PLACE IN RETURN BOX to roman this checkout from your record.
TO AVOID FINES Mum on or baton dat- duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU IcAn Nflmufivc Action/Egan! Opponunlty Institution
Mans-9.1

 

Subthreshold Pion Production From Characterized
Events in 20Ne + 27Al Reactions
By

Stefan Andreas Hannuschke

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

1996

ABSTRACT

SUBTHRESHOLD PION PRODUCTION FROM CHARACTERIZED EVENTS
IN 20NE + 27AL REACTIONS

By

Stefan Andreas Hannuschke

The production of positively charged pions below the free nucleon-nucleon thresh-
old in intermediate energy heavy ion collisions was investigated. The system stud-
ied was 20Ne + 2"A1 at bombarding energies of 90, 110 and 150 AMeV. Pions and
fragments were detected using the MSU 41r Array yielding complete event charac-
terization. Using the Array to determine the centrality of pion producing events,
an apparent enhancement of the production cross section for peripheral events was
found. That trend increases with decreasing bombarding energy. The kinetic energy
distributions measured for protons and pions are in good agreement with BUU model
calculations. The proton spectra are reproduced for all kinetic energies, whereas the
pion spectra are under-predicted at the lower energies. Analyzing the energy spectra
for all detection angles in terms of a classical Maxwell-Boltzmann distribution, the
apparent temperatures for protons and pions were extracted. The values for both,
pions and protons, are in very good agreement with known systematics. The pion
temperatures show no dependence on the event centrality, whereas the ones for pro-
ton emission show a steady decrease with increasing impact parameter. Correlations
of pions with the event as a. whole were also investigated. The azimuthal distribution
with respect to the reaction plane shows a weak in-plane emission for pions in the
forward direction. A transverse flow analysis for pions and light charged particles
shows the typical signal for helium and protons. The pions show an enhancement for

forward rapidities at the highest beam energy.

For Sabine

iii

ACKNOWLEDGEMENTS

I will probably never forget the first experiment I participated in here at the
NSCL. After having looked at the 47r Array and not having the slightest idea how it
works, I was even more confused looking at some on-line spectra. Fortunately there
were several people that helped me in my quest to learn something about nuclear

physics.

Most importantly I would like to express my gratitude to my advisor Dr. Gary
D. Westfall for giving me a chance to learn a great deal about the experimental side
of nuclear physics. Working with him on several experiments, and understanding
more and more about them, was not only a challenge but also a great pleasure. His
guidance during my studies here was always balanced; never too pushy but always
willing to answer any questions I might have had. His great experience in physics

often allowed him to steer me away from dead ends.

The other person I owe a great deal to is Skip Vander Molen. He originally
proposed the experiment that kept me busy for the last few years. His immense
knowledge of the data aquisition system and computers in general (and the ability to
decipher hex numbers in his head) has inspired me to learn something about these
things myself. He told me as much about getting the data to tape as Gary did making
sense out of it. Skips helpful criticism in group meetings often made me sit back and

re—think the results I was so excited about, noticing the one or other flaw in them.

The other members of the 47r group also deserve a great deal of credit for providing
a very pleasant working environment and always an open ear for discussions, not only
about physics. All graduate students I worked with, Tong Li, Eugene Gualtieri,
Jaeyong Yee, Robert Pak, Nathan Stone and Omar Bjarki (in approximate order of

disappearance), always made sure that the next experiment was a full success. The

iv

post—docs I got to know, Roy Lacey, Sherry Yenello and Bill Llope, were all good role
models for a successful career in physics. They taught me how to set up experimental

devices and never got tired of explaining why what I just did wouldn’t work.

I would also like to thank the entire operating staff of the NSCL for providing
the necessary ingredients for the run and analysis of my experiment. Special thanks
goes to the computer group for never complaining when I hugged them to move tape

drives, get more disk space, or even fix something in the middle of the night.

Since my graduate work here at MSU consisted not only of research, but also of
class work, I would like to thank my teachers for a very good education in other fields
of physics. I very much enjoyed their teaching and learned a great deal about gamma

matrices and Schwarzschild metric.

My parents, Sigrid and Klaus Hannuschke, as well as my parents in law, although
not being geographically close, were always with me during the last five years. Their
continuing support, not only in the form of mailings of chocolate, smoked ham and

coffee, made this work possible.

Also I would like to thank all my friends for not being upset when I “had to go

to the lab” during parties and other get-togethers.

Last, but certainly not least, I would like to thank my wife, Sabine Helling, for her
tremendous patience with me. I think the last few years were harder on her than on
me. Although working on her own degree, she was always willing to unburden me of
the “little things”, without even mentioning it. Without her unconditional support I

would not have been able to finish this work.

Contents

LIST OF TABLES vii
LIST OF FIGURES viii
1 Introduction 1
2 Experimental Details 6
2.1 Introduction ................................ 6

2.2 The Michigan State University 41r Array ................ 6
2.2.1 Plastic Phoswich Counters .................... 7

2.2.2 Bragg Curve Counters ...................... 12

2.2.3 Phoswich Calibration ....................... 18

2.2.4 BCC Calibration ......................... 23

2.3 Charged Pion identification ....................... 24
2.4 Pion Energy Calibration ......................... 32
2.5 The Experiment .............................. 35

3 Centrality of Pion Producing Events 40
3.1 Introduction ................................ 40
3.2 Centrality Selection ............................ 40
3.3 Less Central ................................ 41

4 Single Particle Distributions 51
4.1 Polar Angle Distributions ........................ 51
4.2 Kinetic Energy Distributions ....................... 52

5 Azimuthal Distributions and Transverse Flow 73
5.1 Introduction ................................ 73
5.2 Azimuthal Correlations .......................... 74

vi

5.3 Transverse Flow .............................. 79

6 Conclusion 85
A Impact Parameter Selection 88

A.1 Method .................................. 88
LIST OF REFERENCES 95

vii

List of Tables

2.1
2.2
2.3
2.4
2.5

4.1

A.1
A.2
A.3
A.4

Scintillator Characteristics ........................ 11
Phoswich Specifications .......................... 11
BCC Specifications ............................ 18
BCC Specifications ............................ 24
Pion Statistics ......................... ' ...... 39
Pion Temperature Compilation ..................... 58
Impact parameter bins for KE, ..................... 90
Impact parameter bins for Nd, ...................... 92
Impact parameter bins for N lcp ..................... 92
Impact parameter bins for Zer ...................... 92

viii

List of Figures

1.1
1.2
1.3

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20

3.1
3.2
3.3
3.4

Pion slope factors for several systems ..................
Transverse flow for pions at high energies ................

Polar angle distribution for neutral pions ................

47r Array Schematic ............................ 8
47r Module Schematic ........................... 9
Forward Array Schematic ........................ 9
Phoswich Signal and Gates ........................ 11
Ball Phoswich Spectrum ......................... 13
FA Phoswich Spectrum .......................... 14
BCC Diagram ............................... 16
BCC vs. Fast Plastic Spectrum ..................... 17
Ball PID Gates .............................. 20
FA PID Gates ............................... 21
Ball Response Functions ......................... 22
BCC Response .............................. 25
BCC vs. Fast Plastic Template ..................... 26
E” Signal and Gates ........................... 27
Inclusive Ball AE vs. E spectrum .................... 29
Eu gated Ball AE vs. E spectrum .................... 30
Ring distributions for several PID gates ................. 33
Parameters for ring distributions .................... 34
Pion and proton energy calibration from the Plastic Ball ....... 36
Pion energy calibration for plastic phoswich .............. 36
Centrality of pion events, 150 AMeV .................. 42
Centrality of pion events, 90 AMeV ................... 43
Comparison of pion yield with BUU calculations ............ 45
Gated KE. distributions ......................... 47

ix

3.5 Mean KE, values for different gates ................... 48

3.6 Impact parameter distributions for pion events ............. 50
4.1 Laboratory polar angle distributions for several particle types . . . . 53
4.2 Gated lab polar angle distributions ................... 54
4.3 BUU and data comparison of polar angle distributions for protons . . 55
4.4 BUU and data comparison of polar angle distributions for pions . . . 56
4.5 Pion kinetic energy distributions at 150 AMeV ............. 59
4.6 Pion kinetic energy distributions at 110 AMeV ............. 60
4.7 Fit parameters for pions at 150 AMeV ................. 62
4.8 Fit parameters for pions at 110 AMeV ................. 63
4.9 Pion temperature compilation ...................... 64

4.10 Beam energy dependence of pion source velocity and slope parameter 66

4.11 Proton kinetic energy distributions at 90 AMeV ............ 67
4.12 Fit parameters for protons at 90 AMeV ................. 68
4.13 Beam energy dependence of proton source velocity and slope parameter 70
4.14 Comparison of spectral shapes with BUU for protons ......... 71
4.15 Comparison of spectral shapes with BUU for pions .......... 72
5.1 Reaction plane determination method .................. 75
5.2 Azimuthal distributions for He ions at 150 AMeV ........... 76
5.3 Azimuthal distributions for He ions at 90 AMeV ............ 76
5.4 Azimuthal distributions for pions and protons at 150 AMeV ..... 78
5.5 Transverse flow for helium ........................ 80
5.6 Transverse flow for protons ........................ 81
5.7 Transverse flow for pions ......................... 82
5.8 Summary of transverse flow for helium, protons and pions ...... 84
A.1 Probability distributions for centrality observables ........... 91
A.2 Estimate of maximum impact parameter ................ 94

Chapter 1

Introduction

The study of meson production below the free nucleon—nucleon threshold can provide
valuable information about the formation of hot nuclear matter far away from the
ground state and lead to a better understanding for the nuclear equation of state
(EOS)[Brau 87, Gutb 89, Dani 88]. Because mesons must be created in the reaction
rather than be merely liberated, they are dominantly emitted from the hottest and
most dense regions created in central collisions [Suzu 91a]. Pions, being the lightest
mesons, have been observed from collisions at incident energies as low as 25 AMeV.
The production of pions can be understood in terms of the BUU model except at the
very lowest incident energies where an abnormally high momentum tail of the Fermi

distribution of the constituent nucleons has to be assumed to explain the observed

data [Niit 91].

A great deal of work has been done in understanding the inclusive production
of pions from a variety of systems. In general, the production cross sections and
energy spectra can be understood in terms of BUU [Li 91b]. One striking feature
that has emerged recently is the small variation in the slope parameter, T0, of the
pion invariant cross section kinetic energy spectra at 90° in the center of mass frame

for beam energies below 100 AMeV [Suzu 91b] (see Figure 1.1).

 

 

 

 

 

To (McV)

 

 

 

 

Figure 1.1: Slope factors (To) for 1r‘ spectra at 90M together with the temperatures
(T‘) deduced from 1r° distributions. The inset shows the shape of the momentum
distribution used in the calculation. From [Suzu 91a].

 

 

on + .1
at.
“‘01- .... -I
U'
v .3.
o A
9
t

 

 

 

Figure 1.2: < qr; >y vs. rapidity y for 7r+ produced in Ne—Pb collisions at 800
AMeV. qt: is the transverse momentum, normalized to the pion mass, in the esti-
mated reaction plane. Experimental results (filled circles) are compared to the results
of intranuclear-cascade (INC) calculations (open circles) for collisions with squared
reduced impact parameter b2 / (R1 + R2)2 z 0.18. From [Goss 89].

Pion production from characterized events has been studied at Saclay at high
energies (400, 600, 800 AMeV) using Diogene [Goss 89]. Figure 1.2 shows the pion
transverse flow in the estimated reaction plane. Except for the point at the lowest
rapidity the flow is positive for all rapidities. This positive flow was attributed to

absorption of the pions in nuclear matter.

At intermediate energies pion production has been studied using the MUR at
GAN IL in coincidence with a single pion detector. The system studied was 94 AMeV
O+Al [Aiel 88]. The authors found that coincident particle distributions are very
similar for high energy proton and pion triggered events but different from those
in inclusive reactions. In a similar experiment, pion production in coincidence with
fission fragments was studied using the system O+Th at 95 AMeV [Eras 88]. Through
an analysis of the impact parameter distributions obtained from the fission fragment
folding angles, the authors concluded that pion production requires a large overlap

of the target and projectile nuclei.

In a recent experiment [Schu 94] polar and azimuthal distributions of subthresh—
old neutral pions were measured in coincidence with projectile-like fragments (see
Figure 1.3). The findings are that the final-state interaction of pions with the nuclear

medium seems to play an important role.

We studied 20Ne + 27A1 reactions at 90, 110 and 150 AMeV with close to 41r
coverage for pion detection and event characterization. The good solid angle cover—
age of the device enables us to perform a detailed analysis of event properties such
as reaction plane, impact parameter and degree of multifragmentation for inclusive
events and events in which a pion was detected. The range of bombarding energies

studied covers the balance energy for this system where the transverse collective flow

disappears.

 

 

 

 

 

..... ”first--.”
2’(o) inclusive Au ‘
IO M1
i a
A ’ 1
3 ° ‘
\10 {V1
9 : c 3
5 ’ . . 1
$433: $‘f‘CCI‘4ivw
C: I
1: .(b) Lynn-17 ,
E > c 1
‘O r + <
. r W1.
: i
* Au
axgal4_xxaxl JJJJJ ‘
O 60 120 180
0... (deg.)

Figure 1.3: (a) Inclusive 1r° polar distribution measured for 36Ar + 19"An and
36Ar + 12C at 95 AMeV, transformed into the N~N cm frame. (b) same as (a),
but for very peripheral collisions, selected by requiring Zpr in the range 14 -— 17.
The solid curves are shadowing calculations normalized to the integral of the data.

From [Schu 94].

The remainder of this study is organized as follows. Chapter 2 contains a descrip-
tion of the technical details of the experiment, including a description of the MSU 41r
Array and its subelements, as well as information about the electronic modules and
logic used to record the data. An outline of the on-line and off-line data analysis and
the detector calibrations is also given. The pion detection and identification method
is explained in detail. In Chapter 3 we investigate the centrality distributions and
compare events where a pion was identified with inclusive events. Different meth-
ods for determining the approximate impact parameter of the collision are presented.
Chapter 4 deals with single particle observables for pions and protons. Comparisons
of angular and kinetic energy distributions are made with BUU model calculations.
Inverse slope parameters for the pion and proton kinetic energy spectra are deter-
mined and compared with known systematics for similar systems. In Chapter 5 the

correlation of the pion with global event properties is investigated and the results

compared with those for protons and helium. In particular we show the azimuthal
distributions with respect to the approximate reaction plane and the transverse flow
in that plane. In Chapter 6 we summarize the results of this study. Appendix A dis-
cusses the experimental determination of the centrality of an event, and the technique

of impact parameter determination based on different global observables.

Chapter 2

Experimental Details

2.1 Introduction

The 411' Array, as instrumented for this experiment, provided close to 471' detection of
light charged particles, intermediate mass fragments, and positively charged pions.
Most previous experiments studying subthreshold pion production did not have cov-
erage as complete as that provided by the 41r Array, either in geometric acceptance

or range of particle types identified.

The following sections in this chapter describe in detail the 41r Array, its various

components and their acceptance, and the methods used to calibrate them.

2.2 The Michigan State University 47r Array

The MSU 4w Array [West 85] consists of a 32-faced, aluminum, truncated icosahedron
housing several different detector subsystems. Of the 32 faces, 20 are of hexagonal
shape and 12 are pentagonal. If one were to paint the hexagons white and the pen-
tagons black the Array would look like a giant scoccer ball. On all of the hexagonal
and on 10 of the pentagonal faces aluminum plates are mounted that serve as back-

plates for the 30 modules of the main Ball. One of the remaining pentagons serves

as the mount for the beam entrance pipe as well as the target mechanism. The other
one supports the Forward Array and the exit beam pipe. The shape of the Array is

shown in Figure 2.1.

The 30 modules of the main Ball are each divided into 6 (hex) or 5 (pent) triangular
sub-modules of close packed fast / slow plastic phoswich detectors. Mounted in front
of each of the 30 modules are gas ionization chambers that are capable of functioning
as Bragg curve counters or serve as AE detectors for low energy particles that stop
in the fast plastic scintillator. The 5 most forward of the gas counters are further
segmented into 6 separate detectors. A schematic view of a Ball hexagonal module is
shown in Figure 2.2. In total the main Ball consists of 170 plastic phoswich detectors
and 55 gas ionization chambers covering polar angles from about 18° to 162° . Mounted
on the most forward pentagonal face is the Forward Array consisting of 45 fast / slow

plastic phoswich counters, covering approximately 54% of the solid angle from 7° to

18° .

2.2.1 Plastic Phoswich Counters

The 170 plastic phoswich counters in the main Ball are composed of a 3 mm thick layer
of Bicron BC-412 fast plastic scintillator (AE component) which is optically coupled
to a 250 mm thick block of Bicron BC-444 slow plastic scintillator (E component).
The terms “fast” and “slow” refer to the rise time of the light pulse in either of
the components for charged particle energy deposition. The specifications for the two
scintillator materials are summarized in Table 2.1. The solid angles of each of the sub-
modules in the hexagonal and pentagonal modules are 66 msr and 50 msr respectively.
The total solid angle subtended by the main Ball detectors is therefore 10420 msr or
83% of 41r. The phoswich detectors in the Forward Array are composed of the same

scintillator material. They also come in two different shapes. There are 30 cylindrical

 

 

 

 

 

 

 

 

   

¥-----

   
 

Figure 2.1: Schematic diagram showing the underlying geometry of the 47r Array.

SUBARRAY 0F MULTIPARTICLE ARRAY

FAST/SLOW PLASTIC SCINTILLATORS

LOH PRESSURE

§\ .5 "we
: !Ilmm

 

 

 

F::::::::::::::::M
i BRAGG CURVE
,fl SPECTROMETER

 

\
g‘

 

 

 

 

 

 

 

 

 

b

Figure 2.2: Schematic diagram showing the components of a 47r module.

    

EEC; "
T9969
@ as 32 ..

 

 

 

 

 

 

 

 

Figure 2.3: The layout of the 45 Forward Array detectors.

10

and 15 truncated pyramidal detectors. The fast (AE) component is only 1.6 mm thick
and the slow (E) component 150 mm for the cylinders and 130 mm for the truncated
pyramids. The thinner AE component allows for a lower kinetic energy threshold for
the heavier fragments in the forward direction. The solid angles are 3.02 msr and
2.75 msr for cylindrical and pyramidal, respectively, therefore covering about 54% of
the total solid angle between 7° and 18°. A summary of low energy threshold, angular

coverage, and Z identification capabilities is given in Table 2.2.

Energetic charged particles penetrating a phoswich detector will produce two dif-
ferent flashes of light. The first one originates from the fast AE component, which
is proportional to the rate of energy loss in that medium, and the second one comes
from the slow E component. If the particle stops in the second component that sig-
nal will be proportional to the total energy of the ion after passing through the fast
component. The combined light pulse is transformed into an electronic signal and
amplified via 8-stage Amperex photo—multiplier tubes. The resulting signals are then
approximately separated into the fast and slow components by means of two different
gates to charge-to-digital converters (QDC, Lecroy FERA 4301B). A schematic of the

signal with the corresponding gates is drawn in Figure 2.4.

Figures 2.5 and 2.6 show examples of the 2-dimensional spectra obtained by plot-
ting the fast (AE) signal against the slow (E) signal. The strong band along the AE
axis is from particles that stop in the fast plastic layer and have therefore no slow
signal. The fact that a small amount of E is present is simply due to the integration
of the tail of the fast signal in the E gate to the F ERA. Similarly, the line at the
bottom of the spectra is caused by particles such as neutrons or photons that deposit
no or very small amounts of energy in the fast layer. The tilt of this line arises from
integration of a part of the slow signal in the AE gate to the FERA. Naturally all

charged particles approach that line as their AE goes to zero. In the spectrum for

11

Table 2.1: Characteristics of the two types of scintillator used in the phoswich detec-
tors.

 

BICRON Plastic Rise time (ns) Fall time (ns)
BC—412 (fast) 1.0 3.3
BC-444 (slow) 19.5 179.7

 

 

 

 

 

 

 

Table 2.2: Specification of the Ball and Forward Array phoswich detectors.

 

 

 

 

 

 

 

 

Characteristic Ball Phoswich FA Phoswich
Polar Angle region ° ) 18 - 162 7 - 18
Solid Angle coverage (%) 84 54

Z identification 1 — 8 1 - 10
Energy Threshold (AMeV)

Pion 8 N / A
Proton l2 7
Helium 17 12
Carbon 32 22

 

 

 

 

 

 

 

I(-—250 nsec—-)I

Figure 2.4: Diagram of the phoswich signal and gates.

12

the Ball detector (Figure 2.5) lines can be observed for Z = 1 to 3, possibly four, with
isotope resolution for Z = 1. If one displays these spectra in a higher resolution even
3He and ‘He can be separated. The Forward Array spectrum also shows lines for Z
= l to 3, again with isotope resolution for Z = 1. With more statistics higher Z lines
can be observed. The bin width in both histograms is 16 FERA channels, so that the

actual resolution is better than the figures indicate.

2.2.2 Bragg Curve Counters

In addition to the 170 main Ball phoswich counters and the 45 forward array counters
the 41r Array contains 30 gas-filled ionization chambers (Bragg Curve Counters). The
ion chambers are directly mounted on the face of the main Ball phoswich modules.
They are of either hexagonal or pentagonal pyramidal shape depending on which type
of Ball module they are mounted on. A 2.5 pm thick aluminum coating is evaporated
on the face of the phoswich fast plastic layer and serves as the anode for the BCC. In
the most forward ring of the main Ball modules (5 hexagons) the anode is separated
into 6 electrically isolated segments corresponding to the 6 phoswich submodules. The
total number of BCC is therefore 55 with only 30 separate gas volumes. The front
pressure windows are made of 900 pg/cmz, aluminized kapton foil. These windows
are epoxied to a stainless steel frame that serves at the same time as the cathode for

the BCC. The perpendicular distance from the anode to the cathode is 13.36 cm.

In front of the anode at a distance of about 1 cm a Frisch grid is installed in the
BCCs. It is made of 12.5 pm gold plated tungsten wires spaced .5 mm apart, and
epoxied with conductive epoxy to a copper strip on the BCC frame. The Frisch grid
is held at ground potential in order to shield the anode from the image charge induced
by the drifting electrons. In order to produce an approximately radial electric field

inside the BCC chamber, a shaping grid is installed inside the housing. It consists

13

Main Ball Phoswich Spectrum

 

IIII'IIIIIIIIIIIITIIIWIIIIIVII[IVIWY'TVTIVII

     

2000

l

1

1750

1250

1000

AE (ch)

 

.‘-'-TTIIIIIIIIIII[llIIllllIIlllI

   

 

o 250 750 1000 1250 1500 1750 2000

E (ch)

Figure 2.5: Typical raw spectrum from a Ball phoswich for Ne + A] at 150 AMeV.
Lines for particles of Z = 1 - 3 are identified with isotopic resolution for Z = 1.

14

Forward Array Phoswich Spectrum

 

IIIIIIIIIIIITTIITHI'IIIITIIIIIIIII[ITWII

2000

‘_‘—‘II

1750

1500

1000

AE (ch)

750

TIIIIIIIIIIIIIIITIIIIITIIIIIIIIifiTII

 

 

llllijlllllilljlllllll‘

i'IIllllllllLlllllllILJIIILIIIIJIIIIIII

 

0 ' 250 500 750 1000 1250 1500 1750 2000

E (ch)

 

13

10

Figure 2.6: Typical raw spectrum from a Forward Array phoswich for Ne + A1 at 150
AMeV. Lines for particles of Z = 1 - 3 are identified with isotopic resolution for Z =

1.

 

15

of 21 parallel copper strips, each encircling the volume of the chamber between the
Frisch grid and the cathode. The strips are connected by 21 1.55 MO resistors creating
a 21 stage voltage drop between the cathode potential and ground. A schematic view

of a BCC chamber is given in Figure 2.7.

Positive ions entering the chamber through the front window will produce electron-
ion pairs as they lose energy along their trajectory. The functional dependence of the
rate of energy loss on the distance of penetration is the well known Bragg curve. It

typically has a strong peak close to the end of the particle track.

The electron-ion pairs created by the ionizing particle will drift along the electric
field lines towards opposite sides of the detector. The negative signal from the anode
is fed into a charge-sensitive pre-amplifier and integrated. The resulting signal is
supplied to a shaping amplifier that provides a fast (differentiated) output and a slow
(2 x differentiated and 2 x integrated) output. If the ionizing particle stops in the
gas volume of the BCC detector, the peak height of the fast output is proportional
to its charge whereas the slow one represents the total energy. For particles not
stopping inside the BCC counter the slow output is still proportional the energy loss
in the detector volume. In the latter case that signal together with the corresponding
signal from the fast plastic behind the BCC can be used for AE vs. E particle
identification. Since there are 170 phoswich counters with BCCs in front of them,
there are effectively 170 BCC / fast plastic telescopes as well. Figure 2.8 shows such a
spectrum. The lowest Z line above the noise is for He ions, the one above it for Li.
Again, with more statistics higher Z lines can be observed. The bin width here is 16

FERA channels in x-direction on 32 Silena channels in y-direction.

Originally the BCCs were intended to be operated with 500 Torr of P5 gas (95%
argon, 5% methane), and with -1200 V and +500 V on the anode and cathode re-

16

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i
i
I
I Anode

Frisch Grid:
I
I
C II I :
l
l
I
<3st Gas at 125 Torr :

: Pro-amp
i
I
H I
Field Shaping Grid '
I
T ~ ~ I
~ ~ I

§
~ ~ I
‘ ~ I
..__ I
~
1’— star chain -—° 1
600 V =' +150 V

Figure 2.7: Schematic of the MSU 47r Array Bragg curve counter.

 

17

BCC vs. Fast Plastic Spectrum

16

 

TTTWTTITIITWTIPTIIIIIIIIIIIIIIrIllITIII

3500

ITJlrIIIjIIIIIITIleIITTIIIIr-J

   
   

 

   

  

V I.
.
1500 t
t5
s
x
s,
:4
a
_ 2 as . ..
e
"' u g. 1:. ,-; .x v.
_ ‘3‘ A" j»: .2 “”31
m . .‘v: ‘3 a: :- :- ,. F n V .‘v. .
' ' .19}? 3; n i g. a i at \ ,_ .1! ' ' x‘
- ., 7.1 ,fi 9), Is gal» ”a. ’9’}. “a: gap 1...: m . .
.3". ( " - 5' figs (' I“; ‘ .,-. If) ? ;i‘r- " ‘.~
1° 0'; as" I -»«‘ -' fig '- V

 

0 250 500 750 1000 1250 1500 1750 2000

E (ch)

Figure 2.8: BCC vs. fast plastic spectrum for Ne + A1 at 90 AMeV. The lowest Z
line above the noise is for helium, the one above for lithium.

18

Table 2.3: Specifications of the Bragg curve counters.

 

 

 

 

 

 

 

 

Characteristic BCC vs. FP BCC E vs. Z
Polar Angle region (° ) 18 - 162 18 -162
Solid Angle coverage (%) 84 84

Z identification 2 - 18 3 - 18
Energy Threshold (AMeV)

Lithium 4.0 2.0
Boron 5.0 3.0
Carbon 5.5 4.0

 

 

 

 

spectively. For the present experiment however, the BCCs were filled with 125 Torr
of CzFe and operated at -500 V and +150 V. The lower gas pressure puts less strain
on the front windows and the heavier gas compensates for the loss in stopping power.
Since for such a light system 20N e + 27Al heavy fragments are not expected, only the
BCC/fast plastic identification method was used. A summary of the characteristics

of the BCCs is given in Table 2.3.

2.2.3 Phoswich Calibration

Because of the large number of detectors in the 47r Array, a method had to be devel-
oped to keep the time needed for detector calibration within reasonable limits. The
basic idea is [Cebr 90, Cebr 92] to create two-dimensional calibrated templates for
each of the detector systems to which all the individual AE vs. E spectra are then
mapped. The template consists of a set of gate lines for the observed Z lines to which
the spectra can be matched as well as calibration curves for the Z lines that are used

to map matched channel numbers to incident particle energies.

To obtain the gate lines a typical spectrum is transformed so that the punch-in line
and neutral line coincide with the y and x axis. Then lines are drawn on either side

of the Z lines in that spectrum. These lines are the gate lines. The transformation

19

equations are
CH; = (AEdl — Y0) — (Edl — X0)M,,
CH, = (Ed1 — X0) — (AEch — Yo)/Mp, (2.1)

where ABC}, and Ed. are the fast and slow raw channel numbers, Mn and Mp are
the slopes of the punch-in and neutral line and X0 and Y0 are the coordinates of the
intersection of the two lines. C H I and C H, are the transformed fast and slow channel

numbers.

Using these gate lines one can assign each point in the mapped spectrum an A
and Z value. The atomic mass number used is the most common isotope for the
cases where isotope resolution is not given from the gate lines. All phoswich raw
spectra can now be gain matched and transformed to fit the template. The matching
parameters and the gains are stored in a file and are used in further steps of the data
analysis. Figures 2.9 and 2.10 display the gate lines for the Ball and Forward Array

phoswiches used in this experiment.

The second ingredient for the energy calibration are response functions that map
the transformed fast and slow channel numbers to energies deposited in the cor-
responding plastic scintillator. These response functions were determined from a

previous calibration experiment [Cebr 90], and are of the form:

CH, = aEslA/AOA 20.8
CH} 2 (JET;5 — C. (2.2)

The inverse of these equations converts the transformed fast and slow channel numbers
into the energy deposited in the corresponding plastic. The arbitrary constants a,b,
and c are determined by fitting the lines following this functional form to the same
representative spectrum used to create the gate lines. The final response functions

used for the Ball are shown in Figure 2.11.

20

Main Ball Gatelines

 

AEch (arb. units)

 

 

 

 

 

 

 

 

 

 

 

Ecll (arb. units)

Figure 2.9: The particle gate lines for 1r, p,d,t and Z = 2 - 3 for the Ball phoswich
detectors.

21

Forward Array Gatelines

 

 

 

 

 

AEch (arb. units)

 

 

 

 

 

 

 

 

 

 

 

 

: ‘l' I I
o I I l l I I I I I I j J J I I l I I I I I r I I I

0 100 200 300 400 500
Ech (arb. units)

 

Figure 2.10: The particle gate lines for p,d,t and Z = 2 - 10 for a Forward Array
phoswich detector.

22

Ball response functions

 

PTIIITT‘IFTITIIIITIIIII

500

400

300

200

DE channel #

100

 

 

 

I
I
0111111411111114;;111111

o 100 200 300 400 500
E channel #

 

 

 

Figure 2.11: The response functions for p,d,t and Z = 2 - 5 for a Ball phoswich.

 

23

As a last step one has to obtain the value of the incident energy of a given particle
by simply looking up the well known energy loss curves for that particle type. In
our case the energy loss program DONNA was used to calculate AE and E vs. Einc

providing it with the densities, composition and thickness of the detector media.

To summarize, calibrated templates are generated for the Ball and Forward Array
detectors to which all raw phoswich spectra are matched. From this template look-
up tables are made which map raw channel number into particle type and incident
energy. The angles of the detected particles are assigned as the geometric mean angle
of the corresponding detector. Using these tables, the raw data tapes are sorted onto
“physics” tapes which contain information regarding the event multiplicity and the
atomic mass number, charge, 9, <1), and kinetic energy of each of the particles in the

event.

2.2.4 BCC Calibration

Since the nature of the BCC vs. fast plastic spectra is also AE vs. E, the calibration
of those is accomplished in a very similar way to the phoswich detectors. The main
differences are that the gate lines as well as the response functions are generated from
a known functional form and since both AE and E originate from separate signals
no transformation of the spectra is necessary. The response for the fast plastic is
identical to the slow plastic in the phoswich calibration, since here it is the stopping
detector. The form is

CH, = aE}°“/(A°°“Z°'8). (2.3)

During a field test using a BCC with P5 gas and corresponding specifications listed

in Table 2.4 [Cebr 91] the response function for the BCC was originally determined

24

Table 2.4: Specifications of the Bragg curve counters.

 

 

 

 

 

 

 

 

 

 

 

 

Characteristic BCC vs. FP BCC E vs. Z
Polar Angle region (° ) 18 - 162 18 -162
Solid Angle coverage (%) 84 84
Z identification 2 - 18 3 - 18
Energy Threshold (AMeV)
Lithium 4.0 2.0
Boron 5.0 3.0
Carbon 5.5 4.0
to be linear
CHBCC = flEBCC (2-4)

(see Figure 2.12). In that test run, it was determined that the BCC energy response
was independent of particle type. However, in the present experiment, it is necessary
to introduce a charge dependence into the energy calibration as an exponent in the

energy term.

CHBCC = 513%) (2.5)

In the same fashion as for the phoswiches a common template is made to which
all the BCC vs. fast plastic spectra are gain matched. The energy loss calculations
are performed using the ELOSS program. The template used in this experiment is

shown in Figure 2.13.

2.3 Charged Pion identification

The positively charged pions were detected using AE vs. E particle identification
(PID) in the fast/slow plastic phoswich counters of the main Ball, similar to the

method used by the Plastic Ball group [Bade 82, Gutb 89]. In order to distinguish

25

 

I
J
.4
.4
.4
—1
.4
.1
.1
.1
—
_.
_.
.i
.4
———1

500

400

300

Channel

200

100

IITIIIIIIIIIIIIITIIVIIIIITI

 

 

1111ILLIJIIILIIILIIIJIILII

 

h—

 

o JJIIIIIILTII4II

100 150

50
Energy (MeV)

Figure 2.12: Bragg curve response function from test run.

26

BCC v. Fast Plastic PID gates

 

        

 

 

— 500
Q)
=
g 400 b
.:
U
H 300
4
200
100 L
£75
F l

 

 

 

1 l l 1 .7 i l l i l l l l
300 400 500
E Channel

Figure 2.13: Template for a BCC vs. Fast Plastic spectrum.

1 I I l
100 200

27

 

7’

{A E- E E I‘

 

 

I( 700 nsec—-—)I(—-—- 2 nsec )I

Figure 2.14: Diagram of the phoswich signal and gates for an incident pion.

real pions from background we used the dominant decay of positively charged pions,

7r+ —+ 11+ + Z A = 26 nsec, pm = 30MeV/c

[1+ -—) 6+ + '17;+ V" A = 2.2 nsec, pm = 53MeV/c. (2'6)

The energy loss of the positron from the 11+ —+ 6+ decay was recorded using an
additional bank of QDCs (also Lecroy FERA 4301B) with a gate of 2 nsec width
that was delayed by 700 nsec with respect to the AE gate (See Figure 2.14). Any
hit in that delayed gate will be called an E” gate, irrespective of the particle it was
associated with (if any). In order for a hit in the AE vs. E 1r particle identification
gate to be identified as a real pion we require a coincidence with an Eu gate. In a
test run where the Eu signal was recorded for only 16 detectors, the time signal from
the decay was also recorded. In that case an exponential fit to the time spectrum

resulted in A = 2.2 :l: 0.4psec.

The resulting pion identification is demonstrated in Figures 2.15 and 2.16. The
upper panes in both figures show gain matched and added AE vs. E spectra for all

detectors in the indicated polar angle range. In the lower pane the projection of a

28

vertical slice of the 2-dimensional data is shown for E channels between 100 and 200.
In the inclusive distributions (Figure 2.15) an expected line in the pion identification
gate is completely hidden by the background. The cut at the indicated E channels
(lower right) reveals no structure in the resulting AEch distribution in the area where
a pion peak should arise. However, if one requires a coincident signal in the delayed
Eu gate (Figure 2.16) the same data reveals a clear line below the protons with a very
small contribution from background signals. The same cut as for the inclusive data

now shows a strong peak at the expected position.

Due to the unusually long gate (2psec) for the type of QDC used (Lecroy FERA
4301B, rated up to 512 nsec gates), one can expect several problems in the pion

identification method.

The first is false signals in the delayed gate that arise from random noise accumu—
lation, accidental pile up from uncorrelated events and possibly large initial AE/ E
signals that might leak into the delayed gate. The random noise contribution is small
for low pion energies and might increase somewhat for the higher energies, as can be
seen from the lower panel in Figure 2.16. The polar angle dependence of Eu gated
PID distributions indicates the importance of accidental pile up, since at forward an-
gles many more protons and neutrals have an associated Eu signal than at backward
angles. This indicates that false Eu signals are mainly related to high count rates in
the phoswich detectors. In fact, at the very forward angles in the Ball (rings 1 and 2
at 23° and 32° ) the pions cannot be separated from the background. The total polar
angle coverage for pion identification is therefore from 46° to 157° in the laboratory

frame.

On the other hand, the method used will misidentify some real pions as noise since

the finite width and position of the Eu gate only captures those decays that fall within

29

 

IITITT‘IITIITTTTIITTYIITITIIITIIIIIIIITIIITT—TI

, 86. S 0 S 95°

AEcI

 

--:0, .32., .

8
3

 

IILIIIlllllIllllljlllllllilllljlll1141111111[All

 

"‘ i . i‘ , l. "T
"1 ”-rLLJFLIAIIIIILIAILII

. V - ‘ ' .\- . ' x
, A
. . -,.I . r.

Eek

IIII[UITTTITITIIIrTTrIITT'fIIIITTTIIIIII]ITWTITII

1” 100 5 Ed 5 200

y-

 

 

Yield
? i i 5 3 i I
I l I I I V I T I I

'5

IIIJILILIIIILIJILLLIllllllllllslllllllllq

 

 

 

.
D
b
’
r
h
b
D
I
m—
h
p
L
.hllll llll lLlllllIllllllIIIIIIJHJIIIIIIII
ouiulummmmmmm

AEcll

Figure 2.15: (a) Inclusive Ball AE vs. E spectrum summed over all detectors in the
indicated polar angle range and (b) resulting AEch distribution

30

 

 

 

  
       

 

TrT T TrTT T TD I I I T I I I I T I I I I I I I I I T I I I I I I I I I I

- -4
_ I T l I l l I l I _‘
- 4
. a) .
*— fl
I- -I
u- q
I. '4
I- Q 0 -1
» 86 < 0 < 95 ~
I — — .1
j a
q
q
i- —
i ..
i 13': d
F ' 4
I -4
f- -—d
d
d
d
— —‘l
.4
l ~- p «
q
' ~.. —I
. I 1
d
.4
—l
.1
d
d

-4 .
_
q
d
.1
d
d
._ d
1' i‘ A 1
.’ 1. Q '1

0 100 2“ 3” 4“ 500 6. 700 I“ 900 1000

Ech

 

WTTTIIIIIIIITTTTTTI'IITIrIIIIITIIIIIIIrIIIII'IIIT

f—b) loosschszoo

IIIIIIIIII
Lllllllll[1111111111111IIIIIIIIIIIIIIII

 

 

lIIllllllllllllllllllllllllLJJlllLllll
50 I“ 150 2“ 250 3“ 350 400 450 5”

AEch

I
r

 

° fir,

Figure 2.16: Same as Figure 2.15 with Eu gate applied.

31

the gate. Also, depending on the stopping position of the muon, some positrons might
escape the detector without leaving enough energy. This will be especially important
for pions with low incident energy, since these will not penetrate the phoswich deep
enough to enable the resulting positron to deposit enough energy in the detector to
be detected. The low energy threshold for the muon to be detected was determined
to be about 5 MeV.

An additional problem arising from the long gate is related to the charge inte-
grating ADC used to record the Eu signal. The FERA measures charge by charging
a capacitor with the input pulse and discharge it through an RC circuit. Since the
discharge process starts immediately after the gate opens (or the signal arrives) a
variation of measured charge with arrival time will occur. That variation is compen-
sated for gate widths up to 500 nsec and can be adjusted for gate widths up to 1 nsec.
Since that gate width is too short to capture a significant amount of the decaying
muons it was decided to compromise the constancy of the E” signal and use a 2psec
gate. For gate widths above 2psec all signals arriving more than 2psec before the end

of the gate are completely decayed and therefore not recorded.

In order to overcome the above mentioned problems we apply lower 13,, cuts for
several detectors and exclude the first two rings of Ball detectors (23° and 32° ) for
pion identification. The resulting pion identification is demonstrated in Figures 2.17
and 2.18. In Figure 2.17 we show the number of hits in a given PID gate as a function
of the ring number, in the Ball, that was hit. The PID gates are for neutrals (n), pions
(1r), between pions and protons (7r - p) and protons (p) which includes both regions
adjacent to the pion PID gate (see Figure 2.9). The solid histograms represent the
inclusive data, i.e., all bits in the corresponding PID gate are accepted. Note that
there is no obvious difference between the pion and the data in the two neighboring

PID gates. The triangles show the data if a coincidence with an E” signal is required.

32

Now the slope for the data in the pion PID gate is very different from the ones in the
other PID gates. Both the inclusive and the gated data are area normalized to one by
fitting an exponentially decaying function to the data and integrating the area below
that function. In Figure 2.18 the inverse slope and the total area for both inclusive
(squares) and gated (triangles) data are displayed in the upper two panels. As could
already be seen in Figure 2.17 the inverse slope for the pion data with an Eu gate is
much larger than the one for the inclusive data, whereas the other PID gates show
no significant change in the slope whether the Eu gate is applied or not. From that
we conclude that for hits in the pion PID gate a coincident Eu signal is mainly due
to the decay products, whereas for neutrals and protons the number of coincident
Eu signals is a constant fraction of the total number of counts in that gate. This is
further demonstrated in the bottom panel of Figure 2.18 where the ratio of the total
yield with a corresponding Eu signal and the inclusive yield is shown. That ratio is

at least a factor of two larger for pions than for the other particle types.

In summary, the detection efficiency for positively charged pions depends not only
on polar angle but also on the energy of the incident pion. The most forward angles do
not provide a clean separation for pions from background. The yield for low energy
pions will be underestimated due to the method of identification. Absolute cross
section cannot be obtained at the current level of analysis. The total polar angle

coverage is from 46° to 157° in the laboratory frame.

2.4 Pion Energy Calibration

In order to obtain an energy calibration, one could simply use equation 2.2 with the
appropriate mass scaling for the pion mass (A = 0.15). This would imply a factor

of about 1.7 more light produced for a pion, than for a proton depositing the same

33

 

 

150 AMeV
l . 1
: A n ; 1t

    
 

I j TI IITI'

I I IIIIIII

I IIIIIII'
I IIIIIII'

.3
IO

 

T 1 IIIIIII
I llllilll

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

a 4 1 1 1 1 4 1 1 1 1
A i. 1 1111 1111 1111 11'. 11 1111 1111 11L1 11
a no IS 20 25 1o 15 zo 25
Q l l _
E E n- 5
an : p : p
-l
I. E' E
: c
p- .—
.1
1° F 5'
I I
-J
10 E- 10 :_ A
I I
I0 1111111111L111L1114LJ 'o 11111+JLLJM14L1L1111
no 15 20 25 1o IS 20 25
ring number (@1111)

Figure 2.17: Inclusive (histograms) and Eu gated (symbols) probability distributions
for detector hits in the main Ball as a function of ring number.

33

 

 

 
  

 

 

 

 

 

 

 

 

 

  

l . l -
h- —
P —
’ 11 3 11:
IA -
h P
b D
-l

10 r' r-
h r-
b n-
p v-
n- r-
. p
I- r-
P -

o"
L—

l :—
- P
n- r-
- 1-
I- >-
F r
1- L-
P b

.J

I. :- :-
b I-
l- r-
: I
n- r-
h- n—

30 . .
g "411111J—1111111111111 '0 11‘11111111LJL1LJ1141
GI 10 IS 20 25 IO 15 20 25
1: l. l_
P r-
n- >-
2 . mp . p
A. ~ -
n- .-
L-
4 4

no r no t
I -
r- P-
n- >-
b- .-
b —
i- I—

.1 -1

10 r' I. :-
h- I-
P b
D h
n- r-
P h
n- u-
r- 1—

4 -3 A

10 r- 10 r
I —
P h
h h
D P
I- n-
»- >—
I. >-

4
1.41111111l111111141J1 l“ nilnlnnIlllnanJnlnn

 

 

 

 

 

 

10 IS 20 25 10 15 20 25

ring number (9»)

Figure 2.17: Inclusive (histograms) and Eu gated (symbols) probability distributions
for detector hits in the main Ball as a function of ring number.

33

 

 

   

l . I .
h I—
r- r-
' [1 h 1!
CA -
h P
D —
.|

I. r' :-
I Z
P i-
n- n—
i- .-
n- 1-
F r-
4
I- n-

10 '- '-
P I—
h 1—
P b
P p
l- .—
i- r—
n— F-
.3

I. r- :-
b I-
i- n—
h n-
y- b
D h
i- I-
'- 1-

'.4 111111111111111111'n-‘llllllllllllllllllll

 

 

 

 

 

 

I. IS 20 25 10 15 20 25

 

 

M)

P

Probability

I I IWIIII

I ITTIIIII

I I nrrnrq

   

I I I FITII'
I I I IIIIII

I IfIIIII'
I ITIIII'

I

 

 

 

 

 

 

4 4
I. 111111111111l1111l111“ lllllllllJJlllllllll
1. l5 2. 25 10 15 20 25

ring number (9“,)

Figure 2.17: Inclusive (histograms) and E“ gated (symbols) probability distributions
for detector hits in the main Ball as a function of ring number.

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

150 AMeV
15
[2] Incl.
. . A E mod
10 j u "
m C
\
fl 1—
I 5 __ A
{I} fir»: g
0 i 1 1 1
n 1: n-p p
10'_
no”; r”
g s n as
0 6 U
... 10 r
>"
"‘ 5
3 10 .r
G : A A
in! . u L“
1:- «A
’ 1 1 1
n 1: n-p p
0.5 _
= 1
g 0.4 L—
F‘ I
2 «a g—
‘5 ~ A
a 0.2 - T l
0.1 E— l ¢
0 : l l l
n 1: nt-p p
pid

Figure 2.18: Inverse slope, total yield and ratio for detector hits in the main Ball,
inclusive and Eu gated.

35

energy in the detector. This is clearly too high, since even an electron produces
only about 1.6 times as much light as a proton for a deposited energy of 160 MeV
in a plastic scintillator [Birk 64]. Obviously the well known energy calibration of
the 41r Array phoswich detectors for particles with mass number A Z 1 cannot be
extrapolated to pion masses. Figure 2.19 shows the energy calibration for protons
and pions obtained by the Plastic Ball group [Bade 82]. The two curves show a very
similar response, with slightly more light produced from pions than from protons
for the same deposited energy. Since the stopping plastic scintillator in the Plastic
Ball is very similar to the one used in the MSU 47r Array, the pion kinetic energies
are calibrated relative to the well known proton calibration. The resulting energy
vs. light curve is shown in Figure 2.20 as the solid curve. The dot-dashed curve is
the proton response and the dashed line is obtained by using the mass scaling from

equation 2.2.

2.5 The Experiment

The experiment was performed in February 1993 at the National Superconducting
Cyclotron Laboratory (NSCL) at Michigan State University (MSU). The K1200 su-
perconducting cyclotron was used to accelerate 20Ne beams at Eben“ = 90, 110 and
150 AMeV that bombarded a 5 mg/cm2 27Al target. The average beam intensities
were between 10 and 40 pA , resulting in about 2000 triggers per second, depending

on the hardware trigger condition.

The analog data from all the phoswich detectors are electronically split three ways
to extract the AE and E information and to provide additional trigger information.
The AE and E signals are delayed and fed into 16 channel Lecroy 4301B FERAs.

The trigger signal again split two ways, with one of the signals being supplied to an

36

 

n—n
A
O
I
l

—I— Protons 4
—e— Pious .

_ _

8 '5’

“1...,
o
1

Energy Deposited (MeV)
00
O

 

 

 

 

0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 100 200 300 400 500
Light (channels)

Figure 2.19: Pion and proton energy calibration from the Plastic Ball. From
[Bade 82].

37

additional bank of FERAs that record the Eu signal. The other signal is fed into 16
channel Phillips 7106 discriminators where sum and individual outputs are provided.
The individual channel outputs are again delayed and fed into 16 channel Lecroy 4303
Time-to-FERA converters (TFCs) that provide an analog time proportional signal to
another bank of FERAs. The sum outputs are fed into two EG&G octal constant
fraction discriminators CCF 8000. One of these provides scaler information for the
detector subsystems (BALL and FA), whereas the other is used to determine the user
selectable trigger condition (MASTER). The trigger condition consists of the detector
subsystem (or a combination thereof) and a hit multiplicity. The triggers used in this
experiment were FA2 (two hits in the forward array), 32 (two hits in the main Ball)
and B3 (three hits in the main Ball). The MASTER signal in coincidence with a signal
from the data aquisition module, indicating its “readyness” to accept data make up
the MASTERLIVE signal. Another sum output from the Phillips discriminators in
coincidence with MASTERLIVE is used to provide individual gates to the AE and
E FERAs for the main Ball and Forward Array subsystems. The Silenas (BCCs) and
the bank of FERAs for the Eu signal are both gated with appropriate signals derived
from MASTER.LIVE.

The digitized data from the F ERA QDCs and Silena ADCs are read out by ECL
line using a VME based data-bus to buffer-memory interface module and stored in
local VME memory. From there it is accessed by an INMOS T-800 transputer linked
to a SUN Sparc workstation. The VME transputer packs the data and supplies
it to a host process running on the Sparc workstation. The host process on the
SUN feeds the data to a general purpose router (also on the SUN) which in turn
distributes the data to a number of consumers. The most important consumer is the
taping process, which writes the data to 8mm Exabyte magnetic tapes. The other

important consumer is a program that supplies the data to consumers running on

38

different hosts over the Ethernet. Two such consumers are the online data display
and analysis program XSARA and a scaler program, both running on VMS DEC
Alpha computers. For a more detailed description of the data aquisition system see

References [Vand 94, Vand 91].

Over the time of 10 days beam time we collected a total of several billion raw
events. The analysis was done using only the B2 trigger data due to some detector
problems in the initial phase of the experiment (B3 trigger). In order to reduce
analysis time two types of physics tapes were prepared. The first includes about
600000 events of inclusive data for each beam energy and is used to get all distributions
not involving pions. The second type consists of all events from all raw tapes that
had an Ep signal anywhere in the event (not necessarily in coincidence with a pion).

The total numbers of pions for the B2 trigger are summarized in Table 2.5.

39

 

Plon Energy Calibration
I I Y I 1' Y I Y I Y Y T V Y 'Y Y T 1 Y ‘I Y I T T T Y T fT—fifif T Y Y I I I T Y Y Y I T
I. >- /_1
~ nfrom[Bade82] ,2 .
m~ ----nfrommasaacaling —

Energy (at. units)
a

 

 

* - - --- proton

   
 

 

 

“ 1—
I
I '— .1
r . -n
1‘ // :
. V l l 1441 1 l L 1 1 1 L14 1 1 LL 1 1 1 1 A 1 l 1 1 1 1 L 1 J 1 kg) 1 l 1 L4
0 I“ I“ 3“ U 5“ aa 7. 90 non
Light output (channels)

Figure 2.20: Pion energy calibration for plastic phoswich detectors. The pion energies
are calibrated relative to the well known proton calibration using the solid line.

Table 2.5: Total number of identified pions for B2 trigger.

 

if of events

 

 

 

 

 

 

 

# of approximate .
Ebem(AMeV) with one or identified number of pnons per
more E1: pions total events event
150 4437537 47675 100 M 4.8 x 10-4
110 445309 19742 170 M 1.2 x 10‘4
90 243182 7291 135 M 5.4 x 10‘5

 

 

Chapter 3

Centrality of Pion Producing
Events

3.1 Introduction

In some of the previous experiments that measured pions below the free nucleon-
nucleon threshold, indications were seen that a large overlap of the projectile and
target nuclei is necessary to produce a pion [Eraz 88, Mill 87]. Also, in the picture of
individual nucleon-nucleon collisions producing the pion at the bombarding energies
in question, a strong correlation between the number of collisions, and therefore the

centrality of the reaction, and the number of pions produced can be expected.

3.2 Centrality Selection

The impact parameter or centrality of a nuclear reaction is conventionally determined
by dividing the possible values of some event observable into a given number of bins
and assume that the values of the observable increase (or decrease) monotonically
with decreasing impact parameter. Examples of such observables are total transverse
kinetic energy KB. or momentum Pt, charged particle multiplicity N ch or midrapidity

charge Zn". For a detailed analysis of advantages and disadvantages as well as possible

40

41

auto correlations see Reference [Llop 95]. In this experiment we choose KEt as the
main centrality observable. Since the total number of nucleons in the system is only
47, all of the multiplicity related observables are very limited in resolution and do not
provide a continuous distribution to determine event centrality. For a more detailed

description of the centrality selection see Appendix A.

3.3 Less Central

In Figures 3.1 and 3.2 we show the centrality for inclusive and pion gated events
as measured by four different event observables. In the case of the total transverse
kinetic energy KE. (upper two panels) the available phase space is divided into 10
bins ranging from central (high values of KEt) to peripheral (low values). Since
the displayed data is for the B2 hardware trigger the most peripheral collisions still
require two particles in the main Ball, i.e. polar angles above 23° . The absolute
normalization of centrality versus impact parameter remains therefore in question,
but the trend from central to peripheral events is still valid. The multiplicity related
observables Nd, (number of charged particles, excluding pions), N13,, (number of light
charged particles) and Z," (midrapidity charge) are, in this reaction, too small to
allow for good impact parameter selection. For these we divide the available phase
space into only 4 bins. All distributions are area normalized to one. All statistical
errors are smaller than the line width or symbol size. The fact that the inclusive
centrality distributions for Nah, N16,, and Zmr are not flat at a value of one (like the

KB. distribution) is due to the limited resolution in these observables.

For the data at 150 AMeV (Figure 3.1) the pion gated distributions (diamonds)
produce higher values of the respective observable, indicating more central events.

This result is in good agreement with the findings of other authors [Eraz 88, Mill 87],

n3

8

i.

Yield (arb. units)
a

42

 

 

  
   

 

 

 

 

 

 

IIIII

 

'QTITIIII TTII
'

 

 

 

 

 

 

 

5 I.- A .1 ,. 1. 1.2. .
observable

 

 

2 27

”NH Alat 150 AMeV

.- 2 r-

: —lacLeventa E

L O plgatedeveata ‘5 C

: E—OOO-Q-e'v‘ ,_. ’27

. 1,

~ ; (>00
:1111111111111111111

 

0.2 0.4 0.6 0.8 l

 

[III]
O

O

IIIIIITTI

TL

 

 

InaM

 

IIII

1111111111111111111

 

 

 

 

 

 

 

0.25 as 0.75 n
:1LIJL111414LLJL1J1111
0.25 05 0.75 n
p
L

  

 

 

~1111111l11111111114_.1

 

0.25 0.5 0.75 l

centrality

Figure 3.1: Centrality of pion events at Ebem = 150 AMeV

15

10

Yield (arb. units)
8 8 i

0.4

0.3

0.2

.01

43

 

 

 

   

 

 

 

 

 

20 27
Ne 4' Al at 90 AMeV
2 h
~ — Incl. eve-ta E
1 0 pl gated events 15 C“
— +
: 1 WW
1 t
_ t
1— 0.5 1—-
r .
“ E
11111111 .L11i11L1111111111111
0 0.1 0.2 0.2 0.4 0.6 0.8 I
2
{— ns C 0
E E
7 0
W
:1 1 l 1 1 L 1 i 1 1 1 1 l 1 1 1 1 l 1
0.25 0.5 0.75 l

 

 

 

 

 

 

 

 

observable

 

‘nnninnnnlnlnl

  

 

ITIII]

 

 

 

J 1 L l L 1 l l 1 1 I 1 1 L 1 1 i 1 1
0.25 0.5 0.75 l
E 0 <> <>

 

TI;

 

 

LilllllillllLlllllll

 

0.25 0.5 0.75 l

centrality

Figure 3.2: Centrality of pion events at Ebem = 90 AMeV

'13 N

11112

44

where different methods were used to determine centrality in pion producing events.
At the lower bombarding energy of 90 AMeV (Figure 3.2) the total number of pion
producing events is significantly lower than for the 150 AMeV case (z 50000 at 150
AMeV vs. 5:: 7000 at 90 AMeV). While a preference for central events is still present
in these data, it is much less pronounced than for the 150 AMeV data, possibly
indicating a transition to some more collective process and a less dominant production

from individual nucleon-nucleon collisions.

In Figure 3.3 we show a comparison with BUU model calculations [Bane 89,
Li 91a]. The BUU calculations were done for the impact parameters determined
in Appendix A, which are 2.0, 3.43, 4.43, 5.24 and 5.93 fm. Both the data and
the calculations are normalized to unity at the most central bin. At all three beam
energies the BUU predictions show a much steeper decrease of the total pion yield
with impact parameter than do the data. The BUU calculations were done using a
parameterization for a medium equation of state for nuclear matter. Employing a
stiff or soft parameterization does not change the results, i.e. the number of pions
produced for a given impact parameter. One rather obvious explanation of the dis-
crepancy would be that in peripheral collisions other more collective processes are
responsible for the production of pions. On the other hand, it is possible that the
total transverse kinetic energy (KE.) does not provide a good centrality selection for
events that produce a pion since the energy necessary to produce the pion is missing

from the system, possibly reducing the values of KEt.

In order to further investigate that possibility we can make use of different cen-
trality observables and look for a change in the centrality as determined by KEt for
events classified as peripheral or central by these other observables. In Figure 3.4 the
KB, distributions for all events and events with an identified pion are displayed for

the global observables N ch, Nlcp and Zm.

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: 150AMeV
n an
r-
: 0 a a
05—
» 1:1 Data 0
~ 0 BUU o
1 0 BUU,illtered
I o-
. 1111111111L1Lll111111111l11111l111llllllJJJllllll
0 0.n 0.2 0.5 0.4 05 0.0 0.7 0.0 0.0 n
E 1
,0 _ 110AMeV
s. 1 1.
fl .
.2 _
9' _
'5 ~ 0
g 0.5 r-
“ I-
a 1 °
n... - o
9 1 o
a . 11L1111111LL11111111111111111111_ILJ_L1111111111111
0 0.n 0.2 0.1 0.4 0.5 0.0 0.7 0.0 0.0 n
; 90AMeV
I & L—{IIkl—fifi
.
0.54 °
_ o
' o-
. 1111111L111111111L111111111111111111111[111111911
0 0.n 0.2 05 0.4 05 05 0.7 0.0 0.0 n
b[bum

Figure 3.3: Comparison of total pion yield as a function of centrality with BUU
calculations.

46

The circles are for ungated events and are naturally identical for the three observ-
ables, the squares are for events with a value of less than 5 for the above observables,
representing a peripheral cut, and the triangles for events with a value larger or equal
to 5, representing a central cut. The value of 5 represents the point where about 50%
of the events are classified as central. The panels in the left column (open symbols)
are for events without a pion gate and the right column (filled symbols) for events
that had an identified pion. In all cases the central cut shows significantly higher
values of KEt, as expected, whereas the peripheral one represents most of the low
values. In order to be a little more specific, we can determine the mean values for
KE. for all these event classes. In Figure 3.5 the average KEt is shown for the three
different global observables. The symbols have the same meaning as in Figure 3.4.
For all three observables the pion requirement increases the average KEt for the in-
clusive and the peripheral gate. For the central gate, on the other hand, gating on
events with a pion decreases the average by about the same amount, indicating that
indeed producing a pion in a central event lowers the average value of KEt. Since the
overall size of that change for all event classes is much smaller than the change by
going from peripheral to central, we conclude that the requirement of a pion in an
event does not significantly change the apparent centrality of the event. Therefore
the enhancement of the total pion yield for peripheral events as compared to BUU

(see Figure 3.3) could be a real effect.

In order to demonstrate the effect of the pion gate on the centrality of the event in a
more direct comparison with impact parameter, we show the probability distributions
as a function of reduced impact parameter in Figure 3.6. The open circles are obtained
from events with no gating condition and the filled circles are for events where a pion
was detected. For all three beam energies the curves for pion events rise faster than

the inclusive ones, indicating more central events. After going through a plateau

47

 

 

 

   

 

 

    

 

 

 

 

 

 

 

 

 

 

2 27
°Ne+ Alat 150AMeV
all events pi events
40000 4000 _
: F
1—- M >—-
” “*1. n“?
1.0 -. I.
a... ; w ; I-
_ 15’ 2000 _- ... «.2
P (5)0 : g o '5'
.. .. I
I“ - 1m _ x
a
. ‘.’ ..... .
0 0.05 0.1 0.15 0.1 0.25 0 0.05 0.1 0.15 0.2 0.25
40000 _ 4000 _
. - s
.o . I
'2 . ' ° 2
.2 I“ i.—
>" c
10000 L
a
. .
0
40000
+-
a
10000 _—
a
0 P
0 0.1 0.15 0.2 0.25

KE

t

Figure 3.4: Inclusive (circles), central (triangles) and peripheral (squares) KE; distri-
butions for inclusive (open symbols)and pion gated (filled symbols) events.

<KE,>

48

 

 

 

 

 

 

 

 

20Ne + "Al at 150 AMeV

0.12

’ A

: ’3 0 A
0.1 — ‘
0.08 -

: . 0 g
0.06 '— O O Q

I a B B
0.04 -

f
0.02 — 0 C] A nllevenb(llcll0lv0,<5,25)

» CIA plevenh(lncln0lv0,<5,25)

0 i 1 1
Na NI” Z.“

0.12 _ A

3 1
0.11 —

i A
0.1 L A A

: . O Q
0.09 —
0.08 —

* O I I
0.07 r - D C]
0.06 b 1 I

Nell Nlcp Zmr

Figure 3.5: Mean KE. values and width for the gates from Figure 3.4.

49

at about 0.6b/bmax the gated distributions rise again at the most peripheral impact
parameters. It should be noted that this effect does not depend on the detection
angle of the pions, so that contamination from neutral particles in the pion gated

events is unlikely.

50

 

 

 

 

 

 

 

 

 

 

 

 

0.3
~ 0 inclusive events 150 AMCV
- 0 pi gated events
0.2 *- Q
. O 0
: . 0 9 '
o 0
0.I : . O
. o O
_ O
6
. llJllllllJlllllLllLllllllllJllLllLllLiLllllllJllI
0 0.1 0.2 03 0.4 0.5 0.0 0.7 0.0 0.0 1
0.3
_ 110 AMeV
.: . O 0
00 _ o o
.9 . O o
c r 0 o
a 0.1 r . O
. o
_ 8
Q
. llUlllLlJlll111111llLLLlllLlllLillllllllllllllll
0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 00 0.0 1
0.3
I 90 AMeV
0.2 — Q
C 0 °
C
: 8 e 9
.01 F g
L O
: 8
_ o
o lllllllllllJJl_lllllllllllllllllllllllllllLJJlllll
0 0.1 02 03 0.4 0.5 0.0 0.7 0.0 0.0 1
b/bm“

Figure 3.6: Impact parameter distributions for pion events (filled circles) compared
to inclusive events (open circles) for the three beam energies.

Chapter 4

Single Particle Distributions

4.1 Polar Angle Distributions

Polar angle distributions in the laboratory frame in general show a strong forward
focussing for all particle types (in fixed target experiments). The heavier the parti-
cles the more forward boosted it appears in the laboratory frame. The laboratory
polar angle distributions for pions, protons, Helium and Lithium ions are shown in
Figure 4.1 for impact parameter inclusive events at the beam energy of 150 AMeV.
As expected the pions are much less forward focussed than the other particle types.
The enhancement at backward angles can be attributed to a combination of enhanced
emission from a target like source and shadowing from the target holder and the target
itself. The first effect can be clearly seen in Figure 4.2 where the same distributions
are shown as in Figure 4.1 but this time only for particles from central (squares) and
peripheral (triangles) events. For protons and Helium ions a clear enhancement at
around 130° in the laboratory frame can be observed. For Lithium ions the effect
seems to be present, but the statistical errors are too large to make a strong state-
ment. The fact that the pions do not show any difference between the central and the
peripheral gates, indicates that no pion emission from a target like source is present

and the suppression at angles around 90° is entirely due to shadowing by the target

51

52

frame and the target itself.

In Figures 4.3 and 4.4 we show the polar angle distributions in the laboratory
frame for both protons and pions as solid histograms. The symbols indicate BUU
calculations at impact parameters of b = 2.0, 3.43, 4.43, 5.24 and 5.93 fm. The di—
amonds are raw calculations, whereas the crossed points are obtained after all test
particles from the calculation are subjected to a possible rejection by a software replica
of the detector acceptance of the 47r Array. For the first frame in the figures (BINO),
which shows the impact parameter inclusive distributions, no BUU calculations were
done. For all but the very peripheral collisions (BIN5) the filtered BUU calculations
reproduce the data very well for protons as well as for pions. While the raw BUU
calculations do not change appreciably with impact parameter, the filtered ones and
the data show an enhancement at the backward angles for the more peripheral re-
actions. This seems to indicate a change in the detection efficiency by going from
central to peripheral events. That can be expected since particles from a target like
source will have lower kinetic energy in the lab frame and are therefore more affected

by absorption in the target frame and the target itself.

4.2 Kinetic Energy Distributions

The kinetic energy distributions for different particle types are important to under—
stand the reaction mechanism in nuclear collisions. By assuming thermal equilibrium
in the hot overlap region of projectile and target, the slopes of the kinetic energy dis-
tribution give direct access to the temperature, and therefore the excitation energy of
the reaction zone. Especially particles that have to be produced in the reaction are
supposed to carry information about the properties of the medium in which they are

produced. Previous experiments show that temperatures extracted from pion energy

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E,” - 150 MeV
: .
E " E
-1 -I
I. :- I. :-
-2 -2
I. :- 10 E
- 1-
® I. Ill 1L1+lllllll l '. l llllLJlJlLJLl l
E 0 50 100 150 0 50 100 150
a - .
: He : Li
~ r
r- 1-
-I -I
I0 :- 10 :7
P h
L -
-2 -2
I. :- 1. L-
i T.
P P
‘..J lllllllJlllLl [1.Jl lllllllllll 7111
0 50 100 150 0 50 100 150
®|0b

Figure 4.1: Laboratory polar angle distributions for several particle types at Ebem =
150 AMeV.

54

 

 

Ebeun - 150 MeV
E
b 1t : -A-_A_ P
i W : DD
Q U 1:}

¢ 10 "

r 1171 TTT
W TIIIIITI
I?
Cl

 

 

 

 

 

 

'1 -z 'A'
10 :— 10 :— ¢' {39313.4(
~ A peripheral ~
g i. .3 l L l l l 1 J J 1 J J 1 1 1 l l 1 l. .3 l l I l J 1 l 1 1 l 1 1 1 1 #1 1
E 0 50 100 150 0 50 100 150
"’
a He : é, Li

CH5
ODD
[31>-
—§B

 

 

 

 

 

 

 

 

 

 

.1 -l -
I. E- 1. _:_
E 5123 E is
I '4 : {1
Cl .
., - .0, q: .1.

10 _— +£$éf+ 10 E (
W + i A-
l.-3,,..1..1.L11..1l.,“-3HHIIH. .1 .1
0 5° 100 '5' 0 50 100 150

69M)

Figure 4.2: Same as Figure 4.1 for particles from central (squares) and peripheral
(triangles) events.

55

 

 

   

 

 

 

 

 

 

 

 

 

 

BIN2

150 AMeV, p
l : I
E BIN]
ol - -I
I. .‘:— I.
.3 -1
I. E- 10 E
1.4. 1 LL 1 l l l l l l l l l l l 1.4 1]
-1
I. f

-
' I 'Q’T T1 11111 .
‘._
J

 

 

 

 

   

 

 

 

 

 

 

10'
fig
-2 -2
I. 5- |. E-
C I
r- J -
I. l llJlJllllllll ' 1.. J LillLlJlllll
50 I” 150 50 100 IS.
I I

1.0
.
0
‘
I 'w' 'II'I'I .
0
-
1 11 111] 1 1111111 .

T I VTII‘HI
I l l'llll'

 

 

   

 

U
\

 

 

 

 

14l1111l111117

0 50 100 150 0 50 100 150

69M1

llllllllJllll 1..

—
e
b

 

Figure 4.3: Comparison of proton polar angle distributions (histograms) with raw
(triangles) and filtered (crosses) BUU calculations for centrality bins from central
(BINl) to peripheral (BIN5).

56

 

 

      
     

 

 

 

 

 

 

 

     

 

 

 

 

 

 

 

 

 

 

 

      

 

 

 

 

 

 

 

 

150AMeV,1t
I : I
E BINO BIN]
: I
L l-
.1 -I
I. :— [Q :—
E s
I C
4’ -1
I. F I. E—
l I
1.6.1.111411....1 11.41.11....1...11,
0 50 100 150 0 50 100 150
l 1
E BINZ ; BIN3
,. ..
.J t
I. E- ? I:
E t
G: 3 E
4
l0 :- a-
l' 1-
1.4 I I I I I I I I I I I I ll , I 1.4 I I IJ II I I4 I I I 14 7 L
0 50 I“ 150 0 50 100 150
l 1 =
E BIN4 5 13le
.1. __
I. :— =—
E 5
i I
-1
I. :—

E a
1.4111il1141l1111l1|..31L11111111411] 1
0 50 100 150 0 50 100 150

9h!)

Figure 4.4: Comparison of pion polar angle distributions with raw and filtered BUU
calculations for several centrality bins.

57

spectra are lower than those from proton distributions for bombarding energies above
95 AMeV [Naga 81]. One experiment (‘60 + 27A1 at 94 AMeV) [Barb 90a] found that
the temperature extracted for protons (17 MeV) can be used to fit the positive pion
spectra as well. At a lower bombarding energy of 41 AMeV Suzuki et al. reported
a temperature of 16 MeV for negative pions [Suzu 91a] whereas the proton tempera-
ture for a similar reaction was determined to be around 9 MeV [Glas 83]. Table 4.1
gives an overview for most of the published data for pion temperatures in heavy ion

collisions both above and below the free nucleon-nucleon threshold.

As far as the source of pions is concerned it is generally assumed that they are
dominantly produced from the intermediate (cm) source in a spectator-participant
model. One experiment [Bada 93a] determined a source velocity between the center
of mass and the projectile-like source for neutral pion emission. In Figures 4.5 and 4.6
we show the pion kinetic energy spectra in the laboratory frame for angles between
45° and 153° at the two higher beam energies. The different panels in the figures show
the results for inclusive and centrality gated reactions (BINl being central, BIN5
peripheral). All spectra show the typical exponential decrease for higher energies as
well as a bump at low energies. The data for 45° show an enhancement for higher
energies, which is probably due to contamination from high energy neutrons that
leak into the pion PID gate. All distributions are solid angle normalized, but do not

include any correction for pion detection efficiency.

The solid lines in Figures 4.5 and 4.6 are obtained by fitting the two-dimensional
dN/dEdfl spectra with a boosted Maxwell-Boltzmann distribution. As in other ex-
periments a single source of pions is assumed, but the velocity of that source (8,)
is left as one of the fit parameters. The other fit parameters are the pion tempera-

ture (in the emitting frame) 1',r and an overall normalization factor A. Explicitly, the

58

Table 4.1: Compilation of pion temperatures from different experiments.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

reference system Ebwn (AMeV) pion charge 1' (MeV)
:Barb 90a] 16O+TTA1 94 +1 17.1
:Joha 82] 12C+12C 85 +1 14
12C+197Au 85 +1 15
Ban 84]“ l2C+12C 85 +1 17
'Bada 93a] 160+27A1 94 0 22.1
:Lebr 9015 160+x 93 o 10
:Grim 85]c 120+120 48 0 13.5
”C+"C 60 0 15
l2C+12C 74 0 17.5
12C+1’C 84 0 19.5
[Naga 82] l4N+NaF 400 -1 39
1‘N+NaF 183 -1 25
[Mill 87] 139La+139La 138 -1 14
139La+139La 183 -l 21
139La+139La 246 —1 25
:Haya 88] 139La+139La 800 -1 56
:Suzu 91a] 1“NJfiC 135 -1 16:1: 1
l4N+12C 80 -1 15:1: 1
l4N+12C 67 -1 13:1: 2
1“N+12C 41 -1 163: 2
[Naga 81] Ar+Pb 800 -1 72
Ar+KCl 800 -1 66
C+C 800 -1 60
Ne+NaF 800 -1 62

 

 

 

 

 

 

 

“same for a"
5T. S 30MeV
‘1' from Bose-Einstein statistics, day/tip3 = 1/(exp(E/1') — l)

59

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

150 MeV,1r
10’: 10’:
I f:
_ % . 1..
f° " Incl. : BIN]
10 -. 10 1.-
E, :
t F
I C
I :— u I E'—
: ° :
C I
1..I 1 1 1 1 l 1 1 L1 19 AI 1.4
10 50 100 150 I 50 100 150
10 . -
A E E
g : E BIN3
=3 ’ l
g "E E
v I :
© 1- 1-
'5 ‘2’ :—
g E E
10"
0 0
I01: :
E 5 eu(°)o45 481
: : .117.153 BINS
1' F E‘
E E
I C
I 'E— 5—
10'l
O 0

 

 

Figure 4.5: Pion kinetic energy distributions at 150 AMeV for several angles and
centrality bins. The solid lines are for moving source fits.

dN/dEd@ (arb. units)

-0
.

10‘

10

fl
.
N

60

110 MeV, 11

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

   

I 1.2:
L' L'-
' ° : BINl
: 1ncl. .
E’ " E'.°°
.. O
b E “ .‘
h '- 0
o
0
t." I :0.
E : 4
Z I
-I
I. 1 I I I
0 0
10’-
: E
3 : BIN3
f- I-
|—- r—
5 E
: :ach D
.. 1- "“1390
v- 1-
5- :"
I- P
0 I 50 1“ I50
E E o
i- It
.. 1. 0 "7 .153 BINS
» L
“=- 1. 5‘
t E
E __ ‘Than 111'
- 1. n O a
.
in
5 ° 1:
*’ u
1. D O
.1 l a u
1 I I I L I I

 

 

     

 

 

 

 

 

  

 

 

E (MeV)

Figure 4.6: Same as Figure 4.5 for 110 AMeV.

61

equation used is

 

 

 

d2N P d2N

dEdfl ‘ AFdE'dn' (4'1)

CPN 00 I T,

dE'dQ' ‘ 41rm3fiexp(—;) (4-2)
B" = 7,,(E — 3,1) cos 0) (4.3)

where the primes denote cm quantities and 7,, = l/‘/1 — B3,. The resulting values
of 7,, fl, and A for 150 AMeV and 110 AMeV are shown in Figures 4.7 and 4.8 for
all centrality bins. The bin labeled 0 represents the results for the impact parameter

inclusive fits.

One interesting result is that none of the parameters depend on the centrality of
the event. This finding is expected for emission from a completely thermalized source.
The normalization factor A for the impact parameter inclusive bin (BINO) is naturally
about 5 times larger than for the 5 different centrality bins. Again the constancy of

A with centrality is rather surprising, but follows the findings from Chapter 3.

The slope parameters 'r,r are in very good agreement with the values from Table 4.1.
In Figure 4.9 we present the data from Table 4.1 (open symbols) and include the points
for our measurements (filled stars). The data from this experiment link the positive
and negative pion data at low energies to the data for negative pions at the higher
energies. The trend for neutral pions seems somewhat different than the one observed

for charged pions.

Figure 4.10 shows the beam energy dependence of the source velocity and the slope
parameter (open symbols) for impact parameter inclusive events. The reversed trend
in the source velocity 19,, as compared to the values of the cm velocities, could be
due to the lack of identified pions in the forward direction. Although the polar angle

distributions for pions are not as forward focussed as the ones for other particles, the

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

150 MeV, 11
30
r
2' T—A——A A 4 1 —1——
1: I
P >-
10 —
. PI I I I I I I I I I I I I I I I I I I I I I I I I I I I I L
0 1 2 4 5
f.
0.4 —
L
a? »
A I
0.2 u ‘9 4 ¢__ 4 ___¢__
1.
0 I I I I L I I L 1 I I I I I I I I I I I I I I I I I I I I I
1 2 3 4 5
10’_
E C
.3 .
é —_—A———_
E I. L—
G : —A_‘-
. —A—
a A __¢———A——
I I I I I I 14 i J 4 I I I I I I I I I I I I I I I 4 4 4L ;
0 1 2 3 4 5
BIN

Figure 4.7: Resulting fit parameters from a moving source fit to a Maxwell-Boltzmann
distribution for pions at 150 AMeV. The solid line in the middle frame indicates the
value of [36,...

63

 

 

 

 

 

 

 

 

 

 

 

 

 

110 MeV, 11
30
20 — l l
:——A——¢——A—— ‘r‘ '1’ —(X—*
1: .
P l—
10 —
” PI I I I I I I I I I I I I L I I L I I I I L I I L I I L L I
0 1 2 3 4 s
0.4 L
F
C
0.3 -
1- 1 L
1: L— __ _
n 0.2 - 4‘ 1‘ l l l f
: I T T
L.
l—
0.1 r
. TL; I J I I 1 I I I I I I l I I I I I I I L I I I4LI I I
0 1 2 3 4 s
10‘_
g I
:g .
00 10 L—
E E—A—
c I
E _

1. __¢___
I11l1111l111LI117AT—1—‘1—1—Afl'11é11

0 l 2 3 4 5

BIN

 

 

 

 

 

 

Figure 4.8: Same as Figure 4.7 but for 110 AMeV.

64

 

—4

Cl
:1
.1.
0000-1

* present study

A
A
° AAO?*°
A o 0
A

0
IIIIIIIIIIIIIIIIILJIIIIIIILLIIIII

TillIT—TTTIIIIIIIITIlIIIIIIIIIIIWIU

 

 

I I I I I J I I I I I I I l I

2 3
IO 10

rrTII‘fijTjT—FIIIITTTITIIITIIITIIITIWITrT

 

 

T. (MeV)
: O

15

10

TTIIITIIIIIITTIIIPTIIIIIIIIII
0

D
C]
0
I11IIIIIIIIHIIIIIIILIIIIIIll

 

 

. IIIIIIIIIJIIIIIIIIIIIIIIIIIJLLIILIIIIII

20 40 60 N 100 120 I40 I60 I” 200

Em (AMeV)

 

Figure 4.9: Compilation of pion temperatures from different experiments. The lower
panel displays the data up to 200 AMeV on a linear scale. The open symbols represent
the data from Table 4.1. The errors are typically of the order of 1 -— 2 MeV. The errors
for this study are statistical only.

65

effect is still present and a larger number of pions will not be detected at the higher
beam energies. In order to further investigate the possibility of a misidentification
of the pion source that may be related to detector acceptance or pion identification
problems, we performed another set of fits to the data; again using equation 4.3 but
this time keeping the source velocity fixed at the value for the intermediate (i.e., cm)
source. These values are indicated in the figure as filled symbols. Even though the
source velocities in both cases are quite different, the values of 7',r are essentially the

same.

In order to check the assumption of pions being emitted from an equilibrated
source in the cm system, we apply the same method to the proton kinetic energy
spectra. Figure 4.11 shows the data together with the obtained fits. The overall
agreement with the data is good for the inclusive as well as the more central bins. In
peripheral collisions the data can probably not be described with a single emitting
source since strong contributions from a target like source, especially at the backward
angles, can be expected. A contribution from a projectile like source does not seem

to be present in the data, since the smallest angle included in the fits is 36° .

In Figure 4.12 the resulting parameters of the fits are displayed. In contrast to
the pion result the slope parameter ‘rp decreases with centrality. In this figure, the
impact parameter inclusive bin (BIN = 0) shows the weighted average. The apparent
source velocity ,3, also decreases from values slightly above to somewhat below the
cm velocity, again indicating target like source contributions for peripheral events.
The value obtained for the impact parameter inclusive fit is within a few percent of

the cm velocity.

In Figure 4.13 we compare the results obtained for “r? and flp at all three beam

energies. The general trend is that 7,, as well as 6,, decrease with decreasing centrality

66

 

15

0,. (MeV)

10

 

 

_r’r1 II 1*11’f' T 11 I TI’TTTI I II II’T IT IT

I IIILI,II II II II II II II LI II II LI,II II II II IILII L4 II I

00 90 I“ 110 120 130 140 150 160

 

05

 

0.4

0.35

0.3

B. (e)

0.2

0.15

0.1

0.05

IIIIITTI'ITIII'rTTIIIIIIITIIIIIIIlIIIIIIIII'ITTTT

 

 

. I II II II I LI,II II LJ I II II I II II I IJIIJ,I IIIII I II II II

80 90 100 110 120 130 140 150 160

ElmIn (AMeV)

 

Figure 4.10: Beam energy dependence of pion source velocity and slope parameter.

67

 

 

  
 
  
 
   

 

 

 

 

90 MeV, p
10 ‘ 10 ‘
incl. BIN]

10 3 10 3
101
10

1
I." 1.1.1.10... " °

0 50 100
10‘

 

 

—
.
U

  

 

 

dN/dEdO (arb. units)

IMJILIIIII

 

 

 

 

0 50 100 150
10‘
BIN4
10 3
9.. (°) '
a 45
. 01
. 117
. 153

 

 

IIIIIIIIII

100 150 200

 

Figure 4.11: Proton kinetic energy distributions at 90 AMeV for several angles and
centrality bins.

68

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

90 MeV, p
9 1—
E
4' r
30 C
=- L
P E A
2. :- 13 —A—
1- —A——_
10 _— —A—
. A
. P LI I I I I I I I I I I I I I I I J I I I I I I l I 1 I l I
0 1 2 3 4 5
0.4 -
E-
0.3 —
I
n. ~ _ __
m. u — . A 1
u If
; —A—‘-—-A—
. —A——
0.1 —
. -I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
0 1 2 3 4 5
103
s s——A—
‘5 _A_
00 1'1 =- ——A—
. E A A —A_
a E
g I0 5-
: E
l I L L L I I I I I I I I I I I I I I I I I I I I I I I I I J
0 1 2 3 4

Figure 4.12: Resulting fit parameter from a moving source fit to a Maxwell- Boltzmann
distribution at 90 AMeV. The solid line in the middle frame indicates the value of
flan. All statistical errors are smaller than the symbol size.

69

(increasing impact parameter) and decreasing beam energy. The solid lines in the
upper panel are the 7,, values extracted from BUU calculations at the three different

beam energies. In the bottom panel the solid lines are at the values of Ban.

As a last step in the analysis of the spectral shapes for kinetic energy distributions
we compare in Figures 4.14 and 4.15 the experimental results for 150 AMeV with the
filtered BUU results. In both figures the 2-dimensional spectra are normalized to
unity for angles between 45° and 153° . The energies considered for the normalization
are 10 — 150 MeV and 20 — 150 MeV for pions and protons respectively. The proton
spectra are well reproduced at all angles for the more central bins. In peripheral
collisions the shapes for backward angles are still in good agreement, whereas for the
forward angles the data drops much faster than the calculations. For the pions the
agreement is relatively good for the higher pion energies, whereas for the lower ones

the calculations under-predict the data by a factor of two.

70

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35
3- i— —<*—
: BUU 150
G 0t -—
25 ;— O ——{A}-——
E
,1 _ C} Q— C BUUatno—
a __2,_ 1111110100—
3- : —D—-—
P . —o——-
15 r A
E __U_
1. E o 150 AMeV _—A_
: D 110 AMeV D:
5 _— A 90AMeV A
. pI I I I IL1 1 I I 1 1 1 I LI 1 I I 1 I I I I I I I I I 1 I
0 1 2 3 4
0.3 _
0.275 L
E —o—
0.25 E
. 8 ° 150AMeV—
0125 ~_-—-O——
a : _A_ ¢
en. .1 .LU__ 3 110AMeV—]
;_A__ It. ”AMeV-fl
0.175 _— —£3—
E ——A——- $
0.15 :-
I _{j___ __
0.125 :-
t
..l P.1 I I I I I I I I I I I I I 1 1 LI I I I I I I l I I I I 1
0 1 2 4 5

Figure 4.13: Beam energy dependence of proton source velocity and slope parameter.
All statistical errors are smaller than the symbol size.

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

150 MeV,p
10"E 1o"_
BIN] E 13er
1.4::- "E"
4. _
" F 5'
4’- h
10 .
40 40
’5 10 P
'3 r
:1 .2"
e I. E
5 :
% 104E-
% ;
I0 .‘
10"
BINS histograms: data
-1
'° symbols: BUU
ICJ noun a: a D450 A 81°
‘..“. . . 0 ll7°<> 153°
"4 .11..111L1I
0 I00 150 2.

 

E (MeV)

Figure 4.14: Comparison of kinetic energy spectral shapes with BUU calculations for

protons at 150 AMeV.

-1
I0

10'

.3
10

4
l0

.1
l0

dN/dEdQ (arb. units)

72

 

 

 

 

 

-1
10 _

4
10

 

4
l0

 

 

 

 

 

 

 

 

 

    

150MeV,1:
-l
10 :
BIN] E BIN2
'Lr' -1_
I131, ' " '
1' I ' o E v
IIA 10"?
. .
#11 135111an 10
50 100 150 40
10 .
E
: BIN4
4’-
E— 0
_T
E
1 [1L .
1 1 II 1 17
0 50 100 150

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

histograms : data
symbols: BUU
o 45 ° I 81 °
A 117 ° V 153 °

Figure 4.15: Comparison of kinetic energy spectral shapes with BUU calculations for
pions at 150 AMeV.

Chapter 5

Azimuthal Distributions and
Transverse Flow

5.1 Introduction

In the study of the properties of hot, exited nuclear matter it is important to separate
collective effects from statistical ones. Collective effects such as rotation or collective
expansion can distort certain experimental quantities such as kinetic energy spectra

and severly affect the results obtained from model comparisons to the data [Hsi 94].

One of the goals for this experiment was to investigate the azimuthal correlations
and the possibility of transverse flow for pions produced below the free nucleon-
nucleon threshold. The azimuthal correlation, or the relative azimuthal angle of
emitted nuclear particles with respect to the reaction plane of the event, can give
a picture of the event shape in momentum space. Preferential emission in (or out
of) the reaction plane can be easily identified. After having found an approximate
reaction plane, the transverse motion in that plane can be determined for different

particle types and give a representation of the event shape.

Since for such kind of analysis it is important to have good event characterization

one needs to record the properties of as many particles in the events as possible. The

73

74

41r Array with its large solid angle coverage is well suited for this type of experiment

at intermediate energies and results for several such experiments have been published

[Wils 92, West 93].

In this experiment the small system size and the relatively high beam energies put
some restrictions on the completeness of the event characterization. The total system
mass in the 20Ne + 27Al reaction is only 47 amu, with the total charge being 23. This
results in rather low multiplicities in the events. For example, the average number of
charged particles in inclusive events is only about 4 at all three bombarding energies.
The average number of intermediate mass fragments (Z > 2) varies from 0.11 at 150
AMeV to .26 at 90 AMeV. Since both azimuthal correlations and transverse flow are

much stronger for heavier particle types, these low numbers affect the analysis.

5.2 Azimuthal Correlations

For the determination of the reaction plane in nuclear collisions several methods have
been devised. In general these methods rely on either some collective motion of
nuclear matter [Cugn 83, Dani 83, Dani 85, Wils 92] or the detection of projectile

like fragments (see e.g. [Schu 94]).

For the analysis in this experiment, we use a slightly modified version of the
azimuthal correlation method [Wils 92] to determine the reaction plane. The angle of
the approximate reaction plane with respect to the x-axis in the laboratory frame (Pap
is found by minimizing the sum of the squared distances of the transverse momenta
of all particles in an event to a common axis with slope A. In order to avoid auto-
correlations, reaction planes have to be determined for every particle in the event
by excluding that particle of interest (POI). Because of the exclusion of the POI we

require a minimum charged particle multiplicity of Nd, 2 3. This is at the same time

75

pm. .

 

 

 

1 RP
r01 ~. d.

d) .

tbRp-arctaMA)

0‘ d2
‘ ‘ >
B: s‘ (I" 32 p‘
‘. d3
3;

 

Figure 5.1: Reaction plane determination using azimuthal correlations. The particle
of interest is POI, the reaction plane is RP and 13: are the remaining particles in the
event.

the only restriction on the impact parameter of the reaction. The above procedure
will only give the value of the slope of the common axis but not the orientation along
that axis. Whereas the original method used the transverse momentum method to
determine the forward (positive) side of the reaction plane, the modified method

calculates a weighted projection of the transverse momenta onto the found axis, i.e.
PA = 2112515} - ff,

where A. is a unit vector along the direction of A and w,- is +1(-1) for particles with
positive(negative) cm rapidities. The orientation of if is given by the requirement that
—90° S <I>Rp S +90° . The forward side of the reaction plane can now be determined by
the sign of PA and does not rely on the transverse momentum method. A schematic
diagram showing the involved quantities is given in Figure 5.1. This modified method

has also been used in another recent experiment and yields distributions very similar

to the original method [Pak 95].

76

 

 

 

 

 

 

 

 

Helium at 150 AMeV, Nch23
incl. central
FT—TT j T T Y T fffir fir Y j r T j' T Y fir T Tfi 7 fl T I I T 7 T 1 1' V
1.2 — 4 e
- L +++ .
—¢— A —A— . e
1 - _¢_ —¢— — — i‘ .4 V
‘75— “A“ »+—— — I
F —A— 1. _ _ 4 0
"H4 + —+— >
r 4 ~ 4
Z: ’ l ’ 4
§ ” ‘ ’
A I A J; L A 41 J. L I 1 A A J. L L 1 1 I I l. J I L I L l l I 1 I I i 4 I
00
g T T # l’ T T j fir T 7 f T T ‘1 fl fir V Y I I V V Y 1' ‘I’ 1 j j f T Y Y Y
1.: — _ a
A. , l , +_ .
> '1 #- — — d
1. _A_++ 4 r+— +7 +-_ _ 4 7
. :¢- —¢— a _ i
—A— ——¢-—4 _ ‘j E
++‘¢‘ 1 * +7 >1
. J . I} _+_+ .
u .- — 1—
A I L L I I 4 ++ I l l A g _1# 41 4 L__L A I I A I l l l 1 .L I 1 I J
0 I” 200 0 I“ 1”
(bar (bar

Figure 5.2: Azimuthal angle distributions with respect to the approximate reaction
plane for He ions at 150 AMeV.

 

 

 

 

 

 

 

 

Helium at 90 AMeV, N¢23
Incl. central
fifr I T T f W 1 V T V T I Y I I ‘T ‘7 Y Y r I V V V l V I ' T l' I Y VJ
1.3 '- : ~ :
" 4 1. <
> -l r- 1 e
. -l P 'l
._ ”flat ++-v!
3' . J L .
g l L l l. l j. I l J. 1 L L_L I l A J L l I 1 1 I L J 4 l_l 4 L 1 4 l
C
r Y V V I V I I Y I I T ‘r 17 r j Y Y T Y Y 'I I I T ‘ Y I V Y 1 T I
I? 1.2 _ — — ~
Bun . . .
1- 4 r- -1
. a .4 .. .l A
—0- -O— —0—
.+ «H— .0. _+ +++++ ,1 ,9
,. -J 1- 4
4 h 1
01 - 1 r— d
L l A J #4 l 44L A l L L J I L A I A A 1
0 I” I“ I“ 2“
on, on,

Figure 5.3: Same as Figure 5.2 for 90 AMeV.

77

In Figures 5.2 and 5.3 we present the azimuthal distributions with respect to the
reaction plane for helium ions for the energies of 150 AMeV and 90 AMeV. In each
figure the two panels on the left are for impact parameter inclusive events, whereas
the two on the right are obtained for events within a 10% central cut on KE.. The
upper two are for backward, the lower two for forward center of mass rapidities of the
particle of interest. One effect that can be seen is that the centrality cut enhances
the correlation more for the higher beam energy. Whereas for the lower beam energy
the central distributions show a peak in the negative side of the reaction plane for
backward rapidities and a peak in the positive side for forward rapidities — as expected
for an ellipsoidal shape in momentum space, the data at 150 AMeV show a persistent
peak in the forward side even for the backward rapidities. The application of a recoil-
correction [Wils 92] has no effect on these distributions, since all the particles have

relatively small masses. The distributions for 110 AMeV are somewhere between the

ones for 90 and 150 AMeV.

The distributions for protons and pions in central events at 150 AMeV are dis-
played in Figure 5.4. Similar to the helium data the protons show an in-plane en-
hancement in the forward side of the plane for both rapidity gates. As far as the
pions are concerned the statistical errors tend to be rather large for these cuts, but at
forward rapidities a possible enhancement in the forward (positive) side of the plane
along with a suppression in the backward (negative) side can be seen. For all of the
more inclusive cuts, either in rapidity or centrality, the distributions are flat within
the error bars. Also, at the two lower beam energies the distributions for protons
show no correlation and for pions the errors are even larger than for 150 AMeV and

no correlation can be seen.

78

150 AMeV, Nflz3, central

 

'2 '- l. _1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

z. r
E "' "
I m. 1_L
I
.9 j ' w 1 1 l w l r T T r
E “ " ‘ ’ ‘
f -1l-— J
)v 4
5 1 ‘9‘ —i‘— 6
. _ +- +1,» 1, :¢~ + =1— —14 “1
Hi:— r —+ >11
1 _,,_ 1 -¢
0.8 r- -4 —
1 1 7 1 1 I 1 L 1 1 a 1 a
0 I. I“ 0 I. 2"
(DR? (DR?

Figure 5.4: Azimuthal angle distributions with respect to the approximate reaction
plane for pions and protons from central events at 150 AMeV.

79

5.3 Transverse Flow

One important collective mode is transverse directed flow. This mode is a collective
motion of the nuclear matter in the reaction plane and is observed in reactions at

both high [Dani 88, Gust 84, Gutb 89] and [Ogil 89, 81111 90, West 93] low bombarding

energies.

In general the interpretation is [Moli 85] that at low relative energies the attrac-
tive part of the nuclear potential is probed resulting in negative scattering angles,
whereas for high (relativistic) energies the repulsive hard core interaction dominates
the collision yielding positive flow angles. Since in an experiment only the absolute
value of the flow angle can be determined, that value should go through a minimum
at a bombarding energy, termed the balance energy EM, where the scattering angle
crosses zero. Several experiments have been performed to study that disappearance
of transverse flow [Ogil 89, Krof 89, 81111 90, Zhan 90]. One publication [West 93] re-
ports the balance energies as a function of the combined system mass. One of the
systems measured was Ne + Al, where the balance energy was found to be around
110 AMeV. Since transverse flow for pions has been observed at beam energies of
800 AMeV [Goss 89] and was found to be positive (same direction as fragments) for
all rapidities, we hoped to be able to determine the flow for subthreshold pions at

energies on either side of the balance energy of 110 AMeV.

Figures 5.5 to 5.7 display the average normalized transverse momentum in the
reaction plane < Px/Pt > as a function of center of mass rapidity ch for helium,
protons and pions for the three beam energies. All distributions are for a 10% central
cut in KEt. In all three figures the values of the projectile and target rapidities
are indicated by arrows. The cm rapidity is marked by a vertical line at ch = 0.

Whereas for helium the typical “S”-shaped curves are observed below and above the

80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

He, Nch23, central
“.2 I I I I 1 I I T If I T111 I I I I I Ifl Ifljerfirf‘I I I erl I I IT—TTj
r- 1
0.1 '- -1
: _,a_._—+— I ] i 9
0 _——‘ +—+—‘ E
p- . + __ -<
r- —+— - g
4.] — ~
‘1 ’- I I I I I I I I IJ L I I I I I I I I I I I I I I I I I I I I I I I I_LI I I I l I l I I I I I d
4.5 4.4 4.3 -0.2 JJ 0 0.1 0.2 0.3 0.4 0.5
.1 '- r17 T T I V Y F r I Y I I U I I I 1 r r I T I I I I U V I V T r I T r l T r 1 T I V T V 1 q
l' 1
0.1 —- -1 >
a“ _ —+——-+— ++—l——]— ‘ 5
~_—— '+ + 4
flu L ‘ 6
V )- 1 fl
* —1
JJ — ._._. ‘1
i \l \ :
‘1 I I I I I L I I I I I I I I J I I I I I J I I I I I I I I I I I I I I I I I I I I I I I I I
4.5 -0.4 4L3 4.2 JJ 0 0.1 0.2 0.3 0.4 0.5
.01 _T T l 1' I V r I V I U T T I I F V Y I I T T I V I I I r I T 1 I I I I I U I T I I I I I I I T I 1
)- -1
... _ J, + J >
- __ + —+—- 1
- + —+—+ . v
__ l —+—- —+-— j 5
P I
0 ..__
" + “ a
1- -* fi
401 h- _
~ +
4.2 '- I I I 7 I I I I I I L LI_L I I I I I I I I_I_I I l I I I I I I I I I J4 I I I L I I I I I I I d
-0.5 4.4 4.3 ~03 -0.1 0 0.1 0.2 0.3 0.4 0.5
ch

Figure 5.5: Average transverse momentum in the reaction plane as a function of
rapidity for helium at the three different beam energies. The arrows indicate the
target and projectile rapidities. The balance energy is 110 AMeV.

0.2

.0!

JJ

NJ
E...
“\7

4.1
0.1

4.1

4.1

p, Nch.>_3, central

81

 

l

TIILTIIITITWTIIIITI

 

IIIIIITT‘IIIIIITTIIITTTII

IIIIIIIILIIIIIIIIIIIIII

 

rII‘IIIIIIIIIITTI

IIIIIIIIIJIIIJIIIIIIIIII

IjI IIIT

_

l
IIIIIIIIII

 

IIIIIIIII

 

b
h

4.4 4.3

4.1

4.1

0.1

0.3

0.4 0.5

 

TIIIIIITTII

TIIITI

++

IIIILIIIIIIII

TIIIITTIIITWTIIITjIIIII

_+_—-I'—'—+-"

+++

*IIIIIIIII

TIIIIIIIITTIIII—rIITI I11

IIIIIIIIIIIIIIIIIIII

”PW—I“ +

«J

J

-

—J

4

d

4

—

_Il——

 

 

4.5

4.4 4.3

4.2

4.1

0.1

0.1

0.3

E
gIIIIIILII

0.4

 

 

TIIIIITjTIIIIIIT—TWTIITIT

 

IITWIrIIIIIIIjITIIITIjTT

.- .4
b '4
v- d
F.- —4
p d
l— l ————-4‘
p- d
L ..
t .4
b c-
p -4
r- 4
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I l I I I I L I I I I I

 

 

 

4.5

4.4 4.3

Figure 5.6: Same as Figure 5.5 for protons.

4.2

JJ

Y

0.1

cm

0.2

0.3

0.4 0.5

110 AMeV 90 AMeV

150 AMeV

<P/P.>

IIIIIIIIIIIIjIII—TT

0.2

82

1:, N ch23, central

 

T t I T T I I I I I I I T I I I I I I I I I I I I

__ l l l l T l l l q

l“ '4

r- .4

y- a

0.1 ~— —
>- __4__ J

. ,_ .1

- 1

v- -1

. __ ___0___ —4p—.

I— 4

l- a

D «II

,_ fi— 1
4.1 — —— d
r- d

I- —— u

L M a

r- -4

I I I I

4.1

IIIIJIIIII

 

 

 

 

 

 

 

 

 

II IIIIIIIIJ IIIIIII

III

 

I
—

.1 TITT

4.8

4.6 4.4 4.2 O 0.2

IA 0.6 0.8

~

 

0.1

4.1

TTT IT‘IWTTTITIII

 

IIIITII]

iflflflfiifli

 

IIIIIIrTjI

IIIIIILIII

 

IIJ.IIII.JHIIIIJIIIIII

IIIILI

 

IIII

 

‘1 J44

4.8

4.‘ 4.4 -I.2 O

0.8

—

 

.1 I-IT ITII IT ITII ITTII I I TTI.rIT .II I ISIEI II I IT—4

. .J

0.1 — '-
.— i H ++ '

- -<

-0.l — —

3 I

 

4.2

 

IIIIIIIIIILIIIIIIILL

 

 

IIIIIIIIIIIIIIIIIII

 

 

43.8

4.6 4.4 4.2 O 0.2

Y

cm

0.4 0.6 0.8

Figure 5.7: Same as Figure 5.5 for pions.

_

110 AMeV 90 AMeV

150 AMeV

83

balance energy, the data for protons are flat for all beam energies. In fact the data
at 90 AMeV show a slightly negative slope. This does not present a problem, since
the slopes for all higher charges are positive. The distributions for pions at the two
lower beam energies are strongly affected by the centrality cut. The statistical errors
are too large to allow the extraction of a slope at midrapidity. For the 150 AMeV
the statistics is much better and a sharp rise at positive rapidities is seen, indicating
a preferred emission in the projectile direction. The fact that above a rapidity of
ch z 0.4 the < Par/P, > is zero is only due to the missing acceptance for pion

detection at polar angles below 45° .

To summarize the values of the slopes at midrapidity for the three particle types,
we show in Figure 5.8 d < Px/Pg > /dY6m|ch=0 as a function of beam energy. Again,
due to the large statistical errors at the lower two beam energies, no values for pions

are reported for these.

84

0.5

 

DI.
at:
G

IITTITFIIITTITTITT

d<P,/P,>/dv|y_,
:

 

l Tr I I I I

1 t

 

 

 

. .—
i- +
..‘IIIlIIIILIIIILJIIIIIIIIIILLIlllllIIlIILIIlLJI
so so m m m 130 m 150 m
Ebeanl

Figure 5.8: Slopes of the average transverse momentum in the reaction plane at
midrapidity. Due to the large statistical errors at the lower two beam energies, no
values for pions are reported for these.

Chapter 6

Conclusion

The production of positively charged pions below the free nucleon-nucleon threshold
in intermediate energy heavy ion collisions was investigated. The system studied was
20Ne + 27A] at bombarding energies of 90, 110 and 150 AMeV. Pions and nuclear
fragments were detected using the MSU 41r Array yielding complete event character-

ization.

Pion detection and identification

The pions were detected using fast /slow phoswich AE/E detectors for polar angles
from 18° to 162° and all azimuthal angles. The separation of the pion signal from the
background is accomplished by using the delayed 11+ —) 6+ decay in the pion decay
chain. That decay can be easily detected in the phoswich detectors. Unfortunately
the background contamination at angles below 45° is too large to extract reliable pion
signals. The absolute cross section for pion production is not readily available due to

the method of identification.

Pion event centrality

The fragment information from the 47r Array was used to determine the centrality

of pion producing events. A surprising enhancement of the production cross section

85

86

for peripheral events was found when compared to BUU model calculations. The
nuclear equation of state used for the calculations has no impact on the number of
pions produced for any given impact parameter. The peripheral enhancement seems
to be independent of the observable chosen to determine the centrality. The similarity
of inclusive and pion gated impact parameter distributions is found to increase with
decreasing beam energy, suggesting more cooperative phenomena for the production

of pions at subthreshold energies.
Polar angle distributions and kinetic energy spectra

The polar angle distribution in the laboratory frame shows the expected forward
focussing, increasing with particles mass. For pions, strong effects of target shadowing
are found. Both proton and pion distribution are very well reproduced with BUU
model calculations after taking into account the detector acceptance. An analysis of
the kinetic energy spectra in terms of a classical Maxwell-Boltzmann source, yields
pion and proton temperatures well within the systematics for similar systems and are
reproduced by BUU model calculations. The pions temperatures show no dependence
on the impact parameter of the collision, as can be expected for emission from a
completely thermalized source. For protons a significant decrease in the extracted
temperatures with increasing impact parameter is observed. The spectral shapes are
well reproduced by BUU calculations for central events. For low energy pions the

data are under-predicted by about a factor of 2.

Azimuthal distributions and transverse flow

Azimuthal distributions with respect to the estimated reaction plane were found to
be more strongly correlated with that plane for heavier particles. The correlation for

pions from central events shows a weak in-plane emission in the forward direction

87

for the highest beam energy. At the two lower beam energies, as well as for more

inclusive cuts, no correlations are found.

The average transverse momentum in the reaction plane as a function of rapidity
shows the typical “S”-shaped curves for helium fragments, both below and above the
balance energy. For protons the data show only flat distributions at a value close
to zero, which is expected for light particles at energies rather close to the balance
energy. For pions, on the other hand, a steep rise at forward rapidities is found at
the highest bombarding energy, indicating a preferred emission towards the nuclear

matter flow. At the two lower energies the statistics do not allow any conclusions.

Appendix A

Impact Parameter Selection

A.1 Method

In experimental studies of nuclear reactions it is highly desirable to determine the
(approximate) impact parameter on an event by event basis. This becomes especially
important when comparisons with theoretical model calculations are necessary, since
these usually require the impact parameter as one of the inputs. Whereas the ex-
clusive measurement of events of a certain class, such as peripheral or central, can
usually be achieved with few specialized detectors, the classification of all possible
events according to their centrality requires recording as much information about the
particles in an event as possible. For that purpose 47r detectors, such as the MSU
41r Array are well suited. While the impact parameter of a nuclear collision is not
directly accessible from an experiment, several “centrality” variables have been shown
to be correlated with impact parameter [Cava 90, Phai 92]. The observables used in
this experiment are the number of charged particles Nah, the number of light charged

particles Nlcp, midrapidity charge Zm, and the total transverse directed kinetic energy

KEt.

The number of light charged particles is defined to include only particles of Z S 2.

Both Nd. and Nlcp do not include the pion that might be produced. The midrapidity

88

89

charge is the sum of the charges of particles with a center of mass rapidity y’ between

one half the target and projectile cm rapidity, i.e.
531:. S y' S .5y,',,- (A-l)

Again pions are not counted in Zm. Since kinetic energy is not a directed quantity,

the transverse kinetic energy is derived from transverse momentum, i.e.

2 .
K13. = z: .2331— (A.2)

In order to obtain the approximate impact parameter from these variables, the

geometrical prescription of Reference [Cava 90] is used. It is assumed that a given

observable q is monotonically related to the impact parameter b in a way that

2 bdb
«:2 =if(q)dq, (A.3)

max:

 

with bma, being the maximum impact parameter of the reaction and f (q) the proba-
bility density function of q. That is f (q)dq is the probability of detecting a collision
with a value of q between q and q + dq. The function f (q) is therefore normalized to
unity. The plus (minus) sign indicates an increase (decrease) of q with increasing b.

Integration of equation A.3 from a given 6 to bma, yields

 

bma: 21rbdb 9(bm03) I I

/. «b3... — a: [m f(q )dq. (AA)

If we define

bemazl
F = i ' d ', A.5
(q) [is f(q) q ( )
then

b/bmar = 1 — F(q). (A.6)

Using equation A.6 one can easily obtain an estimate for the impact parameter

in any given event. In practice, we divide the possible values of the observable q into

90

Table A.1: Impact parameter values for bins in KEt

 

 

 

 

 

 

i F(KE.) i, in <3> 3.. j
3 3-3 333 0.00 0.32 0.45 1
Z 33 3:: 0.45 0.55 0.63 2
2 33 333 0.63 0.71 0.77 3
3 33 3;: 0.77 0.84 0.89 4
30 33 3:32 0.89 0.95 1.00 5

 

 

 

 

 

 

 

a number of bins with an equal number of events in each bin. For these bins we find

the appropriate F (q) by integrating the distribution function f (q)

Figure A.1 shows the distributions of the four “centrality” observables used in
this experiment. On the left the probability densities f(q) are shown. The hatched
areas under the curves indicate the bins for each variable. In the case of KE, there
are ten bins. For the other three variables only four bins are used, since the limited
range of values does not allow for a finer distinction. Even for four bins the resulting
integrated numbers of events in each bin, displayed on the right, is not constant, as it
is the case for KEt. Here all bins have approximately the same number of events and
the normalized distribution is flat at a value of .1. In the later stages of the analysis
these bins can be grouped to yield any possible cut on centrality. For the comparison
with model calculations in Chapter 3 the bins in centrality are grouped in pairs of
two so that an estimate of impact parameter can be made for the center of the bin
as well as for the upper and lower limit. The resulting values for f) = b/bmax obtained

for the different observables are listed in Tables A.1 to AA.

As the final step in the determination of an approximate impact parameter one

0.3

0.18
0.12
0.“

91

2"Ne + "A1 at 150 AMeV, Nd, 2 2

 

b'

 

  

II I

II II II II II II II II II II

II

IIIIIIIIIIIIIIIIII

 

IIII

 

I
h

J .

 

.
quvaLLLLLIIIIIIIIIIII

0.05 0.1 0.15

“mm...

0.2

E

 

IIITIIIIIIIIIIIIIIII

 

T T71 I I I I I I I I I I I I‘T I T

I I I I I I

 

 

3 “ninliruluuluulurr‘

 

 

TTIIIIIIIIIIITTIIIIILL

 

an

T’I I T I I I I T‘I“T T I I’I I I I

 

I I

 

g "nqunlunlquun‘

 

 

 

I I

‘

IIIIIIIIIIIIIIIIIIIII'I"

 

0.2
0.16
0.1 2
0.“
0.04

0.5
0.4
0.3
0.2
0.1

0.5
0.4
0.3
0.2
0.1

0.5
0.4
0.3
0.2
0.1

 

 

EAAAAAAAAAA
E—
:I I I I III I IIIIIII I I I I I I I I

 

2 0 0 s
centrality

l0

 

-
p
h
p
P
~ A
b
p
_
i—-
p
b
F A A
p-
p
P
b
. A
p
p
p
p
I I I IIJ III I I I I I I I I I I I I

 

 

1 z 3 4
centrality

 

A

 

JIIIIIIIIIIIIIIIIIIIIIII

I I III I_I I I I I I I IIIII I I I I

 

1 2 3 4
centrality

 

A A

III IIII IIII IIII IIII
l I l I

 

I I I I I I I I I I I I I I I I,I I,

 

1 2 3 4
centrality

Figure A.1: Probability distributions for centrality observables.

 

 

 

 

Table A.2: Impact parameter values for bins in NC},

92

 

 

 

 

 

 

 

i F(Nch) I1 I71 < I) > 0,;
1 1.00 0.00

2 0.68 0.56 0.00 0.56 0.69
3 0.52 0.69

4 0.16 0.92 0.69 0.92 1.00

 

Table A.3: Impact parameter values for bins in Nlcp

 

‘H

 

 

 

 

 

 

i F(Nlcp) i; 6, <3> 6..
1 1.00 0.00

2 0.72 0.53 0.00 0.53 0.67
3 0.56 0.67

4 0.18 0.91 0.67 0.91 1.00

 

Table A.4: Impact parameter values for bins in Zmr

 

 

 

 

 

 

 

i F(Zmr) E E, <6> 6,.
1 1.00 0.00

2 0.71 0.54 0.00 0.54 0.76
3 0.43 0.76

4 0.26 0.86 0.76 0.86 1.00

 

 

 

 

 

 

 

93

needs to obtain an estimate for bmax. Since the experimental hardware trigger con-
dition naturally presents a centrality bias, one can estimate bmax by comparing the
total cross sections of the trigger used in the data (EX) and a minimum bias trigger

(MB). Assuming a geometrical cross section for the minimum bias trigger , i.e.
0M3 = 0m: = 7r(R,,, + 3:6)2 (A.7)
with RP, and Rm being the projectile and target radii, we can write

bmaz: = EE'(Rpr + Rta)- (A-8)
0MB

The transverse kinetic energy distributions used for the above procedure are shown
in Figure A.2 for 150 AMeV. The histogram labeled FA2M1 is the data taken with a
hardware trigger requiring a minimum of two detector hits in the forward array and
one identified charged particle in the whole array. It is assumed to be the minimum
bias trigger for the experiment. The curve labeled B2M2 represents the trigger that
was used for the data analysis. I required at least two phoswich detector hits in the
main ball and also two identified particles in the whole array. The two histograms are
normalized by minimizing the sum of the squared differences for values of the reduced
KE. larger than 0.025. That value is where the B2M2 data has its maximum. The
assumption here is that for values of KE:ed above the maximum the trigger bias

becomes negligible. The ratio of the two cross sections is

082M2
R =
0FA2M1

 

= 0.90. (A-9)

Using RP, + R... = 1.124(A;{3 + A33) = 6.42 fm for the sum of projectile and target
radii, we obtain bm” z 5.8 fm from equation A.8, which turns out to be independent
of the beam energy. Combining the values of I) from Table A.1 with the estimate for
bmu. we obtain average impact parameters of < b > = 2.0, 3.4, 4.4, 5.2 and 5.9 fm

for the five centrality bins in KEV

Yield

10‘ —

94

2'Ne + 27A] at 150 AMeV

 

 

I

I I

l_.I

ITTITIIITTIIIII'IIIIIIIfIIllIIITj—TIIIIIIIIITTI

FAZMI

IIIIILILJJIIIILIAIJIJIIIIILIIIIIIIIIIIIIIJ

0.025 0.05 0.075 0.1 0.125 0.15 0.l75 0.2 0.125

“mm...

Figure A.2: Estimate of maximum impact parameter.

I IIIIIII

 

 

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