MEASURING NEUTRONS IN HEAVY ION COLLISIONS

By

Kuan Zhu

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics — Doctor of Philosophy

2020

ABSTRACT

MEASURING NEUTRONS IN HEAVY ION COLLISIONS

By

Kuan Zhu

The behavior of the symmetry energy above nuclear saturation density plays a significant

role in the properties of neutron stars, the structure of heavy nuclei, and the dynamics of

nuclear reactions. To improve constraints on the symmetry energy term in the Nuclear Equa-

tion of State (EOS), neutrons and charged-particles were measured with beams of 40,48Ca

at 56,140 MeV/u on targets of 58,64Ni and 112,124Sn. The updated High Resolution Array

(HiRA10) was used for charged-particle detection. A charged-particle veto wall was designed

and constructed to eliminate charged-particle contamination in neutron spectrum measured

with the Large Area Neutron Arrays (LANA). Several innovative methods were developed to

improve LANA’s calibration and neutron/gamma discrimination procedures. Neutron light

output are compared to the simulation results from SCINFUL-QMD to test the validity of

neutron measurements and calculate the neutron detection efficiency. Various analysis pro-

cedures needed for neutron measurements are demonstrated and a preview of the data to

come is provided.

ACKNOWLEDGMENTS

First and foremost I could not have accomplished any of this without the guidance of my

advisor, Professor ManYee Betty Tsang. She was always available for idea and discussion.

I would like to further acknowledge my graduate guidance committee members: William

Lynch, Pawel Danielewicz, Mark Dykman and Morten Hjorth-Jensen. Thank you for your

time and thoughtful advice. Thanks to all previous and current HiRA lab members: Kyle

Brown, Giordano Cerizza, Daniele Dell’Aquila, Genie Jhang, Pierre Morfouace, Chenyang

Niu, Cl´ementine Santamaria, Rensheng Wang, Adam Anthony, Jon Barney, Justin Estee,

Sean Sweany, Tommy Tsang, Chi-En Fanurs Teh and Joseph Wieske. It has always been

joyful to keep learning and work with you. I would also like to thank the many talented

undergraduates I worked with: Corinne Anderson, Hananiel Setiawan, Suhas Kodali, Mira

Ghazali, Shuqi Han and Jiashen Ron Tang.

Special thanks to Zbigniew Chajecki group in Western Michigan University. The ex-

periments and the construction of the Charged-Particle Veto Wall can not be accomplished

without the strong collaboration with his team.

Last and certainly not least, thank you to all my fellow graduate students for your

help and support. Maxwell Cao, Mengzhi Chen, Brandon Elman, Rongzheng He, Kuan-Yu

Lin, Hao Lin, Dan Liu, Han Liu, Tong Li, Didi Luo, Xingze Mao, Samuel Marinelli, Pierre

Nzabahimana, Omokuyani Udiani, Qi Wang, ChunYan Jonathan Wong, Huyan Xueying and

Faran Zhou, thank you for your encouragement and friendship.

This work was in part funded by National Science Foundation (NSF) and Michigan State

University (MSU).

iii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 The Atomic Nucleus
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Nuclear Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Probing Effective Mass Splitting in Heavy Ion Collision . . . . . . . . . . . .
1.4 Neutron Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5
Improvements from Previous Experiment . . . . . . . . . . . . . . . . . . . .
1.6 Organization of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2

Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Microball
2.2 HiRA10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The Large Area Neutron Array (LANA)
. . . . . . . . . . . . . . . . . . . .
2.4 Forward Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Charged-Particle Veto Wall
. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Design and Prototype
. . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3

Data Analysis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Microball Impact Parameter Determination . . . . . . . . . . . . . . . . . .
3.2 LANA Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 LANA Calibration using cosmic rays . . . . . . . . . . . . . . . . . .
3.2.1.1
Impact position calibration . . . . . . . . . . . . . . . . . .
3.2.1.2 Time resolution and time offset calibration . . . . . . . . . .
3.2.1.3
Light attenuation length and photomultiplier gain-matching
. . . . . .
Light output calibration and position corrections
3.2.1.4
3.2.2 Time calibration with the Forward Array . . . . . . . . . . . . . . . .
3.2.3 Geometry Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Background Scattering Efficiency . . . . . . . . . . . . . . . . . . . .
3.3 Charged-Particle Veto Wall Pulse Height Calibration . . . . . . . . . . . . .

1
1
3
10
12
16
21

22
27
29
33
43
48
49
50

60
60
62
62
63
70
71
75
80
86
90
96

Chapter 4

Performance of LANA . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.1 Neutron/γ Pulse Shape Discrimination . . . . . . . . . . . . . . . . . . . . . 104
4.1.1 Traditional PSD & VPSD comparison . . . . . . . . . . . . . . . . . 106
4.1.2 PSD efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2 Neutron Light Output Comparison with SCINFUL-QMD . . . . . . . . . . . 120
4.3 Preliminary Neutron Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 129

iv

Chapter 5

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

v

LIST OF TABLES

Table 1.1: Neutron designation table for different energy ranges. This table is adopted
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

from Ref. [1]

Table 3.1: bmax table for all 16 beam-target-energy combinations in our experiment.
The unit is barn, 100 fm2. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 3.2: The ∆X and v of each back LANA (NWA) bar.

. . . . . . . . . . . . . .

Table 3.3: The ∆X and v of each front LANA (NWB) bar.

. . . . . . . . . . . . . .

Table 3.4: The light attenuation length λ of each back LANA (NWA) bar. . . . . . .

Table 3.5: The light attenuation length λ of each front LANA (NWB) bar. . . . . . .

14

62

67

67

73

73

vi

LIST OF FIGURES

Figure 1.1: The schematic showing the“plum pudding model”proposed by J.J. Thoma-
son (left) and the model proposed by Rutherford (right) after his discovery
experiment that showed back scattering of alpha particles. Alpha particles
penetrating atoms are represented by horizontal black arrow. Blue circles
represents electrons and red area shows the region with positive charge.
The sizes of electrons and nuclei are not drawn in scale. . . . . . . . . . .

Figure 1.2: Density dependence of the symmetry energy from the Skyrme interactions
used in Ref. [2].The shaded region is obtained from HIC experiments.
Picture is adopted from Ref. [3]. . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.3:

(top panels) Y(n)/Y(p) ratios as a function of kinetic energy for 124Sn+124Sn
at b=2fm. (bottom panels) DR(n/p) ratios as a function of kinetic energy.
From left to right, the beam energies are 100 MeV, 150 MeV, 200 MeV,
. . . . . . . . . .
300 MeV per nucleon. Figure is adopted from Ref. [4].

Figure 1.4: Neutron reaction cross sections adopted in SCINFUL-QMD model. Pic-
. . . . . . . . . . . . . . . . . . . . . . . .

ture is adopted from Ref. [5].

Figure 1.5: neutron/proton double ratio for 124Sn +124 Sn/112Sn +112 Sn reaction
systems at 120 MeV/u for central collisions. The symbols are experimental
data. Red line shows calculation using SLy4 which has m∗
p while
blue line comes from calculation using SkM∗ which has m∗
p. The
picture is adopted from Ref. [6]. Open circles are the original version and
the close circles are data of the most updated version. The original data
points did not take into account the efficiency corrections for charged-
particles [7, 8].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n < m∗
n > m∗

Figure 1.6: Neutron Wall light vs TOF, where TOF is the time of flight for the ob-
served particle to travel to the neutron walls. The prompt γ ray peak,
charged-particle punch-through, and charged particle stopping PID lines
are marked. Picture is adopted from Ref. [9].
. . . . . . . . . . . . . . .

Figure 2.1: Experimental setup overview. Microball, Forward Array and HiRA10 are
placed inside a vacuum chamber. The target is inside the Microball at the
center of the chamber. The lid of the vacuum chamber is removed for this
picture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.2: A schematic showing the experiment setup. It is a not-to-scale version of
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.25.

2

7

13

15

17

20

23

24

vii

Figure 2.3: Schematic diagram showing a vertical section of the Microball. The CsI(T1)
crystals are shown in grey. The blue trapezoids behind crystals are light
guides. The beam enters from the left. The numbers 1,2,3,to 9 are the
ring numbers. The polar angular coverage for each ring are also shown
together with the number of crystals contained in each ring. This picture
is adopted from Ref. [10].
. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.4: Ten microball detectors removed to allow charged particles emitted in reac-
tions to be detected by HiRA10 without materials without going through
blocking materials. The beam enters from left. . . . . . . . . . . . . . . .

Figure 2.5: The target ladder used in the experiment.

. . . . . . . . . . . . . . . . .

Figure 2.6: Angular coverage for Forward Array, Microball, HiRA10 and LANA in lab
Φ-Θ coordinates. The dashed blue rectangle represents the coverage of the
Forward Array, green regions represent Microball, red regions represent
twelve HiRA10 telescopes arranged in 4 towers, and the purple region
represents LANA coverage. Ten crystals in total are removed on Microball
ring #3, #4 and #5 leaving a direct path for the fragments to be detected
by HiRA10. There is no such accommodation for LANA. Microball ring
#6 is removed for target structure. The Microball covers part of the
forward array from Θ = 13° to Θ = 28°. In the adopted co-ordinate from
0 and 360 deg, the coverage of LANA is split at 0 and 360 degree (top
panel). The bottom panel shows LANA in continuous angular coverage
by plotting the φ range from -60° to 300°.
. . . . . . . . . . . . . . . . .

Figure 2.7:

(Left panel) A mechanical drawing of a HiRA10 telescope with its alu-
minum container and associated electronics. The DSSSD (not shown) is
placed in front of CsI crystals. (Right panel) A schematic drawing of a
HiRA10 telescope showing the front and back sides of the DSSSD placed
in front of the 4 CsI crystals.
. . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.8:

(Left panel) 12 HiRA10 telescopes arranged in 3 towers used in the present
experiments. The mounts are designed in approximately in an arc so that
the center of each telescope is located at 35 cm from the target. (Right
panel) Angular coverage of 12 telescopes in HiRA10 on a (θ, φ) plane
measured by Romer arm technology [11]. Each point represents a DSSSD
(1.95mm × 1.95mm) pixel. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.9: Particle identification of a HiRA10 telescope. The Y axis is the calibrated
DSSSD energy loss (∆E) versus the ADC channels of the residual energy
(E) in the CsI 2D plot. The top right inset shows an extended plot up to
120 MeV of energy loss in DSSSD. Red lines are PID lines from simulation
for various isotopes. This figure is adopted from Ref. [12].
. . . . . . . .

25

26

28

30

32

34

35

viii

Figure 2.10: Mechanical cutaway drawing of one wall of the Large Area Neutron Array.
[13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.11: One of LANA walls is illuminated with ultra-violet light after the front
. . . . . . . . . . . . . . . . . . . . . . . . .

aluminum cover is removed.

Figure 2.12: 3D mechanical overview drawing showing the position of LANA being
limited by the vault wall. During the move, some floor panels had to
be removed. These panels were installed back again after the moving of
LANA was done.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.13: Angular coverage of the front LANA (NWB) and back LANA (NWA) in
. . . . . . . . . . . .

the lab frame based on laser position measurement.

Figure 2.14: Schematic of the electronics setup (for one PMT) used to process signals
from the LANA when the walls are used in standalone mode. An ex-
act reproduction of these circuits is used to process signals obtained with
each of the 100 individual PMTs. “Fast” and “total” are two copies of the
original anode signal but integrated respectively by using a fast gate (con-
taining only the fast component of the signal) and total gate (containing
the whole signal) for PSD analysis. PMT dynode signals are used for the
timing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.15: The front and back views of the original Forward Array without PMT
bases. The front side of Forward Array is covered by a thin layer of
Sn/Pb foil to protect itself from δ electrons emitted in reactions. . . . . .

Figure 2.16: The front and back views of the original Forward Array assembled with
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

its backing.

Figure 2.17: The side and back views of the upgrade Forward Array placed in position
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

during experiments.

Figure 2.18: 3D sketch showing how 3 Charged-Particle Veto Wall scintillator bars are
. . . . . .

assembled at the bottom end with T-Slotted aluminum frame.

Figure 2.19: Professor Chajecki is studying the signal characteristic of Charged-Particle
Veto Wall bar prototype (at the right of the figure) with his students at
Western Michigan University.
. . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.20: Light guides are being glued on PMTs at Western Michigan Universty.

.

36

38

40

41

42

44

46

47

51

52

53

ix

Figure 2.21: (top left panel) Professor Chajecki is testing the Charged-Particle Veto
Wall frame.
(top right panel) Undergraduate students from Western
Michigan University and Michigan State University are moving Veto Wall
bar. (bottom left panel) Veto Wall bars are being taken out from shipment
packages. (bottom middle and right panel) NSCL and WMU researchers
are installing the Charged-Particle Veto Wall in front of LANA.
. . . . .

Figure 2.22: Charged-particle Veto Wall construction in progress. 22 bars have been
installed in place. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.23: The Charged-Particle Veto Wall installed in front of the LANA. In the
top panel, the red and yellow tape marks on the ground indicate the polar
angle with respect to the beam direction in lab frame.
. . . . . . . . . .

54

55

57

Figure 2.24: (Top panel) 3D sketch of the Charged-Particle Veto Wall. (Bottom panel)

3D sketch of the Charged-Particle Veto Wall and the LANAs nested together. 58

Figure 2.25: Top view of experimental setup schematic. The schematic reflects the sizes
and distances to the target of the Charged-Particle Veto Wall (VW) and
LANA (NWA and NWB) in scale. The VW+LANA assemble is moved
to 39.37 ° . All distances are drawn to scale and determined from laser
measurements.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.1: Correlations between the induced impact parameter ˆb and Microball mul-
tiplicity Nc for 16 reaction systems. On the upper right corners of two
panels, the reaction systems are labeled as target+beam. The top panels
are for Ni target reaction systems and the bottom panels are for Sn target
reaction systems. The left panels have lower beam energy of 56 AMeV
and the right panels have higher beam energy of 140 AMeV.
. . . . . . .

Figure 3.2:

(top panel) Time difference, tleft-tright distribution for cosmic muons ob-
tained with bar #8 of the LANA. A numerical differentiation of this spec-
trum (bottom panel) is used to determine the position of right and left
edges of the tleft-tright distribution consistently as indicated by the dashed
lines, which correspond to − L
2 respectively. . . . . . . . . . . . . .

2 and L

Figure 3.3: A schematic drawing of a cosmic muon track penetrating 10 consecutive
bars in the wall. Red stars represent the hit positions. The reconstructed
muon track (blue slanted line) is obtained by fitting the measured hit
positions on the bars with a straight line. ∆X indicates the position
deviation between the expected and the actual hit position. ∆di,ref is the
theoretical distance between two hits on a certain bar and reference bar
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

61

65

66

x

Figure 3.4: Position deviation distribution for bar #8.

. . . . . . . . . . . . . . . . .

68

Figure 3.5: δi,ref distributions for each of the bar in the array before (top panel) and
after (bottom panel) the peaks are aligned. Y-axis is the bar number while
i,ref − ∆T th
X-axis shows the corresponding ∆T exp
i,ref distributions. Bar #12
is used as the reference bar; therefore δ12,ref =0.
. . . . . . . . . . . . . .

Figure 3.6: Time deviation distribution for bar #8. . . . . . . . . . . . . . . . . . . .

Figure 3.7: Equation (3.8) as a function of the position X along the bar #8 for cosmic
ray data. The red dashed line is a linear fit of the distribution. The
intercept of the best fit line is compatible with (0,0), indicating a good
left-right matching of the PMT gains. The slope allows to extract the
attenuation length of the bar.
. . . . . . . . . . . . . . . . . . . . . . . .

69

72

74

Figure 3.8:

(Top panel) Uncalibrated left-right GM as a function of the position along
bar #8. Vertical cosmic rays are selected by restricting data to impinging
angles −10° ≤ θ ≤ 10° with respect to the axis perpendicular to the bar
length. Black points are the position of the cosmic ray MPV deduced with
a Landau fit of data for each position bin. The blue line is the result of
a quadratic fit of the cosmic MPV position dependence. (Bottom panel)
Same as top panel after light calibration and position dependency correction. 76

Figure 3.9: An example of a Landau fit of the GM distribution for the position bin
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-20 cm ≤ X ≤ 0 cm.

78

Figure 3.10: Position corrected light output spectrum obtained with an AmBe source
for bar #8. The Compton edge is fitted with a Fermi function and the
deduced position associated to the 4.44 MeV transition in 12C is indicated
by an arrow and a dashed line. The theoretical value of the Compton edge
is 4.2 MeV.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.11: The cosmic-ray energy-light calibration curve (red line) obtained by using
the 11.96 MeVee constraint of the cosmic muons and the zero-offset (blue
solid circle and blue square, respectively). The open star corresponds to
the Compton edge discussed in Figure 3.10. The open blue circles are two
additional light-energy calibration points obtained by select cosmic muons
that punch through the detector at 44.4 ± 5 and 56.3 ± 5 degrees with
. . . . . . . . . . . .
respect to the axis perpendicular to the bar length.

79

81

xi

Figure 3.12: A time of flight spectrum from NWB with log (top panel) and linear
(bottom panel) scale. The narrow peak at the left of the spectrum comes
from prompt gamma rays, which arrives the LANA all together and earlier
than any other particles. This plot is from 48Ca+124Sn at E/A = 56M eV
reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.13: 2D plot of FA segment QDC raw channel versus the timing subtraction
between NWB and a FA segment. Top panel is before walk in effect
correction and bottom panel is after correction. The red curve in top
panel is a fitted function in form of Eq. 3.11. . . . . . . . . . . . . . . . .

Figure 3.14: Normalized ToF spectrum from NWB with FA Time Min (top panel) and
. . . . . . . . . . . . . . . . . . . . . . .

FA Time Mean (bottom panel).

Figure 3.15: Hit distribution pattern in Φ-Θ plane for NWB using Geant4 simulation.
In simulation, the LANA is placed in the same position as measured by
laser measurements [14] in experiments. Then particles are simulated to
emit from target uniformly in Φ-Θ plane. We can see that for different Θ,
LANA’s coverage in azimuthal direction is different resulting in a geomet-
ric efficiency difference. The red window is 0.2 ° wide binned at Θ = 30°.

Figure 3.16: LANA fractional azimuthal coverage fΦ for front (NWB, top panel) and
. . . . . . . . . . . . . . . . . . . . . .

back (NWA, bottom panel) wall.

Figure 3.17: A shadow bar used in experiments for background neutron scattering ef-
. . . . . . . . . . .

ficiency correction. Picture is adopted from Ref. [15].

Figure 3.18: NSCL staff is removing part of aluminum floor in S2 vault for leaving space
in order to nest the LANA. Above S2 vault’s concrete floor, an aluminum
. . . . . . . . . .
layer of floor was built on which vacuum chamber sits.

Figure 3.19: The front LANA’s (NWB) neutron hit pattern with 4 shadow bar in-
stalled in Φlab-Θlab coordinates. 4 square areas with less counts of hits
corresponds to 4 shadow bars labelled with A, B, C, D as shown. NWB
bars are labelled from #1 to #25 corresponding to from the bottom bar
to the top bar.Shadow bar A and B fully cover NWB bar #16 and shadow
bar C and D fully cover NWB bar #8. The reaction system for this plot
is 48Ca +124 Sn at E/A = 56 M eV .
. . . . . . . . . . . . . . . . . . . .

Figure 3.20: (left panels) Neutron hit position spectrum corresponding to shadow bar
B (top) and D (bottom). Red lines indicates the fitted functions. (right
panels) Scaled fitted functions indicating the background scattering neu-
tron fraction. The lowest points’ Y values are both 0.26. The light output
threshold is set to 5 MeVee for all 4 plots here.
. . . . . . . . . . . . . .

83

85

87

88

89

90

91

93

94

xii

Figure 3.21: (left panels) Neutron hit position spectrum corresponding to shadow bar
A (top) and C (bottom). Red lines indicates the fitted functions. (right
panels) Scaled fitted functions indicating the background scattering neu-
tron fraction. The lowest points’ Y values are 0.27 and 0.29 for A and C
respectively. The light output threshold is set to 5 MeVee for all 4 plots
here. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.22: Light output versus ToF 2D spectrum from front LANA (NWB). The top
panel is the spectrum without using any VW information. The bottom
panel is the same spectrum but with the condition that VW should not
be triggered. We can clearly see that by requiring no hit in VW, the
charged-particle events (those slanted lines in the top panel) are removed
completely while keeping the rest of the spectrum undisturbed.
. . . . .

Figure 3.23: Light output versus ToF 2D spectrum from front LANA (NWB) gated on
the events that must have VW triggered. The blue window (around 20
MeVee on Proton line) gating on proton line selects the events where a
proton’s normalized ToF is in range [41.5, 43.5] ns and its light output is
. . . . . . . . . . . . . . . . . . . . . . . . .
in range [19.5, 20.0] MeVee.

Figure 3.24: VW Geometric Mean(cid:112)Qtop ∗ Qbottom versus VW bar number 2D plot.

95

97

99

The top panel is before geometric mean calibration and the bottom panel
is after geometric mean calibration using GMcalibrated = α ∗ GMraw.

. . 100

Figure 3.25: VW bar #18’s geometric mean versus Y position 2D plot for events sitting
in the blue window of Fig. 3.23. We can see that it is almost flat comparing
to the top panel of Fig. 3.8.

. . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure 3.26: VW calibrated geometric mean versus NWB light output 2D plot. . . . . 103

Figure 4.1: A schematic of different pulse shapes for neutron and gamma rays. The
peak heights are normalized to be the same. This picture is adopted from
Ref. [9].

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 4.2: LANA geometric mean versus fast geometric mean 2D plots from a typical
bar. The data was taken with 48Ca+124Sn at E/A = 56 MeV reaction.
The top panel focuses on the low value end, which is a zoomed-in version
of the bottom panel. We can barely see two lines in each panel, which are
gamma rays (top) and neutrons (bottom).

. . . . . . . . . . . . . . . . . 107

Figure 4.3: LANA flattened geometric mean versus fast geometric mean 2D plot. The
data is the same as shown in figure 4.2 but the clustering of gamma rays
(top) and neutrons (bottom) is much clearer.

. . . . . . . . . . . . . . . 108

xiii

Figure 4.4: A two-dimensional histogram of (Qf ast, Qtotal) from the left end of a
LANA bar. The two solid curves are quadratic fits on the gamma ray
cluster (top) and neutron cluster (bottom) respectively. Qf ast and Qtotal
correspond to SHORT Q and LONG Q in this plot. This picture is taken
from Ref. [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 4.5: 2D vL,R plots for all the nine segments of one LANA bar, with 1/9 repre-
senting the leftmost segment and 9/9 representing the rightmost segment.
The solid line represents the n/γ separation line, while the dashed line is
the line perpendicular to the solid line that pass through (-0.5, -0.5). This
picture is taken from Ref. [16]. . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure 4.6: PSD results comparisons between traditional flattened PSD method (left
column) and VPSD method (right column) for both best (top row) and
worst (bottom row) performance bars.

. . . . . . . . . . . . . . . . . . . 113

Figure 4.7:

(top panel) Neutron/γ pulse shape discrimination obtained by PPSD
method. The X and Y axes correspond to vL and vR of Figure 7 in
Ref. [16], after rotation to match for different segments on LANA bar.
The light output threshold is set to 2 MeVee. Gamma rays aggregate in
right bubble and neutrons are clustered in left bubble. (bottom panel) 1D
projection plot from the plot in top panel. Two Gaussian functions are
fitted to γ events peak (red dash line) and neutron events peak (green dash
line). The blue solid line represents the sum of two Gaussian functions.
Taking events with gate of P P SD-X < −0.6 ensures getting neutrons
with nearly no gamma contamination.

. . . . . . . . . . . . . . . . . . . 114

Figure 4.8: Gamma contamination as a function of particle incident energies, if the
scintillation material used in this experiment to detect neutron has no
PSD capability. The data was taken with 48Ca+124Sn at E/A = 56 MeV
reaction. The light output threshold is set to 5 MeVee.

. . . . . . . . . . 115

Figure 4.9: Pure neutron TOF spectra obtained by two correction methods. Black
dash line is calculated based on the Gaussian fits in figure 4.7: Take
neutron events with ”PPSD X>0.6” and then correct for 94.2% efficiency.
Green solid line is the same green line shown in figure 4.10 using gamma
peak matching method.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 117

xiv

Figure 4.10: (top panel) Same as the bottom panel in figure 4.7 but set a gate at
“P P SD-X = −0.1” to get pure gamma ray events and neutron with
gamma contamination. (bottom panel) ToF spectra with different gate
conditions. Spectrum of neutron and gamma where charged-particles are
vetoed is drawn in black. Red line shows pure gamma ray events with
condition “P P SD-X > −0.1” while blue line shows neutron with gamma
contamination with condition “P P SD-X < −0.1”. Green line displays the
ToF spectra after correction using gamma peak matching method, which
is the same line drawn also in green in figure 4.9.

. . . . . . . . . . . . . 119

Figure 4.11: Comparison of neutron light output spectra from experiments and SCINFUL-

QMD with different incident neutron energies at 20 MeV (top panel) and
40 MeV (bottom panel).

. . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Figure 4.12: Comparison of neutron light output spectra from experiments and SCINFUL-

QMD with different incident neutron energies at 60 MeV (top panel) and
80 MeV (bottom panel).

. . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Figure 4.13: Comparison of neutron light output spectra from experiments and SCINFUL-

QMD with different incident neutron energies at 100 MeV (top panel) and
120 MeV (bottom panel).

. . . . . . . . . . . . . . . . . . . . . . . . . . 126

Figure 4.14: Comparison of neutron light output versus incident neutron energy 2D

plots from experiment data (left) and SCINFUL-QMD simulation (right). 127

Figure 4.15: The neutron detection efficiency of LANA as a function of neutron incident
energy. Detection efficiencies for neutrons with incident energies more
than 25 MeV are used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Figure 4.16: Neutron energy spectrum measured by the front LANA from 48Ca+64Ni
at E/A = 140 M eV reaction. The data come from a batch of continuous
runs of around 18 hours. The Y-axis is counts per bin and the X-axis
is neutron energy in MeV in lab frame. The black line represents the
raw spectra and the red line shows the spectra after detection efficiency
correction using the efficiency data from Fig. 4.15. All data shown here
have a deduced impact parameter gate from [0,0.4). . . . . . . . . . . . . 130

xv

Figure 4.17: Neutron energy spectrum from 48Ca+64Ni at E/A = 140 M eV reaction
with angular cuts. The Y-axis is count per bin from a batch of continuous
runs of 48Ca+64Ni at E/A = 140 M eV reaction and the X-axis is neu-
tron energy in MeV in lab frame. The error bars only reflect statistical
uncertainties. From red, green and blue lines, different polar angular cuts
from around 32°, 38° and 46° are applied respectively. Solid lines show the
result after fitting with moving source model. The surface temperature of
the moving source model is extracted to be 26±1 MeV. Similar moving
source fits of the proton spectra in the same angular range yield similar
results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

xvi

Chapter 1

Introduction

1.1 The Atomic Nucleus

All visible things on earth are made of atoms. Each atom consists of a nucleus at the

center and a cloud of electrons. Although this is common knowledge nowadays, atoms were

regarded as the most fundamental particles until early 19th century. In 1897, Joseph John

Thomson measured the charge-to-mass-ratio (e/m) of cathode ray particle using deflection

in both electric and magnetic field. He discovered that the cathode ray particle turned out

to be 2000 times lighter than hydrogen (the lightest atom). This discovery, for the first

time, showed that atoms are not the indivisible particles of matter. With the discovery

of electron, J.J. Thomson incorrectly postulated the “plum pudding model” assuming the

negative-charged electrons were distributed throughout the atom in a uniform sea of positive

charge.

In 1919, with the help of Hans Geiger and Ernest Marsden, Ernest Rutherford

devised an experiment that observed the deflection of alpha particles bombarded at a thin

sheet of metal foil [17]. He expected that the positively charged alpha particles would pass

straight through the foil with little deflection if “plum pudding model” was correct. However,

Geiger and Marsden spotted that some alpha particles deflected at very large angles as shown

in the left panel of figure 1.1. Considering the mass of an alpha particle is about 8000 times

that of an electron, Rutherford realized that the mass of the atom must be concentrated

1

Figure 1.1: The schematic showing the “plum pudding model” proposed by J.J. Thomason
(left) and the model proposed by Rutherford (right) after his discovery experiment that
showed back scattering of alpha particles. Alpha particles penetrating atoms are represented
by horizontal black arrow. Blue circles represents electrons and red area shows the region
with positive charge. The sizes of electrons and nuclei are not drawn in scale.

at a small point with positive charge. Almost all of the mass of an atom is located in the

nucleus, with a very small contribution from the electron cloud. The radius of the atom can

be from about 20,000 (uranium) to 60,000 (hydrogen) times bigger than the nuclear radius,

which means the density of nucleus is extraordinarily high, in the order of 1017 kg/m3.

The atomic nucleus composes of even smaller constituents. Every nucleus consists of

protons and neutrons. In experiments that impinge alpha particles into pure nitrogen gas,

scintillation detectors showed the signatures of typical hydrogen nuclei as a product.

In

1919, Rutherford interpreted this observation as the process of alpha particle knocking a

hydrogen nuclei out of nitrogen. After observing Blackett’s cloud chamber images in 1925,

Rutherford realized that the actual process was the opposite case: the alpha particle is first

2

Thomson ModelRutherford Modelcaptured by nitrogen, then a proton is emitted and an oxygen nucleus is left. This was the

first reported nuclear reaction: 14N + α = 17O + p. Several years after the discovery of

proton, in the year of 1930, Walther Bothe and Herbert Becker found that an unusually

penetrating radiation was produced when energetic alpha particles were ejected on certain

light elements such as beryllium, boron or lithium. In 1932, James Chadwick determined

that this new type of radiation was not gamma rays but uncharged particles with about

the same mass as the proton [18]. These particles are neutrons. Nuclear strong force binds

protons and neutrons together against the repulsive electrical force between the positively

charged protons. Studying the inner structure and interaction of such matter constituting

of neutrons and protons is the topic of nuclear physics.

1.2 Nuclear Equation of State

People have been attempting to understand nuclei through a variety of models such as

liquid drop model (LDM) [19], droplet model (DM) [20], Thomas-Fermi model and density

functional methods [21]. Here I will discuss the LDM, the simplest one among them. It was

first proposed by George Gamow and further developed by Niels Bohr and John Archibald

Wheeler [19]. This model was first formulated in 1935 by German physicist Carl Friedrich von

Weizsacker. Based on the short range nature of the nuclear interaction and the saturation

property of nuclear matter, LDM treats the nuclei as macroscopic drops of incompressible

fluid of nuclear matter [22].

In LDM, the nuclear binding energy (the minimum energy

required to completely disassemble a nucleus into separate protons and neutrons) of a nucleus

3

of protons Z, neutrons N and mass A=Z+N is written as:

B(A, Z) = avA + asA

2
3 + ac

Z2
1
3

A

(N − Z)2

A

+ aa

+ O(A, Z)

(1.1)

The first term with av is the volume term: the binding energy is proportional to the volume

of the nuclei, so it is also proportional to the mass A, the total number of nucleons. The

second term with as is a correction to the volume term: the strong force that binds the

nucleons together has a very limited range and a nucleon only interact strongly with its

closest neighbors. Therefore, the nucleons on the surface of the drop has less neighbors

to interact with, thus reducing the binding energy. The third term starting with ac takes

the Coulomb repulsion between protons into account. The next term with aa is known

as the asymmetry term. Based on the Pauli exclusion principle, no two identical fermions

can occupy the same quantum state within a quantum system simultaneously. Consider a

nucleus with imbalanced number of protons and neutrons, e.g., with more neutrons (N > Z),

neutrons have to occupy higher single particle energy levels than protons, reducing its binding

energy, when compared to a nucleus with equal number of protons and neutrons (N = Z).
We call the excess in the proton or neutron number as the isospin asymmetry δ = N−Z
Z .

The last term O(A, Z) is called pairing term to refine the model. Due to Pauli principle, a

nucleus would have lower energy if the number of protons with spin up equals to the number

of protons with spin down.

To describe the collective state of a macroscopic system such as neutron star, we must

move beyond the liquid drop model. Nuclear equation of state (EOS) is used to describe

the relationship between pressure, temperature, energy, and density of the system. Nuclear

EOS can be approximately expressed (at zero temperature) in terms of the sum of energy

4

from a term that describes the symmetric nuclear matter with equal densities of neutrons

and protons and energy from an asymmetric term consisting of nuclear matter with different

densities of proton and neutron:

E(ρ, δ) = E(ρ, δ = 0) + S(ρ)δ2

(1.2)

Isospin asymmetry δ here is more generally written as:

ρn − ρp
ρn + ρp

δ =

(1.3)

where ρn and ρp is the density of neutron and proton. We call the later term S(ρ)δ2 the

symmetry energy. It is approximately the energy cost of converting symmetric nuclear matter

into pure neutron matter. Nuclear EOS governs many fundamental properties of the nuclear

matter and plays a crucial role in understanding not only terrestrial nuclei and nuclear

reaction process, but also the evolution of nuclear structure and many astrophysical objects.

Over the last four decades, much knowledge about the E(ρ, 0) term in Eq. 1.2, which is the

EOS of symmetric nuclear matter, has been obtained through the hard work of scientists in

both nuclear physics and astrophysics [23].

In more recent years, significant efforts have been taken to explore the relatively poorly

known S(ρ). The symmetry energy plays a fundamental role especially in the stability

of neutron stars. The pressure that supports the neutron star against the collapse from

gravitational force, mainly comes from the symmetry energy [24]. It also strongly influences

neutron star structure, radius, moment of inertia, cooling process and prevents the collapse

of a neutron star into a black hole [25, 26, 27, 28, 29, 30]. The first observation of a neutron-

5

star merger event in 2017, GW170817 (GW), has provided new insights to the equation of

state of neutron star [31, 32, 33, 34, 35, 36]. Much progress has been made in constraining

the two coefficients S0 and L in the Taylor expansion of S(ρ) around the saturation density

ρ0 (0.16 nucleon/fm3):

S(ρ) = S0 +

(ρ − ρ0) +

L
3ρ0

Ksym
18ρ0

(ρ − ρ0)2 + O((ρ − ρ0)3)

(1.4)

Constraints of S0 and L at sub-saturation density was obtained through various types of

laboratory experiments including excitation energies of Isobaric Analog States (IAS) [37],

Pygmy Dipole Resonances (PDR) [38, 39, 40], atomic mass analyses [41, 42], electric dipole

polarizability [43, 44], neutron skin thickness of heavy nuclei [45] and isospin diffusion in

heavy ion collision [46, 47, 48, 49, 50].

While much knowledge is obtained about S(ρ) at sub-saturation density, the high density

behavior of S(ρ) remains rather uncertain. A set of Skyrme parameterizations, which is

selected based on the fit of binding energy difference between 100Sn and 132Sn nuclei, gives

very different predictions about the energy per nucleon in pure neutron matter at densities

above saturation density [3]. Figure 1.2 shows that the uncertainties remain large when S(ρ)

with ρ > ρ0 with selected Skyrme interactions from Ref. [2]. For simplicity, it is common to

write the density dependence of S(ρ) in the following form:

S(ρ) = Skin(

ρ
ρ0

2
3 + Sint(

)

)γ

ρ
ρ0

(1.5)

The first term with Skin is the Thomas-Fermi kinetic energy. In a uniform system of Fermions

of spin S = 1

2 in 3 dimensions, the relationship between Fermi momentum kF and the

6

Figure 1.2: Density dependence of the symmetry energy from the Skyrme interactions used
in Ref. [2].The shaded region is obtained from HIC experiments. Picture is adopted from
Ref. [3].

density ρ is: kF = 3πρ3. Then the kinetic energy is proportional to the square of the

Fermi momentum kF

2. Overall, the kinetic energy part in S(ρ) depends on ρ

2
3 . The second

term with Sint is the interaction energy term. It is modeled to have power law of density

dependence with factor γ. The value of γ is usually chosen between 0.5 to 2. The symmetry

energy is “soft” when γ < 1 and “stiff” when γ > 1.

It is worth mentioning that the symmetry energy S(ρ) is closely related to the neutron-

proton effective mass splitting. From the Fock exchange term, finite range and correlation

effects, the nuclear mean-field potential has momentum dependencies [51, 52, 53, 54]. The

concept of effective mass was introduced to simplify the description of nucleons that are

moving in a momentum-dependent mean-field potential. Consider the following Hamilton’s

7

Equation for a nucleon:

˙x =

=

∂H
∂p
p
m

+

∂V
∂p

Define the effective mass m∗ such that:

˙x =

p
m∗

Combine Eq. 1.7 and Eq. 1.8, we have:

m∗
m

=

1
1 + m
p

∂V
∂p

(1.6)

(1.7)

(1.8)

(1.9)

Nucleons can be described as moving with their effective masses, instead of with their free
masses in a momentum-dependent potential. An isoscalar effective mass m∗
the mean-field potential with m∗

s is derived from
≈ 0.65 − 0.75 where mN is the nucleon mass [7, 55]. Due

s
mN

to the momentum dependencies in the isovector mean-field potential, the effective masses for
neutron m∗

p are different from each other [52], resulting in the effective mass

n and proton m∗

splitting:

∆m∗

np =

m∗
n − m∗
mN

p

(1.10)

Based on the well-known Lane potential [56], the single nucleon potential Vτ (ρ, k, δ) in

8

Equ. 1.9 can be well approximated by:

Vτ (ρ, k, δ) = V0(ρ, k) ± Vsym(ρ, k) · δ

(1.11)

where the V0(ρ, k) is the nucleon isoscalar potential and Vsym(ρ, k) is the isovector (sym-

metry) potential for nucleons with momentum k and isospin asymmetry δ at density ρ.

τ = n for neutrons and τ = p for protons. With the isoscalar asymmetry δ considered,

equations 1.10 can be written as:

∆m∗

np =

(1 +

mN
¯h2kF
mN
¯h2kF

(dVp/dk − dVn/dk)

dVp/dk)(1 +

mN
¯h2kF

dVn/dk)

(cid:12)(cid:12)(cid:12)(cid:12)kF

(1.12)

For practical systems, δ is small and can be neglected in the denominator, but the leading

order term in the numerator is proportional to δ. So to a good approximation:

∆m∗

np ≈ −2δ ·

= −2δ · (

dVsym

mN
¯h2kF
dVp/dk)(1 +

dk

mN
¯h2kF

dVsym

dk

)

mN
¯h2kF

(cid:12)(cid:12)(cid:12)(cid:12)kF

dV0
dk )2

mN
¯h2kF
)2 · (

(1 +
m∗
s
mN

(cid:12)(cid:12)(cid:12)(cid:12)kF

(1.13)

(1.14)

Here, m∗

s is the nucleonic effective mass in symmetric matter, where Vsym vanishes. On

the other side, the symmetry energy Esym(ρ) and its slope L(ρ) can be expressed as:

Esym(ρ) =

L(ρ) =

1
3

2
3

¯h2K2
F
2mN
¯h2K2
F
2mN

+

+

1
2

3
2

Vsym(ρ, kF )

Vsym(ρ, kF ) +

∂Vsym

∂k

(cid:12)(cid:12)(cid:12)(cid:12)kF

kF

(1.15)

(1.16)

Combining equations 1.12 to 1.16, the effective mass splitting depends on asymmetry δ

9

in such form [57]:

∆m∗

np ≈ δ ·

3Esym(ρ0) − L(ρ0) − 1
mN
m∗
3
0
mN
m∗
)2
0

EF (ρ) · (

EF (ρ0)

(1.17)

where m∗0 = 0.7mN at normal density.

This effect influences the magnitude of shell effects in nuclei far from stability and some

properties of neutrons star especially the cooling process via neutrino emission [58, 59].
However, both the sign and magnitude of the effective mass splitting ∆m∗

np are poorly

determined. Different Skyrme parameterizations contained different effective mass splitting.

Moreover, some microscopic calculations performed in Landau-Fermi-liquid theory [60] and
the nonrelativistic Brueckner-Hartree-Fock approach [61] have predicted that m∗

n > m∗

p

while other calculations using relativistic mean-field theory and relativistic Dirac-Brueckner
theory [52, 62] predict that M∗

p . Additional experimental data and theoretical studies

n < M∗

are urgently needed to resolve this issue.

1.3 Probing Effective Mass Splitting in Heavy Ion Collision

Heavy Ion Collision (HIC) is one of the main tools used to explore the density dependence

of the symmetry energy and the momentum dependence of the symmetry potential. A large

range of densities can be obtained in HIC by choosing different projectile-target systems [63,

64, 65] and bombarding energies. In the energy above the Fermi energy but below around

150 MeV per nucleon, nucleons that participate in the collision first form a compressed,

high-density region, then expand with the emission of light clusters. The emitted particles

carry the information of nuclear symmetry energy because the motions of ejected particles

10

are determined by the nuclear interaction during such compression-expansion process. The

measurements of particles emitted from HIC include neutron/proton yield ratio spectra and

isospin diffusion. This strategy has been successfully applied to constrain the symmetry

energy at sub-saturation density using Sn+Sn collisions [64, 66, 47, 67, 68, 69].

Transport models that take EOS as an essential input is used to interpret the results

measured in HIC and to constrain EOS quantitatively. Calculations performed in trans-

port models have been successful in describing observables in HIC such as isoscaling ratios

and elliptic flow [50, 70]. Calculations typically employs a set of parameterizations such as

Skyrme interactions that characterize the density dependence of the nuclear matter energy

including the symmetry energy. Aside from the density dependence of the symmetry en-
ergy, other inputs such as neutron-proton effective mass splitting ∆m∗

np that results from

a momentum-dependent mean-field potential and in-medium nucleon-nucleon cross sections

δN N also impact the propagation of nucleons in collisions. Results from transport model

calculation predict that neutrons with high momentum emitted from the compressed par-

n < m∗

n < m∗

p and calculations using

p, compared to protons with same momentum [4, 22]. This effect will enhance

ticipant region will experience a more repulsive potential thus a higher acceleration process
if m∗
ratio of neutron over proton (n/p) at high momentum for m∗
m∗
n > m∗

p give predictions that the acceleration of protons are enhanced, resulting in a lower

n/p spectral ratio.

If we use M to represent the multiplicities for a certain particle, the

differential yield defined as Y (n) = dMn

dE and Y (p) =

dMp
dE and the spectral yield ratio of n/p

is written as:

Rn/p =

Y (n)
Y (p)

=

dMn/dE
dMp/dE

(1.18)

11

Eq. 1.18 is called “single ratio”. Another observable is defined as “double ratio”:

DR(n/p) =

(Rn/p)system1
(Rn/p)system2

(1.19)

which takes the ratio of single ratios from two reaction systems. Double ratio is commonly

used to take the advantage of cancellation of systematic errors which are difficult to determine

experimentally such as detector efficiencies and to a certain extent, inadequacies in models.

such as the Coulomb effects and clustering mechanisms.

Figure 1.3 shows simulation results of Rn/p and DRn/p using Improved Quantum Molec-

ular Dynamics (ImQMD) model [71, 72, 73] with two Skyrme interaction parameter sets,
SLy4 [74] and SkM∗ [75]. SLy4 and SkM∗ have similar symmetry energy coefficient S0, slopes
of symmetry energy L and isoscalar effective mass m∗, i.e., S0 = 32 ± 2MeV, L = 46MeV
and m∗/mN = 0.7 ± 0.1. However, the effective mass splitting is different with m∗
n < m∗
for SLy4 and m∗
p for SkM∗. In figure 1.3, DR(n/p) is roughly flat or decrease slightly
with nucleon kinetic energy for SkM∗ while they increase for SLy4. The sensitivity of the

n > m∗

p

DR(n/p) to effective mass splitting decrease with greater incident beam energies due to in-

crease in nucleon-nucleon scattering [4]. These calculations suggest incident energy less than

200 MeV is best for the effective mass splitting study.

1.4 Neutron Detection

Neutron detection is very difficult and this is why the discovery of neutron was relatively

late in 1932 by Chadwick. Unlike protons and other charged-particles, neutron has no

electric charge and does not interact with other particles through electromagnetic force.

12

Figure 1.3: (top panels) Y(n)/Y(p) ratios as a function of kinetic energy for 124Sn+124Sn
at b=2fm. (bottom panels) DR(n/p) ratios as a function of kinetic energy. From left to
right, the beam energies are 100 MeV, 150 MeV, 200 MeV, 300 MeV per nucleon. Figure is
adopted from Ref. [4].

Neutrons are stable when bounded in nuclei. However, as a free particle, neutron beta decays

with a half-life of about 880 s. It primarily interacts with other particles by strong force

(hadronic interaction), which is much stronger than electromagnetic interaction but with

very limited range of a few fermi. As neutral particles, neutrons do not ionize directly and

their paths are weakly affected by electric and magnetic fields. They are usually detected by

nuclear interactions that produce secondary charged-particles with relatively low interaction

probability. Because the nuclear force has extremely short range, neutrons need to be very
close within around 10−15 m of another nucleus in order for scattering to take place. Given

13

the radius of a nucleus is at least 10,000 times smaller than the radius of an atom, the

probability of neutrons interact with normal material is relatively low. Thus, the detection

of neutrons represents a considerable technical challenge.

The energy of neutrons to be detected can vary from below meV (milli-electron volt)

called ultracold neutrons up to more than TeV (Tera-electron volt) which are mainly created

in large accelerators or in certain astrophysical activities. Neutrons are commonly classified

according to their energies as listed in the following table [1]:

Designation
Ultracold neutrons
Cold neutrons
Thermal neutrons
Epithermal neutrons
Intermediate neutrons
Fast neutrons
High-energy neutrons

Neutron Energy
< 0.2 meV
0.2 meV - 2 meV
2 meV - 100 meV
100 meV - 1 eV
1 eV - 10 keV
10 keV - 20 MeV
> 20 MeV

Table 1.1: Neutron designation table for different energy ranges. This table is adopted from
Ref. [1]

Neutrons at different energy range require different detection techniques. The energy

range of neutrons we measured in our experiment is from tens of MeV to a couple hundred

MeV; the fast and high energy neutrons. The principles of detection of fast neutrons are

based on ionizing radiation. Because neutrons do not directly ionize in material, charged-

particles need to be induced by neutrons first, and then the energy of charged-particles are

converted into different types of signal through ionization processes. The main interactions of

neutrons with nuclei are the following three processes: elastic scattering, inelastic scattering

and radiative neutron capture [1]. The most important process for such neutrons is elastic

scattering on light target nuclei, especially elastic n-p scattering due to the higher cross-

sections compared to other reaction channels, as shown in figure 1.4.

14

Figure 1.4: Neutron reaction cross sections adopted in SCINFUL-QMD model. Picture is
adopted from Ref. [5].

Popular types of neutron detectors include gas-filled detectors, semiconductor and scintil-

lators [76]. Organic plastic and liquid scintillators composed of large percentage of hydrogen

are widely used in neutron measurement. Not only are they fast detectors, a requirement

for Time of Flight (ToF) measurement to determine the energy of the detected neutrons,

but they are robust and relatively cost effective to build a large detector like LANA. Since

recoiling protons is the dominant neutron interaction in scintillators, neutrons and charged-

particles emitted from nuclear reaction cannot be distinguished from the light they produced

in the scintillator. This is why we designed and built a thin plastic scintillator wall which

has 1% neutron detection efficiency and 100% charged-particle detection efficiency. It will be

placed in front of existing Large Neutron Area Array (LANA) at NSCL to provide extra in-

formation in order to distinguish and veto charged-particle events from neutrons detected in

LANA. This wall is called Charged Particle Veto Wall (VW) and its detail will be presented

15

in Chapter 2.

1.5

Improvements from Previous Experiment

Due to difficulties in measuring neutrons, few experimental data on neutron and protons

yield or spectra ratios exist. In 2009, the HiRA group measured the neutron and protons

spectra emitted from Sn+Sn reactions

[6, 7]. Conclusions from that study regarding the

effective mass are ambiguous both due to quality of the data. In the current experiment,

We studied smaller, near symmetric reaction systems such as Ca+Ni and Ca+Sn to allow

extensive calculations with CPU intensive transport models such as the AMD models which

have sophisticated treatment of cluster production. We also study very asymmetric systems

such as Ca+Sn to study the in-medium NN cross sections. Based on experience with previous

experiments, we have also made major improvement in the experimental setup regarding

detection of charged particles and the neutrons. The work of this thesis mainly focuses on

the improvement made in neutron detection while the thesis of Sean Sweany focuses on the

improvement in detecting charged particles in this experiment.

Fig. 1.5 shows the DR(n/p) spectral double ratios measured in previous experiment on

central collisions of 124Sn+124Sn and 112Sn+112Sn systems at E/A=120 MeV. The red

and blue shaded bands correspond to the predictions from ImQMD using SLy4 and SkM*

interactions. As expected the results split starting at center of mass energy of the nucleons

around 50 MeV/u. Unfortunately due to limitation of the charged particle detector, the

data does not extend beyond 80 MeV/u in the center of mass energy. The large statistical

uncertainties mainly arise from contamination of charged particles in the neutron spectra due

to deficiencies of the old veto arrays. Because of the difficulties for most transport models

16

Figure 1.5: neutron/proton double ratio for 124Sn +124 Sn/112Sn +112 Sn reaction systems
at 120 MeV/u for central collisions. The symbols are experimental data. Red line shows
calculation using SLy4 which has m∗
p while blue line comes from calculation using
SkM∗ which has m∗
p. The picture is adopted from Ref. [6]. Open circles are the
original version and the close circles are data of the most updated version. The original data
points did not take into account the efficiency corrections for charged-particles [7, 8].

n > m∗

n < m∗

17

in producing the relative abundances of light isotopes in HIC, instead of comparing free

neutrons and protons spectra, we use the observable the coalescence invariant (CI) neutron

and proton spectra by combining the free nucleons with those bound in light isotopes with

1<A<5 are calculated according to Ref. [6]. The open and closed symbol correspond to

data before and after correction to the charged particles due to reaction loss in the detector.

Before the corrections were applied, the data (open points) seem to be more consistent with

the SLy4. After the corrections, the data appear to be more consistent with the SkM* even

though both sets of double ratio data are within experimental uncertainties. The observable

double ratios work as designed that most of the systematic errors are cancelled out. The

residual errors are associated with the construction of coalescence invariant of the neutron

and proton yields that involve clusters. Subsequent efforts to use Bayesian analysis [7] failed

to extract a definitive conclusion on the sign and magnitude of the effective mass splitting.

However, the previous experiment paved a path forward to measure the neutron to proton

ratios using the HiRA and LANA arrays.

To improve the design of the previous experiment, we need to:

1. Improve the quality of the neutron spectra and the statistical errors so that we can

construct the free neutron/proton ratios rather than relying completely on the coalescence

invariant of the n and proton yields. At high nuclear energy, contribution of the clusters

on the n/p ratios are minimal since the production cross-sections of clusters drop off much

faster than neutron and protons. Thus at high energy, the free n/p ratios can be compared

to the n/p ratios from models. This is the subject of this section.

2. Extend the energy spectra of the charged particles to the high energy region where

the effective mass splitting effects becomes larger. The improvements of charged-particle

measurements including extending the length of crystal to allow the detection of higher

18

energy charged-particles and correction of reaction losses in the detector will be detailed in

Sean Sweany’s thesis.

To improve neutron detection from previous experiment, we must understand the prob-

lems. The top panel of Fig. ?? shows the layout of full setup in previous experiment and

the bottom panel is the image of veto arrays (left) and veto paddles (right) used to veto

charged-particles in the forward angle LANA wall and backward angle LANA wall respec-

tively. The forward angle veto arrays are made of 13 BC-408 scintillator bars of 3/8 inch
thickness. Each bar is a 2.35×27.4 cm2 rectangular. The backward angle veto array consists
of four 16×16 cm2 square BC-408 scintillator paddles. The forward LANA covers angles
from 7° to 29° while the backward LANA covers angles from 34° to 59°.

The forward veto array covers the angle from 8° to 30° in lab frame so the edges of

forward LANA are not well covered. There were also several gaps between veto paddles

shadowing the backward LANA. These problems can be partly rectified by excluding the

exposed edges and gaps in the offline analysis. The major problem is the long distances

(more than 5 meters) between the veto arrays/paddles and the neutron walls. Because of the

coarse granularity of veto position resolutions, the one-to-one charged-particle hit correlation

constructed for the hits on veto arrays/paddles and the LANA is ambiguous. This means

for events with both neutrons and charged-particles hitting the LANA, we were not able

to identify charged-particles based on their hit positions on veto arrays/paddles. Therefore,

for high multiplicity events, we needed to either abandon the whole events or tolerated the

charged-particle contamination (this is especially true for the forward veto array because

every event is accompanied by at least one charged-particles hitting it). Considering LANA

detecting charged-particle at 100% efficiency and neutron at less than 10%,even a 90% vetoing

accuracy is not acceptable. Figure 1.6 shows the charged-particle contamination over a wide

19

Figure 1.6: Neutron Wall light vs TOF, where TOF is the time of flight for the observed
particle to travel to the neutron walls. The prompt γ ray peak, charged-particle punch-
through, and charged particle stopping PID lines are marked. Picture is adopted from
Ref. [9].

region of the neutron spectrum in that experiment.

20

To completely veto the charged particles from the neutron detectors, we designed and

constructed a large Charged-Particle Veto Wall to be placed about 0.5 m in front of LANA,

the closest distance that is mechanically feasible. This new veto wall was designed to fully

cover LANA without gaps. Moreover, instead of the forward-backward wall configuration

(Figure ??) we used in previous experiment, we focus on detecting neutrons in one angle,

around 90 deg in the center of mass. The nesting of both walls increase our efficiencies by

nearly a factor of two.

1.6 Organization of Dissertation

The rest of this thesis is organized as follows. Chapter 2 provides the details of experimental

setup used in experimental campaign during February and March of 2018 at NSCL. The ex-

perimental setup consists of Microball, HiRA10, LANA, Forward Array and Charged-Particle

Veto Wall, the last of which was designed and constructed specially for the experiments. This

thesis mainly focuses on the neutron wall detector with the veto wall and the forward array.

Analysis of charged particles from microball and HiRA10 is the thesis topic for another stu-

dent, Sean Sweany. Chapter 3 details the analysis with LANA and the energy calibration of

the Charged-Particle Veto Wall. A calibration method using high-energy muons produced

in cosmic ray showers to calibrate the position, time and light output of LANA is described.

Chapter 4 presents the results of the analysis. Finally, Chapter 5 contains the summaries

and conclusions.

21

Chapter 2

Experimental Details

The experimental campaign took place from the beginning of February to the end of March

in 2019 at NSCL S2 vault. K1200 cyclotron produced 40Ca and 48Ca beams at E/A =

56 MeV and 140 MeV which were incident on 58Ni, 64Ni, 112Sn and 124Sn targets. The

thicknesses of these four targets are: 5.0 mg/cm2 for 58Ni, 5.3 mg/cm2 for 64Ni, 6.1mg/cm2
for 64Ni and 6.47mg/cm2 for 124Sn. There are 2 (beam isotopes) × 2 (beam energies) × 4

(targets) = 16 reactions in the experiment. Targets are located at the center of a thin-wall

aluminum chamber. The experimental setup consists of the the following five main detector

systems: (1) Microball, for impact parameter determination (2) HiRA10 (High Resolution

Array with 10 cm long CsI crystals), for measuring charged-particles (3) Forward Array, for

reaction start time determination in Time of Flight (ToF) technique to measure the energy

of neutrons (4) LANA (Large Area Neutron Array), for neutron detection, providing stop

time in ToF method. (5) a large Charged-Particle Veto Wall placed in front of LANA to

veto charged-particles in offline analysis.

Figure 2.1 shows a picture of experimental setup taken right after the experiment cam-

paign finished and with the lid of the vacuum chamber removed. Each detector system is

labelled. Figure 2.2 shows the top view of the relative positioning of every detector systems.

The remainder of this chapter details the design of each detector system.

22

Figure 2.1: Experimental setup overview. Microball, Forward Array and HiRA10 are placed
inside a vacuum chamber. The target is inside the Microball at the center of the chamber.
The lid of the vacuum chamber is removed for this picture.

23

Figure 2.2: A schematic showing the experiment setup. It is a not-to-scale version of Fig-
ure 2.25.

24

VWNWBNWABeam LineHiRA10NSCL S2 VaultTargetMicroballForward ArrayFigure 2.3: Schematic diagram showing a vertical section of the Microball. The CsI(T1)
crystals are shown in grey. The blue trapezoids behind crystals are light guides. The beam
enters from the left. The numbers 1,2,3,to 9 are the ring numbers. The polar angular
coverage for each ring are also shown together with the number of crystals contained in each
ring. This picture is adopted from Ref. [10].

25

Figure 2.4: Ten microball detectors removed to allow charged particles emitted in reactions
to be detected by HiRA10 without materials without going through blocking materials. The
beam enters from left.

26

2.1 Microball

The original Microball, on loan from Washington University at St. Louis, is made of 95

CsI(T1) crystals arranged in nine rings with increasing forward segmentation [10]. These

crystals are closely packed to cover the angular range 4.0°-172.0° as shown in figure 2.3 and

figure 2.5. Crystals on rings are made of CsI with high thallium concentration (1200ppm).

The thickness of each CsI varies from 3.66 mm (Ring #9) to 9.85 mm (Ring #1). To protect

the crystals from light, their front surface are covered by a thin 0.9 mg/cm2 Al foil. Since a

lot of delta electrons are emitted in heavy ion collisions, the front of each crystals are also

covered with high Z materials: Sn/Pb foils. The thickness of Sn/Pb foils vary from 73.5

mg/cm2 for the most forward Ring #1 to 9.8 mg/cm2 for the most backward ring #9.

At the Coupled-Cyclotron Facility (CCF), beams (even for stable beams such as 40Ca

and 48Ca) are produced as secondary beams. Secondary beams from cyclotrons have large

emittance resulting in large beam spot. For this experiment, typical beam spot size is 10

mm accompanied with a large beam halos. To protect the crystals in Ring #1 and Ring #9

from being hit by the beam particles especially those in the beam halo, we removed these

rings in the experiment. Ring #6 at polar angle 90 ° is removed to accommodate the target

structure. The targets are mounted on a target ladder as shown in figure ??. The bottom of

the target ladder is attached on a vertical stainless steel rod which is half inside the chamber

and half outside the chamber. By pushing or pulling this stainless steel rod from outside

the bottom of the chamber, the height of target ladder can be adjusted so that different

targets can be aligned with beam. Removal of ten crystals, four from ring #3, three from

ring #4 and three from ring #5 allows particles to be detected directly by HiRA10 as shown

in Figure 2.6. Each HiRA10 telescope is represented by the red ”squares” in the figures. To

27

Figure 2.5: The target ladder used in the experiment.

28

create the opening for HiRA10, new mounts in the shape of a ”C” than full circles must be

designed to hold the remaining crystals in each ”ring”. The designs of these rings are very

complicated and expensive to machine.

Instead, we 3D-printed using VeroWhite, a very

dense polyjet 3D printing materials. The choice of the materials is very important as these

3D parts are placed in the chamber so they must not outgas into the vacuum. In addition,

the quality of printing is also critical to prevent mciro-bubbles that may trap gas during the

printing process. The 3D printing precision we used is better than 0.05 mm (600 DPI) which

ensures the accuracy of the prototyping.

Unlike protons, the cross sections for neutron interacting with Microball crystals is esti-

mated to be less than 5% based on the density and thickness of crystals. Thus, no crystals

are removed on the opposite side of HiRA to allow neutrons to be detected by LANA un-

blocked by the Microball crystals. In any case, it would be very difficult to fabricate a strong

structure consisting of only two arcs to support the top and bottom detectors.

2.2 HiRA10

HiRA10 is an updated version of HiRA (High Resolution Array) [77]. While the original

HiRA with 4 cm CsI crystals is well suited for experiments with low energy charged-particles,

it is not able to measure the energy of high energy charged-particles produced in our experi-

ment. For high energy light charged-particles such as protons, deuterons and tritons, limited

to the 4 cm length of CsI(Tl), they will punch through HiRA crystal and deposit only a

small portion of their kinetic energies. With longer crystal length, HiRA10 can measure

protons with kinetic energy up to 200 MeV, compared to 116 MeV for the original HiRA.

The design of HiRA10 is based on modular strip Si-CsI telescopes which have been widely

29

Figure 2.6: Angular coverage for Forward Array, Microball, HiRA10 and LANA in lab Φ-Θ
coordinates. The dashed blue rectangle represents the coverage of the Forward Array, green
regions represent Microball, red regions represent twelve HiRA10 telescopes arranged in 4
towers, and the purple region represents LANA coverage. Ten crystals in total are removed
on Microball ring #3, #4 and #5 leaving a direct path for the fragments to be detected
by HiRA10. There is no such accommodation for LANA. Microball ring #6 is removed for
target structure. The Microball covers part of the forward array from Θ = 13° to Θ = 28°.
In the adopted co-ordinate from 0 and 360 deg, the coverage of LANA is split at 0 and
360 degree (top panel). The bottom panel shows LANA in continuous angular coverage by
plotting the φ range from -60° to 300°.

30

MicroBallLANAHiRA10Forward Array-50MicroBallLANAHiRA10Forward Arrayadopted by the physics community in the past two decades to detect charged particles in

nuclear structure and nuclear reaction experiments. The Si-CsI telescopes utilize the energy

loss technique [12, 77] includes LASSA [78], MUST2 [79] and FARCOS [80].

The upgrade design and testing of HiRA10 was mainly done by Sean Sweany, who will

describe HiRA10 in details in his thesis. In this thesis, only a brief description of HiRA10

is given to allow a self-contained description of the experiments. HiRA10 consists of twelve

identical telescopes grouped into three towers with four telescopes in each tower as shown in

figure 2.8. Each HiRA10 telescope is composed of a 1.5 mm double sided Si strip detector

(DSSSD) backed by four 10 cm CsI scintillator crystals as shown in figure 2.7. The increase

from 4 cm to 10 cm CsI crystals to allow detection of protons up to 200 MeV is the main

upgrade designed specifically for this experiments. Both the front and back side of each

DSSSD have 32 strips. Every strip is 1.95 mm wide and the strips on the front and back are

perpendicular to each other, allowing for high resolution position measurements of events.

Given the width of every strip, the angular resolution for HiRA10 at 35 cm is 0.32°. Taking

the uncertainties from beam spot into account, the angular resolution is better than 0.5° [12].

For a particle that is fully stopped in the CsI crystal, the correlation between the energy

deposited in DSSSD and the residual energy deposited in corresponding crystal can be used

to identify the mass and charge of this detected particle. This particle identification method

is called energy loss technique. Figure 2.9 is an example showing the result of energy loss

technique, which is produced by 16 strips, front and back, in one quadrant of one HiRA10

telescope and their corresponding CsI crystal. The energy calibration for DSSSD was care-

fully done with 232U α source which has 4 peaks with energies spanning from 5.41 MeV to

8.58 MeV. The energy calibration for CsI crystal is based on proton-recoil scattering data

with punch-throughs of p,d,t and low energy elastic scattering of protons on 40,48Ca targets

31

Figure 2.7: (Left panel) A mechanical drawing of a HiRA10 telescope with its aluminum
container and associated electronics. The DSSSD (not shown) is placed in front of CsI
crystals. (Right panel) A schematic drawing of a HiRA10 telescope showing the front and
back sides of the DSSSD placed in front of the 4 CsI crystals.

32

CsI(Tl) CrystalDouble Sided Silicon StripPhotodiode preamplifier boardLight guideCluster of 4 CsIcrystalsat incident energies of 28 MeV/u, 56.6 MeV/u, 39 MeV/u and CH2 target at incident energy

of 139.8 MeV/u. The relevant details can be found in Ref. [12].

2.3 The Large Area Neutron Array (LANA)

Despite recent advance in new scintillation materials, liquid scintillator is still the most cost

effective way to build large area neutron detectors. The Large Area Neutron Array (LANA) is

composed of two large neutron walls. Each wall consists of 25 independent neutron detection
bars that cover a total area of 2×2 m2. The scintillator bars are horizontally stacked as

schematically shown in Figure 2.10. Taking into account the thickness of the Pyrex glass (3
mm) and a gap of 3 mm between bars, the total active geometrical area of the 2×2 m2 wall

is reduced by about 12% [13]. To maximize detection efficiency, the LANA features small

dead space between scintillators and minimum inactive mass through which the neutrons

must pass [13].

Each detector cell is a 2m-long Pyrex glass container, with a rectangular cross section of

NE-213 with height h = 7.62 cm on the vertical direction and depth w = 6.35 cm as indicated

in the upper corner of Figure 2.10. Both ends of each Pyrex bar are coupled with 7.5 cm

diameter Philips Photonics XP4312B/04 photomultipliers (PMTs), to detect the scintillating

light produced in the bar by an incident radiation. Typical high voltage employed on PMTs is

2200 volt. Each cell is filled with liquid organic scintillator NE-213 [81]. NE-213 was chosen

for its excellent efficiency for detecting fast neutrons and its pulse shape discrimination

(PSD) properties that enable the discrimination between neutrons and gamma-rays [82, 16].

Liquid scintillator that has PSD characteristic is especially desirable for heavy-ion collision

experiments where copious photons and neutrons are produced and must be identified in

33

Figure 2.8: (Left panel) 12 HiRA10 telescopes arranged in 3 towers used in the present
experiments. The mounts are designed in approximately in an arc so that the center of
each telescope is located at 35 cm from the target. (Right panel) Angular coverage of 12
telescopes in HiRA10 on a (θ, φ) plane measured by Romer arm technology [11]. Each point
represents a DSSSD (1.95mm × 1.95mm) pixel.

34

Phi (deg)Theta (deg)01234567891011Figure 2.9: Particle identification of a HiRA10 telescope. The Y axis is the calibrated DSSSD
energy loss (∆E) versus the ADC channels of the residual energy (E) in the CsI 2D plot.
The top right inset shows an extended plot up to 120 MeV of energy loss in DSSSD. Red
lines are PID lines from simulation for various isotopes. This figure is adopted from Ref. [12].

35

Figure 2.10: Mechanical cutaway drawing of one wall of the Large Area Neutron Array. [13]

36

data analysis. The LANA is designed to detect neutron from about a couple MeVs to about

300 MeV when it is placed at 4.5 meters from the target.

The physical location of each bar is determined by laser measurements made on the sur-

face of the wall with respect to a global reference frame in the Facility for Rare Isotope Beams

(FRIB) Laboratory [14]. Such measurements allow one to determine not only the absolute

position of each bar with respect to the target during an experiment, but also the relative

positions between bars of each wall, which is relevant for the time calibrations described

below. The distance from the target to the front LANA (NWB) and back LANA(NWA) is

441.6 cm and 517.5 cm, respectively. Two walls are placed at 39.37° with respect to beam

direction. Please note that the most bottom bars of two walls are not used due to shadowing

and lack of electronics channels so only 24 bars are used in each wall. Figure 2.13 show their

angular coverage.

The LANA was constructed in 1997. The frames were designed to allow nesting of the

two walls so that one wall is located in front of the other. This configuration increases the

efficiency of neutron detection at the expense of covering a wide angular range. The NE-213

liquid scintillator is flammable and hazardous. Furthermore, with the size and weight of the

two walls in addition to the large number of cables which have to be first disconnected from

the electronics, moving and nesting the two walls required a lot of advanced planning and

safety precautions. Figure 2.11 shows the inner structure and liquid scintillator bars of one

LANA wall after the front aluminum cover is removed under ultra-violet light. For clarity,

after nesting, the front wall is labelled as NWB while the back wall is labelled as NWA.

LANA refers to both walls in this thesis.

To study particles emitted in the overlapped compressed zone in central collisions, the

LANA should be placed at polar angle around 90° in the center of mass frame in order

37

Figure 2.11: One of LANA walls is illuminated with ultra-violet light after the front alu-
minum cover is removed.

38

to minimize contributions from projectile-like and target-like fragments. For symmetric

projectile and target systems, this corresponds to around 45° in lab frame. Unfortunately,

we are limited by the walls in the vault as shown in Fig. 2.12. LANA was eventually placed

at 39.37° with respect to beam in lab frame (the accurate measured angles come from the

laser measurements).

In order to implement the detector capabilities described above, we used the electronics

setup schematically shown in Figure 2.14 for one PMT. An analogous electronics chain is

replicated for each of the 100 PMTs in the two neutron walls. Each PMT has an embedded

passive voltage divider circuit as described in Ref. [13]. Such a circuit, omitted in the drawing

of Figure 2.14 for the sake of clarity, allows one to use both the anode and the last dynode

signals, labelled respectively as “anode” and “dynode” in the figure. The anode signal is

a negative-voltage pulse that contains the charge from the multiplier chain and is used to

produce the integrated charge signals. To enable the PSD analysis, the anode signal is

initially split into two equal signals by means of an NSCL passive splitter module. One split

signal, named “total” in Figure 2.14, is sent to a channel of a common gate CAEN V792

charge-to-digital converter (QDC) [83] for the integration of the total charge. The other
split signal is integrated for its fast component (≈ 30 ns). To successfully implement the

detection of more than a single particle in an event, which is required for high-multiplicity

heavy-ion collision experiments, the gate for the fast component integration is generated

independently for each hit within an event. The gate is generated from the dynode signals

by using a Lecroy 1806 16-channel constant-fraction discriminator (CFD) [84] and a CAEN

C469 16-channel gate and delay generator [83]. These gates are used to digitize the fast

component of the anode signals using a CAEN V862 individual gated QDC [83]. This allows

the PSD technique to be applied exclusively to single-particle events. The logic chain, which

39

Figure 2.12: 3D mechanical overview drawing showing the position of LANA being limited
by the vault wall. During the move, some floor panels had to be removed. These panels were
installed back again after the moving of LANA was done.

40

Beam LineS2 VaultNested LANAGround Panels Need To Be RemovedFigure 2.13: Angular coverage of the front LANA (NWB) and back LANA (NWA) in the
lab frame based on laser position measurement.

41

•Front LANA•Back LANAFigure 2.14: Schematic of the electronics setup (for one PMT) used to process signals from
the LANA when the walls are used in standalone mode. An exact reproduction of these
circuits is used to process signals obtained with each of the 100 individual PMTs. “Fast” and
“total” are two copies of the original anode signal but integrated respectively by using a fast
gate (containing only the fast component of the signal) and total gate (containing the whole
signal) for PSD analysis. PMT dynode signals are used for the timing.

42

totalCFD(LRS 1806)ORGate GeneratorCommon gate QDC(CAEN V862)Individual gate QDC(CAEN V792)TDC(CAEN V1190A)NSCL Passive SplitterTrigger&glob. busyclearother PMTsdynodeanodefastfastgatetotalgatecomp.busytriggerRight PMTLeft PMTref.Gate Generator for fast gate&glob. busyfast busyglob. busyincludes trigger, gates, and timing, is implemented by using the dynode signal from the

PMT voltage divider fed into the CFDs. The trigger to the acquisition system is produced

by a logical “OR” of all the CFD signals for each PMT in the walls in anti-coincidence with

a global busy signal, generated as the “OR” of the computer busy and a fast busy signal,

obtained by stretching a copy of the trigger itself. The latter prevents multiple triggers at

a time interval shorter than the time required by the circuit to generate the gates and to

process the event. The trigger signal is used to produce the total gate for the commonly

gated QDCs, which is a logic signal of about 3 µs in length, as well as the time reference

and trigger signals for the CAEN V1190A time-to-digital converter (TDC) [83]. This TDC

records the time difference between the individual dynode CFD signal and this reference

signal, which are used for the position and time calibrations of the wall. Finally the trigger

is sent to the data acquisition to enable the readout of each module. In the latest experiment

using LANA, digital electronics was set up in parallel to the analog electronics for 8 bars.

Analysis using digitized waveforms to devise software algorithm to improve neutron/gamma

pulse shape discrimination (PSD) is discussed in Ref. [16].

2.4 Forward Array

Time of Flight (ToF) technique is a method for measuring the energy of particles based on

the time they travel between a start-time and a stop-time detectors. Given the distance

between start-time and stop-time detectors known as D and the time of flight measured as

∆t, the speed v of a particle can be calculated by v = D

∆t. The Forward Array is used as

the start-time detector for the neutron ToF measurement while the LANA is the stop-time

detector.

43

Figure 2.15: The front and back views of the original Forward Array without PMT bases.
The front side of Forward Array is covered by a thin layer of Sn/Pb foil to protect itself from
δ electrons emitted in reactions.

44

The Forward Array was originally constructed for experiment in Ref. [85]. It was up-

graded to increase its forward angle coverage. The original forward array is composed of

16 wedges of NE-110 plastic scintillator, all of which are placed on a partial annulus whose

inner diameter is 1 inch and outer diameter is 4.5 inches. The annulus has a 72° cutout

to allow charged particles to be detected by the Large Area Silicon Strip Array (LASSA)

which is a prototype of HiRA) in Ref. [9]. Each scintillator wedge is first painted with Bicron

BC-620 reflective paint to enhance light internal reflection before it is detected by the PMTs.

The wedge is then wrapped in aluminized mylar foil to prevent cross talks between adjacent

detectors. Hamamatsu R5600U PMT is attached on the back of each scintillator wedge as

shown in Figure 2.15 and an E5780 base is coupled with each PMT during experiments.

In our experiments, we are able to eliminate the 72° cutout angles by adding two more

wider but shorter scintillator wedges. Each new wedge covers angular range of 36° with the

outer radius of new wedges to 3 inches. The shorter scintillator wedges as indicated by the

indentation of the blue dashed rectangle representing the FA in Fig. 2.6 ensure that HiRA10

is not shadowed. The original 16 PMTs are not suitable for PMTs of new wedges. If similar

PMTs are installed at the side surface of new wedges, their shadowing can go up to around

45° in polar angle which will surely shadow HiRA10. The two PMTs for the new shorter

scintillator wedges were attached perpendicular to the wedge plane at the back. The photos

in Fig. 2.16 show the two holes for the PMT’s.

A new mount supports the Forward Array in place. It also provides the platform where

two additional scintillator wedges are attached. To accomplish this, we 3D-printed the

support using Connex350 3D-printing facility at MSU electrical and computer engineering

department [86]. Figures 2.16 show how the original Forward Array is assembled with new

components. We used the VeroWhite materials for its excellent properties in vacuum.

45

Figure 2.16: The front and back views of the original Forward Array assembled with its
backing.

46

Figure 2.17: The side and back views of the upgrade Forward Array placed in position during
experiments.

47

The upgraded Forward Array is placed about 12 cm from the target downstream with

the beam axis passing through the center hole as showed in Figure 2.17. To measure the

neutron ToF, we use the Forward Array triggering time as the start time and the LANA

triggering time as the stop time. The Forward Array is triggered mainly by the abundant

charged particles emitted in the forward angles. Being placed only 12 cm from the target

while LANA is placed 4.5 m away, the differences in the time arrivals of the particles to the

forward array is negligible. Details about neutron ToF analysis will be discussed in Section

3.2.2.

2.5 Charged-Particle Veto Wall

In general, neutrons are difficult to measure. When neutron interacts with the protons in

the scintillator, the recoil proton is usually detected. Similarly, if a proton (or charged

particles) is detected by a neutron detector, it cannot distinguish proton from neutrons.

Although NE-213 attains excellent discrimination of γ rays and neutrons utilizing Pulse

Shape Discrimination (PSD) technique, it cannot by itself discriminate charged particles

produced in the target from these recoil protons that are produced by the neutrons we want

to measure.

To ensure near 100% rejection of charged particles from the target, we designed and built

a large Charged-Particle Veto wall (VW). The project is a collaboration between the HiRA

group and Professor Zbigniew Chajecki at Western Michigan University (WMU). Professor

Zbigniew Chajecki is also the spokesperson for one of the experiments.

48

2.5.1 Design and Prototype

The Charged-Particle Veto Wall consists of 25 vertically-placed 1 cm thick plastic scintillator

bars in front of the LANA. Only 20 bars are needed to cover LANA. Nonetheless, 5 extra

bars are mounted to provide spares in the event that one of the bars failed in the middle of

the experiment so that the failed bars can be replaced quickly. We choose 1-cm-thickness of

plastic scintillator to ensure sufficient strength of the bar which is 2.5m long while minimizing

interaction of neutrons with the veto bars. The density of EJ-200 (1.02 g/cm2) is about

17% higher than the density of NE-213 (0.874 g/cm2) but NE-213 used in LANA is 5.65

times thicker. The loss of about 20% neutrons in the veto wall will need to be corrected

in determining the neutron cross-sections. With the current design, we are assured that a

signal from a charged particle hitting LANA will be detected 100% while less than 2% of the

neutrons will be detected assuming the neutron detection efficiency is 10%.

To ensure that 100% charged-particle will be vetoed, firstly, these scintillator bars are

required to fully cover the LANA with no gap when looking from the target. Secondly,

because the scintillator bars are placed vertically, the horizontal hit position resolution i.e.

the width of the veto bar should be similar to the resolution of the neutron bar which is

about 8 cm. 3 mm overlap is designed to ensure that there are no gaps between neighboring

veto bars taking into account possible inaccuracy in the veto wall installation. Thirdly, the

Charged-Particle Veto Wall should be placed as close as possible in front of the LANA to

better correlate the hits in Veto Wall and the LANA. The bars are made of EJ-200 [87]

scintillator material coupled with PHOTONIS XP3462 PMTs. The PMTs were harvested

from the MSU 4π array [88]. The outer diameter of each PMT’s shielding tube is 8.74 cm

which impose the main limitations on the width of the veto bars.

49

The final design consists of the scintillator bars with dimension of 9.4 cm wide x 250 cm

tall and 1 cm thick. The ends of each bar are tapered to 5.65 cm in order to couple with

a 7.62 diameter light guides which are first glued onto the PMT’s as shown in Fig. 2.18.

Precision grooves are machined on the side of the light guides coupled to the veto bars. The

tapering at veto bar ends is necessary in order to insert and secure the veto bars into the

grooves in light guides as shown in Fig. 2.20. SYLGARDT M 182 Silicon Elastomer [89] is

used as the gluing material between veto bars and light guides. As shown in right bottom

panel of figure 2.18, the extra spaces at two ends of grooves on light guide allow extra silicone

between the bar and the light guide contact to be squeezed out. Skill is needed to ensure

no tiny air bubbles exist between in the silicon at the junction of the veto bar and the light

guide contact. Scintillator bars are staggered back and forth to ensure 3 mm overlap between

neighboring bars.

To test the design and to develop the complicated procedure in coupling the veto bar

to the PMTs, we first built a prototype 30 cm veto bar. The prototype is identical to a

full-sized bar including bar width, light guides and PMTs. Figure 2.19 shows the testing

of the Veto Wall bar prototype in Chajecki lab at Western Michigan University. Similarly,

3D printed parts are used extensively in the design and testing of most of the parts in the

construction of the Veto Wall.

2.5.2 Construction

After the prototype veto bar was tested successfully. Two full size bars were ordered from

Eljen and tested at Western Michigan University before 24 more were ordered. At the end,

25 veto bars were selected to be used in our experiment. Each bar was constructed and tested

at WMU. Finally, all 25 veto bars are assembled into a veto wall as designed. Before the VW

50

Figure 2.18: 3D sketch showing how 3 Charged-Particle Veto Wall scintillator bars are
assembled at the bottom end with T-Slotted aluminum frame.

51

Figure 2.19: Professor Chajecki is studying the signal characteristic of Charged-Particle
Veto Wall bar prototype (at the right of the figure) with his students at Western Michigan
University.

52

Figure 2.20: Light guides are being glued on PMTs at Western Michigan Universty.

53

Figure 2.21: (top left panel) Professor Chajecki is testing the Charged-Particle Veto Wall
frame.
(top right panel) Undergraduate students from Western Michigan University and
Michigan State University are moving Veto Wall bar. (bottom left panel) Veto Wall bars
are being taken out from shipment packages. (bottom middle and right panel) NSCL and
WMU researchers are installing the Charged-Particle Veto Wall in front of LANA.

54

Figure 2.22: Charged-particle Veto Wall construction in progress. 22 bars have been installed
in place.

55

commissioning experiment at NSCL in December of 2017. The wall was disassembled and

reassembled in the S2 vault and coupled to LANA. The veto bars were packaged into wooden

transportation boxes padded by foam. Special liquid foam packages that can conform to the

shape of the cargo, were used to protect the fragile end of veto wall bars where PMTs are

attached. Due to its length (2.5 m) and thinness (1 cm), customized aluminum structure

was designed for support in taking veto bars on and off veto wall frame safely as shown in

the upper two panels of Figure 2.21. The special aluminum structure prevents the veto bar

from bending or even breaking during short distance transportation from veto wall frame to

storage container and vice versa. Figure 2.22 and 2.23 show the scene while the Charged-

Particle Veto Wall was being built.

The veto wall is placed at 393.3 cm away from the target. The distance between the VW

and NWB and NWA was 48.3 cm and 124.2 cm respectively. Figure 2.24 shows how the

Charged-Particle Veto Wall was nested with NWA and NWB. Figure 2.25 is a top view of

experimental setup schematic. The beam direction is labelled. The dashed circle on the left

upper corner represents the aluminum vacuum chamber used in experiments. The sizes and

relative relationships between VW, LANA and target are drawn in scale. VW, NWB and

NWA are parallel (< 1 °) with each other. The gold line pointing to VW is perpendicular to

VW front surface in figure 2.25. This line is 39.37 ° with respect to the beam line. VW bars

are labelled from from right to left as 0 to 24 as shown in Figure 2.25. Using this numbering,

VW bar #12 is the middle bar. LANA is fully protected by VW bar #3 to #22.

56

Figure 2.23: The Charged-Particle Veto Wall installed in front of the LANA. In the top
panel, the red and yellow tape marks on the ground indicate the polar angle with respect to
the beam direction in lab frame.

57

Figure 2.24: (Top panel) 3D sketch of the Charged-Particle Veto Wall. (Bottom panel) 3D
sketch of the Charged-Particle Veto Wall and the LANAs nested together.

58

Figure 2.25: Top view of experimental setup schematic. The schematic reflects the sizes
and distances to the target of the Charged-Particle Veto Wall (VW) and LANA (NWA and
NWB) in scale. The VW+LANA assemble is moved to 39.37 ° . All distances are drawn to
scale and determined from laser measurements.

59

Beam LineHiRA10NSCL S2 VaultTargetMicroballForward ArrayChapter 3

Data Analysis

3.1 Microball Impact Parameter Determination

In beam-target collision experiments, collisions are often characterized according to their

impact parameter b. Typically, collisions with smaller impact parameter have more nucleons

participating in compress-expand process, resulting in more particles emitted and larger

multiplicity (number of particles detected in a given detector).

The Microball is used to measure the charged-particle multiplicity, which is assumed

to decrease monotonically with impact parameter b. The probability of producing particles
with multiplicity ≤ Nc is proportional to the geometrical area of a disk with radius b(Nc), we
can calculate the deduced impact parameter, ˆb = b/bmax, which is a dimensionless variable

associated with the centrality of the collision, using the following formula [90, 91, 92, 93, 94]:

(cid:115)∞(cid:80)
(cid:115) ∞(cid:80)

Nc

ˆb(Nc) =

b(Nc)
bmax

=

P (Nc)

P (Nc)

(3.1)

where Nc is the number of charged-particle detected in Microball, P (Nc) is the probability

of events with multiplicity equal to Nc. The probability of event having Nc multiplicity is

Nc=1

60

Figure 3.1: Correlations between the induced impact parameter ˆb and Microball multiplicity
Nc for 16 reaction systems. On the upper right corners of two panels, the reaction systems
are labeled as target+beam. The top panels are for Ni target reaction systems and the
bottom panels are for Sn target reaction systems. The left panels have lower beam energy
of 56 AMeV and the right panels have higher beam energy of 140 AMeV.

61

calculated using:

P (Nc) =

C(Nc)

∞(cid:80)

C(Nc)

(3.2)

Nc=1

where C(Nc) is the counts of events with Microball multiplicity Nc.

The relationships for all 16 reaction systems between the induced impact parameter ˆb and

Microball multiplicity Nc are shown in figure 3.1. The top panels of figure 3.1 summarize

the ˆb-Nc correlations for Ni target while the bottom panels are for Sn target. With the bmax

given in table 3.1, we can calculate the impact parameter of any event using equation 3.1.

The majority of the work mentioned in this section was done by Sean Sweany.

systems
40Ca, 56
MeV/u
40Ca, 140
MeV/u
48Ca, 56
MeV/u
48Ca, 140
MeV/u

58Ni

5.78

5.85

5.63

5.05

64Ni

5.64

5.92

5.65

5.95

112Sn

124Sn

7.91

7.61

7.61

7.45

7.38

7.47

7.17

7.25

Table 3.1: bmax table for all 16 beam-target-energy combinations in our experiment. The
unit is barn, 100 fm2.

3.2 LANA Analysis

3.2.1 LANA Calibration using cosmic rays

Typically, calibration of a neutron detector requires the use of radioactive sources that pro-

duce gamma rays with well-known energies [13, 95]. Nearly all of these sources have low

energy gamma < 5 MeV. For large detector array, calibration has to be done at various po-

62

sitions along individual detector to determine the position dependence of the light collection

of the photo-multipliers incorporated in the neutron detectors. Such procedures are tedious

and time-consuming especially when the area of the arrays is large. Alternatively one can

use nuclear reactions that produce neutrons at fixed energies for calibrations. The latter

method requires accelerated ion beams which may not be readily available [96, 97].

The section below describes a method that uses high-energy muons produced in cosmic-

ray showers to calibrate the light response of a large neutron array [98, 99, 100, 101]. The
mean muon energy is ≈ 2 GeV [102]. This section will also show how the time and position

resolutions of the array can be obtained and how to match the time difference of each neutron

detector without an external timing detector. The method can be applied to other neutron

detectors.

3.2.1.1

Impact position calibration

When an ionizing radiation strikes one of the bars of the neutron wall, scintillation light is

isotropically produced in the NE-213 liquid scintillator along the ionization path. The X-

position of the hit on the horizontal axis is extracted by comparing the time signals recorded

by the PMTs at the two ends of the bar, while the vertical Y-position is constrained by the

physical dimension of the scintillation fluid inside the bar.

Given tleft and tright as the absolute times which correspond ideally to the arrival times

of the scintillation light at the left and right PMT photocathodes, the horizontal position of

the particle hit along the bar, with respect to the bar center, is given by:

tleft − tright − τ

2

¯v

X =

(3.3)

63

where ¯v is the average horizontal speed of the light propagating through the bar and τ is

the residual delay since the timing for the left and right PMT and electronics channels are

not exactly the same due to different cable length, different delays in electronic channels or

modules etc. Because the cosmic rays hit the neutron wall bars with no preference, the hit

distribution along one bar should be uniform. By using data collected with cosmic rays,
we produced the time difference, ∆t = tleft − tright distribution shown in the top panel of

figure 3.2 for bar #8 of the LANA walls. As expected, the distribution is almost flat with two

sharp edges, corresponding to the geometrical left and right ends of the bar. To determine

the left and right edge consistently for all the bars, we perform a numerical differentiation

of the time difference distribution spectrum. The result exhibits two sharp peaks, where

the time difference differential diverges negatively at ∆tmax or positively at ∆tmin as shown

in the bottom panel of Figure 3.2. A numerical peak finding method can then be used to

infer the positions of the two edges. An analogous procedure is applied to all the bars. The

following equations can be used to obtain the position calibration parameter of a bar:

τ =

¯v =

∆tmax + ∆tmin

2
2L

∆tmax − ∆tmin

(3.4)

where L is the bar length.

After the position is calibrated, we define a cosmic track by fitting the impact positions

measured in at least ten consecutive bars as schematically shown in figure 3.3. (Except in

Section 5, no other conditions are imposed on the cosmic tracks.) From the fitted track (blue

diagonal line passing through the bars in Figure 3.3) we can calculate the deviation (∆X)

between the impact position and that extracted from track reconstruction. Figure 3.4 shows

64

Figure 3.2: (top panel) Time difference, tleft-tright distribution for cosmic muons obtained
with bar #8 of the LANA. A numerical differentiation of this spectrum (bottom panel) is used
to determine the position of right and left edges of the tleft-tright distribution consistently as
indicated by the dashed lines, which correspond to − L

2 and L

2 respectively.

65

20-10-0102030counts per 250 ps500100015002000 (ns)right-tleftt20-10-0102030 derivative plotright-tleftt1500-1000-500-05001000Figure 3.3: A schematic drawing of a cosmic muon track penetrating 10 consecutive bars in
the wall. Red stars represent the hit positions. The reconstructed muon track (blue slanted
line) is obtained by fitting the measured hit positions on the bars with a straight line. ∆X
indicates the position deviation between the expected and the actual hit position. ∆di,ref is
the theoretical distance between two hits on a certain bar and reference bar respectively.

66

the ∆X distributions for Bar #8 with a FWHM of 6.92 cm, comparable to the position

resolution obtained in Ref. [13]. The obtained position resolution is averaged over a LANA

bar. It is worse towards the end of the bar due to attenuation of the light signal from the

PMT located at the opposite end. It is worth noting that the above resolutions include the

uncertainty in the track reconstruction. The X position resolution is similar to the height

of the NE-213 liquid inside the Pyrex cell which determines the Y position resolution. The
mean position resolution for all 25 bars is 8 ± 1.5 cm which is consistent with the position

resolution obtained in Ref. [13] suggesting that the PMTs in LANA wall have not deteriorated

even after 25 years.

Bar #8 of NWB is used as example in the analysis of Chapter 3.2.1. Table 3.2 and 3.3

list the ∆X and v of 48 LANA bars. Please note that we have in total 50 LANA bars. The

bottom bars of the two LANAs are not used in our experiments because of the shadowing

by the stainless steel stand that holds the shadow bars.

NWA Bar#

∆X FWHM (cm)

v (cm/ns)
NWA Bar#

∆X FWHM (cm)

v (cm/ns)

1

7.60
14.5
13
6.17
14.3

2

7.15
14.3
14
6.29
14.6

3

11.4
14.7
15
6.89
14.2

4

9.18
14.6
16
6.44
14.4

5

9.34
13.8
17
7.05
14.7

6

8.95
14.9
18
8.32
14.5

7

11.6
14.6
19
6.78
14.5

8

6.02
14.7
20
6.82
14.8

9

6.88
15.0
21
6.99
14.7

10
6.09
14.4
22
6.76
14.4

11
6.87
14.9
23
7.96
15.1

12
8.20
14.2
24
10.1
14.5

Table 3.2: The ∆X and v of each back LANA (NWA) bar.

NWB Bar#

∆X FWHM (cm)

v (cm/ns)
NWB Bar#

∆X FWHM (cm)

v (cm/ns)

1

6.02
15.5
13
7.27
15.5

2

6.97
14.9
14
7.34
14.9

3

12.9
15.4
15
8.90
15.4

4

6.35
14.9
16
6.72
14.9

5

5.77
16.0
17
8.03
16.0

6

6.01
14.7
18
6.42
14.7

7

6.48
15.5
19
9.50
15.5

8

6.92
14.5
20
6.29
14.5

9

6.17
15.4
21
5.71
15.4

10
5.84
15.0
22
7.12
15.0

11
5.91
15.4
23
7.35
15.4

12
6.18
14.8
24
6.57
14.8

Table 3.3: The ∆X and v of each front LANA (NWB) bar.

67

Figure 3.4: Position deviation distribution for bar #8.

68

X (cm)D20-020counts per 0.5 cm050010001500200025003000FWHM = 6.92 cmposition deviation distributionFigure 3.5: δi,ref distributions for each of the bar in the array before (top panel) and after
(bottom panel) the peaks are aligned. Y-axis is the bar number while X-axis shows the
corresponding ∆T exp
i,ref distributions. Bar #12 is used as the reference bar; therefore
δ12,ref =0.

i,ref − ∆T th

69

 (ns)thi,refTD-expi,refTD10-010bar number510152025 (ns)thi,refTD-expi,refTD10-010bar number5101520253.2.1.2 Time resolution and time offset calibration

Cosmic muons travel at nearly the speed of light. As illustrated in Figure 3.3, theoretically,

one can calculate the expected arrival time difference of a cosmic muon track between two

bars since we know the position of the bars accurately. The expected time difference of the

signal recorded in a bar used as the reference and the i-th bar of a wall is given by:

∆T th

i,ref =

∆di,ref

v

(3.5)

where ∆di,ref is the theoretical length of the cosmic muon path from the i-th bar to the
reference bar determined by the track fit, and v ≈ c is the speed of the cosmic muon. The

time difference measured experimentally with TDC is given by:

∆T exp

i,ref =

(tleft + tright)ref

2

− (tleft + tright)i

2

+ δi,ref

(3.6)

where δi,ref is the time difference between bars arising from differing cable and electronic
delays. Figure 3.5 shows the distribution of δi,ref = ∆T exp

i,ref for each of the bars in

i,ref − ∆T th

a LANA wall. The Y-axis is the bar number, i. Bar #12 is chosen as the reference bar with

the obvious result δ12,12 = 0. Deviation of δi,ref from zero suggests that time delays arising

from the differences in cable and electronic delays, etc are different for each bar. While we

cannot determine the absolute time offset or delays for each bar, we can align the peaks of

δi,ref to zero as shown in the lower panel of Figure 3.5. Figure 3.6 shows a Gaussian shape

distribution of δi,ref for bar #8 with FWHM of 751 ps. The time resolution, FWHM, for bar
#8 involving two PMTs can be deduced as: 751 ps√
= 531 ps. The average time resolution
2
for all 24 bars is 504± 106 ps. However, this time resolution cannot be compared directly to

the time resolution of 1 ns obtained in Ref. [13] which involves the use of an external time

70

zero Si detector. Our time resolution reflects the time response of the PMTs which are quite

similar as reflected by the standard deviation of the mean.

3.2.1.3 Light attenuation length and photomultiplier gain-matching

When an incident particle interacts with the NE-213 liquid, only a small fraction of the

produced optical photons directly reach the PMTs, while some photons are lost completely

and the rest of the photons experience multiple reflections on the surface of the Pyrex glass

cell before being collected by the PMTs. The photons that reach the photocathodes are

detected by the left and right PMTs attached at the end of the Pyrex tubes and converted

to charge by the QDC in Figure 2.14. The measured charge is a function not only of the

number of photons produced by the incident particle (and therefore of the energy deposited

by the particle in the material) but also of the hit position X as described below:

Qright(N, X) = gright

Qleft(N, X) = gleft

− L/2−X

λ

− L/2+X

λ

N
2
N
2

e

e

(3.7)

where gright and gleft are the gain of the corresponding PMT, L is the bar length, N is

the total number of photons emitted and λ is the technical attenuation length of the scin-

tillator material in our detector to optical photons. The attenuation length describes the

self-absorption in the material and also includes the effect of geometry. λ is therefore, nor-
mally smaller than the material bulk light attenuation length, which is ∼270 cm [81]. The

logarithm of the ratio of Equation (3.7) gives a linear expression:

ln(

Qright
Qleft

)(x) =

2
λ

X + ln(

gright
gleft

)

(3.8)

71

Figure 3.6: Time deviation distribution for bar #8.

72

 (ns)thi,refTD-expi,refTD2-02counts per 0.5 ns05001000150020002500FWHM = 0.751 nstime deviation distributionwith a slope equal to 2

λ and an intercept ln(

gright
gleft

). Figure 3.7 plots the gain ratio of the

two PMTs ln(

Qright
Qleft

)(X) as a function of X for bar #8. The distribution is mostly linear

with some curvature at large absolute X values due to the light collection efficiency near the

end of the bar. The red dashed line is the result of a linear fit of data from -90 cm to 90 cm

to avoid any possible effect from the end of the bar. We have varied the range of fit from
(−80 cm, 80 cm) to (−90 cm, 90 cm) and find that the fitting results are stable to within
1%. The mean λ value for all the bars in the array is 94 ± 8 cm. Thus the light attenuation

effects are significant in the LANA bars, due to their size and geometry.

Table 3.4 and 3.5 below list the λ of 48 LANA bars. We can see that in general NWA

bars have shorter attenuation length, this is probably because the liquid scintillator leaking

problem is more severe for NWA so that an air gap was created between liquid scintillator

and the pyrex container walls, resulting in less efficient photon reflection.

λ (cm)

NWA Bar# 1
66
NWA Bar# 13
79

λ (cm)

2
59
14
79

3
60
15
69

4
80
16
79

5
66
17
83

6
92
18
74

7
62
19
79

8
89
20
80

9
85
21
88

10
78
22
81

11
81
23
80

12
68
24
59

Table 3.4: The light attenuation length λ of each back LANA (NWA) bar.

λ (cm)

NWB Bar# 1
90
NWB Bar# 13
108

λ (cm)

2
102
14
84

3
82
15
84

4
102
16
101

5
107
17
84

6
101
18
88

7
95
19
90

8
88
20
87

9
85
21
92

10
109
22
96

11
87
23
102

12
102
24
99

Table 3.5: The light attenuation length λ of each front LANA (NWB) bar.

Equation (3.8) also facilitates matching the gain of left and right PMTs of each bar to

allow for uniform performance along the bar using the following procedure. A cosmic ray

run is performed to produce a plot similar to Figure 3.7. The intercept extracted with a

73

Figure 3.7: Equation (3.8) as a function of the position X along the bar #8 for cosmic ray
data. The red dashed line is a linear fit of the distribution. The intercept of the best fit line
is compatible with (0,0), indicating a good left-right matching of the PMT gains. The slope
allows to extract the attenuation length of the bar.

74

X (cm)100-50-050100)left/Qrightln(Q4-2-024020406080100120140160180200220linear fit is the left-right gain ratio. Using the power-law of the high voltage (HV), gain
∼ (HV )N , (e.g. N ∼ 8 for LANA) a new gain setting is chosen to minimize the intercept.

It takes about 3 iterations to adjust and match all HV for 100 PMTs in LANA in order to

consistently equalize the PMT gains for all the bars with (

gright
gleft

), close to one. One can also

use the vanishing intercept in Equation (3.8) to judge the quality of the gain matching in

offline analysis. In our case, the statistics from an overnight cosmic run is sufficient for one

iteration. The same method can also be used between experimental runs to monitor the gain

of the neutron detection array.

3.2.1.4 Light output calibration and position corrections

To determine the light output threshold and to calculate neutron detection efficiency from

simulation, we need to calibrate neutron signal’s light output to MeV electron equivalent

(MeVee). Cosmic muons reaching the sea level have a mean energy of 2 GeV [102, 99, 101].

The most probable energy deposited in the scintillator material by such muons depends on

the length of their path in the material. We simulate the interaction of 2 GeV muons with

the NE-213 material by using the GEANT4 toolkit and the standard electromagnetic physics

list. Our simulation indicates that, if muons punch through the bar vertically, the expected

deposited energy has a Landau distribution whose most possible value (MPV) is 11.96 MeV.

To calibrate the neutron detectors, we require the incident angles of the cosmic muon

track to the axis to be within 10 degree perpendicular to the horizontal central axis of the

bar. This is to ensure the shortest track path in the scintillating liquid in the neutron bar to

be consistent with the simulations, in order to achieve accurate determination of the energy

loss by the cosmic muons. The 10 degree condition is chosen so that the uncertainties of

transverse length of the track in a bar is consistent with the position resolution of the bars.

75

Figure 3.8: (Top panel) Uncalibrated left-right GM as a function of the position along bar
#8. Vertical cosmic rays are selected by restricting data to impinging angles −10° ≤ θ ≤ 10°
with respect to the axis perpendicular to the bar length. Black points are the position of the
cosmic ray MPV deduced with a Landau fit of data for each position bin. The blue line is
the result of a quadratic fit of the cosmic MPV position dependence. (Bottom panel) Same
as top panel after light calibration and position dependency correction.

76

X (cm)100-50-050100 (arb. unit)leftQrightQuncalibrated 0500100015001-10110Quadratic FitX (cm)100-50-050100Light Output (MeVee)05101520251-10110To minimize the position dependence, the geometric means (GM) of the charges in the left

and right PMTs defined below is typically used for the energy-light calibrations of neutron

detectors:

(cid:113)

Qleft(N, X)Qright(N, X) = f (N ) =

(cid:113)

N
2

gleftgrighte−L/λ

(3.9)

Figure 3.8 shows the GM distributions of bar #8 with a bin width of 20 cm. Consistent with

the GEANT4 simulations, the GM distribution shown in Figure 3.9 has a Landau shape. The

black squares in Figure 3.8 (top panel) show the MPV of the Landau GM distributions of

vertically-penetrating cosmic rays as a function of X position. The statistical uncertainties

of the black squares are smaller than the size of the marker. Despite using the GM of

Equation (3.9), there is still some position dependence, most likely coming from the position

dependence of the light collection due to scattering and reflections along the bar. This

residual position dependence can be corrected empirically by flattening the experimental

GM distribution for each X position using a parabolic fit of MPV (blue line in Figure 3.8

(top panel)). The flattened or corrected GM vs X-position spectrum is shown in Figure 3.8

(bottom panel), where the MPV of the GM has been calibrated to 11.96 MeVee.

To validate the cosmic ray energy-light calibration procedure, we placed an intense

Americium-Beryllium (AmBe) neutron source at a distance of about 60 cm from the front of

the LANA walls. Such source emits a mono-energetic 4.44 MeV gamma-ray from the reaction
of α + 9Be → n + 12C∗. A typical AmBe gamma spectrum obtained with bar #8 is shown in

Figure 3.10. The sharp Compton edge expected to lie at 4.2 MeV, can be easily defined. We

calibrate the Compton edge of the gamma spectra by fitting it with the sum of a Fermi func-

tion and a linear background. The Fermi function is of the form f (x) =

exp

, where

+1

a0
x−a1
a2

a0,a1,a2 are free parameters. The position of the Compton edge is determined from the a1

parameter by using the method proposed in Reference [103]. The open star in Figure 3.11

77

Figure 3.9: An example of a Landau fit of the GM distribution for the position bin -20 cm
≤ X ≤ 0 cm.

78

 (arb. unit)leftQrightQuncalibrated 050010001500counts020406080100Figure 3.10: Position corrected light output spectrum obtained with an AmBe source for bar
#8. The Compton edge is fitted with a Fermi function and the deduced position associated
to the 4.44 MeV transition in 12C is indicated by an arrow and a dashed line. The theoretical
value of the Compton edge is 4.2 MeV.

79

Light Output (MeVee)34567counts per 35 keVee05001000150020002500AmBe source dataFermi fitshows that the 4.2 MeV from the Compton edge calibration lies along the red line obtained

from the cosmic calibration at 11.96 MeVee and the zero offset of the electronics confirming

the validity of our calibration procedure. The statistical uncertainties of the blue square,

open star and blue circle points are smaller than the size of the marker in Figure 3.11.

By selecting cosmic tracks at large incidence angle, the calibration can be extended to

higher energy depositions. We select cosmic muons that punch through the detector at 44.4
± 5 and 56.3 ± 5 degrees with respect to the axis perpendicular (0 deg) to the bar length.

According to the GEANT4 simulations, such muons should deposit 15.4 and 19.8 MeVee.

These points are added to Figure 3.11 as the blue open circles. It appears that the light

response remains linear out to 20 MeV.

3.2.2 Time calibration with the Forward Array

We use Time of Flight (ToF) technique to measure the velocity and therefore energy of

neutron. In ToF measurement, the upgraded forward array is used as start-time detector

and the LANA is used as stop-time detector. The distances between the target and LANA

are 4.42m for the front wall and 5.18m for the back wall. After a nucleon-nucleon collision,

because of the large angular coverage of forward array at forward angle, it is almost certain

that several emitted charged-particles will hit the forward array. To accommodate multi-

hits, forward array has 18 scintillation segments which greatly reduce the chance of having

two particles hitting on one segments and thus improves time resolution. The earliest time

recorded by a forward array element is assumed to be tstart and tstop is the time triggered
by a particle detected at LANA. Assuming this is a neutron, it takes tstop − tstart to fly

from the target to LANA neglecting the short time for the detected particle to reach the

forward array which is located at around 10 cm from the target. and therefore its velocity is

80

Figure 3.11: The cosmic-ray energy-light calibration curve (red line) obtained by using the
11.96 MeVee constraint of the cosmic muons and the zero-offset (blue solid circle and blue
square, respectively). The open star corresponds to the Compton edge discussed in Fig-
ure 3.10. The open blue circles are two additional light-energy calibration points obtained
by select cosmic muons that punch through the detector at 44.4 ± 5 and 56.3 ± 5 degrees
with respect to the axis perpendicular to the bar length.

81

Energy (MeVee)05101520 (arbitrary unit)leftQrightQuncalibrated 05001000Pedestal90.0 Degrees constraintOther Degrees constraintCosmics calibration curve0.0) Compton EdgefiC*(4.4412vneutron = D/(tstop − tstart) where D is the distance between target and where this neutron

hits the LANA. In principle, the subtraction between two timings tF A and tLAN A directly
recorded by two detectors will be tstop − tstart + Crandom. Crandom is a random time offset

caused by different cable lengths and electronic module channels.

We use prompt gamma to do ToF time calibration. Prompt gamma rays are emitted

immediately after or during the nuclear reaction. Because photons always travel at the

speed of light, we can utilize them to calibrate time. Figure 3.12 is a time of flight spectrum

from the LANA and forward array. The narrow peak at the left of the spectrum comes from

prompt gamma rays.

By checking the signal of prompt gamma rays using 2D plot as shown in the top panel of

figure 3.13, we can correct ToF for forward array time walk and synchronize all 18 forward

array segments to compensate for time delays from different cable lengths or electronic

module channels. The y-axis in figure 3.13 is raw QDC channel for a certain forward array

segment and the x-axis is the average timing for the left and right PMTs on NWB minus

forward array timing before (top) and after (bottom) time walk correction. The light blue

region in the center of the plot corresponds to the events of prompt gamma rays. Ideally,

the time of flight of prompt gammas should be independent of the magnitude of the gamma

signal, which means the red line in top panel of figure 3.13 should be vertical independent

of the energy of the particle. Instead, in the top panel of figure 3.13 we can see that the

light blue region is tilted towards right which results from the fact that a stronger FA signal

would cause an earlier triggering time. This dependence of the trigger time on the signal’s

magnitude is called time walk effect. To correct for this effect, first we fit the light blue

82

Figure 3.12: A time of flight spectrum from NWB with log (top panel) and linear (bottom
panel) scale. The narrow peak at the left of the spectrum comes from prompt gamma rays,
which arrives the LANA all together and earlier than any other particles. This plot is from
48Ca +124 Sn at E/A = 56 M eV reaction.

83

ToF (ns)020406080100120140160counts per 100 ps210310410ToF (ns)020406080100120140160counts per 100 ps050001000015000200002500030000350004000045000region using a function in form of:

or we can write this relationship:

Channel = (ln

∆t − a

b

)/c

∆t = a + b ∗ ec∗Channel

(3.10)

(3.11)

where a, b, c are three free fitting parameters. Please note that other forms of function that

can reproduce the time walk effect are also acceptable. Then we can calculate corrected FA

trigger time using:

tcorrected = t − (a + b ∗ ec∗Channel)

(3.12)

Equation 3.12 also synchronizes 18 forward array segments at the same time. Figure 3.13

shows the difference before and after time walk effect is corrected. After correction, the

arrival time of prompt gamma rays is independent of signal amplitude.

After the time walk effect is corrected for each FA segment, we need to choose the start

time from eighteen FA segments’ time signals. We can either choose the earliest time among

eighteen FA segments’ signals (FA Time Min) or calculate the average time among them

(FA Time Mean). To decide which value to choose, we compare the resolution of the prompt

gamma ray’ peak. A better choice of FA start time should result in a smaller FWHM of the

peak thus better time resolution. Because different positions on NWB have different distances

to the target (4.42 meters to 4.53 meters), in order to accurately reflect the time resolution,
we normalize the ToF spectrum which is a histogram of T oF ∗ Dshortest

. Dshortest here takes

D

the minimum distance between the target and LANA but other values such as the average

84

Figure 3.13: 2D plot of FA segment QDC raw channel versus the timing subtraction between
NWB and a FA segment. Top panel is before walk in effect correction and bottom panel is
after correction. The red curve in top panel is a fitted function in form of Eq. 3.11.

85

distance also work. The idea behind normalized ToF is to cancel out the time differences

brought by different flight distances. Figure 3.14 shows the FWHMs of normalized ToF using

minimum (top panel) and mean (bottom panel) value from FA segments time signal. The

time resolution is found to be 1.53 ns and the time resolution difference between these two

choices is negligible.

3.2.3 Geometry Efficiency

Figure 3.15 displays the hit distribution pattern Φ-Θ plane for the front LANA (NWB)

using Geant4 simulation. Geant4 generates 1 million test particles and emits them from the

position of target uniformly in Φ-Θ plane. For test particles that hit LANA scintillation

material in simulation, we record the spherical coordinates (Φ, Θ) of the hits. In simulation,

the LANA is placed in the same position according to laser measurements [14] done in

experiments. In laser measurements, the positions of 4 fiducial marks were measured in each

LANA wall. From the 3D mechanical drawings of LANA, we know the accurate positioning

of all LANA bars. For different Θ, LANA’s coverage in azimuthal direction is different. To

correct for this, we calculate the fractional azimuthal coverage fΦ as a function of polar angle

Θ which represents LANA’s coverage fraction of 2π in azimuthal direction at a certain Θ.

By using the simulation done within Figure 3.15, we can calculate fΦ in this way: at certain
Θ, we choose a small bin of Θ (for example, 0.2 °) and then fΦ(Θ) =(number of particles

detected at this bin)/(number of particles emitted at this bin). Figure 3.16 shows the fΦ

as a function of polar angle Θ for LANA. With fΦ, we can calculate the observable we are

interested at, such as dM
dEk

using

dM
dEk

=

dMmeasured
dEk ∗ fΦ(Θ)

86

(3.13)

Figure 3.14: Normalized ToF spectrum from NWB with FA Time Min (top panel) and FA
Time Mean (bottom panel).

87

Using FA TimeMinFWHM: 1.53 nsUsing FA TimeMeanFWHM: 1.53 nsFigure 3.15: Hit distribution pattern in Φ-Θ plane for NWB using Geant4 simulation. In
simulation, the LANA is placed in the same position as measured by laser measurements [14]
in experiments. Then particles are simulated to emit from target uniformly in Φ-Θ plane.
We can see that for different Θ, LANA’s coverage in azimuthal direction is different resulting
in a geometric efficiency difference. The red window is 0.2 ° wide binned at Θ = 30°.

88

Figure 3.16: LANA fractional azimuthal coverage fΦ for front (NWB, top panel) and back
(NWA, bottom panel) wall.

89

Figure 3.17: A shadow bar used in experiments for background neutron scattering efficiency
correction. Picture is adopted from Ref. [15].

If we want to use

dM
dEkdΩ, then it is

dM
dEkdΩ =

dMmeasured

dEkdΘdΦdsin(Θ)fΦ(Θ).

3.2.4 Background Scattering Efficiency

Inevitably, there are much materials around the target including the floor and the LANA

which can potentially scatter neutrons and protons emitted from target. Figure 3.18 shows

the structure of aluminum floor under vacuum chamber. For neutrons that have experienced

scattering before hitting LANA (indirect neutron), the determination of their ToF is in-

valid, resulting in incorrect kinetic energy and position information. Those indirect neutrons

contribute a certain portion in the neutron spectrum we measure with LANA. We need to

determine the fraction of background scattering neutrons in the neutron spectrum and has

to be corrected accordingly.

To determine the neutron background i.e. neutrons that do not come directly from beam

induced reactions in the target, we block some areas of LANA and then compare the number

of neutrons detected in blocked and unblocked areas of LANA. Four 30-cm-long brass shadow

bars are used to block about 2% of NWB detection area. They are placed at about 1.7 m

90

Figure 3.18: NSCL staff is removing part of aluminum floor in S2 vault for leaving space in
order to nest the LANA. Above S2 vault’s concrete floor, an aluminum layer of floor was
built on which vacuum chamber sits.

91

from the target outside aluminum vacuum chamber. Figure 3.17 shows one of the shadow

bars used in the experiments. Figure 3.19 shows the neutron hit distribution of NWB in

lab Θ-Φ coordinates with 4 shadow bars installed. Red indicating area being hit by neutron

more frequently than orange, yellow and blue. Areas labelled with A, B, C, D have less

counts due to blocking of the shadow bars. Certain portions along LANA bar #8 and #16

are fully shadowed by shadow bars. The top left plot in figure 3.20 is a neutron hit position

distribution plot of NWB bar #16 with the position range which is shadowed by shadow bar

B. The red line in this plot indicates a fit function using the following form:

(1 + 0.5 ∗ erf (−x − x0√

) + 0.5 ∗ erf (

x − x1√

2σ1

)) ∗ a + b + c ∗ x

(3.14)

) part shows the area between x0 and x1 is

where (1 + 0.5 ∗ erf (− x−x0√
2σ0

2σ0

) + 0.5 ∗ erf (

x−x1√
2σ1

shadowed with associated standard deviation σ0 and σ1 coming from the LANA position

resolution. The values of σ0 and σ1 are very similar. The rest of the term in Equation 3.14

indicates the general hit count drop when the X position is smaller (Θ is defined to be

zero at the beam line). To get the fraction of background scattering, we scale the form in

Equation 3.14 by:

(1 + 0.5 ∗ erf (− x−x0√
2σ0

) + 0.5 ∗ erf (
a + b + c ∗ x

x−x1√
2σ1

)) ∗ a + b + c ∗ x

(3.15)

The right two plots in Figure 3.20 display the fit function after scaling. At the lowest Y

value, the fraction of background scattering is 0.26 for shadow bar B and D area. Same

analysis is also applied to shadow bar A and C area as shown in figure 3.21, the fractions of

background scattering are found to be 0.27 and 0.29 for A and C respectively. The fitting

uncertainty for this method is less than 1%. The slightly higher background from the A C is

probably related to their polar angular positions. More neutrons are emitted in the forward

92

Figure 3.19: The front LANA’s (NWB) neutron hit pattern with 4 shadow bar installed in
Φlab-Θlab coordinates. 4 square areas with less counts of hits corresponds to 4 shadow bars
labelled with A, B, C, D as shown. NWB bars are labelled from #1 to #25 corresponding
to from the bottom bar to the top bar.Shadow bar A and B fully cover NWB bar #16
and shadow bar C and D fully cover NWB bar #8. The reaction system for this plot is
48Ca +124 Sn at E/A = 56 M eV .

93

1357911131517192123Figure 3.20: (left panels) Neutron hit position spectrum corresponding to shadow bar B
(top) and D (bottom). Red lines indicates the fitted functions. (right panels) Scaled fitted
functions indicating the background scattering neutron fraction. The lowest points’ Y values
are both 0.26. The light output threshold is set to 5 MeVee for all 4 plots here.

94

Figure 3.21: (left panels) Neutron hit position spectrum corresponding to shadow bar A
(top) and C (bottom). Red lines indicates the fitted functions. (right panels) Scaled fitted
functions indicating the background scattering neutron fraction. The lowest points’ Y values
are 0.27 and 0.29 for A and C respectively. The light output threshold is set to 5 MeVee for
all 4 plots here.

95

angles resulting in higher signal to backgound.

3.3 Charged-Particle Veto Wall Pulse Height Calibration

Charged-Particle Veto Wall (VW) provides critical information to identify and veto charged-

particle signals from neutron spectrum measured by LANA. Fig. 3.22 displays 2D plots of

NWB light output versus normalized ToF. In the bottom panel of Fig. 3.22, the charged-

particle events are vetoed from the spectrum after requiring there is no hit in VW and the

top panel has no such requirement. Clearly there are charged-particle contamination lines

over neutron spectrum in the top panel. The parabola edge of neutron spectrum is caused

by the fact that the maximum light output a neutron could produce is proportional to the

kinetic energy of neutron and thus the square of its velocity in non-relativistic case. And

neutron velocity is inversely proportional to its ToF. For both plots in Fig. 3.22, most gamma

events are filtered out by PPSD described in Ref. [16].

We calibrate the QDC pulse heights of 20 VW bars (only VW bars from #3 to #22

are needed to provide complete coverage of LANA) such that when a charged-particle with

certain energy passes through any of 20 VW bars, we will have same QDC pulse height

channel value. One way to do this is to use radioactive sources such as 60Co and 137Cs so

that the QDC channels of Compton edge of the gamma spectra from several decay channels

of 60Co and 137Cs can be calibrated to one value among 20 VW bars. This method is used

during setup. It is time-consuming considering moving radioactive sources all over the VW

and waiting for adequate statistics to identify Compton edges. Here we use the data taken

from experiments with beams to calibrate the QDC pulse height of VW efficiently.

The calibration procedure is based on the fact that a certain charged-particle (for exam-

96

Figure 3.22: Light output versus ToF 2D spectrum from front LANA (NWB). The top panel
is the spectrum without using any VW information. The bottom panel is the same spectrum
but with the condition that VW should not be triggered. We can clearly see that by requiring
no hit in VW, the charged-particle events (those slanted lines in the top panel) are removed
completely while keeping the rest of the spectrum undisturbed.

97

ple, proton) at a fixed energy should produce the same light output in any VW bar when

traversing it. We select protons with certain energy and check the VW QDC pulse height

of all bars when these protons passing through them. Fig. 3.23 is a 2D Light output versus

ToF plot from NWB gated on the events that must have VW triggered. We can see proton,

deuteron and triton lines from left to right. By choosing a small window (blue window) on

the proton line as shown in Fig. 3.23, we can select protons with ToF in range [41.5, 43.5]

ns, corresponding to [58.6, 65.0] MeV in energy or [10.16, 10.7] cm/ns in velocity.

Based on LISE++ calculation [104], these protons should deposit 11.7 ± 0.7 MeV in

1-cm-thick BC-200 scintillator every time. Selecting on these events, then we plot the VW

geometric mean value(cid:112)Qtop ∗ Qbottom for every bar as shown in the top panel of Fig. 3.24

where Qtop and Qbottom are QDC values for top and bottom PMT. Due to PMTs’ dif-

ferent gains, different VW bars have different geometric mean value although protons de-

posited about same energy in every bar. By assigning every bar one coefficient α such that
GMcalibrated = α ∗ GMraw, we calibrate all VW bars’ geometric mean to be the same for

those proton events, as shown in the bottom panel of Fig. 3.24.

Similar to what we do in Chapter 3.2.1.4, we can also investigate the geometric mean

position dependence of VW bars. For a certain VW bar, we can check its geometric mean

versus position 2D plot for events sitting in the blue window of Fig. 3.23 as shown in Fig. 3.25.

Comparing Fig. 3.25 to the top panel of Fig. 3.8, we can see that the geometric mean of VW

bar is much less dependent of VW bar’s Y position, varying within 5% over the length of

the bar.

Fig. 3.26 is the ∆E-E plot for VW and NWB. The Y-axis is VW calibrated geometric

mean and the X-axis is NWB’s light output. The three slanted charged-particle lines are

protons, deuterons and tritons, from bottom to top, respectively. Because the proton line

98

Figure 3.23: Light output versus ToF 2D spectrum from front LANA (NWB) gated on
the events that must have VW triggered. The blue window (around 20 MeVee on Proton
line) gating on proton line selects the events where a proton’s normalized ToF is in range
[41.5, 43.5] ns and its light output is in range [19.5, 20.0] MeVee.

99

Figure 3.24: VW Geometric Mean(cid:112)Qtop ∗ Qbottom versus VW bar number 2D plot. The

top panel is before geometric mean calibration and the bottom panel is after geometric mean
calibration using GMcalibrated = α ∗ GMraw.

100

Figure 3.25: VW bar #18’s geometric mean versus Y position 2D plot for events sitting in
the blue window of Fig. 3.23. We can see that it is almost flat comparing to the top panel
of Fig. 3.8.

101

vanishes at around (X = 25,Y = 500) in Fig. 3.26, any charged-particle that punches

through VW and leaves a signal in LANA should deposit a signal in VW greater than

500 ADC channels as VW calibrated geometric mean. We can set 200 ADC channels as the

threshold to indicate whether VW is triggered by any charged-particle and take events below

threshold as noise. Bars need to be well calibrated among VW and LANA in order to see

charged-particle lines as shown in Fig. 3.26.

102

Figure 3.26: VW calibrated geometric mean versus NWB light output 2D plot.

103

Chapter 4

Performance of LANA

4.1 Neutron/γ Pulse Shape Discrimination

Pulse shape discrimination (PSD) technique is commonly used to distinguish whether a light

signal from the scintillator originates from neutron or gamma ray. This technique is based

on the characteristic of certain organic scintillators which have longer scintillation decay

time for proton (induced by neutrons) and charged particles emitted from nucleus-nucleus

collisions than for gamma rays [105, 106]. For scintillator molecules in configurations where

π-electron spins are fully paired, singlet states (S1) are created. Configurations with unpaired

π-electron spins give rise to triplet states (T1) where 3 spin component values are allowed:
ms = −1, 0, 1. The de-excitation of excited S1 results in the short decay component while

the kinetic of the excited T1 diffusion process and the following triplet-triplet interaction
and annihilation including T1 + T1 → S0 + S1 is responsible for the long decay component.

High concentration of triplets states are created from the short range of energetic protons

knocked out by neutrons. Therefore, compared to gamma rays, neutron contributes a larger

proportion in the long decay component of scintillation pulses. Figure 4.1 shows a schematic

drawing of the different pulse shapes for neutron and gamma ray signals.

104

Figure 4.1: A schematic of different pulse shapes for neutron and gamma rays. The peak
heights are normalized to be the same. This picture is adopted from Ref. [9].

105

4.1.1 Traditional PSD & VPSD comparison

In experiments, we applied two different gate widths to obtain the total (340 ns) and fast

component (first 30 ns) of light signals from LANA. Details about the electronics that we

used to enable PSD is described in Section 2.3. To minimize the position dependence of the

light output and to utilize signals from both the left and right PMTs in each neutron bar, the

geometric mean ((cid:112)Qlef t ∗ Qright) of the total and fast are constructed. Figure 4.2 shows a

2d plot with the GM of total component of light signals versus GM of fast component. Two

groups representing gamma rays and neutrons can be seen. In the past [9] we calculate a

value called “flattened geometric mean” to replace geometric mean in figure 4.2 so that the

splitting between gamma rays and neutrons is enhanced, as shown in figure 4.3. Flattened

geometric mean is calculated from the difference between total GM and scaled fast GM:

GMF lattened = GM − constant ∗ GMF ast

(4.1)

While traditional PSD analysis method cancels out some of the position dependence effect

due to the signal attenuation when the light travels along a scintillator bar to the PMT, this

method compromises the signal resolution as it includes the light signal from scintillator

bar’s far end which can worsen the resolution because the light transmission through the

scintillator to the far phototube reduces the signal size and consequently, the photon statistics

for that signal. An innovative method called ”Value-assigned Pulse Shape Discrimination”

(VPSD) [16] which takes full advantage of the light signal that comes from one end with

good resolution. The VSPD is mainly developed by Fanurs Teh, a graduate student in our

group. For illustration, we use data obtained from Americium-Beryllium neutron source as

described in section 3.2.1. In this method, instead of combining the information from left

and right PMTs of a bar at early stage by calculating geometric mean, we retain the left

106

Figure 4.2: LANA geometric mean versus fast geometric mean 2D plots from a typical bar.
The data was taken with 48Ca+124Sn at E/A = 56 MeV reaction. The top panel focuses on
the low value end, which is a zoomed-in version of the bottom panel. We can barely see two
lines in each panel, which are gamma rays (top) and neutrons (bottom).

107

Figure 4.3: LANA flattened geometric mean versus fast geometric mean 2D plot. The data
is the same as shown in figure 4.2 but the clustering of gamma rays (top) and neutrons
(bottom) is much clearer.

108

Figure 4.4: A two-dimensional histogram of (Qf ast, Qtotal) from the left end of a LANA bar.
The two solid curves are quadratic fits on the gamma ray cluster (top) and neutron cluster
(bottom) respectively. Qf ast and Qtotal correspond to SHORT Q and LONG Q in this plot.
This picture is taken from Ref. [16].

109

Figure 4.5: 2D vL,R plots for all the nine segments of one LANA bar, with 1/9 representing
the leftmost segment and 9/9 representing the rightmost segment. The solid line represents
the n/γ separation line, while the dashed line is the line perpendicular to the solid line that
pass through (-0.5, -0.5). This picture is taken from Ref. [16].

110

right information on individual PMT i.e. we analyze the signal to the left and right PMTs

separately. Figure 4.4 is an example of such 2D plot for the left end of a LANA bar. Two

quadratic functions are fitted along the neutrons and gamma lines over the range of interest

in figure 4.4. Then, we assign the value -1 and 0 to the points lying on the neutron and

gamma fitted lines respectively. Each pulse is assigned a value according to:

vL,R(Qf ast, Qtotal) ≡ QL,R
qγ(QL,R

f ast − qγ(QL,R
total)
total) − qn(QL,R
total)

(4.2)

where qγ and qn are the fitted quadratic functions for gamma rays and neutrons, respec-

tively. We called his procedure “valued assigned pulse shape discrimination” (VPSD). Note

that VPSD does not correct for the position dependence of the neutron light output signal.

To examine the position dependence, we plot the VPSD values from the left PMT (vL) vs.

the right PMT (vR). Figure 4.5 shows the 2D histograms of vR versus vL for nine segments

along the position of LANA bar. Near the ends of the bar, one can clearly see the separations

of neutrons from gammas. To take into account the position resolution, we rotate the plots
in figure 4.5 around point (−0.5, 0.5) by position dependent angles such that the green sepa-

ration lines are all vertical. This allows data from different segments along LANA bar to be

plotted cumulatively together while retaining the maximal separation between neutron and

γ. To be specific, mathematically, we propose a PSD metric named PPSD-X and PPSD-Y

(position-corrected VPSD) that is defined as:

P P SD-X(x, vL, vR) =

P P SD-Y (x, vL, vR) =

cos(θproj) + sin(θproj)

vLcos(θproj) + vRsin(θproj)

cos(θproj) + sin(θproj)

−vLsin(θproj) + vRcos(θproj)

(4.3)

where x is the hit position within range [−l/2, l/2] (l is the scintillator bar length), vR

and vL are the values calculated in VPSD as described in Equation 4.2. For a certain hit

111

position x, θproj is calculated as:

θproj(x) =

π
2

· x + l/2

l

(4.4)

This gives θproj = 0 for x = −l/2 and θproj = π

2 for x = l/2. The dominators in Equa-
tion 4.3 serve to normalize the projected neutron peak to be at P P SD-X ≡ 1. Figure 4.6

compares the PSD results using traditional flattened PSD method(left) and PPSD method

(right) for both best (top row) and worst (bottom row) performance bars. The advantage of

using the PPSD based on the VPSD method to separate the neutrons from gamma is clear.

The top panel of figure 4.7 shows the well separated neutrons and gamma in PPSD from

48Ca+124Sn at E/A = 56 MeV reaction. By projecting the PPSD spectra onto the x-axis,

we can get a PSD spectra with two peaks representing neutrons and gammas. Their relative

abundance can be obtained using a double Gaussian fit. This improves the resolution near

the ends of the bar because you can rely essentially on the near phototube and ignore the

far phototube because it is not required to resolve neutrons and gammas. As the separation

achieved is quite good, there is little ambiguity in the determination of percentage of gammas

which would be misidentified as neutrons if the neutron detector does not have PSD capability

as is the case for plastic scintillator bar. For plastic scintillator bars, one can only set a gate

to exclude prompt gamma-rays that travel to the bar from the target at the speed of light.

Other gamma rays are created by reactions of gammas, neutrons and charged particles that

come from the target and react with nuclei in the floor of the vault, for example creating a

gamma that hits the LANA device. For 48Ca+124Sn at E/A = 56 MeV reaction, the fraction

of such gammas that arrive after the prompt peak are shown in figure 4.8 as a function of

neutron energy that would be computed from their time of flight. It varies from around 10

112

Figure 4.6: PSD results comparisons between traditional flattened PSD method (left col-
umn) and VPSD method (right column) for both best (top row) and worst (bottom row)
performance bars.

113

Flattened PSDVPSDBest CaseWorst CasePPSDPPSD-X (arb. unit)PPSD YPPSD YPPSD-X (arb. unit)-1.4-1.2-1-0.8-0.6-0.4-0.200.20.4PPSD-Y (arb. unit)PPSD-Y (arb. unit)-1.4-1.2-1-0.8-0.6-0.4-0.200.20.40-0.2-0.40.20.4-0.3-0.10.10.30-0.2-0.40.20.4-0.3-0.10.10.3NeutronGammaNeutronGammaNeutronGammaNeutronGammaFigure 4.7: (top panel) Neutron/γ pulse shape discrimination obtained by PPSD method.
The X and Y axes correspond to vL and vR of Figure 7 in Ref. [16], after rotation to match
for different segments on LANA bar. The light output threshold is set to 2 MeVee. Gamma
rays aggregate in right bubble and neutrons are clustered in left bubble. (bottom panel) 1D
projection plot from the plot in top panel. Two Gaussian functions are fitted to γ events
peak (red dash line) and neutron events peak (green dash line). The blue solid line represents
the sum of two Gaussian functions. Taking events with gate of P P SD-X < −0.6 ensures
getting neutrons with nearly no gamma contamination.

114

Figure 4.8: Gamma contamination as a function of particle incident energies, if the scintil-
lation material used in this experiment to detect neutron has no PSD capability. The data
was taken with 48Ca+124Sn at E/A = 56 MeV reaction. The light output threshold is set
to 5 MeVee.

115

percent for 20 MeV neutrons to more than 50 percent for 200 MeV neutrons. For nuclear

reaction studies above Fermi energies, where no sharp peaks of neutrons are observed, it is

important to retain the ability to resolve gamma and neutrons in the neutron detectors.

4.1.2 PSD efficiency

In previous section, I give a brief summary and comparison of both tradition PSD and

VPSD analysis method. While more details of VPSD can be found in Ref. [16], we can

further illustrate the superiority of VPSD over traditional method with its application. In

the following, based on the results from VPSD method, I will show how to estimate neutron

PSD efficiency, gamma contamination and extract the corrected neutron spectrum.

To quantify the gamma ray background in neutron events, we examine the bottom panel

of figure 4.7 which contains the 1D vertical projection plot of its top panel. We found that

the sum of two Gaussian functions could reproduce the shape pretty well. Based on Gaussian

fits, if we take events with ”PPSD X<-0.6” condition, we will obtain 94.2 percent efficiency

of the neutrons with gamma contamination less than 1 percent. The efficiency corrected

neutron TOF spectrum using this method is shown in black dash line in figure 4.9. This is

one way to get the neutron spectrum.

There is another way to obtain the neutron spectrum to verify the above estimation.

To do this, we generated a series of TOF 1D spectra as shown in the bottom panel of
figure 4.10. This time, we set a gate at “P P SD-X = −0.1” as indicated in the top panel
of figure 4.10. We take all events with “P P SD-X > −0.1” as pure gamma ray events and
the rest with “P P SD-X < −0.1” as neutron with gamma contamination. The time of flight
spectrum for pure gamma events with “P P SD-X > −0.1” are shown in the bottom panel
of figure 4.10. ToF spectrum for “P P SD-X < −0.1” corresponding to neutron with gamma

116

Figure 4.9: Pure neutron TOF spectra obtained by two correction methods. Black dash
line is calculated based on the Gaussian fits in figure 4.7: Take neutron events with ”PPSD
X>0.6” and then correct for 94.2% efficiency. Green solid line is the same green line shown
in figure 4.10 using gamma peak matching method.

117

Corrected using Gaussian Fit MethodCorrected using Gamma Peak Matchingcontamination is drawn as the green line in figure 4.10. Red line representing pure gamma

ray events has a strong prompt gamma peak at around 16 ns. It also has a long tail from

reactions on surrounding material that looks like neutrons. While the majority of blue line

includes ALL of the neutron events, there are also gamma ray events from the tail of the

gamma ray Gaussian, and the (n,gamma) background reactions mixed in. To get rid of the

gamma contamination in blue line, we first assume that the gamma events mixed in blue

line have the same ToF spectrum shape as pure gamma ray ToF spectrum in red with some

scaling constant. Then we use the prompt gamma peaks in red and blue lines as an indicator

of this scaling constant. We can calculate this scaling constant by doing division between

the prompt gamma peak count heights of red and blue lines.

In the case of figure 4.10,

the scaling constant is 0.449. To get pure neutron spectrum after correction, we multiply

the pure Gamma Tof spectrum by 0.449 and subtract it from neutron ToF with gamma

contamination. The neutron ToF after correction is shown in green line both in figure 4.10

and figure 4.9.

Figure 4.9 compares the pure neutron ToF spectra after correction using two methods

described above. The black dots are the pure neutron spectrum rescaled by 1/0.94 as dis-

cussed in the first procedure. The green line is what we did second by taking everything

in the neutron PSD peak and subtracting the gamma contamination. These two spectra

agree with each other within 2 percent. The gamma contamination rate in these spectra is

within 1 percent based on previous analysis and indeed we can see a small prompt gamma

peak at around 16 ns. Because the speed of neutrons emitted from our experiments can

not be close to the speed of light, particles with TOF below 20 ns will be eliminated from

neutron events in further neutron energy and momentum spectra analysis. This will make

the gamma contamination in neutron spectra much smaller than 1 percent.

118

Figure 4.10: (top panel) Same as the bottom panel in figure 4.7 but set a gate at “P P SD-X =
−0.1” to get pure gamma ray events and neutron with gamma contamination. (bottom panel)
ToF spectra with different gate conditions. Spectrum of neutron and gamma where charged-
particles are vetoed is drawn in black. Red line shows pure gamma ray events with condition
“P P SD-X > −0.1” while blue line shows neutron with gamma contamination with condition
“P P SD-X < −0.1”. Green line displays the ToF spectra after correction using gamma peak
matching method, which is the same line drawn also in green in figure 4.9.

119

Neutron + GammaPure Gamma RayNeutron with Gamma ContaminationPure Neutron after correction4.2 Neutron Light Output Comparison with SCINFUL-QMD

To successfully detect a neutron in LANA, the neutron needs to interact with the scintillating

material and deposit enough that it is above a threshold value for which electronics can

generate a trigger signal reliably. Because neutrons are neutral, a neutron interacts with the

detector via the strong interaction making the detection probability significantly less than

unity (<10 percent) for a thickness of 6.35 cm of the LANA scintillator bars. There are two

different ways that one can define the efficiency; therefore it is easy to become confused about

what one is discussing. This is because the efficiency can be defined in a way that it includes

the solid angle and it can also be defined in a way that it includes only the probability that a

neutron interacts deposits energy above the threshold value if it goes through the solid angle

subtended by the detector.

For the following discussion, we take the second definition and define the neutron de-

tection efficiency as the probability of detecting a neutron that traverses a detector with a

particular incoming kinetic energy. Determining this efficiency is indispensable in extracting

the absolute magnitude and shape of neutron energy spectrum. It depends on the thickness

of the scintillator and of the electronic threshold applied to the scintillator signal that must

be overcome by the induced signal.

The NE213 scintillator in LANA is a hydrocarbon fluid containing both protons (hydro-

gen nuclei) and carbon atoms in it. Neutrons below 10 MeV are typically scattered elastically

by these protons and subsequent interactions of the recoiling protons with the scintillators

create the photons to be detected. Neutrons can be detected also through inelastic, fusion,

or breakup nuclear reactions on the carbon nuclei in the scintillator fluid. This becomes

increasingly important for more energetic neutrons. When a neutron reacts with a carbon

120

nucleus, one or more charged particles can thereby be generated. Besides considering various

reaction channels between incident neutrons and scintillation material, we need to take how

the scintillator geometry influences the induced signal into account because events can occur

that involve recoiled protons escaping the detector without depositing all of their energies.

The resulting signal may be above the detection threshold and be counted or below the detec-

tion threshold and be lost. Developing a simulation codes that can handle all these processes

is a complex task because some of the reaction channels are not well described in current

detector simulations and it is an ongoing project for one of our Korean collaborators. To

obtain preliminary neutron spectra in this thesis, we used a code called SCINFUL-QMD [5]

developed by Satoh et al. at the Japan Atomic Energy Agency. This code is one of the more

complete simulation in modeling neutron reaction processes in the detector and reproducing

experimental data. Using SCINFUL-QMD, we are able to determine the neutron detection

efficiency in LANA. To validate the code, we compare the simulated neutron light response

function to our experimental data.

SCINFUL-QMD code simulates the NE-213 scintillator light response of neutrons from

0.1 MeV to 3 GeV using the Monte Carlo technique. Above 150 MeV, multiparticle breakup

is an important decay mode and to model this, SCINFUL-QMD incorporates a quantum

molecular dynamics model (QMD) and the statistical decay model (SDM). The QMD semi-

classically describes the behavior of nucleons and mesons during nucleus collision and thus

simulates the process for these more complicated nucleon reactions. The current version of

SCINFUL-QMD code restricts the configuration of detector to be in the shape of a cylinder

with radius and height as input variables. We adjust the input variables including cylin-

der’s height, radius similar to the geometry of our unit cell of 6.35cm and 7.62cm as depth

and height, and light attenuation factor is then adjusted by comparing the simulated light

121

response to the data.

Figures 4.11 , 4.12 and 4.13 show a more comprehensive neutron light response compar-

ison between experimental data and SCINFUL-QMD simulation using neutron light output

versus incident neutron energy. Figure 4.14 shows a two dimensional representation of the

light output response as a continuous function of the neutron energy En. In general, we find

that SCINFUL-QMD reproduced the shapes of light output spectra pretty well for different

incident neutron energies. This is consistent with the study by Coupland et al. [9]. For that

work, accuracy in the shape of the spectrum was extremely important as the veto wall was

not available then to eliminate charged particle contamination in the neutron walls. So it

was necessary to know details of the light output response in the regions of neutron energy

and light output where the charged particle contamination was absent.

The efficiency for detecting a neutron of a given energy in a given scintillator bar corre-

sponds to the probability of getting a signal in the neutron wall that is over the experimental

threshold when a neutron of that energy hits that bar in the neutron wall. To calculate the

efficiency for a neutron at certain energy,we need to choose the threshold in the geometric

mean signal in the bar the neutron signal must exceed. During the experiment, we set a

hardware threshold on the bars so that a signal of 3 MeVee would be detected everywhere

on the bar. Here, we raise that threshold to 5 MeVee. To calculate the efficiency for detec-

tion of an energy deposition above this threshold, we integrate the properly normalized light

output spectra e.g. figures 4.11 , 4.12 and 4.13, over all light output values higher than that

threshold value. Each of these light output curves gives the efficiency at one energy. Doing

this at one MeV intervals in the incident neutron energy provides the neutron efficiency as

a function of energy.

There are discrepancies between the observed light output in Figures 4.11, 4.12 and

122

4.13 and the simulation. These discrepancies between data and simulation may be caused

by the significant limitations of changing the detector geometries and moving the position of

neutron source in SCINFUL-QMD code. It is also hard to reproduce the light attenuation,

scattering and collection processes in simulation. Ongoing efforts are being taken to embed

SCINFUL-QMD into GEANT4 platform to make the code more versatile and more accurate

for our purposes. The final neutron spectra will be obtained after that effort is complete.

Nevertheless, we now examine the neutron spectra using the present efficiency calculations.

Based on SCINFUL-QMD simulation with a threshold of 5 MeVee, the neutron detection

efficiency of LANA for neutrons with energies greater than 25 MeV is calculated as shown

in figure 4.15. Low energy neutrons have larger contamination due to scattering from the

beam dump and the floor and ceiling of the experimental vault and we have not studied that

contamination extensively. 25 MeV also corresponds to the energy threshold of the charged

particle detected in HiRA.

123

Figure 4.11: Comparison of neutron light output spectra from experiments and SCINFUL-
QMD with different incident neutron energies at 20 MeV (top panel) and 40 MeV (bottom
panel).

124

Figure 4.12: Comparison of neutron light output spectra from experiments and SCINFUL-
QMD with different incident neutron energies at 60 MeV (top panel) and 80 MeV (bottom
panel).

125

Figure 4.13: Comparison of neutron light output spectra from experiments and SCINFUL-
QMD with different incident neutron energies at 100 MeV (top panel) and 120 MeV (bottom
panel).

126

Figure 4.14: Comparison of neutron light output versus incident neutron energy 2D plots
from experiment data (left) and SCINFUL-QMD simulation (right).

127

ExperimentSCINFUL-QMD100Figure 4.15: The neutron detection efficiency of LANA as a function of neutron incident
energy. Detection efficiencies for neutrons with incident energies more than 25 MeV are
used.

128

4.3 Preliminary Neutron Spectrum

We extracted preliminary neutron spectrum from 48Ca+64Ni at E/A = 140 M eV reaction

as shown in figure 4.16. Firstly, when calculating the raw energy spectra of neutron drawn in

black, we adopt a light output threshold of 5 MeVee to ensure the whole LANA can detect

particle hits uniformly. The majority of gamma contamination comes as prompt gamma

so they are filtered out naturally by the time-of-flight gate cut. For gammas that hit the

LANA within the time window of neutrons, most of them come from the experiment vault

background. Most of them are eliminated by utilizing the neutron/γ discrimination method

described in Chapter 4.1. To measure the neutrons from central collisions, a deduced impact

parameter gate from [0,0.4) is applied. The red line above the black line in figure 4.16 takes

the detection efficiency correction into account by using the SCINFUL simulation results

from figure 4.15.

In figure 4.17, neutron spectra with several angular cuts are shown for the same reaction

system. The Y-axis is count per bin and the X-axis is neutron energy in MeV in lab frame.

A moving source model is applied to extract the following parametrizations of this moving

source: apparent temperatures T , velocities Vs, multiplicities N and Coulomb energy Ec.

Here, the Coulomb energy is the energy gained by Coulomb repulsion of the exciting proton

by the rest of the system. In the context of compound nucleus, that would be called the

Coulomb barrier. In this model, the particles are assumed to be emitted isotropically from

one moving sources, following Maxwell-Boltzman distribution in source rest frame [107]:

d2σ
dΩdE

=

N

2(πT )3/2

(E − Ec)1/2exp[−(E − Ec)/T ]

(4.5)

To apply this model to neutron energy spectrum measured in lab frame, we need to do

129

Figure 4.16: Neutron energy spectrum measured by the front LANA from 48Ca+64Ni at
E/A = 140 M eV reaction. The data come from a batch of continuous runs of around 18
hours. The Y-axis is counts per bin and the X-axis is neutron energy in MeV in lab frame.
The black line represents the raw spectra and the red line shows the spectra after detection
efficiency correction using the efficiency data from Fig. 4.15. All data shown here have a
deduced impact parameter gate from [0,0.4).

130

the following transformation [108]:

d2σ

dΩlabdElab
(cid:48)

E
(cid:48)(cid:48)

E

N

=

2(πT )3/2
(cid:114)
= Elab − Ec
(cid:48) − 2

= E

(cid:48)

)1/2exp[−(E

(cid:48)(cid:48)

)/T ]

(E

(cid:48)

(

1
2

mV 2

s )cos(θlab) +

1
2

mV 2
s

E

(4.6)

(4.7)

(4.8)

where θlab is the emitting angle measured in lab frame, m is the mass of the emitted

particle and Elab is the energy of the emitted particle measured in lab frame. To do this

moving source fit for figure 4.17, because neutron has no charge, we set Ec to be 0. T , N

and Vs are the global free parameters for 3 spectra with different angular cuts. The surface
temperature is determined to be 26±1 MeV from the fitting using moving source model.

The best fit value for the source velocity Vs is found to be 0.48 times of the beam velocity.

The extracted temperature is consistent with a mid rapidity source created in heavy ion

collisions at 140 MeV/u incident energy1. Consider the case of a moving black body:

its

black body spectrum shows a frequency shift due to the relativistic Doppler effect which
depends on the angle α between the observer and the source: f(cid:48) = f

. This leads

1− v

(cid:113)

c cos(θ)
1−( v
c )2

to an angle dependent temperature and the observer will not detect an isotropic black body

spectrum [109, 110].

1Transformation assumes same temperature in the center-of-mass frame. However, recent studies suggest

that the temperature could be different in different frame.

131

Figure 4.17: Neutron energy spectrum from 48Ca+64Ni at E/A = 140 M eV reaction with
angular cuts. The Y-axis is count per bin from a batch of continuous runs of 48Ca+64Ni
at E/A = 140 M eV reaction and the X-axis is neutron energy in MeV in lab frame. The
error bars only reflect statistical uncertainties. From red, green and blue lines, different
polar angular cuts from around 32°, 38° and 46° are applied respectively. Solid lines show
the result after fitting with moving source model. The surface temperature of the moving
source model is extracted to be 26±1 MeV. Similar moving source fits of the proton spectra
in the same angular range yield similar results.

132

Chapter 5

Summary

The goal of detecting neutrons in experiment 14030 and 15190 is to construct neutron/proton

ratios observable to study the symmetry energy. Detection of the charged-particles (including

protons) using the upgraded HiRA10 array has been analyzed. This dissertation describes

the initial effort to analyze the neutrons.

Following is a list of major improvements of this thesis experiment compared to the earlier

version of experiment done in our group:

1. Full removal of charged-particle contamination from neutron spectra using the newly-

built Charged-Particle Veto Wall.

2. Development of an innovative method that can calibrate the time, position and light

output of neutron scintillation detectors using only cosmic rays.

3. Development of a new algorithm for neutron/γ pulse shape discrimination using VPSD

method.

4. Measurement of charged-particles with greater extended kinetic energy ranges. For

example, HiRA10 can measure protons with kinetic energy up to 200 MeV, compared

to 116 MeV for the original HiRA.

The ability to fully remove charged-particle contaminations from neutron spectra is one

of the essential requirements to successfully compare experimental n/p yield ratios with

133

simulation results, especially for the high kinetic energy regions where the observable of yield

is much more sensitive to the effective mass splitting as shown in Fig. 1.3. By successfully

vetoing the charged-particles in the LANA walls, we can successfully measure the neutron

energy spectra beyond 200 MeV which was not achieved in previous study.

This thesis describes the measurement of neutrons emitted in heavy ion collisions. In

experiment E14030 and 15190, we studied 16 reaction systems including 2 beam isotopes of

40Ca and 48Ca, 2 beam energies of E/A = 56 MeV and 140 MeV, and 4 targets of 58Ni, 64Ni,

112Sn and 124Sn. Neutrons and charged-particles were measured in these reaction systems in

order to ultimately identify and construct observables that are sensitive to symmetry energy,

and extract EoS constraints using transport calculations.

The major part of this dissertation focuses on the measurements of neutrons with im-

proved detection equipment and analysis methods. A Forward Array used as the start timing

detector for the neutron wall, was upgraded to increase its forward angle coverage. A new

Charged-Particle Veto Wall was designed, constructed and placed in front of LANA to pro-

duce clean neutron spectrum without charged-particle contamination. An accurate, fast and

convenient calibration method of LANA using cosmic muons was tested [111] and used to de-

termine the intrinsic timing and position resolution of the LANA. Amazingly, the resolution

is nearly the same as 20 years ago. We also developed a new neutron/γ discrimination pro-

cedure based on LANA’s PSD capability which can better separate neutrons from gammas

when compared to the traditional method. The discrimination provides accurate quantita-

tive gamma contamination and neutron loss estimation [16] suggesting that PSD is needed

in heavy ion collisions as contamination from gammas reaches 50 percent for high energy

neutrons. We found that neutron light output spectrum acquired from LANA is comparable

to the simulation results of SCINFUL-QMD code [5] by adjusting the attenuation length

134

parameter in the code. This allows us to use SCINFUL to simulate the neutron efficiencies

of LANA from 10 to 100 MeV neutrons. To validate the analysis procedure, we generate

the efficiency corrected neutron spectra for 48Ca+64Ni reactions at E/A = 140 M eV . Us-
ing a moving source model, the source’s surface temperature (20±1 MeV) and velocity (0.5

vbeam) are extracted. These parameters are reasonable and similar to those extracted from

the proton spectra.

Due to the complexity of the experiment and the large amount of data acquired (27 TB),

only the neutrons emitted in two reactions and WallB of the two LANA walls have been

studied in details. The data presented in this dissertation mainly comes from 48Ca+124Sn

and 48Ca+64Ni reaction system to demonstrate various analysis procedures needed for neu-

tron measurements. Care is needed to extend the analysis to the remaining 14 systems. This

thesis provides more of a preview of the data to come than a conclusion of the project. More

careful investigation in the future is needed to validate every analysis step and determine the

corresponding uncertainties. On the transport model side, efforts are being taken to identify

better observables and address uncertainties in the simulations of heavy ion collisions.

135

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136

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