during the beam spill to trigger the chamber, the CCD's are read
out, and fUrther triggers are inhibited until the current event has been
processed.

One of the problems that had to be solved in order to make this type
of system viable was the handling and storage of the large amount of data
obtained for each recorded event. The read-out of each of the CCD's used
in this system, where the charge accumulated in each of the 22118“ pixels
is digitised to 12 bits, consists of almost 0.5 Mbytes of information. In
order to reduce the amount of data to be transferred to tape, a
previously stored background frame is subtracted and a low-level
threshold applied (see Appendix B for a description of the contritnitions

to the background). The pixels whose content is below the threshold level

50
are discarded, and only the remaining ones are transferred to the dual-
ported memory, together with a series of bit masks, containing the
information on which of the pixels are below or above the threshold.

This type of processing reduces the amount of information that is
stored on tape by 30 to 60%, depending on the event multiplicity and the
number of flares.

After the CPU's have finished processing the current event (a
different view for each system, in parallel), and have stored the non-
zero values and the bit masks in the dual-ported memory, the downloading
of the processed frames to the VAX can start, through the ROC boards, and
the next exposure from the CCD's can proceed simultaneously, thanks to
the use of the dual-ported memory boards.

During data acquisition, randomly selected events can be displayed
on an AED screen, providing on-line monitoring of the experiment. This
has proven to be a very useful diagnostic tool.

As mentioned earlier, one obvious disadvantage of a CCD plus
streamer chamber system is the slow event-rate imposed by the processing
and transferring of the large amount of information collected. The rate
of one event per beam spill, obtained with CCD cameras, should be
compared with that of about three events per spill when film is used.

A total of about 1000 central collisions was recorded at each energy
in about 60 hours. Obviously, a large number of the collected events is
eventually discarded, for several reasons. First, the target thickness is
comparable to the thickness of the several windows, counters, chamber
gas, and air that the beam must go through. This causes a high number of
interactions to occur with nuclei other than those in the target.

Secondly, some rather peripheral collisions, while producing only a few

51
fragments, deposit so little energy in the P-counter that a valid trigger
signal is sent to the chamber.
It is possible that, by using a different trigger system and by ~
allowing the counters in the chamber to be moved vertically (therefore
correcting for the bending of the beam when the magnetic field is

applied), the number of such spurious interactions could be reduced.

Chapter Three

DATA REDUCTION AND ANALYSIS

3.1 Introduction

While a streamer chamber offers several advantages as a An-detecttn~
for heavy-ion collisions, one major drawback is the time-consuming task
of digitizing the images and recognizing the tracks. The amount of time
involved in this part of the analysis is one of the reasons for the low
statistics usually obtained in such experiments, the other being the slow
data acquisition rate.

When the recording medium is photographic film, the fihmInust first
be developed, then scanned on an image plane digitizer by an operator.
The coordinates of the digitized points along each track are stored on
magnetic tape for the spatial reconstruction of the event [Str 8“].

The use of CCD cameras eliminates the necessity of handling and
developing film, since the wholeIdigitized image is directly stored on
magnetic tape during the experiment.

Since parts of the tracks are frequently obscured by flares, the use
of digital image-enhancement techniques is extremely helpful.‘Therefore5
our CCD pictures are first processed to make tracks more visible and to
reduce the background. As a second step, a track-recognition program
attempts to find and‘follow all the tracks in the event. Omissions and
errors can be later corrected by an operator.

Once the coordinates of points along the tracks have been determined
in all three views, the Three View Geometry Program (TVGP) [Som
66] reconstructs the trajectory of each fragment in three-dimensional

space, determining the radius of curvature (R), emission angles (dip and

52

53
azimuthal), and length of the track. If the magnetic field is known, R
provides the magnetic rigidity (p/Z) of a particle, sirune Rsz/Z.
Therefore, determination of the fragment charge is necessary in order to v
find its momentum.

In a streamer chamber, particle identification relies on the
analysis of track intensity. As mentioned before, while the energy loss
of a particle in a gas is proportional to 22, the intensity of the light
emitted in the streamer regime does not show the same charge dependence.
Nevertheless, information about the charge and mass of each fragment can
be extracted by combining the rigidity and intensity information. In this
way, the emitted particles can be identified and their A-momentum
calculated.

‘The rest of the chapter will describe how the various steps of the
analysis are performed. A summary of these steps is given in a flow chart

in Appendix C.

3.2 Image Enhancement and Track Recognition

Several methods have been developed to process digital images in
order to enhance the features of interest, reduce the background, etc. In
the case of streamer chamber events, where particle tracks are to be
recognized and reconstructed, an edge-enhancing technique has been
adopted, which reduces such unwanted features as flares and background
illumination, while making the track narrower and better defined.

The processing consists of calculating the angle between the line
joining a point on the track with the vertex and the horizontal, and then
taking the double derivative of the intensity with respect to this angle

for each point in the image. How this double differentiation operates on

5A
a gaussian-like curve is shown qualitatively in figure 3.2.1. Once the
double gradient has been calculated, the sign of the negative values
found (refer to figure 3.2.1c) is inverted, and the positive ones are set
equal to zero. In practice, the central negative peak in figure 3.2.10
becomes positive and is all that is left of the original track. In this
way, the tracks, characterized by a sharp rise in intensity, become
narrower and well defined, while the background and the slowly-varying
illumination due to flares disappear. Figures 3.2.2 and 3.2.3 show an
event at 100 MeV/nucleon before and after the processing just described.

Using the image-enhanced picture, the track-recognition code starts
scanning in vertical swaths at the right edge, searching for non-zero
points. For each point found, the search is continued in a grid of 3X5
pixels, tilted along the direction of the line joining the point and the
vertex. The intensity-weighted average of the x and y coordinates of the
non-zero points found within the grid is calculated, and the search moved
to the new point.

Before a new point is added to an existing segment, the least-
squares slope of the last six points of the segment is compared to the
slope given by the last three points (including the new one) and, if the
difference is less than 20°, the new point is added to the track.

After the whole picture is scanned, the segments less than 10 points
long are discarded. The remaining ones are compared and the tracks are
reconstructed by matching adjacent segments with similar slopes.

The recognized tracks are then numbered, and a 'track' file is
written to disk, which contains the track numbers, number of points on

each track, and the x and y coordinates of the points.

 

 

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Figure 3.2.1 a) Gaussian-type curve which approximates the intensity

along a cut perpendicular to a track. b) First derivative of
intensity with respect to angle. c) Second derivative of
intensity with respect to angle.

55A

Figure 3.2.2 Nearly-central collision at 100 MeV/nucleon. Unprocessed
event.

 

m

56

 

56A

Figure 3.2.3 Event in figure 3.2.2 after image-enhancing processing.

57

 

58A

Figure 3.2.“ Tracks found for the event in figure 3.2.2.

58

At the present stage, it is still necessary for an operator to
display the processed event and the output of the track-recognition
program on acolor graphics terminal, where corrections and additions to
the tracks can be introduced. The extent of this intervention is strongly
multiplicity-dependent (the higher the number of tracks, the higher the
likelihood of crossing and partially overlapping tracks, which confuse
the search) and it also depends on the overall quality of the image.

After all the tracks have been recognized, the operator introduces
the position of the interaction vertex, which is added as a last point to
all the tracks, and a third degree polynomial is fitted to each track.
The tracks found in the event shown in figures 3.2.2 and 3.2.3 are
plotted in figure 3.2.11. At this point, a new track file is written,
which is used for the next step in the analysis of the event, namely the

three-dimensional reconstruction.

3.3 Three-View Geometry Program

The programs described in this section, WEASEL and TVGP, were
originally written in 1965 to process bubble chamber pictures, and were
later modified to be used with streamer chamber photographs.

After the tracks in three views have been recognized, files
containing the (pixel) coordinates of the track points are created. The
three different views record different projections of an event relative
to fixed fiducial marks. The three-dimensional reconstruction of each
track is based on the fact that, by measuring the projection of a point
on a fixed plane, seen from two different views, the intersection of the
rays from the projected point to the cameras gives the position of the

point in space. In figure 3.3.1 the trajectory of a particle in space,

‘59

 

 

 

 

 

 

 

 

 

 

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CAMERA
1 ‘\
‘\
\‘ss
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\
x
CAMERA

2

 

 

Figure 3.3.1 Trajectory of a particle in space and its projections as
seen from two different views. A is the dip angle.

61
with dip angle A, is shown. From the projections observed from cameras 1
and 2 on a plane defined by a set of fiducial marks of known coordinates,
the trajectory can be reconstructed.

The first step in the spacial reconstruction of an event is the
measurement of the position of the fiducials on the CCD planes. The
(averaged) x and y coordinates of the fiducial marks (iJIIDiXGlS), their
real space coordinates in the streamer chamber geometry, and the
approximate position of the three cameras are the input for WEASEL, a
program that calculates rotation, translation, and magnification for each
camera, and the optical parameters used by TVGP in the track
reconstruction. The system of axes associated with the streamer chamber
in these calculations, and in those performed by TVGP, is centered around
the position of the target. The x-axis is vertical, the y-axis is in the
direction opposite to the beam, and the z-axis is towards the cameras.

This part of the calculations needs to be done only once, in our
case, since the CCD planes, unlike film, do not move from one event to
another.

Before running TVGP, the tracks recognized following the procedure
described in section 3.2 must be matched in the three views. The
coordinates of the matched tracks are then read by TVGP.

The steps of the reconstruction performed by the Three View Geometry
Program are summarized in the following paragraphs.

i- For each view, a circle is fitted through the points, to help

check for bad points (which will be dropped from the
reconstruction); for interpolating between points; and for

getting space-point weights.

ii-

iii-

iv-

vi-

vii-

62
For each view, the good points are rotated to two stereo
systems (given, e.g., by views 1-2 and 1- 3). This is done for
all views.
A new view-loop is started. Here, for all the points in the
primary view, the corresponding points are found, by
interpolation, in the other two views.
For each point, the z-coordinate in each stereo system is
found using the intersection of the rays from the two
projections. The final z-coordinate in space is the weighted
average of the two points reconstructed in the two stereo
systems.
When all the approximate space-points are reconstructed, a
circle is put through the first, middle and last point. At this
stage, for a given track, approximate space points, optical-ray
components, and projected arc-lengths, approximated by circular
arcs in the x,y plane are known.
Now, the corrections due to variations in the magnetic field
and energy loss must be introduced, and a space-curve
calculated such that its projection on the CCD plane minimizes
the distance to the measured track. Such a curve is described
by a set of five parameters and by functions, incorporating
these parameters, from which the points in space can be
calculated.
For each point, the least-squares errors are calculated and
added to the appropriate summation. When all the points have

been used, the error matrix is found by inverting the 5x5

63
summation matrix of derivatives, and the corrections to the
five parameters are found.

viii-Now the five parameters of the fit are available. They are

angles, curvature, and x,z position near the middle of the
track. These parameters, and their error matrix, are then
propagated to the beginning and end of the space-curve, using
the assumed functional form of curvature and slope vs.
projected arc length.

The results obtained from this procedure are the curvature, angles,
and space coordinates at the beginning and end of each track.

The product BR, where B is the magnitude of the magnetic field and R
is the radius of curvature of the track, gives the magnetic rigidity of
the particle, which is also equal to p/Z (momentum divided by the
charge). From the azimuthal and dip angles, the projections of the
magnetic rigidity along the three axis in the chamber geometry are
calculated.

The accuracy of the results calculated by TVGP was estimated by
using computer-generated tracks of known momentum (in magnitude and
direction) in a known magnetic field. The coordinates of three
projections were used as an input for TVGP. For such an ideal case, the
rigidity and emission angles of the reconstructed track deviate very
little (about 0.251) from the original values.

Several factors contribute to a much larger error in the analysis of
'real' streamer chamber tracks. The first is the non-negligible width(3f
the recorded tracks, which introduces an uncertainty in the position of
the points along the tracks themselves. Secondly, the points used as an

input for TVGP are the result of a polynomial fit, and the fitted curve

6A
may, in some cases, deviate slightly from the original trajectory. In the
third place, the high density of tracks around the vertex makes the exact
determination of its position difficult, thereby introducing a further
deviation from the real track in a region where the track is especially
difficult to observe.

Another problem which is encountered in the analysis of the recorded
events, especially at the higher multiplicities, is the difficulty of
matching the tracks in the three views when some of the short tracks are
obscured by flares, or are simply not visible in one or two of the views,
or when several longer tracks are emitted so close together, and are so
similar in intensity, that the determination of the proper match is very
doubtful. This factor limits the success rate for TVGP to about 80% for
the 180 MeV/nucleon data, where the multiplicities are higher, and to a

little better than 90% for the 100 MeV/nucleon data.

3.” Intensity Analysis

The intensity of the light emitted by a charged particle in the
streamer chamber provides information on the energy loss of that particle
as it passes through the gas in the chamber.

In principle, when magnetic rigidity and dE/dx are known, the
identification of the emitted particle is possible, e.g. from a scatter
plot where the intensity is plotted vs. rigidity, in the same fashion as
a common dE vs. E plot. A rather accurate determination of the track
intensity is therefore very important.

In the case of particles emitted in a streamer chamber, up to two or
three hundred points per track are usually visible in a CCD picture (less

for shorter tracks, or for tracks emitted at large angles towards or away

65
from the cameras). Our intensity analysis takes advantage of the fact
that this reconstruction gives us a large number of points along each
track, as described in the following paragraphs.

The starting points for the determination of the intensities are the
'track' file containing the coordinates of the points found along each
track, and the original CCD-recorded event, where the digitized image
contains the available information about the light intensity.

Starting from each point in the track file, a search is made in the
direction perpendicular to the track for the true maxinuun intensity (Hi
the track, and for the minima on either side of the maximum. At the end
of this step, the intensity has been determined along the width of the
track itself, for each point along the track. Now, after subtracting a
locally determined background, the intensities along each out are added,
to give the total intensity for the entire width of the track.

This gives us the light intensity for a large number of points along
the length of the particle trajectory in the chamber.

For the purpose of particle identification, the fragments emitted in
an event can be divided into two groups: those that stop in the chamber
and those that do not. For the first group of particles, the intensity
informatdtni is not strictly necessary, since the fragments can be
identified from their range in the gas and their rigidity, both of‘vuiich
are obtained from TVGP. For these fragments the energy loss dE/dx is not
small compared to the energy, and it increases rapidly, peaking at the
end of the range. The Bragg peak typically observed for stopping
fragments is seen in the streamer chamber in these cases, as shown in

figure 3.14.1. Here the intensity at each point along the track

66

 

 

 

 

 

3000I- _s
.— D J
I “5% ° ‘
A" 'D‘
2000 — (5) _,
>.
.2: - 0 ~
D
a '- C!
o
«.0
.5 - .
1000 —- __
I" .-
- E] q
o l I l l l l L l l I 4 l l 1 l
0 50 100 150
Distance from vertex (in pixels)
Figure 3.11.1 Bragg peak observed for a proton stopping in the gas of the

streamer chamber.

6?
(calculated as described above) is plotted as a function of the distance
from the interaction vertex.

For the fragments that do not stop in the chamber the intensity
(proportional to the energy loss) is a necessary piece of information,
together with the rigidity, to determine A and Z. In this case, the
statistics of the energy loss can be described by a Landau distribution,
which is characterised by a sharp rise on the low-energy side and a
high-energy tail [Igo 59, Seg 611]. The maximum of the distribution
corresponds to the most probable energy loss, as shown in figure 3.14.2.
One advantage of using an energy loss distribution to obtain the track
intensity, rather than calculating the average intensity per unit length,
is that those points along the track which are. obscured by flares will
fall in the high-energy tail of the distribution and will not influence
the evaluation of the maximum. In figure 3.“.3, where the intensity along
a track is plotted as a function of the distance from the vertex, the
localised flares and the areas of relatively constant energy loss are
evident. Some typical intensity distributions for our data, showing the
features of a Landau curve (except for the low—statistics case) are
plotted in figures 3.11.14a, b, and c. This figure also shows the large
range of intensities usually observed in an event.

By these means, magnetic rigidities (rig) and track intensities (I)
are obtained for most of the charged particles emitted in an event. By
plotting each rig,I point on a scatter plot particle identification
should be possible. In practice, for our data, this has proven to be a
rather uncertain enterprise. The first problem, due to a less-than-
optimum performance of the streamer chamber, was that of many flares

along the tracks, which caused large uncertainties in the intensities.

68

 

 

 

    

 

 

300 1 T 1 I I T T
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: I. .-
O_ "i‘ I 'L 1 AM
0 IO 20 30 ‘0 ’0

 

PULSE HEIGNT- ARIITRMY UNITS

Figure 3.11.2 Experimental distribution of energy losses of 31.5 MeV

proton. The corresponding theoretical Landau distribution is
also shown (taken from [Igo 53]).

69

 

 

 

 

 

 

 

 

 

2000 b T r I r ‘I— T T I l I T T T T l T T
)- ..
- -I
1500 — __
_ I
I I
h I' .1
=3 1000 - —I
a . .
0
3 .
,
I -(
500 .4
o l l
D 100 200 300

Position along track (pixels)

Figure 3.11.3 Intensity along a track as a function of distance from the
interaction vertex.

69A

Figure 3.A.A Intensity distributions for three different tracks in a CCD-
recorded event.

TVrTrrTIIIITTIYTTTITVYUTIUTV

 

 

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CCH

IdII<<_<44Jfi4141fi44d‘fi‘44N—1fi41

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100

 

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f

r

I

r i
L

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. 4

T i

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fi i

thL—hPIrPI—IbhbbmhLbLhF-b_rbh
o 0 5 0 5
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200 250

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150

100
YYIfTTYITTYrITW—TY

50

 

 

— d I1 1 I1 — 4 I1

 

rI-ILIbF—b P

 

 

 

 

‘

a... 3.333 .2. 3.58

12000 10000

10000
Intensity

71
This fact is illustrated in figure 3.11.5, where the intensity at each
point along a track is plotted vs. the distance from the vertex. In this
figure, which exemplifies an extreme case of flaring, the track is
obscured by large flares, which saturate the CCD along most of its
length, and the determination of the actual intensity is impossible.

The second problem arises when data from different events are
compared. Since the amount of light emitted by a fragment depends on the
height and duration of the electric pulse applied to the chamber,
variations in pulse height from event to event require that the
intensities be normalized before they can be compared. For our
experiment, a laser beam was to be used for this purpose. The beam,
leaving a constant-ionization track (approximately corresponding to a
mimimum-ionizing particle), would have provided a known reference
intensity for an event-to-event normalization. Unfortunately, the laser
used for this purpose at the LBL streamer chamber was not functioning
properly at time of our experiment, and could not be used. Other ways of
normalizing the intensities in different events had to be considered, and
our criterion for the determination of this normalization factor will be
described later.

Due to these problems, our 2-dimensional (I vs. rig) plot does not
show a distinct isotope separation, and the fragment identification was
based on an algorithm to be described.

An important question to be addressed in dealing with the intensity
of the light emitted in a streamer chamber is how it depends on the
charge and velocity of the particle. It is known that, because of the
statistical process of streamer formation (not all ionization sites

develop streamers), the light does not show the same 2 and v dependence

72

 

T T T T IT—Tj r1 I rTTfi l I T Tl

4000 I—

 

 

 

 

 

 

 

3000 "‘
.I
>. I
s
a 2000
3 d
.5 N ‘
1000 "‘
-I

 

 

 

 

 

 

 

 

 

100 200 300 400
Point 5 Along Track

Figure 3.I-I.S Intensity along a track as a function of the distance from
the vertex. This illustrates an extreme case of flaring
along the whole length of the track.

73

as dE/dx. In order to investigate this dependence, we have tried to
select particles with similar velocity by analysing the fragments emitted
in a narrow forward cone (:8° around the beam direction) and by plotting
an intensity histogram for those tracks with rigidity around twice that
of beam-velocity protons. This should select ions with M/Z=2 (deuterons
and a-particles) and with velocity close to that of the beam. Under these
constraints, if such leading particles indeed exist, the histogram should
show two peaks of area proportional to the ion yield. The position of the
peaks would correspond to the intensity of beam-velocity deuterons and a-
particles. The results obtained for our 180 MeV/nucleon data are shown in
figure 3.11.6 for a sample of 96 events. Here, two peaks are clearly
visible, in spite of the low statistics. The areas are in a ratio of
2.7:1 and the position of the maxima suggests that the intensity varies
linearly with 2.

Our criterion for estimating the normalization factors was based on
the histogram in figure 3.11.6. By comparing the intensity of different
types of tracks (e.g. low-intensity tracks, with rigidity corresponding
to beam-velocity protons; or low- and intermediate-intensity tracks over
a wider range of rigidities), different normalizations were tested. We
selected the factor that gave the best separation between the deuteron
and'alpha peaks in this distribution.

On the basis of the information described above, we have assumed a

simple expression for the intensity, Izconst "Z;- , where the exact
v
. . . . Z rig
dependence on the particle velomty in unknown. Since V=“"fi“‘ ,

substitution for v gives:

7n

 

25 V T' '1' I 1 I I T T T T I T T TTrT

20

15

 

 

 

 

L
L
L
L_
L
I-
L
L
L.
L
L
L
L

10—
I.
L
L
L
I——
L
f
L

lllllllllLLLJlllllJllll

Number of tracks per intensity bin

 

 

 

04 lllLLlLllllll 11

D so 100 150 7 200
Track intensity

I-

 

Figure 3.II.6 Intensity histogram for forward-going particles with
rigidity between 1000 and 11100 MeV/c/Z. Peaks corresponding
to beam-velocity deuterons and c—particles are indicated.

75

1: const * 21-x (M/rig)X 3.1

The scatter plot obtained for rigidities and (normalised)
intensities for the 180 MeV/nucleon data, including all the non-stopping
tracks for 97 events, is shown in figure 3.11.7. Only intensities lower
than 500 are included. The curves are calculated from expression 3.1 with
x=O.5.

These curves were used to select the particle type from the plot.
The percentage of various isotopes obtained with this method is given in
table 3.4.1. These yields agree reasonably well with those obtained from
a code like FREESCO [Fai 86], which simulates the process of statistical
disassembly of a single excited source of given A, Z, volume, and
excitation energy, through a statistical model. The different final
states compete according to their microcanonical weights [Fai 83]. The
input parameters for our calculations were a freeze-out density of 1/3 po
and an excitation energy of the source of 1/2 the beam energy (the other
1/2 of the energy goes into collective effects). The largest
discrepancies in table 3.“.1 are observed for large-mass fragments (A24).
One of the reasons for the presence of a relatively higher number of
heavy fragments in our data is the fact that the calculation was
performed for one source of A=186 and 2:82, i.e. assuming that all the
nucleons in the Nb+Nb system contribute to the excited source. This
assumption is probably not true if the impact parameter is not zero. In
this case, a remaining target-like source, with very low excitation, is
likely to produce a few heavy fragments. The other reason rests with the
uncertainty in the intensities mentioned before. Because of this, some of

the apparently highly ionizing tracks are in reality tracks largely

76

600

 

500

.5
O
O

Intensilu

300

200

100

 

0 1000 2000
Rioidilu (MeV/c)

Figure 3.11.7 2-dimensional plot (intensities are corrected for the dip
angle) for 97 events at 180 MeV/nucleon. The particle-
identification curves shown are calculated from expression

3.1 with x=O.5.

77

Table 3.“.1. Percentages of various isotopes emitted in a Nb+Nb collision
at 180 MeV/nucleon. The values on the left are the yields
obtained from the experimental data using the curves shown
in figure 3.“.7. Those on the right are calculated with the
code FREESCO.

Particle 1 from data 1 from FREESCO
p 2“.2 33.7
d 22.“ 27.7
t 11.7 11.3
3He 12.9 5.“
a “.“ 1“.2
Li 10.9 1.2
Be “.7 not given
B 2.7 not given
C 1.7 not given

much smaller yields
for higher masses

78
obscured by flares.

In this chapter the steps in the analysis of CCD-recorded nuclear
collisions have been described. Computer codes have been developed to
enhance the digitised images, recognize the tracks, and calculate the
tracks mean intensity. The Three View Geometric Program has been adapted
to perform the spacial (three-dimensional) reconstruction of CCD-recorded
events. An algorithm has been developed to identify the charge and mass
of the observed fragments from the information thus extracted.

Much has been learned about the performance of our experimental set-
up and the streamer chamber, and about the analysis of digitised events
obtained with CCD cameras. An evaluation of the data reduction methods,

and ideas for future experiments will be given in the Conclusions.

Chapter “

EXPERIMENTAL RESULTS AND COMPARISON WITH THEORETICAL MODELS

“.1 Introduction
The experiment described in this thesis was performed at the Bevalac

93Nb beam, incident on a 220 mg/crrI2 Nb target, at two

and utilised a
energies, 100 and 180 MeV/nucleon.

Several experiments have previously used the same system at
different energies (150, 250, “OD, 650, 800, and 1000 MeV/nucleon) with
the Plastic Ball spectrometer as a detector [Dos 86]. Theoretical
calculations are available as well, based on the nuclear fluid-dyruunical
model [Buc 8“], the intra-nuclear cascade model [M01 86], and the VUU
theory [M01 85].

In this chapter, the results obtained from our experiment will be

described and compared with previous data and theoretical models.

“.2 Charged-particle Multiplicities

Multiplicity distributions are easily studied without having to
measure the physical characteristics associated with the tracks emitted
in a collision.

Low multiplicity events are usually produced in large impact-
parameter collisions, where projectile and target fragmentation processes
dominater As the impact parameter decreases, fewer heavy fragments and
higher charged-particle multiplicities are expectedL ILLI leading
projectile fragments disappear in the limit of very central collisions.
This effect is illustrated in figures “.2.1 and “.2.2. In the first, a

CCD-recorded image of a peripheral collision is shown, where a massive

79

79A

Figure “.2.1 CCD-recorded image of a peripheral Nb+Nb collision at 180
MeV/nucleon.

Text; .

I.-.
R

1%

 

80

I,

III“)

II

{[IILIII‘i

"'I
IIIL‘,

 

80A

Figure “.2.2 CCD-recorded image of a nearly-central collision at 180
MeV/nucleon.

81

 

   

.1...
.a.

 

his}. I

.....
: . :1 u...

we. .

82
projectile-like fragment produces a bright track, and a {Rue light
fragments are created as well. The second figure shows a nearly-central
collision, where both projectile and target are completely shatterwni and
the fragment distribution extends to backward angles.

The trigger system at the LBL streamer chamber is based on this
effect. The trigger scintillator (the P-counter in figure 2.5.1) is
positioned to intercept non-interacting beam particles and leading
fragments in the forward cone [Lu 81]. By selecting different pulse
heights in the P-counter, it is possible to trigger on events
corresponding to different ranges of impact parameters, from the
"unbiased" mode, where all events are accepted, to a "central" trigger
which corresponds to small pulse heights in the trigger counter and
selects nearly-central collisions. I

For our experiment, we used the central trigger mode, thereby
favouring high-multiplicity events. It has been established from
comparisons between data taken in this and in the "unbiased" mode, that
the central trigger is only minimally biased towards high multiplicities,
within the requirement of nearly-central collisions [Hui 83].

The charged-particle multiplicity distributions for our data at ICH)
and 180 MeV/nucleon, each including about 300 events, are shown in
figures “.2.3 and I4.2.“. The solid lines are the result of a fit with a
Poisson distribution. The centroids obtained from the fits, or mean
multiplicities, are ~“7 at 180 MeV/nucleon and ~3“ at 100 MeV/nucleon.
The fact that the experimental distributions are well fitted by a single
Poisson curve indicates that the central trigger selected a relatively

small range of impact parameters.

83

 

30 I T T T T r T T T I T T T T r T T

 

 

 

 

 

I T T 1
_ a4 2 If I
’ Centroid =- .
25 :u v —:I
I: 1! 1
I.
20 I— j
r -I
I- L ..
3 - L
5 15 t- ‘i
3 : . I i
I" 1 "
: | » .
L y _:
5 I— I J
I I I
o _L l I l 7 l l l l L L l l l l L
0 20 40 00 80

Charged-particle multiplicity

Figure “.2.3 Multiplicity distribution for 300 events at 100
MeV/nucleon. The curve is obtained by fitting the
experimental points with a Poisson distribution.

81%

 

 

 

 

 

 

 

 

 

 

30 T— T r T T T T T T T T T r T T T
T T l 1
C -4
L c t id - 465 j
25 L— on to . _
C I
20 i— [ _
- 4
.. : ., :
a L. r a
g 15_ "I” ‘
o __ 'i
U L. I . ;
L- b d
10 - 4:: —
+ I
5-- .J
r- I
b 1
y.
o l J l L L L L l I l l l

 

 

 

 

 

o 20 f , 40 so

Charged-particle multiplicity

Figure “.2.“ Multiplicity distribution for 300 events at 180 MeV/nucleon.
The curve is obtained by fitting the points with a Poisson
distribution.

85
u.3 u’ Multiplicities

The measurement of pion multiplicities has long been suggested as a
useful tool to probe the nuclear equation of state [Sto 78]. Since pions
are mostly created during the compression stage of the reaction, they
presumably carry information about the high-density nuclear matter formed
at this stage. Also, multiplicities are not much influenced by the
subsequent phases of the reaction (expansion and freeze-out), unlike
other variables such as angular or energy distributions.

Systematic measurements of negative pion multiplicities have been
carried out at the LBL streamer chamber for the reaction Ar+KCl at
energies between 0.6 and 1.8 GeV/nucleon [San 80, Sto 84, and Har 85],
and La+La, at energies between 530 and 1350 MeV/nucleon [Har 87].

The pion yields decrease very rapidly at lower beam energies. For
this reason, digitised and computer-scanned images of streamer chamber
events could offer a distinct advantage in the measurements of n- tracks.
The curvature of these negative particles in the magnetic field of the
chamber makes them easily identifiable by automatic scanning. Figure
ll.3.1 shows an event where a negative pion is produced. For the
measurement described here, the scanning of the images to count the
negative pions was done visually, since the processing and scanning codes
were being developed during the course of the analysis.

The measured 1:. multiplicities, nn-, were 0.05 at 180 MeV/nucleon
and 0.0099 at 100 MeV/nucleon, in both cases for about 300 events
scanned. In order to compare this value with the results for Ar+KC1 from
[Sto 8“], the n' multiplicities must be divided by the number of
participant nucleons, A. Stock et al. give the values of (Q), the mean

number of participant protons, and A can be calculated from a simple

85A

Figure A.3.1 Nb+Nb collision at 180 MeV/nucleon, in which a negative pion
' is created. The particle is clearly recognizable from its
curvature in the magnetic field.

86

 

87
fireball geometry. In our experiment, this number was not determined. We
have therefore assumed that, in the central trigger mode, a range of
impact parameters between 0 and 3 fm was selected. The number of
participant nucleons was then calculated from the fireball geometry for
the various b, and a range of A between 128 and 186 (157:29) was found.
Therefore the error bars for our points include both the statistical

error on n _ and the calculated range of participant nucleons. In figure
n

u.3.2 the points obtained from our Nb+Nb data are compared with the
systematics found for the Ar+KCl experiment.

In a recent preprint, Bonasera et al. have compared the pion yields
from the Ar+KCl, La+La, and Nb+Nb reactions on the basiscfl?a.simple
analytical approximation [Bon 87a].

Assuming that the pions are emitted from a source in thermal
equilibrium, the number of bosons in equilibrium with a fermion gas at

temperature T is given by [Lan 58]:

2
dp
N = I dr dp f B(r, p) = AnB-—§-- I--E ------ “.1
Bose (2nh)3 eE/T_1
where B is a fit parameter.
For pions this expression becomes:
2
- --- --- 3-5.12..-
N - 3: (:1 03) I eE/T-1 1L2

The temperature T is calculated from the beam energy in the

assumption that the nucleons in the source form an ideal Fermi gas.

88

 

 

 

 

 

loo TTTITTTTITTTTITTTTITTTW
I 1
- 4
10-1 5" o 0 "E
" 0 2
C3 o .
_ o q
- o :
(3
10'2 =" 1
Z 1
< ' 0 ‘
\ " .1
I: F d
z
10'3 e:— 1..
10‘4 ._. .5
p :
i- 1
10‘s AIILJLLJIIIIJLIILLIIIII
O 100 200 300 400 500
Ecm (MeV)

Figure li.3.2 Negative pion multiplicities obtained from our data are
compared with the values found by Stock et al. iann Ar+KCl
measurements [Sto 8“]. .

89

\

For a comparison of these results, the negative pion multiplicity

1.5 1. 5
lab’ The factor AElab

compensates for the multiplicity increase with increasing energy and

1.5
lab

plotted in figure 11.3.3 with the curve obtained from expression “.2 with

per participant nucleon (nn-/A) is divided by E

decreasing impact parameter. The experimental yields n"-/AE are
Bzo. 16. At high energies the scaled 11' yields tend to a constant value,
but at lower energies the pion production drops considerably. This is due
to the effect of the pion mass, which is no longer negligible compared
to the beam energy. The experimental results are in good agreement with

this prediction.

4.“ Transverse-momentum Flow Analysis

'The transverse-momentum analysis recently introduced by Danielewicz
and Odyniec [Dan 85] is now recognized as the most sensitive method to
identify collective flow effects in experimental data.

These effects are of particular interest because, in theoretical
calculations, they are associated with the compression of nuclear matter
during a collision. The intra-nuclear cascade model, TMTiCh lacks
compression, does not predict such collective fh»n.1he hydrodynamical
model and the VUU (or BUU) theory, on the other hand, predict a sidewards
flow which varies in magnitude and direction with the beam energy and the
mass of the system.

Experimental results for two-particle correlations [Mey 80, Cse 82],
and from exclusive measurements analysed with the sphericity tensor
method [Gus 811, Ren 8A] have contributed experimental evidence that such

a collective flow indeed exists. But the extraction of information from

9O

 

 

 

 

 

102 T r I r T l T fl 1
«E; i
'T" 101 r "
In. 4
, .
E 100 r X Y —\< x0 0 O 1
2 10"1 g- “a
A? a i
53 i X La+La +
\ 10-3 g- o Ar+KCl
z": U Nb+Nb

10—3 P . . i a L . . . . 1 . . . i g 4

500 1000 1500

Elab /A (MeV)

Figure 14.3.3 Scaled negative-pion multiplicities as a function of
incident energy per nucleon for various systems. The curve
is obtained from the analytical formula described in the
text.

91
the data is complicated by the existence of statistical fluctuations due
to the small number of particles involved [Dan 83].

The method suggested by Danielewicz and Odyniec removes some types
of finite-multiplicity distortions, and has succeeded in finding evidence
of collective motion in a case for which the sphericity analysis was
inconclusive [Str 83].

A detailed description of the method follows. The results obtained
from our data, using the computer code MOMFLOH [Cse 8631, svill then be

shown and compared with previous experimental results.

A. Transverse-momentum Analysis
This method involves calculating the reaction plane for each event,
by defining a vector 0 constructed from the transverse momenta of the

particles observed in that event, 6; :
M «o
6 = Z w p1 4.3
V

where v is an index which runs over all the fragments in the event, and

mv is a weight factor defined as follows:

E
u

+1 for baryons with rapidity yv>ycm+8

-1 for baryons with rapidity yU<ycm-6 A.“

0 otherwise

92

By setting 6 a! 0, particles around mid-rapidity, which contribute
most of the unwanted statistical fluctuations, are removed from the
evaluation of the reaction plane.

The goal of the calculation is to obtain the transverse momentum per
nucleon projected onto the reaction plane. In order to eliminate another
type of finite-multiplicity distortion in this estimate, the self-
correlation term is removed from the calculation of 0. An 'estimated'

reaction plane is thereby obtained for each particle v in the event:
:2 w 5* 14.5

The projected transverse momentum per nucleon of the fragment v,

evaluated with respect to this 'estimated' reaction plane, is therefore:

p : p ----- “.6

When this quantity has been calculated for all the fragments irizill
events, its mean value , (px'>, is evaluated for each rapidity bin. The
obtained (px'>(y) is smaller than the 'true' average transverse momentum
(projected onto 0 rather than 0;) by a factor of (cos ¢>, where ¢ is the

azimuthal angle between 0 and 0;, and

<px(y)> : (px.(y)>/<cos ¢> 4.7

93

In order to estimate (cos ¢>, and also to insure trunz, through the
above procedure, we are indeed estimating a reaction plane, each event is
randomly divided into two sub-events (each containing half‘tflua observed
particles). The reaction plane is then separately evaluated for each of
the two sub-events. Thus, two vectors, 01 and 011, are constructed. The
azimuthal angle ¢ between 61 and 511 is calculated and its distribution
plotted. If a reaction plane really exists, this distributltniivill peak
at ¢=0. Figure u.4.1a shows the results obtained by Danielewicz and
Odyniec for the Ar+KCl reaction at 1.8 GeV/nucleon. In figure A.u.1b the
analogous distribution is shown for Monte Carlo generated events,
obtained by mixing particles from different events in the same
imlltiplicity range. In this case, all real correlations are removed from
the data and the resulting distribution is completely flat.

'The value of 6 in expression A.” is chosen to minimize the width of
the azimuthal angle distribution. This width is then used as an estimate

of the angle ¢ in equation “.7.

B. Momentum Flow Analysis: Experimental Results

The results described in this section were obtained from a total of
75 events at 180 MeV/nucleon. The initial sample of 100 events was
reduced by a number of selections based on:

i) [Anuts setcnithe event normalization factor. Events with a
factor differing from 1 by more than M01 were excluded. Four
events out of 100 were found to exceed the set limits.

ii) Charge conservation check. After the particle types were
identified, the total 2 in each event was calculated. If it was

found to exceed 82 (the total number of protons in the Nb+Nb

914

 

(a) (b)

2.2: H

 

 

 

 

0 so 180 so 180
(p (deg)

Figure Mm a) Distribution of the azimuthal angles between 6, and 0”

obtained by Danielewicz and Odyniec [Dan 85] for Ar+KCl at
1.8 GeV/nucleon. b) Similar distribution for Monte Carlo
generated events, in which a reaction plane does not
exist.

95
system), the event was not included in the momentuuriflxnv
calculations. Fourteen events were excluded for exceeding
(usually by a few units) the total Z allowed.
iii) Energy conservation check. If the total energy of the emitted
fragments was found to exceed the total energy of the beam

(Etot) or to be less than 1/3 E the event was excluded. The

tot’

final energy is expected to be less than Etot because 1)
emitted neutrons are not detected, 2) very low energy
fragments, with a range of less than about 10 cm in the chamber
are not seen, and 3) only about 801 of the observed fragments
were identified. 7 events out of the remaining 82 were found to
be outside the set energy limits.

Figure I4.14.2 shows the distribution of the azimuthal angles between
the vectors 01 and 011 for our 75 events at 180 MeV/nucleon. Except for a
shoulder observed at 90°<¢<120°, the curve peaks at 0° and decreases with
increasing angle. The width of the distribution is about 60°. This is the
value to be introduced in equation u.7 to estimate tine transverse
momentum projected on the true reaction plane.

Figure 9.9.3 gives the projected transverse momenta, (narrected fin:
the deviation from the true reaction plane, as a function of rapidity,
for our 180 MeV/nucleon data. The error bars include only the statistical
errors. Because of detector bias, the curve is not symmetric around the
origin, but the projected momentum does change from negative to positive:
values around zero rapidity. The center-of-mass beam rapidity is
indicated in the figure.

Observing that the (px/A> vs. y curves can be well approximated by a

straight line around mid-rapidity, where detector biases are usually less

96

 

 

 

 

 

 

 

 

 

2| ‘ T T r T T T T [j— T T T T
° I I r
F '1
)- 9] 4
1.5 h_—.. x i-—
.. m V ..
3' f 1r .
z _
E 1.0 L— A 93
r c c ‘
k L p P a
b 4
J. IL
,. ..
(L5 h—’ -
0.0 J l l l J 1 l I 1 l I L l l I J L
O 50 100 150
¢ (den)

Figure 9.9.2 Distribution of azimuthal angles between 01 and 011 for 180
MeV/nucleon Nb+Nb.

97

 

 

 

 

 

 

hr I T T I I I I I I I I T I I I I I I r I I r I I I I I -

L— T .1

200 *— _.

u— )( 4

’1‘ " i ‘

a I 3 ~

\ T

0 .,
\

> 4
0

5 ~ .

A -2oo- —

4 r X A
\

N - -1
n.

V r- -‘

F Y ‘

u I 1 1 1 1 L l 1 1 1 l i l 1 1 l 1 u 1 l l 1 1 l 1 l T

—0.5 —0.25 0 0.25 0.5 0.75
ycnn

Figure 9.9.3 Mean transverse momentum per nucleon, corrected for the
deviation from the true reaction plane, as a function of
rapidity.

98
important, Doss et al. have suggested a definitnm1cn‘the flow as the
slope of the transverse momentum distribution at mid-rapiditgr. In order
to emphasize this fact, the experimental points can be plotted as a

function of the normalised rapidity, y/ypro This plot is shown in

1'
figure 9.9.9.

A least-square fit procedure gives an intercept.cn?;3.9t9.9,
consistent with the expected value of zero, and the flow (slope of the
fitted line) is 97.0111.3 MeV/c. The value of x2 obtained for this fit is
0.97. The slope found by Doss et al. for their 150 MeV/nucleon Nb+Nb data
is 50.023.0 MeV/c.

It must be stressed that, in oum'analysis, the slope and shape of
the transverse momentum distribution were found to be relatively
insensitiveeto small changes in the exponent x (between 0.5 and 0.8) and

the normalization constant (between 65 and 80) in the curves used for the

particle identification (expression 3.1).

9.5 Scaling Behaviour of Transverse Flow Variables.

‘The following derivation is taken from [Bal 89], [Bon 86], and [Bon
87].

The basic equations for a simple hydrodynamical description of a
nuclear collision (non-relativistic and not including viscosity) are the

continuity equation:

which relates the mass distribution p and the velocity distribution J;

the Euler's equation:

200
100
’3
3?
ca
53
O
A
<
\
x
Q
v
‘100
'200

99

 

 

 

 

 

 

 

r I I—T— I T I T I I I I I T I I T I I I I r I TJ
L 9
y- 4
- -1
"" "1
I- 4
"' ‘1
C d
r- 4
)- ..
. 3 Z
—— -—4
- -1
)- -I
P ‘4
r—— --—1
r '4
LL 1 14 X L i u l l l l L 1 1 J l L l_l l l 1"

'2 ‘1 O 1 2
V/yproj

Figure 9.9.9 Mean transverse momentum per nucleon projected onto the

true reaction plane, as a function of the normalized center-
of-mass rapidity. The solid line is the result of a least-
square fit to the experimental points, and its slope
represents the flow obtained for this experiment.

100

-§%- + (G'T)G : - -%- 6P 9.9

and the equation of state, which relates, for instance, the pressure P.

the density p, and the entropy per volume of the system:
P = P(p,s) 9.10

For a non-viscous fluid the entropy can be considered constant

during the expansion, therefore

P

6? z (-g5-)§p : 02 6p “.11

where c is the sound velocity.

Equations 9.8, 9.9, 9.10, and 9.11, with the initial conditions on
u, p, and 3, determine the hydrodynamical evolution of the system.

In [Bal 89], the authors isolate dimensionless, scale-invariant
quantities, which can be used to describe the general properties of a
system, and to compare the hydrodynamical behaviour of systems of
different mass and energy.

A characteristic mass, m1, temperature T1, length 11, and velocity

u1 are introduced:

where m is the nucleon mass and A is the number of nucleon in the system;

U :ICT I: (-r-fi--) 14.13

where E0 is the initial energy per nucleon of the projectile; and

3_9 3
l1 - -3- nro A 9.19

which represents the volume of the system.

1; for the radius, tzt1t for

1T for the temperature (where T1z2/3 E)), equations

9.12, 9.13, and 9.19 are used to define dimensionless quantities, denoted

After introducing the definitions 3:1

the time, and T:T

by a tilde:

. m1 ~ ~ ~
p(r,t) = --3- p(r,t) 9.15
l
1
u(r,t) = u1u(r,t) u 16
T(r,t) = T I(F,E) 9.17

These characteristic dimensionless hydrodynamical functions are
independent of the total mass A and the energy E0 of the system.
Now, since the sound velocity is of the same order as the thermal

velocity of the nucleons, c: u c; with 5&1, the continuity and Euler's

1

equations can be rewritten in dimensionless form:

m1 [-§§- + 35(5 5)] = o 9.18
at

102

~

-ég- . 315.6); = -352-Y§- 1.19
at p

where S=u1t1/l1

In a small system, such as the one formed in a nuclear collision,

is the Strouhal number.

the role of viscosity should not be neglected. Assuming that the

coefficient of bulk viscosity g is proportional to the dynamical

viscosity n, §=qn, where q is a dimensionless constant,anmithat the

kinematic viscosity vzn/p is constant during the expansion, tha Navier-
Stokes equation can be written (again in dimensionless form) as:

~ ~2 55 s

R

-92- + 3(6-5)G = -Sc ------

~

at p

5- [£5 + (q+1/3)6 (6.6)] u.2o

where Re is the Reynolds number: Re=l1u1/v.

With a proper choice of the time scale, t :1 /u

1 1 1’

to 1, and the solutions of the hydrodynamical equations depend on F, t,

S can be set equal

and the Reynolds number Re. In this way, the flow patterns of systems at
different energies and of different masses are similar if the Reynolds
number is the same.

According to this picture, scale-invariant quantities can be
defined, and a deviation from the scale invariance indicates the onset of
physical processes which lead to a non-scale-invariant flow in the
hydrodynamical description, such as a change in the equation of state or
in the reaction mechanism.

Bonasera et al. introduce a scale-invariant transverse momentuun per

nucleon, defined as:

103

/ prol

and a scale-invariant rapidity:

~ _ CM/ CM
y ‘ y yproj

In figure 9.5.1 Ex is plotted for the experimental data obtained
from Ar+KC1 at 1.8 GeV/nucleon [Dan 85], La+La at 0.8 GeV/nucleon [Ren
89], Nb+Nb at 900 MeV/nucleon [Dos 86 and Rit 85], and for our 180
MeV/nucleon Nb+Nb measurement. Some differences are expected, due to
different multiplicity selections, different types of particles detected,
and different detector bias. In spite of this, the various curves show
remarkably similar behaviours, especially for y/yproj greater than -0.5.
At lower rapidities the different biases of the various detectors cause a
rather large spread in the values found for the transverse momenta.

As seen in section 9.3, Doss et al. [Dos 86] have introduced a
parameter F, which they have named 'flow', defined as the slope of the
transverse momentum vs. rapidity curve at mid-rapidity. This parameter,
as a measure of the transverse flow, is less influenced by statistical
fluctuations or detector bias than, for instance, the maximum of the

curve. Bonasera et a1. define a scale-invariant flow, F, as:

In figure 9.5.2 the points for the experiments listed in table 9.5.1

are shown, together with the F = const contour lines, in the A,E plane.

CM
As was mentioned in the introduction, in [Bon 86] the behaviour of the

109

 

 

 

 

F T Y 1 Y Y T
V Nb+Nb 200 MeV/nucl
o <
_ 0.2 f D o 9-
.._°. 0 00 .
E L @6830“;
Q, ; (>890 0 9 e .
\ _ 0% ‘
H 0.0 D ' $9 0 O T
Q. U Q)
T O O
» 0% .
"0.2 —0 0°00 -‘
O D l
t o O ,
1D 0 O 4
h l + 1 l . P1 L 1 . i
-1 0 1

Y/Yproj.

Figure 9.5.1 Scale-invariant transverse momentum vs. scale-invariant
rapidity for Ar+KCl at 1.8 GeV/nucleon (circle) [Dan 85],
La+La at 0.8 GeV/nucleon (diamond) [Ren 89], Nb+Nb at 0.9
GeV/nucleon (square) [Dos 86 and Rit 85], and Nb+Nb at 180
MeV/nucleon (black triangles). From [Bon 86].

105

Table 9.5.1. Flow measured from different experiments, and the

corresponding scale-invariant quantity, F (from [Bon 86]).

lab. CM CM ~
E (MeV) E (MeV) A F (MeV/c) p (MeV/c) Ptcl. F ref.
proj. nucl. proj.

150 37 197 82 265 .310 [Dos 86]
200 99 197 120 306 .391 [Dos 86]
210 51 197 115 319 H .37 [Bee 85]
210 51 197 157 319 He .35 [Bec 85]
210 51 197 220 319 Li .35 [Bec 851
250 61 197 132 393 .385 [Dos 86]
900 96 197 160 933 .368 [Dos 86]
650 150 197 162 552 .293 [Dos 86]
800 182 197 151 613 .297 [Dos 86]
800 182 139 170 613 d .23 [San 89]
150 37 93 50 265 .188 [Dos 86]
180 99 93 97:11 291 .16t.09

250 61 93 102 393 .299 [Dos 86]
900 96 93 130 933 .301 [Dos 86]
650 151 93 190 552 .259 [Dos 86]
800 182 93 136 613 .222 [Dos 86]
1050 233 93 122 702 . .173 [Dos 86]
900 96 9O 76 933 .175 [Dos 86]
800 182 90 190 613 d .19 [San 89]
1050 233 90 72 702 .102 [Dos 86]
1200 263 90 100 750 .13 [Dan 85]

1800 375 90 190 919 .15 [Dos 86]

106

 

 

 

 

 

# ' I "I‘ I r’ I "‘*"1’ ,, ' ' ' I ' ' ' - I *r
9 A v J
’ i-const. 1
' 1
200 1- °45 0.20 -
. 1
P Q 0 0 0 4
P 1
’1; ' 1
5 .
v '
H 100 "' t ‘1
p 4
. 1
. 1
5K) F ‘
b 1
h - . . . 1 ;.L' l ‘
0 50 100 150 200

Mass number

Figure 9.5.2 Contour lines in the A,Ecm plane for F=constant. The dotted

curve represents the prediction for low energies. The
various symbols refer to the experimental values of F listed
in table 9.5.1: o for o.9<1‘=’<0.325, a for o.325<'15<o.275, o
for 0.275<E<o.225, e for o.225<§<o.175, v for
0.175<E<o.125, A for o.125<§<o.1 [Bon 86].

107
experimental F=const. lines are compared with the curves of constant

Reynolds number in the same A,E M plane (refer to figure 1.2.8a). The

C
point added for our system falls between the F: 0.20 and the F:0.25

lines, while our estimated value of F is slightly lower, F:0.16:0.09. It

must be noticed that, in this region of the A,E M plane, the cmonst

C

lines are very close together and an unambiguous attribution of the

experimental points to one or another of them is especially difficult.

Chapter 5

CONCLUSIONS

5.1 Evaluation of the System.

In this concluding chapter, an evaluation of the system (CCD's and
streamer chamber), of the analysis programs, and of the difficulties
encountered in extracting results from our data will be made. The
limitations and advantages of our CCD-camera system will be described and

possible improvements discussed.

A. Electronics and Data Acquisition.

The CCD system we have developed is the first of its kind to have
been used in a streamer chamber experiment.

Several challenges were faced, from the necessity of a reasonably
fast data acquisition rate to the development of all the analysis
software for the digitised images. Some of these problems have been
successfully solved, in others much useful insight has been gained. This
has led to plans for improving and updating the system.

During the experiment, our CCD cameras and electronics performed
very well, allowing us to record events at a rate of about one per beam
spill. Considering the amount of data that has to be read out and
recorded for each event, this can be regarded as a rather fast
acquisition rate.

The main problem found in interpreting our data was that of
obtaining a reliable particle identification. This is a very important

step in the analysis, and it still remains to be shown unambiguously that

108

109
CCD cameras can improve the particle identification capability of the
streamer chamber. 7

One of the principal problems encountered in the present data was
the poor performance of the streamer chamber during the experiment.
Difficulties in regulating the SF6 pressure and the high-voltage pulse
forced us to run at higher voltages than desired, thus producing rather
poor-quality images, with tracks often obscured by large flares. The
fixed position of the target and of the trigger scintillators made it
impossible to tune the beam into the chamber with high magnetic fields,
so that the curvature of the high-energy tracks was extremely small, auui
the errors in the evaluation of their rigidity rather large. All of these
factors were out of our control for the experimental run.

The LBL streamer chamber has recently been modified by narrowing the
Blumlein gap. This will allow running the chamber at considerably lower
voltages than those obtainable during our previous experiment. This fact
alone should help in two ways: one, by reducing the flaring it should
make estimation of the intensities less uncertain; two, by operating the
chamber closer to the avalanche mode a better proporticnnility should be
obtained between intensity of the emitted light and energy loss. Another
advantage would be that of smaller pulse-to-pulse variations, and of a
reduced effect of these variations on the light output, making the event-
to event intensity normalization less important.

Naturally, the price to pay for the advantages of low-voltage
operation is a loss in track brightness. It is possible that CCD's alone
are not sensitive enough to record the dim tracks that will be produced
in this way. The use of image intensifiers could offer a solution to this

problem, and this possibility is currently under study.

110
B. Analysis Software.

All the steps of the analysis have now reached a good degree of
automation, with the exception of the track-recognition code. It is clear
at this stage that the amount of operator intervention in this part of
the analysis depends strongly on the quality of the images and on the
1event multiplicity. Typically, the time required to correct and complete
the track recognition of an event at 180 MeV/nucleon, with an average
multiplicity of almost 50 tracks, was between 15 and 20 minutes. For a
100 MeV/nucleon event (average multiplicity z35, and usually fewer
flares) it was reduced to about 5 to 10 minutes. Inmmovements on the
track-recognition code, which is at the present time the biggest obstacle
to a completely automatic and fast event analysis, are being studied.

A more sophisticated approach to the intensity analysis, including
peak fitting at each point along the tracks, is being investigated.
Currently, this appears to be a very time-consuming method, and its
usefulness has not been demonstrated; but the use of faster routines
and/or more powerful computers might answer the first objection, and

allow a more rigorous evaluation of the method.

5.2 Concluding Remarks.

In conclusion, the development of a CCD system to record heavy- ion
collisions in a streamer chamber has been successfully accomplished. In
the process of analysing the data collected with this system, much
experience has been gained on streamer chamber operations,
characteristics of our system, and what modifications and improvements

are necessary for future experiments.

111

Only limited nuclear physics results were extracted from our data,
because of the impossibility of obtaining a satisfactory particle
identification. Nevertheless, interesting results were obtained about
pion yields in intermediate-energy reactions, where information was
lacking, and a complete momentum-flow analysis has been accomplished at
one energy.

'The particle'identification was the main problem encountered in the
analysis, and suggestions have been made that should help overcome this
limitation.

It appears that the sensitivity of the system can be increased, auni
the streamer chamber performance improved. A successful solution to these
problems should make our CCD system a useful tool for investigating
heavy-ion collisions, especially in the low to intermediate energy
region, where charged-particle multiplicities do not exceed 50-60.
Interesting effects, such as a phase transition and changes in the
reaction mechanism are predicted in this energy range, even for
relatively low-mass systems (refer to figure 9.5.2). Experimental data
are needed to verify the theoretical predictions and expand our

understanding of nuclear matter in its various states.

APPENDIX A

BKGND
DATA
FFRAME
BITMSK
PIX
PIXELS
COMND
PHOTO
CONTRIN
CONTROUT
ROC

COM
NEWFRAME

FASTCL

ENDTRIG

FIFOIN

ONE1

FIFOOUT

ONE2

CHECKSR

SECTION 8
ECU
EOU
EOU
EOU
EOU
EQU
EOU
EOU
EOU
EOU
EOU
EOU

LEA
LEA
LEA
LEA
MOVE.w
Move.w
BTST.L
DBNE
IST.w
BLT
Move.w
CLR.B
TST.B
6E0
Move.w
BTST
SEQ

MOVE.B
MOVE.W
BTST.L
BNE.S
BTST.L
BNE
BTST.L
BNE
BRA

BTST.L
BED
BTST.L
BEO

BTST.L
BNE.S
BTST.L
BNE
BTST.L
ENE
BRA.S

BTST.L
8E0
BTST.L
BEO

$06E000
$001500
$106C08
$100000
SOODTFF
$001800
SFFFCOO
SFFFCDZ
SFFFCOB
SFFFCOA
SFFBOOO
$0003

CONTRIN,A6

COMND.AO
PHOTO.A3
DATA.A1

157FFF,D3

(A6).04
013.04

DS.FASTCL

D3
ERROR

150007.(A0)

FIRST
FIRST
FIFOIN

CONTRIN.07

17.D7
ENDTRIG

l-T,FIRST

(A6).D7
30.07
ONE1
al.07
ERRMESS
e2.07
ERRMESS
FIFOOUT

31,07
ERRMESS
e2.07
ERRMESS

33.07
ONEZ
34.07
ERRMESS
35.07
ERRMESS
CHECKSR

34.07
ERRMESS
e5.07
ERRMESS

Appendix A

PROGRAM CCDSTREAM

FIRST LOCATION OF BACKGND STORAGE AREA

FIRST LOCATION OF DATA STORAGE AREA

FIRST LOC FOR PROCESSED FRAME

DUAL-PORTED MEM INITIAL ADDRESS (FOR BITMASK)

4 COMMANDS WILL BE ENTERED

SET TIMER

CHECK READY BIT

SEND 'FAST CLEAR'
Clear the first time flap.
If first time then skip.

Get trigger...

if still on then...
Loop until it goes away...

iBefore taking a new picture.
! check if FlFO's are in

! synchronism...

l...first FIFO 1N...

9...th0n FIFO OUT...

llf they are not, print
3 error message.

11f they are. start testing

2 for correct bit pattern.

112

EXTRA

READV

BEAMON

EXPOSE

wTRIG

TAKE!

WTREAD

MOVE.w
BTST.L
8E0.S
8TST.L
BEO.S
BTST.L
BEQ.S

(A6).07
312,07
EXTRA
313.07
EXTRA
314.07
EXTRA

BTS
BNE
BRA

T.L
.S

MDVE.W
LEA
LEA
MOVE.B
TRAP
BRA

MOVE.W

MOVE.W
BTST
BNE
MOVE.”

MOVE.
MOVE.
LEA

Iii

MOVE.
BTST.
DBNE
TST.W
BLT
MOVE.W
DBRA

f’t

MOVE.W
BTST
BEQ.S
BTST
BNE
BRA.S

MOVE.W

MOVE.
MOVE.
LEA

MOVE.
MOVE.

:- I"

f’ 6'

MOVE.
MOVE.
BTST.
DBNE
TST.W
BLT
MOVE.H

r'tit

315.07
EXTRA
READV

(A3).(A1)
BJUNK.A5
EJUNK.AB
3227.07
314
FIFOIN

34.CONTROUT

CONTRIN.D7
36.07
BEAMON
32.CONTROUT

3S7FFF.03
3COM.00
TABLE.A2

(A6).04
313.04
03.EXPOSE
03

ERROR
(A2)+.(AO)
00.EXPOSE

CONTRIN.D7
37.07
TAKEl
36.07
NEWFRAME
WTRIG

3581.CONTROUT

3RIX.01
3RlX.02
DATA,A1
391X.06
39!X.05

3S7FFF.03
(A6).04
313.04
03.WTREAO
03

ERROR
382002.(A0)

113

'Test bit pattern

FIFO and test again...
else.

take picture.

SET READY LIGHT AND CLEAR BUSV
Look at beam...

Loop until on...

Set amber waves of lights.

Look at beam..

if EVENT there...

Take event.

If spill gone then

wait for it to happen.
Loop until state changes.

Set red and busy.

Load timeout COunt.

Get status of camera ctller.
Check the ready bit.

Loop until timeout or change.
Check for loop count expiration
And complain about timeouts.
Start read.

AREAD
BREAD
CREAD

DREAD

CLEAR

VAX

INIT

START

NEXTBIT

ERROR:

LEA

MOVE
DBRA
MOVE.
DBRA
MOVE.
DBRA
MOVE.
DBRA
MOVE.

MOVE.
BTST.
DBNE
TST.W
BLT
MOVE.W
LEA
LEA
LEA
LEA
LEA
MOVE.L

r‘i i i i i

MOVE.
BTST
BED
MOVE.
MOVE.
MOVE.
MOVE.

iiiiii

MOVE.
CLR.L

r

MOVE.W
SUB.W
BLE
MOVE.W
BSET

SUBO.L
BGE
MOVE.L
SUBO.L
BGT
MOVE.L
SUB.L
ASR.L
MOVE.L
MOVE.W
MOVE.W
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APPENDIX B

Appendix 8

Sources of Background Noise in CCD's

There are several sources of noise that can affect the performance of
a CCD camera system.

One type of background is due to the production of thermal electrons
(free electrons produced by thermal energy in the silicon lattice), which
cannot be distinguished from electrons liberated by photons. The
dependence of this 'dark current' on the temperature of the CCD is shown
in figure B.1. While the dark current will saturate the CCD in about 1
second at a temperature of 25° C, it will take about 3 minutes to reach
saturation at -H0° C. Therefore, an almost insignificant amount of
thermal background is generated during a Gas second exposure when the
devices are cooled, as was the case during the experiment described here.

An invariant type of noise, which has the effect of somewhat reducing
the dynamic range of the CCD's, is the system noise. This is produced in
the preamplifier, and appears as an essentially constant background,
independent of temperature or exposure time.

Figure 8.2 shows the dark field per pixel (the digitized value,
averaged over 512 pixels), as a function of exposure time, measured at
two different temperatures. The contributions due to the system offset
and the thermal background can be seen as the intercept and the slope of‘
the lines. The graph also shows that, with cooled CCD's and an exposure
time of 0.5 see, the dark current constitutes a very small percentage cm?
the total background.

Other sources of error in a photometric measurement are the presence

of dead or saturated pixels, whose number is very small in a high-quality

116

117

MSU-87-08l

 

SATURATION

‘—

 

 

 

-40 -3o ~20 -IO 0 Jo +720 +30
TEMPERATURE(C‘)

 

Figure 3.1 Dark current vs. temperature.

118

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119

device, and which can, in any case, be ignored for our purposes, and tkua
non-uniform response of the pixels to a uniform light source. This is due
to differences in sensitivity from one pixel to another.

The background subtracted from each event as a part of the data
acquisition process is a readout taken without illumination and allxnaing
the CCD's to integrate in the dark for half a second. This background
includes system offset and dark current, but does not correct for the
sensitivity variations from pixel to pixel. This can be removed by
dividing the exposed field (after subtracting the thermal plus offset
background) by a so-called flat field, the picture of a uniformly

illuminated surface.

APPENDIX C

Appendix C
STEPS OF THE ANALYSIS OF A CCD-RECORDED NUCLEAR COLLISION

 

PROGRAM PIRSTEST
Reads digitised event(s) from tape
Image-enhancing processing
Automatic track-finding
. For all three views

 

 

 

PROGRAM NEHPIT
Operator-assisted corrections to
automatic track recognition.
Fitting of tracks to 3rd degree
polynomial.
Repeat for all three views.

 

 

 

 

 

 

PROGRAM MATCHCOMB
Tracks are matched in the three views
Several possible matches are found
for each track.
An input file is created for TVGP
containing all the combinations.

 

 

 

 

)

PROGRAM TVGP
3-d reconstruction is attempted for
all the combinations found in the
previous step.

 

 

 

 

 

4)

'Correct' match (and 3-d reconstruction)
is selected on the basis of TVGP results
(lower error).

Rigidity, dip and azimuthal angles, and
length of each track are now known.

 

 

 

 

 

120

 

121

1

PROGRAM PARTIDi
An intensity distribution is determined
for each track.
The mean value of the central 5 bins in
the distribution is the intensity
associated with the track.

 

 

i

 

 

PROGRAM PILECOPY
Reads outputs from TVGP and PARTIDI
Writes the values to a master file
containing the information
collected for each track for all
the events analysed.

 

 

 

i

 

 

l

PROGRAM MSORT
Tracks are sorted on the basis of their
intensity, rigidity, emission angles,
and length.
Intensity normalization factors are
calculated.

Distributions of various physical variables

are obtained.

2-d plot (intensity vs. rigidity) is obtained

for non-stopping tracks.

 

 

fl

 

 

M,Z IDENTIFICATION:
PROGRAM STOP
Stopping fragments are identified from
range and rigidity.
PROGRAM MZID
on-stopping fragments are identified with
particle-identification curves from
2-d plot.
M and Z for each particle are written
to master file

 

T

 

 

 

122

1

PROGRAM MOMFLOH
Reads information from master file
[Does momentum flow analysis.

 

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7O
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