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PRODUCTION OF NUCLEI IN NEUTRON UNBOUND
STATES VIA PRIMARY FRAGMENTATION OF “CA

presented by

GREGORY ARTHUR CHRISTIAN

has been accepted towards fulfillment
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5/08 K IProj/Acc8Pres/CIRC/Dale0ue undd

 

 

 

PRODUCTION OF NUCLEI IN NEUTRON UNBOUND STATES
VIA PRIMARY FRAGMENTATION OF 480A

By

Gregory Arthur Christian

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Physics and Astronomy

2008

ABSTRACT

PRODUCTION OF NEUTRON UNBOUND NUCLEI VIA PRIMARY
FRAGMENTATION OF 48CA

By

Gregory Arthur Christian

The method of sequential neutron decay spectrosc0py beginning with a primary
beam of 60 MeV/ nucleon 48Ca was investigated as a potential tool to measure un-
bound resonances in neutron rich nulei. Neutrons were measured in coincidence with
fragments, and unbound resonances were observed for 10Li, 12”Be, and 23O. The
method is currently limited to resonances with small decay energies (Edm,y S, 100
keV) in lighter (Z s 10) nuclei, and the possibility of extending it to heavier, more

neutron-rich nuclei will be discussed.

Contents

1 Introduction 1
1.1 Structure of Neutron Rich Nuclei .................... 1

1.2 Neutron Spectroscopy .......................... 2

2 Experimental Setup and Calibrations 7
2.1 Sweeper Magnet .............................. 10
2.2 MoNA ................................... 13

3 Data Analysis 17
3.1 Particle Identification ........................... 17
3.2 Scattered Background .......................... 23
3.3 Decay Energy Reconstruction ...................... 25
3.4 Monte Carlo Simulations ......................... 26

4 Results and Discussion 31
4.1 Results ................................... 31
4.2 Analysis of Low Energy Decays ..................... 39

5 Future Prospectives 55
6 Summary 58
A Using the MoNA Simulation Code 59
A.1 Introduction ................................ 59
A2 Getting Set Up .............................. 60
A3 Running the Simulation ......................... 62
A.4 Using Flags ................................ 64
A.4.l Decay Energy Model ....................... 67

A42 Stripping Reaction Model .................... 67

A.4.3 GEANT Output ......................... 68

A.5 Analyzing Your Simulation ........................ 69
A.5.1 Parameter Names ......................... 71

iii

A.6 Customizing the Simulation ....................... 73

A.7 Using SVN ................................. 77
B Using ROOT 79
3.1 Introduction ................................ 79
B.2 Installing ROOT ............................. 80
B.3 Files and Trees .............................. 81
B.4 Drawing Histograms ........................... 84
B.5 TCanvases ................................. 87
B.6 Gates ................................... 89
8.7 Creating Pseudo Parameters ....................... 91
8.8 Using Macros ............................... 92
B.9 Various Odds and Ends .......................... 94
Bibliography 97

iv

List of Tables

4.1 Summary of Previous 10Li Ground State Measurements ......... 40
A.1 Simulation Beamline Element Numbering Scheme ............ 72
A2 Simulation Parameter Naming Scheme .................. 72
B.1 Example ROOT TTree ........................... 82

List of Figures

1.1

1.2

1.3

1.4

2.1

2.2

2.3

2.4

2.5

2.6

2.7

3.1

3.2

3.3

3.4

Chart of Light Neutron Rich Nuclei ................... 2
SDNS Setup at Large Angle ....................... 5
Fragmentation Reaction Angular Distribution .............. 5
Sample Zero Degree SDNS Setup. .................... 6
Beam Production .............................. 8
Experimental Setup ............................ 9
TDC Pulser Calibration. ......................... 10
Masked CRDC Position Spectrum. ................... 11
Sample MoN A Bar Time Difference Spectrum .............. 13
MONA Angular Acceptance. ....................... 14
'y-ray ToF .................................. 15
Uncorrected Particle ID. ......................... 18
Focal Plane :c-vs-O. ............................ 19
Particle ID x—correction factors. ..................... 20
Particle ID 0-correction factors. ..................... 20

vi

3.5 Particle ID ................................. 21

3.6 MONA ToF for 10Be Fragment ...................... 22
3.7 Scattered Background .......................... 24
3.8 Tracking of Background Events Through the Sweeper .......... 25
3.9 9Li Fragment Energy Distribution. ................... 26
3.10 Neutron Kinetic Energy Distributions. ................. 27
3.11 Opening Angle Distribution ........................ 28
4.1 Observed Isotopes ............................. 32
4.2 Velocity Difference Spectra ........................ 34
4.3 Decay Energy Spectra .......................... 35
4.4 Event Mixed Decay Energies. ...................... 36
4.5 Event Mixed Decay Energies. ...................... 37
4.6 Efficiency of the Experimental Setup .................. 38
4.7 Simon et al 10Li Decay ........................... 41
4.8 9Li + n Decay Energy Spectrum ..................... 42
4.9 9Li and 10Li Level Scheme ......................... 43
4.10 Deak et al 10Be + 11 Relative Velocity. ................. 45
4.11 Peters et al 11Be Decay. ......................... 45
4.12 10Be + n Decay Energy Spectrum .................... 46
4.13 10Be and 11Be Level Scheme ........................ 47

vii

4.14 Thoennessen et al 12Be + n Relative Velocity. ............. 49

4.15 12Be + n Decay Energy Spectrum .................... 50
4.16 12Be and 13Be Level Scheme ........................ 51
4.17 Schiller et al 230 Decay. ......................... 52
4.18 220 + n Decay Energy Spectrum .................... 53
4.19 22O and 230 Level Scheme ......................... 54
5.1 Neutron TOF at Different Beam Rates ................. 55
B.1 Example 1d ROOT Histograms ...................... 85
B.2 Example 2d ROOT Histogram and Divided Canvas ........... 86
B.3 Example of 2d Gates in ROOT. ..................... 91

Images in this thesis are presented in color.

viii

Chapter 1

Introduction

1.1 Structure of Neutron Rich Nuclei

Nuclei are highly complex, many body quantum mechanical systems consisting of
spin 1 / 2 fermions (protons and neutrons) which interact via the strong nuclear and
coulomb forces. The strong force is attractive and responsible for holding nuclei to-
gether, while the coulomb force provides a relatively small repulsive interaction be-
tween the positively charged protons.

Due to their complexity, phenomenological models must be employed to describe
the structure of nuclei. The most widely used model is the shell model, which subjects
the constituent protons and neutrons in a nucleus to a mean field potential. The form
of this potential is adjusted to reproduce experimental observations. Typical shell
model potentials build upon the Woods-Saxon potential with a spin-orbit coupling

term [1]:
—V0
_ 1+ 6(‘T‘Rl/O‘

 

V(r) — Va. (11)

Subjecting nucleons to a potential well causes them to occupy discrete energy
levels. These energy levels are observed to group into shells, analogous to the case of
electrons in an atom. The energy gaps within a shell are relatively small, and those

between neighboring shells are much larger. Nucleons can be excited to higher energy

 

      
 

I stable I bound
[3 unbound - measured
E] unbound- limit I
X

no bound excited states
I

 

 

 

 

o i 10 20 3o
neutrons

Figure 1.1: Chart of the nuclides showing neutron rich isotopes in the Z S 12 region.
Unbound isotopes and isotopes without any bound excited states are indicated on
the figure [2].

levels within the outermost shell or between shells if enough energy is added to the
nucleus.

There is evidence that the shell structure of very neutron rich nuclei is significantly
different from that of stable nuclei. Shell models describing nuclei in this region are
often tested based on their reproduction of nuclear energy levels. For nuclei lying
beyond the neutron dripline—those for which the number of neutrons is so great that
the nuclei are unstable with respect to neutron emission—the energy of the ground

state with respect to neighboring nuclei is also of interest.

1.2 Neutron Spectroscopy

The excitation spectra of ordinary nuclei are typically studied using 7-ray spec-
troscopy. This involves measuring the energy of the 'y—rays emitted when an excited
nucleus de-excites to a lower energy state. For very neutron rich nuclei, however, ex-
cited states often lie above the one-neutron separation energy, as indicated in Figure
1.1. The lack of bound excited states makes it difficult to study the structure of these
nuclei with 7-ray spectroscopy. Thus other techniques must be employed to observe
unbound excited states, whose decay is dominated by neutron emission.

Single and multiple particle transfer reactions from stable beams have been used

to populate and characterize unbound states in lighter (Z S 4) neutron-rich nuclei
[3,4]. In order to populate heavier nuclei close to the dripline, radioactive beams are
required. In addition to transfer reactions [5—8], fi-delayed neutron spectroscopy [9—11]
and invariant mass measurements following knockout reactions [8,12,13] have also
utilized radioactive beams.

An alternative method to populate excited states of very neutron-rich nuclei with
stable beams is sequential neutron decay spectroscopy (SNDS). In this method the
excited nuclei are produced in heavy-ion reactions and the decay fragments are mea-
sured in coincidence with the emitted neutrons in a collinear geometry.

Early SDNS experiments detected neutrons and fragments at large angles relative
to the beam [14—16]. An example setup, taken from Ref. [15], can be seen in Figure 1.2.
In these early experiments, the angular separation between fragments and neutrons
was needed to allow for event by event separation of neutrons and charged fragments.
Large angle detection is disadvantageous, however, because medium energy fragmen-
tation reactions are kinematically focused near zero degrees. Hence the yield for large
angle fragment-neutron coincidences is rather low. This is demonstrated in Figure 1.3,
which shows a simulated angular distribution, produced by the code LISE++ [17],
for the fragmentation of 18O into 9Li. As can be seen in the figure, the relative yield
peaks at zero degrees and falls off sharply at larger angles.

Later SDNS experiments, beginning with Kryger et al. [18], made use of a magnetic
spectrometer to separate charged fragments from neutrons. In this configuration, the
neutron detector can be placed at zero degrees relative to the incoming beam, resulting
in a greater yield of detected coincidences than in the case of a large angle setup. A
generic schematic of the zero degree setup is shown in Figure 1.4. The higher yield
afforded by the zero degree setup allowed more neutron rich nuclei to be studied,
including nuclei beyond the dripline [18—20].

Zero degree SDNS experiments performed in the past [18—20] have only measured

two observables: neutron velocity (12“) and fragment velocity (Uf). In order to extract

a decay energy from these measurements, the authors must rely on the approximation
that the opening angle between the fragment and the neutron, 60pm, is equal to zero.
This approximation is valid since the angular acceptance of these experiments is small.

In the zero degree approximation, decay energy can be approximated as:

I
E eca 1’ —— -1 , 1.2
d y f‘( /1— ”Eel/02 ) ( l

where u is the reduced mass of the neutron-fragment system. In practice, experiments
using the small angle approximation make use of Monte-Carlo simulations to relate
Ede“), to vrel. These simulation programs model Edecay with a chosen distribution,
then track the fragment and neutron through the experimental system, applying all
relevant resolution and acceptance effects. A simulated relative velocity curve is then
calculated and compared directly to the data.

Although the use of Equation 1.2 proves to be quite useful in extracting decay
properties of unbound nuclei, it is desirable to make a measurement of Edemy directly,
rather than rely on the approximation. This can be achieved by measuring 00pm,

which makes it possible to calculate Edecay directly using the invariant mass method:

 

Edecay = \/m§ + mg + 2 (E,- En — pf - pn - cos (00,...» — m. — m... (1.3)

Until now, the use of zero degree SDNS measurement techniques has been limited
to the study of light nuclei (Z s 4) produced with light primary beams (Z ~ 8).
Moreover, past SDNS experiments have relied on relative velocity measurements to
estimate decay energy [18—20]. In the present work, the feasibility of using zero degree
SDNS to extract a direct measurement of Edecay for heavier isotopes, starting with a

primary beam of 48Ca, is explored.

Neutron Detector

 

    

vane) PLF Telescope

Figure 1.2: Example SDNS experimental setup at large angle, taken from Ref [15].

 

 

 

 

g :
2 I
° -
'57 5i
3 .
5 .
o 4 ‘
“i I
si-
22-
.3.

0 -1o -5 o 5 10 15

Angle(degrees)

Figure 1.3: Simulated angular distribution for the projectile fragmentation reaction
9Be(18O, 9Li)X. [17].

_ Neutron
Incomlng ,5, :. ..,., Detector(s)

/ Beam .\

Bending
Magnet

   
     

Charged
Fragments '

Fragment
Detectods)

Figure 1.4: Generic SDNS setup with neutron detector at zero degrees.

Chapter 2

Experimental Setup and

Calibrations

The experiment was performed at the National Superconducting Laboratory (NSCL)
at Michigan State University. A primary beam of 48Ca was accelerated to 90 MeV/ u
using the coupled K-500 and K—1200 cyclotrons [21]. In order to allow reaction prod-
ucts to be bent by the sweeper magnet (see below), the beam was degraded to 62.8
MeV/ u in the A1900 fragment separator [22]. The reason for first accelerating the
beam to 90 MeV/u then degrading it, as opposed to starting out with a ~ 60 MeV/ u
beam, is that 90 MeV/ u 48Ca is a standard tune of the NSCL’s coupled cyclotron
system. Hence a higher beam quality is achieved by accelerating to 90 MeV/u then de—
grading, as opposed to accelerating directly to ~ 60 MeV/ u. After exiting the A1900,
the beam was delivered to a 94 mg/cm2 beryllium reaction target. A schematic of the
beam production setup can be seen in Figure 2.1.

Charged fragments produced in the reaction of calcium on beryllium were first
sent through a focusing quadrapole triplet and then deflected through a large gap
sweeper magnet [23]. Neutrons produced in the reaction were detected by the Modular
Neutron Array (MONA) [24,25] located at zero degrees. The timing start signal for
all events was provided by the cyclotron radio frequency (RF) signal. A schematic of

the experimental setup can be seen in Figure 2.2.

 

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Raw Sweeper TDC (channel number) Raw MONA TDC (channel number)
Figure 2.3: Example TDC spectra from pulser calibration runs for sweeper TDCs (left
panel) and MONA TDCs (right panel).

2. 1 Sweeper Magnet

The dipole sweeper magnet has a bending angle of 43° and a vertical gap of 14 cm.
During the experiment it was set to a magnetic rigidity of 2.994 Tm, and a tungsten
beam blocker was placed on the low rigidity side of the magnet in order to block
unreacted beam particles. The focal plane box located after the magnet contains
detectors which can be used to measure position, timing, and energy information of
the charged fragments. The present experiment utilized a pair of 30 mm x 30 mm
cathode readout drift chambers (CRDCs) located 182 cm apart to measure focal
plane position and angle; a 65 cm long ion chamber to measure energy loss; and a
thin (4.5 mm) plastic scintillator to measure time of flight (ToF).

The TDCs for each of the timing detectors were calibrated using a pulser set to a
20 ns period; an example calibration spectrum can be seen in the left panel of Figure
2.3. Time offsets were set based on target-out runs with the sweeper magnet set to
beam rigidity. Running at this setting ensures that the central velocity of 48Ca events
in the focal plane is at 10.5 cm/ns, and dividing this into the known path length of

680 cm gives a travel time of 64.8 ns.

 

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~20
CRDC1 X-Position (mm)

Figure 2.4: CRDC 1 y—vs—a: spectrum with a mask placed in front of the detector.

CRDC a: (dispersive) positions were calculated based on the deposited charge on
each pad. The centroid of the charge distribution in pad space is calculated by first
finding the pad with maximum deposited charge and then performing a gravity fit
over all of the pads. A gaussian fitting routine is then called, using the centroid and
width of the gravity fit as initial parameters. The resulting centroid of the gaussian
fit is then defined as the :1: position in pad space. The slope needed to convert pad
position to position in mm is simply the width of each pad: 2.54 mm. Offsets are
determined using mask runs as described below.

Position in the y (non-dispersive) direction is measured based on the travel time
of the avalanche charge from the interaction point to the pads. The slope and offset
needed to turn the raw time signal into a calibrated position in mm is determined by

placing a mask with holes and a slit drilled at known positions in front of the CRDC

11

detector. The beam is then swept across the focal plane to illuminate the entire mask.
The measured CRDC position spectrum, as shown in Figure 2.4, only contain data at
the locations of the mask holes and slit. The slope is calculated based on the spacing
between the holes, while offsets in both the a: and y directions are determined from
the known position of the center hole. The L-shaped pattern seen in the right side of

the figure is used to identify the center hole.

12

 

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0.5

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Ill lIIlIlIIIIlJIlIlIIlIIIJIIIIIIIII IIIIII

-5 -20 -15 -10 -5 o 5 10 15 20 25
Tdm(ne)

 

Figure 2.5: Time difference spectrum for the center bar in MONA’S front layer.

2.2 MONA

MONA is an array of 144 plastic scintillator modules, each 10 cm high x 200 cm
wide x 10 cm deep. The scintillation light is detected on both ends of the modules by
photomultipiler tubes (PMTs). ToF is determined by the mean of the timing signals of
the two PMTs, while horizontal position is determined by the time difference between
the two PMT signals, as explained below. Vertical and lateral position are determined
based on the module in which the neutron interacts.

In order to convert the time difference between the left and right PMTs into a

calibrated position, a simple linear conversion was used:

m=m~t+b, (2.1)

13

 

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83 3
2

8’

32

2

an

I:

‘5

>0

<

2..

E-1

 

Figure 2.6: Plot of MONA y-angle vs. m-angle, demonstrating the limited acceptance
caused by the quadrupole tiplet.

where a: is the position in the bar, t is the time difference between the two PMTs,
and m and b are the linear slope and offset, respectively. The needed parameters
m and b are determined experimentally using cosmic ray muons; Figure 2.5 shows
an uncalibrated time difference spectrum for one MONA bar, taken from a cosmic
ray run. The physical edges of the bar are defined to be at 1/3 of the maximum
height on each edge of the spectrum, based on Monte Carlo simulations. Using the
200 cm length of the bar, along with the position in time space of each edge, m can
be calculated to be:

200 cm

m = —, (2.2)
tright _ tleft

where tfigm and tleft are the right and left edges of the bar in time space. The

14

 

300

counts
w
8

I I I I I I I l I I I I I
——I=_—I_'——

250

 

M I

150

 

I II
................,..,............].]i]lilil]ll

25 30 35 40 45 50 55 60 65 70
ToF(ns)

I I I I I

Figure 2.7: ToF spectrum for 7—rays from the production target to the center of the
front layer of MONA.
offset, b, can then be determined by setting a: = 0 at the halfway point between tleft

and fright, (tlefi, + tright) / 2, and solving for b:

m
b = (tright + tleft) ' 3*. (2.3)

In the present experiment, MONA was arranged in a configuration 16 modules
high by 9 modules deep, and the front face was placed at a distance of 15.38 In from
the reaction target. In this configuration, neutrons are shadowed by the opening bore
of the triplet, resulting in an angular acceptance of :tl.5° in the vertical direction and
3:3: in the horizontal direction, as shown in Figure 2.6.

MONA TDCS were calibrated using a pulser set to a range of 320 ns and period

of 40 ns. The full range of each TDC was set to 350 ns. The time calibrator sends a

15

pulsed signal every 40 us that is read into each MONA TDC spectrum, as shown in in
Figure 2.3. The slope needed to convert raw channels into nanoseconds is determined
by simply dividing the average spacing between the spikes shown in the figure into
40 ns.

The overall time offset for MONA was calculated using 7-rays originating from the
production target. Using the known 'y-ray velocity of 29.998 cm/ns and the measured
distance from the production target to the center of the front layer of MONA of 15.38
m, the TOF of a 'y—ray from the target to the center of the front layer of MONA was
calculated to be 51.3 ns. The TDC offset was then set such that the central 7—ray

TOF falls at 51.3 us, as shown in Figure 2.7.

16

Chapter 3

Data Analysis

3.1 Particle Identification

The charged fragments are separated and identified using energy loss and TOF mea-
surements. The element (Z) identification comes primarily from the energy loss signal
in the ion chamber, while mass number (A) is determined from TOF. As can be seen
in Figure 3.1, the uncorrected TOF signal does not provide sufficient resolution to sep-
arate the fragments, due to the large momentum acceptance of the sweeper magnet.
Hence the TOF must be corrected event by event, based on the magnetic rigidity of
the fragment.

Since position and angle in the dispersive (1:) plane correlate with magnetic rigid-
ity, the needed correction is performed based on a: and 0,, at the focus of the triplet-
sweeper magnet setup. The method used to correct the TOF is to apply linear correc-

tion factors, as demonstrated in the following equation:

tcorr=t+cx-:r+c9-6, (3.1)

where c3 and co are empirically determined constants. Due to nonuniformities of
the magnetic field, the correction factors depend on the location of the particle in

angle-position phase space. To account for this effect, the phase space is divided into

17

 

 

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at
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Energy Loss (au)

102
120

80

60

40

20

 

‘ 5’ so 65 7o ' 75--...- so
ToF (ns)

Figure 3.1: Uncorrected energy loss vs. TOF plot, with selected elements indicated.

a 5 x 6 grid, as shown in Figure 3.2. Separate correction factors are then determined
for each grid region. As can be seen in Figures 3.3 and 3.4, the correction factors c,
and co trend upwards as a; and 0 increase, respectively. Figure 3.5 shows a sample
particle ID plot for one grid region, using corrected TOF.

Neutrons are identified simply by their TOF. Charged particles are deflected by
the sweeper, and the neutrons are cleanly separated from prompt 7-rays as shown in

Figure 3.6. Background neutron events are subtracted as described in Section 4.2.

 

 
 

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Figure 3.2: Focal plane angle vs. position. The black outline indicates events which
are accepted for analysis, and the inner lines are the boundaries of the grids used for
calculating TOF corrections. The peak around 0,, 2 0.04 rad, 1r 2' 0.005 m is composed
primarily of scattered background events, which are excluded as described in section
3.2.

19

 

 

 

 

 

 

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20

 

 

Energy Loss (arbltrary units)
[0 w a a
01 O O

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Corrected ToF (arbltrary units)

Figure 3.5: Sample particle identification plot. The vertical N /Z = 2 and N /Z = 1.5
bands, along with selected isotopes, are indicated in the figure.

21

 

I;
8

llllllllllllllIlllllllllllll

Prompt
Neutrons

     
 

counts

1200

1 000

600

400

200

   

 

 

 

 

IllillllllllllIllllllllllllllllll

350 0 so 100 150 200 250 300
ToF (ns)

 

Figure 3.6: MONA TOF spectrum, gated on 1oBe, showing clear separation between
prompt neutrons and prompt y-rays.

22

3.2 Scattered Background

The upper left panel in Figure 3.7 shows a double peak in velocity for 200. This double
peak structure is present in nearly all of the isotopes observed, and comparison with
coincident neutron spectra rules out the possibility of the double peak structure being
a result of the kinematics of the neutron emission. Further insight into the cause of
this double peak structure can be gained by plotting focal plane dispersive angle (03)
versus fragment velocity, as shown in the remaining three plots in Figure 3.7. Events
falling outside of the outlined oval regions in these three plots are identified to be
background events, as explained below.

The sweeper magnet curves the trajectory of particles with a lower magnetic rigid-
ity more strongly than those with higher magnetic rigidity. A more drastic bending
corresponds to a more negative value of 03. Since magnetic rigidity is proportional to
mv/ q, there is a positive correlation between 6; and vfmg—slower particles are bent
more, making 6,, more negative, while faster particles are bent less making 6,, more
positive. This positive correlation between 01, and 11me can clearly be seen for the
events falling inside the ovals in Figure 3.7. Events falling outside of the ovals have
the opposite correlation—slower fragments come with a more positive angle. This
correlation indicates that these events must not have taken an unobstructed path
through the sweeper magnet.

The events shown in Figure 3.7 which fall outside of the oval regions do come in
coincidence with neutrons. These neutrons have a normal ToF and position distribu-
tion, indicating that they were produced at the reaction target. This makes it unlikely
that the suspected bad events in Figure 3.7 are due to scattered primary beam and
instead indicates that they are due to scattered reaction products.

Tracing the path of the suspected background particles through the sweeper’s
magnetic field provides further evidence that these events must be the result of scat-

tering. The nominal Bp value of the suspected background events is approximately

23

 

 

 

 

8 .
: 20
s - 0
o 5
° :
o 915 1'0 13:5”1‘1” 11:5 12
Veloclty (cmlns)

 

 

E E good:tota| '. 0.71% 150

2 . .,

u

c

<

o

c

L'

n.

10 10.5 11 11.5 12

Velocity (cmlns)

Figure 3.7: Focal plane angle versus velocity plots for selected Oxygen isotopes. The
plot in the upper left corner is a projection onto the velocity axis for 200. Events
falling outside of the indicated ovals are attributed to scattering off the low rigidity

side of the sweeper magnet.

2.8 Tm, based on the velocity of coincident neutrons. Tracking of a 2.8 Tm particle
through the field of the sweeper magnet results in the particle exiting the magnet in
an area covered by the tungsten blocker, as shown in Figure 3.8. Clearly the particles

in question can not have arrived in the focal plane by taking an unobstructed track

through the magnet.

Based on the arguments presented above, events falling outside of the region in

Focal Plane Angle (rad)

I Plane Angle (rad)

:_ good:total = 36%

   
    

 

9.5 10 .15 11 11.5 12°
Velocity (cm/n3)

 

 

3.5 9 9.5 10 10.5 11
Veloclty (cmlne)

which 0,, and 12153,; are positively correlated are excluded from the analysis.

24

 

ylmm)
O
J_

 

 

 

 

.200 _
400 -
£00 -
o
-800 -'
l I l l T T l l
-200 0 200 400 600 800 1000 1200

x(mm)

Figure 3.8: Track of a 2.8 Tm particle through the magnetic field of the sweeper.
The blue curve is the path of the 2.8 Tm particle, while the black line represents the
central trajectory. The location of the tungsten blocker is indicated on the figure.

3.3 Decay Energy Reconstruction

Invariant mass spectroscopy is used to reconstruct Edecay, according to Equation 1.3,

which is reproduced here:

 

Edemy = \/m? + m3, + 2 (E; - En —— pf - pn - cos (Bopen)) — mf — mm.

The equation contains the masses, energies and momenta of the neutrons (mu,
En, pn) and the fragments (m f, Ef, pf) as well as the opening angle Oopen between the
two particles.

The neutron angle is calculated from the measured interaction point in MONA, and
the energy and momentum is calculated using TOF and flight distance. Likewise for the
charged fragment, the energy is calculated using ToF and path length, while the angle

is reconstructed from a partial-inverse matrix produced using COSY INFINITY [26].

25

 

‘OBO'O'II

1" 3 .3...$...3....3...F

  
  

 

so ea 70 72 14 76 n so

 

counts

45- } 22O+n

 

 

 

0 ‘ '.‘._'. .3“ '
53 °

so 54 so so so
Fragment Kl etlc Energy (MeVIu)

 

Figure 3.9: Fragment energy distributions at the reaction point for 9Li 10Be, 12Be and
220. Open circles are the data and solid lines simulation.

3.4 Monte Carlo Simulations

In order to account for the experimental resolution and acceptance effects that are
present in the data, Monte Carlo simulations are performed which fold these prop-
erties into a theoretical lineshape. The code used presently is an extension of a code
originally written by H. Scheit for the analysis of 23O and 24O neutron decays which
were studied in the Sweeper-MONA setup [8,27,28]. The simulation begins by describ—
ing the position, angle and energy of the incoming 48Ca beam, using a GSL gaussian
random number generator [29]. It then strips the beam of the number of protons and
neutrons needed to go from 48Ca to the excited fragment of interest.

An attempt was made to approximate the kinematics of the “Ca fragmentation

26

 

  
  

    

 

 

 

16—
E ’Ll+n

14:

m

1o:—

0:

6:

42 H

2: ‘r + i
m o: ' -' o u." ‘3‘“ .34
‘E 464850525456586002 so 55 7o 75 so 85
3
8 123""

25

 

   

 

 

so 55 so as $0Mososoooozo47o
Neutron Kinetic Energy (MeV)

Figure 3.10: Kinetic energy distributions (open circles) and simulation results (solid
lines) of neutrons in coincidence with 9Li, 10Be, 12Be and 2"’0. Both the data and the
simulation are gated on events with Edemy < 20 keV.

reaction using a Glauber model [30]. However, due to the violent nature of the reac-
tion and the limited Bp acceptance of the sweeper magnet, the shape of the energy
distribution of fragments recorded into the data stream is dominated by acceptance
effects rather than the shape of the kinetic energy distribution at the target. This
results in many of the fragment energy distributions being peaked at values signif-
icantly higher or lower than the incoming beam energy, meaning that the recorded
data are taken from a small slice of the tail of the energy distribution at the target.
Since the precise shape of the energy distribution in this tail region is not known, and

because accepting only a small fraction of the generated events causes the necessary

27

 

 

 

 

 

 

10. 1507
I 0”,," ; 1°BI+n
14:— 14o_— ) ,
12'— 120} l
10_ 100; i ,, l
5.- 30;— i
of— 303 +
4f 403 +
2' .i 20*
s o ...1.. .1. .il..i1.. 1i” g....1....1....1....1....1....
c 11 0.5' "'1'.5" 2' 25' 3 3'.5 11 11 0.5 1 1.5 2 2.5 3 3.5 4
:3
o . .
0 25: 12Bo-bn 25; 2""01I-n
20'—
15}
1, 1
5: i iii
0 . ' g ..+.l...1....1 ......
o 0.5 1 1.5 2 2.5 3 3.511 11 0.51 '1'.'5" "2" '2".'5 3 3'.511

 

 

 

00”,,(degrees)

Figure 3.11: Opening angle distributions for 9Li + n, 10Be + 11, 12Be + n and 22O +
n, for events with Edecay < 20 keV. Open circles are experimental data and the solid
lines are simulation results.
run time of the simulation to become prohibitively large, it was determined that it is
not practical to simulate the fragment energy distributions using a kinematical model.
The method used to describe the fragment energy distribution is to simply give
the incoming beam an energy distribution which matches a fit to the kinetic energy
distribution of the data. Because of the fragment’s heavier mass, calculation of decay
energy is dominated by the kinematics of the neutron; hence the influence of using a
fitted input fragment energy on the final decay energy curve is negligible. Measured
kinetic energy distributions of the four fragments observed with a low energy reso-

nance (9Li, 1086, 12Be and 22O)1 are shown in Figure 3.9 (open circles), along with

 

1It should be noted here that the labels 9Li, 1"Be, 12Be and 220 here refer to the species of

28

fits to the data which are input into the simulation (solid lines). For 9Li, 12Be and
22O, the shape of the energy distribution is approximated as a gaussian, while 10Be
is fit with a gaussian tail on either side of the curve and a flat distribution in the
middle.

The next step in the simulation program is to model the de-excitation of the ex-
cited nucleus via neutron emission. In this step, the excited nucleus loses one neutron,
resulting in a system composed of the neutron and the remaining charged fragment.
The relative energy distribution of the neutron and charged fragment is generated
based on what is known about the spectroscopic properties of the nucleus in ques-
tion. The relative energy distributions used to model the decay of the present data
are discussed in Section 4.2.

After it exits the target, the charged fragment is tracked to the focal plane of
the sweeper magnet using a COSY forward map [26]. Here cuts are placed on the
data such that only those events which fall inside the physical dimensions of the
focal plane detectors are accepted. Software cuts equivalent to those used to filter
out scattered background data are also applied at this time. In order to simulate the
resolution of the CRDC and timing detectors, the position, angle and time values
are given a gaussian spread, based on the known resolutions of the detectors. From
these randomized focal plane positions and angles, the angle of the fragment at the
reaction point is reconstructed using a four parameter partial inverse matrix [31,32]
produced using COSY. The energy of the fragment is also calculated based on the
TOP and mean flight path.

The neutron is tracked to its position in the first layer of MONA. At this point, its
horizontal position is given a gaussian spread to simulate resolution, and its vertical
position is set to the center of the bar in which it interacts. The lateral position
of the interaction is inconsequential to the calculation of neutron energy; hence all

neutrons are assumed to interact in the first layer of MoNA. However, the lateral

 

charged fragment remaining after the excited nucleus decays via neutron emission.

29

position within this layer is randomized to reproduce the effects of ToF resolution.
Neutron energy is then calculated based on the randomized ToF and flight distance,
and the angle of the neutron as it exits the target is calculated from the randomized
interaction point in MoN A.

From the neutron and fragment energies and opening angle, a simulated decay
energy distribution is calculated, using Equation 1.3. Since the parameters that go
into calculating this decay energy include experimental resolution and acceptance
effects the resulting curve can be compared directly to data. Plots of the simulated
decay energy curves for the fragments 9Li, 10Be, 12Be and 22O are presented along
with a discussion of the experimental results in Section 4.2.

As can be seen in Equation 1.3, the parameters which are most important to
calculation of the decay energy are fragment kinetic energy, neuron kinetic energy
and the opening angle between the fragment and the neutron. For the fragments 9Li,
10Be, 12Be and 220, Figures 3.10 and 3.11 show comparisons between simulation (solid
lines) and data (open circles) for kinetic energy and opening angle, respectively. The
figures exclude events for which Edge,y 2 20 keV. This is done to reduce the effect of
background neutron events which dominate at higher decay energies, as demonstrated
in Section 4.2.

Detailed instructions on how to run the simulation program can be found in Ap-

pendix A.

30

Chapter 4

Results and Discussion

4.1 Results

The isotopes which could be identified and separated and which were produced in
sufficient quantities to be studied are indicated on a chart of nuclides in Figure 4.1.
The range of isotopes is determined by the Bp and the momentum acceptance of
the sweeper magnet. For Z > 10 the TOP resolution is not sufficient to separate
neighboring isotopes.

Figure 4.2 shows relative velocity spectra for the three most prevalent fragments
of each element from lithium through neon. The spectra of 9Li, 10Be, 12Be, and 220
show a peak near zero relative velocity, suggesting the presence of a neutron-unbound
state with small decay energy. The enhancement near zero relative velocity in 11Be
is attributed to contamination from 10Be. All other fragments, including those not
displayed in the figure, have a rather broad shape indicative of a background distri-
bution.

The presence of a coherent neutron decay in 9Li, 10Be, 12Be, and 22O can be con-
firmed by doing an event mixing calculation to give an estimate of the background
arising from uncorrelated neutron events. For a given fragment, the event mixing is

performed by pairing each fragment event with a neutron that comes in coincidence

31

 

 

 

-Stable
—Unstable
-Unbound

 

 

 

 

Neutrons

Figure 4.1: Chart of the nuclides. Isotopes outlined in white were observed in sufficient
quantities to be studied.

with a different isotope. The decay energy calculation of Equation 1.3 is then carried
out using the mixed events. Figure 4.4 shows the results of this event mixing calcu-
lation, superimposed with the experimental data, for 9Li, 10Be, ”Be, and 22O. For
each of the four fragments, there is clearly a low energy peak rising above the event
mixed spectrum. In contrast, Figure 4.5 shows event mixed and real data histograms
for four representative fragments that do not have a low energy enhancement: ”B,
18N, 22F, and 26Ne. In this figure, the real data and event mixed histograms for these
fragments show no discernable difference.

As can be seen from Figures 4.2 and 4.3, the majority of the isotopes produced in
this experiment show no evidence of a coherent neutron decay. These isotopes possibly
possess a continuum of states above the one neutron separation energy, and since the
experimental resolution of the present setup is not sufficient to separate closely spaced
states, the resulting spectrum resembles a broad background distribution. Another
possibility is that there is an isolated unbound state present, but that it is at too high
of an energy to be observed, of Figure 4.6.

The observation of only low decay energy states is not surprising and is due to the

32

limited angular acceptance of the experimental setup. Figure 4.6 shows the efficiency
of the entire setup as a function of decay energy for a Monte-Carlo simulation [27] of a
flat decay energy distribution from O to 1 MeV. The efficiency peaks at zero energy and
then falls off rapidly with increasing energy. This demonstrates a major limitation of
the method. The small angular acceptance is determined by the 4 inch bore diameter
of the focusing quadrupole magnet, which is essential for the identification of the
isotopes. In order to increase the acceptance using the present setup, a quadrupole

with a significantly larger bore would be necessary.

33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- V,,- V, (cm/n3) ' V,, - V, (cm/n3) V,, - V, (cm/ns)

Figure 4.2: Velocity difference (neutron minus fragment) for the most prevalent iso—
topes.

34

counts

counts

counts count:

counts

 

 

 

 

 

 

 

 

 

 

 

 

 

 

] ”New
if ”figflefofiow'ffieg

Decay Energy (MeV)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MN? 21O-c-n
§ “Mdfl.Kpn
Mi} ”Ft-n
3 ”#3va?
”W ”11....

_ i“ [“151
Decay1 Energ: (MeV:a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Decay Energy (MeV)

Figure 4.3: Decay energy spectra for the most prevalent isotopes.

35

 

 

 

 

 

 

 

 

 

 

 

2.5 0.5

   

Decay Energy (MeV)

Figure 4.4: Decay energy spectra (open circles) for isotopes showing evidence of a
resonance, with event mixing background (blue histograms) superimposed.

36

 

 

' + 12B-I-n I, . 1"N't-n

 

 

 

 

 

 

 

 

 

Decay Energy (MeV)

Figure 4.5: Decay energy spectra (open circles) for isotopes without a resonance, with
event mixing background (blue histograms) superimposed.

37

 

Efficiency(%)
:3
on

P
N

0.5

0.4

0.3

0.2

lllllllllflllllIlTllllIllllfIlllllllll

 

0.1

 

 

l I l l l i
0.8 1

' Decay Energy (MeV)

 

oil
0
N
P
.5
O
Q

Figure 4.6: Efficiency the experimental setup as a function of decay energy.

38

4.2 Analysis of Low Energy Decays

In the following, the spectra of the four isotopes showing evidence for the presence of
a low energy neutron decay state are analyzed in more detail. Experimental results
from the literature are presented for each nucleus, along with a brief overview of
theoretical considerations. The present data are then compared with past results.
The intent of this analysis is not to make independent measurements of the decay
properties of these nuclei, but rather to confirm that the present data are consistent
with previous measurements.

For each of the four isotopes, Monte Carlo simulations were performed as described
in Section 3.4, with the decay parameters for each individual isotope taken from the
literature. The results of these simulations and experimental data for the fragments
9Li, 10Be, 12Be, and 22O, which originate from states in ”Li, 11Be, 13Be and 230,
respectively are shown in Figures 4.8, 4.12, 4.15 and 4.18. In the figures, background
contributions calculated by event mixing, as shown in Figure 4.4, are subtracted from

the data.

10L1

The ground state of the neutron unbound nucleus 1OLi has been well studied [33], as
knowledge of the ground state properties of ”Li is essential for an understanding of
the Borromean nucleus llLi [19,34]. The general consensus is that the ground state
of ”Li is a virtual s-wave resonance in the 9Li + 11 system [33,34]. Experiments
measuring ground state properties of ”Li are analyzed in terms of the scattering

length as, which is related to decay energy via:

a, = —h/\/211E, (4.1)

where p is the reduced mass of the 9Li + 11 system. A summary of previous results is

presented in Table 4.2. The most recent measurements [34] extract a, = —30:13¥ fm,

39

 

 

Year Authors Reaction —a, (fm) Reference

 

1990 AL. Amelin et al. 11Be(7r—,p) 11Li 30ng [35]
1993 R.A. Kryger et at. “$008 0, 9Li+n)x 2 10 [18]
1994 BM. Young et al. 113(7Li, 8B) 10Li 2 15 [36]
1995 H. Zinser et al. “313001813, 9Li+n)x 2 20 [37]
1998 MG. Gornov et al. 11B(7r_,p)10Li 15330 [38]
1999 M. Thoennessen et al. 9Be(180, 9Li+n)x 2 20 [19]
2001 L. Chen et. al 9Be(113e, X) ”Li 2 20 [39]
2001 M. Chartier et al 9Be( 11Be, X) 10Li 2 20 [40]
2006 HE. Jeppesen et al. 9 Li(2H,p) 10 Li 13—24 [41]
2007 H. Simon et al. natC( 11L1, 9Li+n)X 304513; [34]

 

 

Table 4.1: Summary of previous measurements of the scattering length of the ground
state of ”Li.

and the relative energy spectrum from this measurement is shown in Figure 4.7.

In the present work, the decay energy of ”Li into 9Li + n is simulated assuming
an s-wave interaction, using the model described in Ref. [19]. A fit to the data at
a, = —50 fm, consistent with Ref. [34], is shown in Figure 4.8. This decay is shown

on a level scheme in Figure 4.9.

40

150

. 1
S f. ..e
G.) e
E 100 i 0.. ..
.o ' .
g. 'l. w
a \
[:1 so - 1 -
E I. ‘\ ..°o
\ .0.
'8 .i \~'eo.....e.0 ...
' .ooeoeog.:- ---.- ..

0] r““ "1.. m:

.1 2 .
§+12~ “ 1
‘3‘ 51‘ ””1. i '

1.0 ff + H——+—+—+—+—

1

0.8 n .

0 i 3
E .(Mev1

Figure 4.7: Relative energy spectrum (top panel) for ”Li to 9Li + n from Ref [34].

 

 

 

 

 

 

 

 

41

 

'. “U -> ”Li + n

counts

 

 

 

20 h

10— \
f -41— \ -<>—
- —<>—- —0— —11— —0—
—<1—
N

—1
v A P— l
o I l l I l I J I l l 1 I I T r 1

0 0.2 0.4 0.6 ' 0:3 ' 1
Edecay (MeV)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.8: Background subtracted decay energy spectrum (open circles), with results
from Monte-Carlo simulation superimposed.

42

 

2.7 MeV 1/2-

 

"' 5* (MeV)

1.5

llllllllllllllllllllllllIl

 

210 keV 1+

 

 

0 MeV 312- :(25 keV) 0 keV (1 -,2-)
9Li + 11 10L1

 

0
S1» -25 keV

Figure 4.9: Level scheme showing the measured decay from ”Li to 9Li + n. Levels
are taken from Ref. [42].

43

11Be

11Be is particle bound, with a one-neutron separation energy of 504 keV [42]. The
lowest lying unbound excited state is located at 1778 keV [43]. A low energy neutron
decay originating from 11Be has been observed previously and attributed to a decay
to the first excited 2+ state at 3368 keV in 1"Be [13,15,44]. Deak et al. [15] quote
a decay energy of 19(15) keV and assign this decay to the 3887(15) keV state in
11Be [43]. Peters [44] states a decay energy of 84(15) originating from the 3956(15)
keV 3/2‘ state in 11Be [43]. Pain et al. [13] do not attempt to assign the decay to
a specific state in 11Be and remark that the decay originates from excited 11Be at
approximately 4.0 MeV.

One-neutron knockout reactions selectively only populate specific states; therefore
it is possible that the low energy state at 19 keV of Ref. [15] was not observed
by Refs. [13,44]. The relative velocity spectrum of Ref. [15] on the other hand was
probably not sensitive enough to resolve a possible contribution of the state at 84 keV
observed in Refs. [13,44]. Thus, the present decay of 11Be to 1”Be + n is simulated with
two Breit—Wigner resonances as described in [8]. The energies and widths of the two
decays are Edecay = 19 keV; I‘d,my = 10 keV and Edecay = 84 keV; I‘decay = 10 keV,
based on the level assignments of Refs. [15] and [44], respectively. The widths for
both decays are set to the upper limit of 10 keV, taken from Ref. [42]. Relative
contributions from each of the two states are set as free parameters, and the best fit
to the data is achieved with a 52.7% contribution from the 19 keV decay and a 47.3%
contribution from the 84 keV decay. The fit is shown in Figure 4.12, along with the
contributions from the 19 keV resonance (dashed) and the 84 keV resonance (dotted).
A level scheme including the observed transitions is shown in Figure 4.13.

It should be mentioned that the data could also be described by a single resonance
at Ede“), = 30 keV, I‘decay = 65 keV. This fit is shown as the blue line in figure 4.12.
It is unlikely, however, that the data arise as the result of a single decay, due to the

large width required in order to describe the data with a single resonance.

44

1500

 

'U

3 1°“ ”13 00011 v
. . O
3‘ .

0 _

.2. — L—
...) . 'Be

.9. 500

0.)

m

 

Ea?! = 341.6 keV E

 

 
   
 
   

1—
~15. I?

 

- s .111.
-2 —1 0

3.368Mev

 
 

: 11.0121ro 53°

, = 19 keV, E

am“ ”if!” = 1275 keV

3.887IIQV
——‘I‘< 10 keV

1.778HeV
f— (
I‘= 1 00keV

 

 

 

dV (cm/n3)

Figure 4.10: Relative velocity spectrum (rightmost panel) for ”Be + n from Ref [15].

 

m I I I I I r I
8000 " _
7ooo - 1°Be 2+ __ 1.41 (1.36.145) _
5,2 — 1.04(0.&>7,1.24)
9 p3,2 — 104(0622155)
3 6°00 Thermal — 0%(0874115) ‘
um —
8 sooo 03048-data H—1 -

 

 

 

 

 

1.5 2 2.5
Decay energy (MeV

Figure 4.11: Decay energy spectrum for 11Be to ”Be + n from Ref [44].

45

 

11 10 ‘
300‘, 89') Be '1'"

COUI‘ItS

 

1"

1ooL

 

 

0 1.: - _ . Lli. .i +.lil M

o 0.2 0.4 0.0 0.8 1

Edecay (MeV)

Figure 4.12: Background subtracted decay energy spectrum (open circles), with results
from Monte-Carlo simulations (solid black line) for ”Be + n. The Monte Carlo curve
includes contributions from a 19 keV resonance (dashed line) and 84 keV resonance

(dotted line). A simulated curve resulting from a single Breit-Wigner at E = 30 keV,
P = 65 keV is also included (solid blue line).

46

 

 

 

 

 

 

 

 

 

 

 

 

5.24 MeV - g
_ 5 a
" 11:
I I.l.|
3.37 "av 2+ (84 keV) 3.96 MOV 3,2“ _ 4
(19 keV) 3.89 MeV -
3.41 MeV (112, 312, 512+) :
— 3
2.69 MeV (112, 312,512+) -
1.70 MeV (512, 312+ j 2
— 1
0 M V + _
° 0 320k“ .................. L .............. :1 s," 504 keV
1oBe + n 0 keV 112+ ‘ 0

"Be

Figure 4.13: Level scheme showing the measured decay from llBe to 1”Be" + n. Levels
taken from Ref. [42].

47

13Be

Analogous the case of ”Li, knowledge of the ground state prOperties of neutron un-
bound 13Be is needed to understand the Borromean 14Be nucleus [34]. Theoretical
calculations predict the ground state of 13Be to be an s-wave close to the neutron
emission threshold [45,46], though other models have suggested that it could be a
p—wave at approximately 30 keV above threshold [47].

Experimental investigations into the nature of the 13Be ground state have pro-
duced varied results. An SNDS experiment from a primary 180 beam observed a
low—lying s—wave resonance as the ground-state of 13Be [20]. This study used relative
velocity measurements to estimate the decay energy, and it extracted a scattering
length of a, < — 10 fm. However, the possibility of a p or d state at Edecay = 50(10) keV
with a width of Rim, 3 10 keV could not be ruled out. Subsequent observations us-
ing a single proton-knockout reaction from 14B [48] or single neutron-knockout from
14Be [34] failed to observe this low-lying resonance. Instead a strong resonance at
approximately 700 keV was reported.

The present decay spectrum for ”Be + 11 indicates a low-energy decay similar to
Ref. [20]. Figure 4.15 shows the results of fits using an s-wave (solid line) and a Breit-
Wigner resonance (dashed line). The parameters used for the fits are as = —20 frn
(s-wave) and Edecay = 60 keV, I‘decay = 10 keV (Breit-Wigner), based on the results
presented in Ref. [20]. A level scheme placing the ground state of 13Be slightly above

12Be + n is also shown in Figure 4.16.

48

 

 

 

 

 

VF ‘vn (n3)

Figure 4.14: Relative velocity spectra for ”Be + n from Ref [20].

49

 

13Be -> 12Be + n

COUI‘ItS

    
 

20

 

«>-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m l L 1
0 0.0 1
Edge“ (MeV)

Figure 4.15: Background subtracted decay energy spectrum (open circles), with results
from Monte-Carlo simulations superimposed. Two simulated curves are shown: an

s-wave with a, = —20 frn (solid line) and a Breit—Wigner with Ede,my = 60 keV,
I‘decay = 10 keV (dashed line).

50

 

 

 

 

 

 

 

 

 

_3 s
: o
2.7 MeV ‘ ‘2'
- 1:
42.5"!
2.1MeV 2+ 2" v :
e —2
—1.5
.1
-_1
0.5
. 0 MeV 0+ “° "°"’ o "v 1'2-
...........................‘3 .......................... 81" akov

Figure 4.16: Level scheme showing the measured decay from 13Be to 1zBe + n. The 2
MeV state in ”Be is taken from Refs. [34,48]; all other levels are from Ref. [42].

51

 

 

 

 

counts/20 keV
§ 5 §

 

 

200

100
0o 2.5 3 3.5
decoy energy (MeV)

Figure 4.17: Decay energy spectrum for 23O to 22O + 11 published in Ref [8].

230

The Oxygen isotopes on either side of 230 both show evidence of being magic nu-
clei, thus making knowledge of the excitation spectrum of 230 important for shell
model calculations [8]. An attempt to study the first excited state of 230 using 'y-ray
spectroscopy [49] failed to observe a decay, indicating that the state is unbound with
respect to neutron emission. A recent measurement using neutron spectroscopy [8]
has placed the energy of the first excited state at 2.8(1) MeV. This study employed a
two-proton knockout reaction from 26Ne to observe a decay of 45(2) keV from excited
23O to the ground state of 22O.

The present results shown in Figure 4.18 also indicate a resonance at a very low
decay energy. The fit shown in the figure corresponds to a Breit-Wigner resonance
with Edecay = 45 keV and I‘decay = 5 keV, consistent with the resonance parameters
in Ref. [8]. Figure 4.18 shows a level scheme of 230, including the decay of the first

excited state to the ground state of 22O.

52

 

_ 23
O -> 22O + n

counts

 

 

 

 

 

 

..

' 0.4 0.6 0.8 1

15...... (MeV)

Figure 4.18: Background subtracted decay energy spectrum (open circles), with results
from Monte-Carlo simulation (solid line). The simulation curve is the result of an
Breit-Wigner distribution at Ede“, = 45 keV, I‘decay = 5 keV.

 

 

53

 

 

 

 

5.3 MeV (312,712)- 1 9
" C3
._5 a
j 1:
m
4.0 MeV 312+ -
—4
(45 “Vi 2.79 MeV 512+ ‘- 3
one), 0+" a 31,, 2.74 MeV

   

 

22O+n

0 keV "2+
23 O

 

 

IllllIllJlIlll
‘

 

Figure 4.19: Level scheme showing the measured decay from 23O to 220. Levels for
the two highest excited states in 230 come from Ref. [50], and the lowest lying state
in 230 is from Ref. [8]. Levels in 22O are taken from Ref. [42].

54

counts

 

7000

5000

4000

3000

2000

1000

 

 

IIIITII—IllIIIITIIIIIIIIIIIIIIIIIIIIIIIIITIII

llJIlllllllllIllllIllllIllllIllll

0 50 100 150 200 250 300
ToF(ns)

.gp

Figure 5.1: Neutron TOF for normal (blue) and high rate (black) runs.

55

Chapter 5

Future Prospectives

The present experiment reaches nuclei beyond the dripline only for the lightest el-
ements (”Li and 13Be). Figure 3.5 shows that for heavier elements the populated
nuclei are significantly removed from the dripline. In order to observe decays of more
neutron-rich nuclei, the magnetic rigidity of the sweeper magnet was increased to
Bp = 3.14 Tm. This corresponds to a shift of about one isotope for neon. The cross
section to populate these nuclei decreases, so the primary beam intensity had to be
increased to compensate, and this higher beam rate increased the random background
rate of neutron events. Figure 5.1 shows the neutron ToF for one of the production
runs for the data shown in Section 4.1 (blue line) and a high-rate run (black line).
The periodic features of the random background correspond to the cyclotron fre-
quency. The increasing random-to—real ratio makes it more difficult to extract the
signal from unbound resonances. A shift of only one isotopes towards the dripline
already increases the background rate by about 40%. Thus it was impossible to reach
the dripline for the heavier elements in the current experiment.

In the future SNDS could be extended to higher decay energies as well as heavier
masses. The angular acceptance could be increased by substituting the quadrupole
with the 8800 spectrograph [51]. The target could be placed immediately in front of

the sweeper magnet which would eliminate the shadowing of MoNA due to the small

56

bore of the quadrupole. The increased flight path and higher resolution of the 8800
will also enable isotopic separation up to significantly heavier elements.

However, it does not appear to be possible to populate and measure the decay of
neutron unbound states closer to the neutron dripline with SNDS in the near future.
The small cross section for the production of the dripline nuclei with stable beams
requires large beam intensities which in turn generate a large number of neutrons
from unrelated reactions. In the longer term SN DS could be used at the next genera-
tion radioactive beam facilities [52]. The unbound states could then be populated by

intense secondary beams closer to the dripline nuclei of interest.

57

Chapter 6

Summary

The method of sequential neutron decay spectroscopy (SN DS) has been applied for the
first time using medium mass projectiles (480a). The method succeeded in populating
and identifying unbound ground states of 1"Li and 13Be as well as unbound excited
states in 11Be and 23O. The extracted resonance parameters were consistent with
values reported in the literature. The common feature of these states is their small
decay energy (< 100 keV). The small angular acceptance of the experimental setup for
neutrons limited the observation to unbound states with small decay energies. Isotopic
separation could be achieved up to neon and was limited by the ToF resolution for
the charged particles.

The future study of neutron unbound states with higher decay energies will require
significant modifications of the experimental setup. The measurement of masses of
nuclei beyond the dripline using SNDS will have to wait for the next generation of

radioactive beam facilities.

58

Appendix A

Using the MONA Simulation Code

A. 1 Introduction

This document explains how to run simulations of the MON A-Sweeper detector setup
using the “simple-track” code written by H. Scheit. The code is written in C++ and
uses Monte Carlo methods to simulate the influence that geometrical acceptance cuts
and finite detector resolution have on a measured decay energy spectrum. This allows
simulation results to be compared directly to experimental data. The simulation can
also be useful in determining how the system will respond to experimental setup
changes, such as changing the magnetic field of the sweeper, adding a blocker or
changing the distance of MONA from the target. This information can be very useful
when planning for a new experiment as it allows the Optimal running conditions to
be estimated ahead of time.

The simulation starts with an incoming beam with a gaussian distribution of
position, angle and energy. The beam is then stripped of a set number of protons and
neutrons to arrive at an excited nucleus, which then emits a neutron according to a
set decay model. The resulting fragment is then forward tracked through the sweeper
magnet to its position at CRDC], and the emitted neutron is tracked to its position

in the MONA detector. A .root file is then written containing the energy, position

59

and angle of the incoming beam; energy, position, angle, and time of the fragment
at the target and at CRDC1; and energy, position, angle, and time of the neutron
at MONA. This file can then be analyzed to find the reconstructed target position,

angle, and energy of the fragment, along with the reconstructed decay energy curve.

A.2 Getting Set Up

To start, log into a 64-bit fishtank machine (lobster, shrimp, mussel, oyster,
octopus) with the account from which you plan to run the simulation. Note that you
must run from one of the 64—bit fishtank machines and not one of the 32-bit spice
machines.

In order to run the simulation, you first need to set some new environment vari-
ables for your user account. This will allow the simulation program to source and link
with the correct libraries when you are compiling or running the program. If you plan
to run the simulations as user mona, then these environment variables are already set.
Otherwise if you are running from your own account, the environment variables are
not set by default.

To set up your needed environment variables, cd to your home directory and open

up the .bashrc file. Scroll down to the bottom and add the following lines:

export RO0TSYS=/projects/proj6/mona-sim/soft/root/root_v5.12_00/
export PATH=$RDOTSYS/bin/:$RO0TSYS/include/:$PATH

export LD_LIBRARY_PATH=$RO0TSYS/lib/ : $LD_LIBRARY_PATH
Then save the file and type:
> source ~/.bashrc

at the command prompt. You will now have the proper environment variables set in
your current session as well as any future ones that you start. This also “installs” the

MONA collaboration version of ROOT for use on the fishtank machines.

60

Once you have the environment variables set, you need to set up a new directory
from which to run the simulation. The simulation program is managed with the
Subversion (SVN) repository, and you should start by checking out the latest version.
To do this, first create a new directory to fill with the simulation files. It is suggested
that you make use of the projects space set aside for the MONA simulation, which
is located in /pro jects/ pro j 6/mona-sim/ . Go there and create your new directory;

then cd to it and type:

> svn --username mona co http://www.mpi-hd.mpg.de/cbsvn/st/branches/mona/O.1

with the password mona (if you are prompted for one). Once this process is done
running, type ls, and you should see a new directory called 0 . 1 This directory con-
tains all of the source code for the simulation program. You still need to compile the

program, however, so do:

> cd 0.1/

> make

This will create two new executables, st_mona and mona_analysis, which are the
simulation and analysis programs, respectively. There is still another executable,

st_geant, which needs to be created; to compile this do:

> cd st_geant

> ./compile.sh

It is also suggested that you make use of the /evtdata space set aside for mona
simulations, as the files produced by the simulation program can get rather large, es-
pecially as the number of simulated events increases. To set this up, type the following

commands to create your own directory in /evtdata:

> cd /evtdata/mona-sim-data/

> mkdir mysimdata

Then cd back to your 0.1 directory and make a link to the /evdata space:

61

> ln -s /evtdata/mona-sim-data/mysimdata/ .

Whenever you run the simulation program, save the output files in the mysimdata

directory.

A.3 Running the Simulation

Once you have set up your directory as described above, you are ready to begin
running simulations. All commands described from here on should be run from your
new 0.1 directory unless otherwise specified. The simulation program is run from the
command line and uses flags to set input and output variables. To run the simulation

program, one simply types:
> ./st_mona [-f1ags]

where [-f1ags] represents whichever flags you want to use in running the simulation.

To get a comprehensive listing of the available flags, type:
> ./st_mona -?

The three most important flags are -exp, -n, and -f; these flags set the experiment
number, number of simulated events to be run, and output file, respectively. The
-exp flag is followed by a string that represents a certain experiment number, and by
invoking this flag you set all other variables to their default value for that experiment.
The -exp flag should always be the first one typed after st_mona. Setting a given
—exp flag also instructs the program to use the proper forward COSY matrix for that
particular experiment.

The -n flag should be followed by the integer number of simulated events that you
wish to run. A suggested number which is a good compromise between run time, disk
space and statistics is 100,000 events. You may wish to run more events than this if

you want to eliminate statistical fluctuations in your output or if your simulation will

62

have large acceptance cuts, but anything more than 1,000,000 events is prohibitively
slow and should typically only be used if you want to make “curve-like” histograms
for publication. The default number of events run if you omit the -n flag is one.

As mentioned above, the filename is set using the -f flag, followed by the name of
your output file. The output file needs to have the . root extension, as the simulation
stores its output data in a ROOT file.1 If you forget to set the -f flag, the default
output filename is st_mona.root.

As an example, if you want to run a 100,000 event simulation for the experiment
number 03038, with all parameters set to the 03038 experiment defaults, and write

out the results to a file called Sim-03038.root, then you would type:2
> ./st_mona -exp 03038 -n 100000 -f Sim-03038.root

If you would like to see what the default parameters for the experiment number

you are running, then you will need to view the st_mona. cc file:
> less ./st_mona cc

Scroll down through the file until you find the lines that look like this:3

else if ( x =- "03038") { // Kiss 7H6
INFO(”Using Default Values For Experiment 03038 (Kiss 7H6)");

eBeam a 40.8; //\Beam Energy in MeV/u.

beamA = 8; //\Beam Mass in amu.

beamZ - 3; //\Beam Charge Number

dTarget = 192.2; //\Target thickness in mg/cm“2.

dEbeam = 0.01; //\Sigma of beam energy in percent.

resTime = .3; //\Resolution (gaussian sigma) of time measurements.
resTargetX = 1.; //\Resolution (gaussian sigma) of target X-position.
resCRDC1XY - 1.; //\Resolution (gaussian sigma) of CRDC positions.
resCRDClThetaXY a 1.; //\Resolution (gaussian sigma) of CRDC angles.
resMonaX = 1.; //\Resolution (gaussian sigma) of MoNA X-position.
resMonaBar = 1; //\Turns on/off MoNA bar discreetness (1=0N).
nNeutr = 0; //\Number of neutrons removed from beam.

nProt = 1; //\Number of protons removed from beam.

bSpoth, = 0.004; //\Sigma of the beam position in the X-direction.

 

1It is also possible to have the simulation write out to a gsl ntuple instead of a ROOT file; to do
this, give the filename the .gsltup extension.

2Note that the order of the flags, EXCEPT FOR THE -exp FLAG, does not matter.

3All positions are in meters and all angles are in radians unless otherwise specified.

63

bSpotDy = 0.008; //\Sigma of the beam position in the Y-direction.
bSpotDtx = 0.011; //\Sigma of the beam angle in the X-direction.
bSpotDty . 0.005; //\Sigma of the beam angle in the Y-direction.
bSpotCtx - 0.0; //\Centroid of the beam angle in the X-direction.
bSpoth - 0.0, //\Centroid of the beam position in the X-direction.
bSpotCty - 0.0; //\Centroid of the beam angle in the Y-direction.
bSpotCy = 0.0; //\Centroid of the beam position in the Y-direction.
crdclMaskLeft = 0.086; //\CRDC1 blocker position on the positive-X side.
crdciMaskRight = -0.15; //\CRDC1 blocker position on the negative-X side.
crdc2dist = 1.00; //\Distance from CRDC1 to CRDC2.

monaDist = 8.208; //\Distance from the target to the center of the

//\first bar of MoNA.

}

The comments set off by //\ in the lines above explain what each of the variables
represent. Note that the nNeut and nProt variables are the respective number of
neutrons and protons stripped from the beam to get to the excited nucleus, which
always has one more neutron than the fragment that you see in your particle detectors.
So for example, if you were to simulate a 48Ca beam going to excited 23O, and then
the exited 230 emitting a neutron to become 220 + 11, you would set nNeut and nProt
to 12 and 13, respectively.

In addition to the experiment specific defaults, there are also a number of global
defaults; the most important one is the excitation energy model, which is the type
of lineshape that describes the decay energy of the emitted neutron. The default
is set to be a uniform distribution between 0 and 5 MeV. There are a variety of
excitation lineshapes available, and the decay model can be changed using the -e flag

as described below.

A.4 Using Flags

As has been mentioned previously, nearly any input variable can be changed by using
the proper flags. This is very useful when running simulations as it allows parameters
to be adjusted “on the fly” to quickly see how they affect the overall measurement. The
help invoked by running st_mona -? (or st_mona --help) does a good job explaining
what each flag does For reference the help output is reproduced here (some extra

comments have been added in square brackets, for more clarity):

64

usage:

-v Run verbose
-n Set number of events
-f Set output file name. Extension determines file type.

root -> ROOT file
gsltup -> GSL n-tuple (also a file *.gsltup.dsc is written, describing
the columns)
-geant (filename> Cause st_mona to write out neutron energy & angles to an
ASCII file called filename
-reac Set reaction model
glaub (normal fragmentation w/ glauber kick)
2body <Q-value> <Q-value spread) (two-body stripping)
n.b. spread is relative, e.g. 0.1 a 10% spread

-e Set decay energy model and parameters (MeV)
const <energy> [delta-function spike at <energy>]
uniform <e-low> <e-high> [uniform distribution]
61 <e-low> <e-high>
therm <temp> [thermal with “temperature” <temp>]
gauss <centr> <sigma> [gaussian]
bw <centr> <gamma> [breit-wigner]

asymbw <energy> <Redwidth> <angMom> [energy-dependent breit-wigner]
-be Set beam energy per A
-bZ Set beam Z
-bA Set beam A
-dT Set target thickness
-dbe Set relative beam energy spread (sigma)
-rTx Set resolution of target-x
-rt Set time resolutions (ns)
-rxy Set resolution of CRDC1 xy (m)
-rth Set resolution of CRDC1 theta xy (rad)
-er Set resolution of MoNA X
-rMyz Switch MONA Y and Z discretization on/off (1/0)
-dKE set Kinetic Energy loss/gain from the reaction (in MeV/u).
-strag scale
-glaub scale
-np number of removed protons
-nn number of removed neutrons
-md distance to MoNA (middle of A8)
-cmL position of left edge of blocker (before CRDC1)
-cmR position of right edge of blocker (before CRDC1)
-c2d distance between CRDC1 and CRDC2 (meters)
-ctx centroid of x angle in radians
-cx centroid of x position in meters
-cty centroid of y angle in radians
-cy centroid of y position in meters
-dtx sigma of x angle (rad)
-dx sigma of x posn (m)
-dty sigma of y angle (rad)
-dy sigma of y posn (rad)
-disType type of MONA X distribution
-exp <exp number) set default values for experiment <exp number)
03033 - Nathan’s 230, 220
03038 - Kiss 7He

65

Unless otherwise specified, whenever you invoke a flag, it should be followed by a
number representing its argument(s).
As an example, if I want to run a simulation of the 03038 experiment, with the

following changes made to the default input parameters:

— Decay energy = Breit-Wigner with Edemy = 0.74 MeV, I‘demy = 0.1 MeV
— Beam energy = 42.0 MeV/u with 1% spread
— Centroid of beam :1: position = 0.005 m

— Centroid of beam :1: angle = 0.002 rad

— Centroid of beam y position = 0.004 m

— Centroid of beam :1: angle = 0.002 rad

— Sigma of beam :1: position = 0.003 m

— Sigma of beam :1: angle = 0.001 rad

- Sigma of beam y position = 0.002 m

— Sigma of beam :1: angle = 0.003 rad

— Resolution of CRDC positions = 0.004 m,

then I would type the following:

./st_mona -exp 03038 -n 100000 -f Sim-03038.root -e bw 0.74 0.1 -be 42.0 \
-dbe 0.01 -cx 0.005 -ctx 0.002 -cy 0.004 -cty 0.002 -dx 0.003 -dtx 0.001 \
-dy 0.002 -dty 0.003 -rxy 0.004
Doing this will give me a new file called Sim-03038 . root, with the input param-
eters set as above.
The following subsections explain some of the more commonly used flags in more

detail; if the reader is simply interested in learning how to run the simulation, then

he/ she can safely skip to section A5

66

A.4.1 Decay Energy Model

As mentioned above, the decay energy model can be set using the -e flag. The most
common types of decays are the Breit-Wigner, energy-dependent Breit-Wigner, and
Thermal. The Breit-Wigner and energy-dependent Breit-Wigner represent the two
most common lineshapes for unbound resonances, and they are respectively invoked
with the bw and asymbw arguments to the -e flag. The bw argument expects two
numbers to follow it, representing (in order) central Breit-Wigner energy, and the
width of the lineshape; the asymbw argument is followed by three numbers repre-
senting (again, in order) central energy, reduced width, and angular momentum. The
thermal distribution is characteristic of a neutron background, and is invoked with
the therm argument to the -e flag; therm is followed by one number representing the

“temperature” of the thermal distribution, in MeV. Typical temperatures are usually

on the order of 1 MeV.

A.4.2 Stripping Reaction Model

The stripping reaction model can be changed by invoking the -reac flag. The global
default4 reaction is a simple Glauber model, which conserves the momentum of the
incoming beam. This model allows for the option of setting a momentum kick and
angular straggling scale, using the -glaub and -strag flags, respectively. The -g1aub
and -strag flags are each followed by one number which represents the overall scale
for each parameter; the default value for both -glaub and -strag is 1.

A second stripping reaction model has also been added as it produces a better fit
to the data for the 03038 7He experiment. This is a “two-body” stripping reaction,
which conserves total energy as opposed to total momentum. It can be invoked by
following the -reac flag with the argument 2body; the program will then expect two

numerical arguments representing (in order): Q-value of the stripping reaction (in

 

4Note that since the Glauber model is the default reaction, you do not have to invoke the -reac
flag at all if you wish to use it.

67

MeV) and spread in the Q-value (in percent). So for example, if you wanted to model
your stripping reaction as a two-body reaction with Q = ——8.0 MeV, (IQ = 1%, then

your command to run st_mona should include:

-reac 2body -8.0 0.01

A.4.3 GEANT Output

It is possible to have st_mona write out neutron energy and angles into a text file
which can then be read into a GEANT simulation to more accurately model the
interaction Of the neutrons in MONA. To do this, use the -geant flag, followed by the

name of the text file that you wish to write out, e. g.
-geant geant_out.txt

Note that invoking the -geant flag will not affect the rest of the simulation program;
neutrons will still be tracked to MONA as usual.

As mentioned above, the text file written by using the -geant flag can be read
into GEANT to do a more accurate simulation of the neutron interaction;5 the output
of the GEANT simulation is another text file, which can be integrated into your
existing simulation data using the st_geant executable. This program is located in
the st_geant subdirectory of your 0.1 directory. It takes in two files: a .root file
produced by st_mona, and a text file produced by GEAN T, and merges the data into
a new .root file. This new file links the neutron events produced by GEANT with
the charged fragment events produced by st_mona, and it can be analyzed just like a
normal st_mona output. For more information on how to run the st_geant program,

go into the st_geant directory and type st_geant --help.

 

5Running the GEANT simulation is outside the scope of this manual; for information on how to
do this, contact Artemis Spyrou.

68

A.5 Analyzing Your Simulation

The .root file produced as described in Section A.3, contains only simulated target,
CRDC1, and MONA parameters; it does not include the inverse reconstructed pa-
rameters necessary to compare simulation results directly with data. These inverse
reconstructed parameters can be calculated by using the program mona_analysis.
This program has two basic modes: it can either be used to calculate the needed
reconstructed parameters directly, with the results written out to a .root file, or
it can be used to convert the .root file produced by st_mona into a SpecTcl fil-
ter file which can then be analyzed using the SpecTcl_filter program available on
zuma. iusb.edu or on the NSCL spice machines.

To use mona_analysis to convert a .root file (called, e.g. simfile.root) into a

filter file, simply type:
> ./mona_ana1ysis -f1t -if simfile.root -of simfile.flt

Here the -f 1t flag tells the program to convert the .root file into a SpecTcl file; the
-if flag sets the name of the input file, and the -Of flag sets the name of the output
file. Note that the output file when using the -f 1t option must have the extension
.flt.

If you wish to use mona_analysis to analyze your simulation file directly, then

the procedure is to run the program as follows:
> ./mona_analysis -if simfile.root -Of simfile_ana.root -frag 6He

Doing this would run mona_analysis with on an input file called simfile .root
(set with the -if flag), and it would return a new file, simfile_ana.root (set with
the -Of flag). The -frag flag tells the program what type of analysis to do; it sets
the inverse map to be used; the mass, charge, and brho of the fragment being recon-
structed; and the target thickness and material. So in the example above, the program

would perform the reconstruction using the parameters which are defined for the 6He

69

fragment. Note that the argument of the -f rag flag must be a string which is defined
within the mona_analysis program; to see which strings are available, and the set-
tings used for each string, view the mona_analysis . cc file, and scroll down until you

see some lines that look like this:

else if (frag == "6He") {
INFO("Using settings for fragment 6H6");
e->setMaps(m6He, m6Hei);

e->fragA = 6;
e->fragQ = 2;
e->dTarg = 188;
e—>targA = 9;
e->targZ = 4;

}

Looking at the lines above, you can see that the "6He" flag sets the reconstructed
fragment to be 6He; target thickness to be 188 mg/cm2; and target material to 9Be.
It also tells the program to use the inverse map named m6Hei; the meaning of this
map name will be explained in Section A.6.

Once you have run mona_analysis, you now have a full set of simulated and re-
constructed parameters available to you, contained in the output files of st_mona and
mona_analysis (e.g. simfile.root and simfile_ana.root in the example above).
These files can be analyzed using the ROOT data analysis program. If you are un-
familiar with ROOT, some basic instructions for using it can be found in Appendix
B.

One important consideration to keep in mind is that the simulation and analysis
programs track and store every event, even those which are “unphysical,” such as
events for which the neutron does not hit MONA or events for which the fragment
does not hit CRDC1. The program does flag these events by setting the kinetic energy
of the offending particle to zero. So for example, in an event for which the neutron does
not hit MONA, the parameter representing neutron kinetic energy will be set to zero,

and likewise, for an event where the fragment misses CRDC1 (or hits the blocker),

70

the fragment kinetic energy parameter is set to zero. Whenever looking at simulation
results as a comparison to experimental data, the simulation spectra should always be
gated such that events with KEfmg = 0 or KEmu,ron = 0 are excluded. Depending on
the geometry of your individual setup, you may need to make other cuts as well; for
example the simulation does not flag events for which the fragment hits CRDC1 at a
large enough angle that it misses CRDC2. If you want to exclude those events, then
you need to calculate CRDC2 position based on the simulated position and angle at

CRDCl and then apply the physical cuts directly.

A.5.1 Parameter Names

This section explains the names of parameters stored in the .root files created by
st_mona and mona_analysis. It assumes a basic level of knowledge of the ROOT
program. Readers who are not experienced in ROOT should read Appendix B first
and then return to this section.

The .root files output by st_mona and mona_analysis each contain an incom-
plete set of parameters; the st_mona file only contains simulated and forward-tracked
parameters, while the mona_analysis file only contains reconstructed parameters. In
order to view and compare simulated and reconstructed parameters, you will need to
use the AddFriend command available in ROOT.

Parameters in a file created by st_mona are stored in a TTree called t, and they
are named according to a system which denotes beamline position, particle number
(e.g. fragment or neutron), and parameter name. The system is best explained with
an example: the parameter denoting CRDCl x-position is b7p0x, meaning that we are
at beamline position 7 (crdcl), looking at particle 0 (the charged fragment), and the
final x tells us that we are looking at .r-position. The available parameter numbers are
0 (charged fragment) and 1 (neutron). The beamline numbering scheme is described

in Table A51, and the parameter naming scheme in Table A.5.1.6 For a few more

 

6Each of the parameters listed in Table A51 is not necessarily available for every beamline

71

 

 

 

 

 

Number Location
1 Before Target
2 After Target
7 CRDC 1
13 MONA

 

 

 

 

Table A.1: Numbering scheme for beamline elements as produced by the program
st_mona.

 

 

 

 

 

 

 

 

Name Parameter
Ekin kinetic energy (MeV)

x m-position (m)

y y—position (m)

tx :c-angle (rad)

ty y-angle (rad)
z-position (m)

t time (ns)

 

 

 

 

Table A.2: Naming scheme for simulation parameters as produced by the program
st_mona.

examples, consider the following:

bipOEkin — Beam energy before the target.
b2p0tx — Fragment x-angle after the target.
b13p1t — Neutron TOF to MONA.

Parameters for analyzed .root files are stored in a TTree called at. Because the
analyzed file does not contain parameter values at a variety of beamline positions, it

uses a more straightforward parameter naming scheme, as described below:

deltaE[1] — Energy loss in the target.

exen — Decay energy.

tLab — Opening Angle betwen fragment and neutron.
vRel — Relative velocity betwen fragment and neutron.

nVel — Neutron velocity.

 

element. To get a full listing of the available parameters, from within ROOT, use the t.Print()
command. There are also a few parameters specific to b2 which are not included in Table A.5.1;
these are: TP (position of the interaction within the target), dE (energy loss in the target), and
R.exen (excitation energy).

72

fVel — Fragment velocity.

f ragKinE — Fragment Kinetic Energy.
neutronKin — Neutron Kinetic Energy.
nTheta — Neutron 6.

nPhi — Neutron d.

fTheta -— Fragment 6.

fPhi — Fragment (0.

prTA — Fragment x-angle at target.
prTA — Fragment y—angle at target.
pr’I‘A — Fragment y-position at target.
fop — Fragment y-position at CRDC1.
fop — Fragment y-angle at CRDC1.
fop — Fragment :c-position at CRDC1.
fAfp — Fragment :r-angle at CRDC1.

There are more parameters present in the at tree, but they are not needed for a

typical user.

A.6 Customizing the Simulation

It is likely that at some point you will need to add code to the simulation in order to
continue with your analysis. Since the code is managed with SVN, modifying it is a
fairly low-risk task, even for those who are inexperienced in C++. As long as the user
does not “check in” his/ her changes, the worst case scenario of a bad modification
is that the code in the user’s directory has to be scrapped, and the current version

re—checked out from the repository.
The most common type of modification is to add a new experiment option to

the simulation. In order to do this, you need to modify three files: st_mona.cc,

73

mona_analysis.cc, and mk_maps_icc.sh. The first file that you should modify is

st_mona. cc. Open up this file and scroll down until you see lines that look like:

else if ( x =3 "05039") { // Hoffman 250
INFO("Using default values for experiment 05039 (Hoffman 250)");

eBeam = 84.0;
beamA - 26;
beamZ = 9;
dTarget a 500.0;
dEbeam = 0.025;
resTime = 0.3;
resTargetX = 0.0007;
resCRDC1X a 0.0013;
resCRDClThetaX 8 0.0013;
resCRDClY = 0.0013;
resCRDClThetaY = 0.0013;
//resMonaX1 - 0.04;
//resMonaX2 - 0 10;
//resMonaP = 0.66;
//resMonaBar = 1;
nNeutr = 0;
nProt = 1;
bSpoth = 0.005;
bSpotDy = 0.004;
bSpotDtx = 0.009;
bSpotDty = 0.0035;
bSpotCtx a 0.008;
bSpoth = 0.00;
bSpotCty = -0.001;
bSpotCy = -0.001;

crdclMaskLeft = 0.15;
crdciMaskRight a -0.15;
crdc2dist a 1.88;
monaDist = 8.20;

Copy and paste these lines to create a new experiment. In the new lines, replace the
05039 in the line else if ( x == "05039") with the name that you want for your
new experiment. You should also change the string in the line beginning with INFO
to something sensible for your new experiment. All of the other variables should be
set to their proper values for your experiment. An explanation of what each variable
represents is given in Section A.3.

The next lines that you should edit look something like this:

74

else if ( beamA - nProt - nNeutr == 25 && \
beamZ - nProt == 8 && beamZ == 9) {
dipole = new StPropMapCosy(m240);
dmona = new StPropDrift(monaDist - m240.getLen());
INFO("using 24o map for 05039");
}

As before, copy and paste these lines, and change the line reading
beamA - nProt - nNeutr == 25 && beamZ - nProt == 8 && beamZ == 9)

to reflect your new number of total particles lost, number of protons lost, and beam
Z. Recall that the final mass number should be that of the excited nucleus, before
emitting the final neutron. You also need to change the map name in the second and
third lines. In the example shown above, the map name is m240, so you would replace
m24O with your new map name. At this point the map name can be anything you
want; you will give it a meaning later when you modify mk_maps_icc . sh. Finally you

should change the string coming after INFO to reflect the new map and experiment.

The final change to make to st_mona. cc is to update the help message to include
your new experiment. This is not necessary for the code to run properly, but doing
it will make everyone’s life a little easier. Scroll up near the top of the file until you
find the lines:

" -exp <exp number> set default values for experiment <exp number> \n"
" 03033 - Nathan’s 230, 220\n"

" 03038 - Kiss 7He\n"

" 03048a - 12Be g.s. to 1OBe\n"

" 03048b - 11Be Coul to 1OBe\n"

" 05039 - Hoffman 250\n"

Pick a line to copy and paste, and update the <exp number> and description fields
to reflect your new experiment.
The next file that you should edit is mona_analysis. Only one set of lines needs

to be updated here: those that look like:

75

else if (frag == "240") {
e->setMaps(m240, m240i);
e->fragA = 24;

e->fragQ = 8;
e->dTarg = 500;
e->targA = 9;
e->targZ = 4;
}
Copy and paste these lines, and then change the text reading frag == " 240 " to

reflect your new fragment name (in this example, you would replace 240 with the
new name. The new name can be anything you like (but it must be unique), and it
is what follows the -f rag flag when you run mona_analys is, as described in Section
A.5. Next you should update the line reading e->setMaps (m240, m240i) ; This line
is what sets the names of the forward and inverse maps. The name of the forward
map, which in this example is m240, must match the new map name that you set in
st_mona. cc. The name of the inverse map—m240i—can be anything you want since
it has not yet been set elsewhere, but it is suggested that you stick to the convention
of simply adding an i to the end of the forward map name. Finally you will need to
update the remaining lines to reflect the correct variable values for your experiment;
the meaning of each variable is explained in Section A.5.

The last file that you need to edit, mk_maps_icc . sh is what ties together the map
names that you set in st_mona. cc and mona_analysis . cc to the actual COSY map

files. In the mk_maps_icc . sh file, copy and paste the lines that look like:

echo "// forward map"

mkMapEntry m240 24 8 1.5741 3.77548 24o-cosy.map
echo "// partial inverse map"

mkMapEntry m240i 24 8 1.5741 3.77548 24o-sch.imap

You need to edit the two lines beginning with mkMapEntry. These two lines set

variables for the forward map (top line) and inverse map (bottom line). The expla-

76

nation of each entry in these lines is given below”8

m240 and m240i - Name of the forward and inverse maps, as assigned in
st_mona. cc and mona_analysis . cc.

24 — Mass of the tracked/ reconstructed fragment (the fragment that is left
after neutron emission).

8 — Charge of the tracked/ reconstructed fragment.

1 . 5741 — Central track distance from the target to CRDC1.

3.77548 — Brho setting of the map file that you are using.

24o-cosy .map and 24o-sch. imap - Filenames of your COSY forward and

inverse map files.

Once you have edited these lines and saved all of your files, you should be ready
to recompile the programs. To do this, from within the 0.1 directory, type make,
and if there are no errors you should end up with new executables that include your

changes.

A.7 Using SVN

If you have made modifications to your simulation code that you think might be
useful to the rest of the collaboration, then you should check these changes into the
respsitory so that others can access your updated code. It is also a good idea to
regularly update your own directory so that your code always contains the latest

implementations. Below are some of the basic SVN commands that you will need:

> svn update — Update to latest code version.

 

7Note that both the forward and inverse map files must be in “COSY format” (without line
headers) and not “SpecTcl format” (with line headers). If need to convert a map file to COSY format,
use the program spctkl2cosy, which is located in /projects/proj2/sweeper/bin/. This program will
only run on 32-bit spice machines and not the 64-bit fishtank machines.

8It is recommended that you DO NOT follow the past practice Of copying individual map files into
the 0.1 directory, as doing this leads to clutter and compatibility issues between different versions.
A better method is to simply include the full filepath of the map file in its original location, e.g.
/ projects / pro j2 / sweeper / maps / . . . / * .map

77

> svn add <filename> — Add a file to the repository.
> svn ci <filename> — Check in file to SVN (must be added first).
> svn co <filename> — Check out file from SVN.

> svn stat — View status of all SVN files.

As explained above, if you want to check in your changes to the repository, use
the command svn ci <filename>, where <filename> is the name of the file that
you are checking in (you can also use svn ci without the <filename> argument to
check in all files in your directory). When you use the svn ci command, a vi editor
will automatically open up to allow you to make a comment on the changes that you
are adding. To begin inserting text, press 1, and when you are done writing your
comment, hit the esc key, followed by :wq and then hit the Enter key.

Before you check in any changes, your new code should be well tested to ensure
that there are not any bugs. You should also be sure that your new code does not cause
any incompatibilities with the existing code. This can be checked using the svn stat
command, which lists all edited files in the directory with a status character before

the filename. The status characters are as follows:

M—modified (not checked in yet)

A—added

?—unknown (not added yet)

C—conflict (please edit to agree with checked out version)

U—updated

If one of your files is flagged as having a conflict, you must edit the file until the

conflict is resolved. Once you have done this, type:
> svn resolved <filename>

to tell subversion that you have resolved the conflict. For more information on

using SVN, see the documentation at: http : //subversion.tigris.org/.

78

Appendix B

Using ROOT -

B. 1 Introduction

ROOT is an “object oriented data analysis framework” written by programmers at
CERN. It is particularly suited for analysis of the large data sets found in nuclear
physics. It is capable of performing basic analysis tasks such as gating, histograming
and fitting, in addition to much more complex tasks. ROOT is primarily command
line driven, using the CINT C/C++ interpreter.

This manual is intended to introduce those who are new to ROOT to some of its
basic functions. After reading this manual you should have a “SpecTcl like” level of
functionality in using ROOT, i.e. you should be able use ROOT perform all of the
tasks that are possible in SpecTcl (plus a few more).1 At times the manual may gloss
over some of the more subtle subjects involved in using ROOT; this is done in the
interest of promoting simplicity and quick learning of the program. The manual also
makes purposeful use of imprecise terminology as Opposed to technically correct C++
jargon, with the hope that it will be better understood by readers with little or no
knowledge of C++.

 

lSpecTcl is just being used as an analogy here; if you aren’t familiar with SpecTcl, don’t worry
about it.

79

B.2 Installing ROOT

Before you can start to use ROOT, you need to “install” it (e.g. set the needed
environment variables) on your N SCL user account.2 If you have already set up your
account to run st_mona simulations—as outlined in Appendix A—then you are all
set and can begin using ROOT on any of the 64—bit fishtank machines. Otherwise,

open up your "/ .bashrc file, and add the following lines to the end of the file:

export ROOTSYS=/projects/proj6/mona-sim/soft/root/root_v5.12_00/
export PATH=$ROOTSYS/bin/:$ROOTSYS/include/:$PATH

export LD_LIBRRY_PATH=$RO0TSYS/lib/ : $LD_LIBRARY_PATH

Then save the file and type
> source ~/.bashrc

Once you have done this, the command to begin the ROOT program is:
> root.exe

When you type this at the command line, ROOT should start up and you should

see something like this:

*******************************************
WELCOME to ROOT
Version 5.12/00 10 July 2006

You are welcome to visit our Web site
http://root.cern.ch

********
********

*******************************************

FreeType Engine v2.1.9 used to render TrueType fonts.

 

2If you are logged into the N SCL servers as user mona, then the environment variables are already
set; in this case you can go ahead and begin using ROOT on the 64—bit fishtank machines.

80

Compiled on 15 November 2006 for linux with thread support.

CINT/ROOT C/C++ Interpreter version 5.16.13, June 8, 2006
Type ? for help. Commands must be C++ statements.
Enclose multiple statements between { }.
root [0]
ROOT’S command line works much like a BASH shell: you can scroll through your
most recent commands by hitting the up—arrow key, and auto-complete recognized

commands using the Tab key. You can quit the program by typing .q at the command

line. Also note that all commands in ROOT are case sensitive.

B.3 Files and Trees

ROOT reads data that is stored in a binary file with the .root extension. These
files are capable of storing many types of objects, but for the purposes of this doc-
ument we will focus on the most basic one: the TTree. There are two example files,
example1.root and example1_ana.root located in the /projects/proj1/MONA/ROOT/
directory. It is suggested that you use those two example files to practice the com-
mends being presented throughout this document.

To read data from a root file, you must first read the file into ROOT’S memory.
There are two ways to this. The easiest is to simply follow the root.exe command

by the name of the file, e.g.
> root.exe examplei.root

The second way is to open up the file once you have already begun the program;

you can do this using the following command:
TFile * _file0 = TFile::Open("example1.root");

One note about this method: the _file0 can be thought of as a “variable” name
(more accurately, it’s the name of the pointer to the TFile object). It could be set to

anything that you wish.

81

 

 

Event # Value of P1 Value of P2

 

1 74.689 5670.4
2 93.452 6987.6
3 45.657 3331.4
4 22.389 3787.6
5 61.723 2229.3

 

 

Table 8.1: Simple example of the type of data stored in a TTree.

Now that you know how to read a file into ROOT, we’ll go a bit into what makes
up a ROOT file. As mentioned above, the most fundamental part of a ROOT file is
the TTree; a TTree is essentially a collection of “events” and parameters. Each event
is a collection of data values for all of the parameters present in the file. As a simple
example, consider a TTree that stores two parameters, P1 and P2, and five events.
The structure of the data might look something like what is shown in Table B.3, with
each event number being associated with specific values of P1 and P2.

Each TTree has a “name” associated with it, and in order to perform operations
on the tree, you must know what that name is. To see the names of all the trees

contained with the file you have open, use the command:
.13
and you should see something like:

root [2] .13

TFile** example1.root
TFile* example1.root
KEY: TTree t;1 simple-track tree
Here the line KEY: 'I'I'ree t;1 simple-track tree tells you that you have a

TTree with the name t stored within this particular ROOT file.
The parameters in a TTree are given names by the person or program who writes

the ROOT file; to see a list of all of the parameters stored in your particular 'I'I‘ree,

typez3

3Throughout this document, we will use the tree name “t” to represent a generic T'Dee, and

 

82

t->Print("all");

doing this will show you a bunch of entries that look like this:

* ............................................................................ *
*Br 4 :b1p0Ekin : b1p0Ekin/D *
*Entries : 100000 : Total Size= 802866 bytes File Size = 697625 *
*Baskets : 25 : Basket Size= 32000 bytes Compression= 1.15 *
* ............................................................................ *

The lines above give information about the parameter called b1p0Ekin. For the
purposes of this document, you just need to be able to read off the parameter name
from lines like the one above: as you can see the name, b1p0Ekin, is located on the
first row directly after the first colon.

One useful (and necessary if you want to look at MONA simulation data) feature
of ROOT trees is the ability to merge TTrees from separate ROOT files together,
by adding the second tree as a “friend tree” to the first. Essentially, when you add
a friend tree to an existing tree, the existing tree looks as if it contains all of the
parameters present both in itself and in the friend tree. As as example, consider
the files example1.root and example1_ana.root. Start up ROOT and load in the
file example1.root. Now add as a friend the tree contained in examplel_ana.root"

(which is named at) by doing the following:
t->AddFriend("at=at","example1_ana.root");

Once you have done this, you can seamlessly work with parameters in
example1_ana.root, just as if they were contained in examplei .root.

In addition to the parallel merging capabilities of AddFriend, it is also possible to
merge multiple files in series, such that a group of files can be used as if it were one
large file. A grouping of files in series is called a TChain, and the syntax to create one

is:

 

all “operations” on a TTree will assume that the tree name is “t” (unless specifically specified
otherwise).

83

TChain * mychain = new TChain("t");

Note that the t in the expression above should be substituted with the actual
name of the TTrees in the files that you are chaining together.
The new TChain() command shown above only creates a new TChain; you still

need to add files to it using:

mychain->Add("file1.root");
mychain->Add("file2.root");
mychain->Add("file3.root");
mychain->Add("file4.root");
mychain->Add("file5.root");
mychain->Add("file6.root");
mychain->Add("file7.root");

Once you have done this you can treat mychain as if it were a “normal” TTree

name.

B.4 Drawing Histograms

Histograms are one of the most commonly used methods of viewing data in nuclear
physics. A histogram in ROOT can be thought of as the analogy of a spectrum in
SpecTcl: for a given parameter it displays the number of counts falling within a user-
defined bin range. The command used to draw a histogram is best illustrated with an
example: lets say I am interested in seeing a histogram of the parameter b1p0Ekin,
and I want to let ROOT set the histogram limits and bin ranges automatically. In

order to do this, the command is as follows:
t->Draw("b1p0Ekin");

The histogram drawn by this command is shown in Figure B.1(a). Now lets say
that I want to draw another histogram of b1p0E1kin, but I want to manually set it to

display from 2960 to 3070 in 300 bins. The command to do this is as follows:

84

t->Draw( "b1p0Ekin>>hst (300 , 2960 , 3070) ") ;

which draws the histogram seen in figure B.1(b). The instructions to set the binning
and ranges are contained in the characters >>hst (300,2960,3070). Here hst is the
histogram “name,” and could be set to anything.4 The 300, 2960, and 3070 represent

the number of bins, low bin and high bin, respectively.

 

 

 

 

 

 

 

 

 

 

 

 

[Jr—............o —n-—.............
M ”17 “I ”17
00° Ln mu ’ m.
mo ‘ ‘
anon
mo
anon
mo
mo
no
° m mo m 3020 m no no
bipown

(a) (b)

Figure B.l: Example ROOT histograms; the histogram in the left panel is drawn with
automatic binning and ranges, and the one in the right panel is manually set to go
from 2960 and 3070 in 300 bins.

The syntax to draw a two-dimensional histogram is an extension of the 1d syntax
shown above. For example, if I want to plot the parameters b1p0Ekin vs. b2p0Ekin,

with b1p0Ekin displayed on the y-axis from 2960 to 3070 in 300 bins, and b2p0Ekin

displayed on the x-axis from 400 to 800 in 300 bins, the command is:
t->Draw("b1p0Ekin:b2p0Ekin>>hst(300,400,800,300,2960,3070)");

Note that the syntax for specifying parameters is Y:X, while the syntax for setting
bin and axis ranges is (somewhat unintuitively): (xbins, xlo, xhi, ybins, ylo, yhi).

The 2d draw command shown above will display the desired histogram using a
2d black and white scatterplot. It is usually desirable to view histograms in color,
with different hues representing different z-axis values. Before you try drawing a 2d

histogram in color, you should change the color scheme from the default (which is

 

4Although histogram names can be reused, doing so will delete the current histogram with that
name from memory. Reusing histogram names can also lead to segmentation faults, so it is advisable
to choose a. unique name for each new histogram that you draw.

85

ugly and hard to decipher) to a more traditional blue—green—red. You can do this with

the command:
gStyle—>SetPalette(1);

Now that you have a nice palette, the command to draw a 2d histogram in color

t->Draw("b1p0Ekin :b2p0Ekin>>hst (300 ,400 ,800 , 300 , 2960 , 3070) " , " " , "col") ;

It should be obvious that the "col" is what tells ROOT to draw the histogram in
color. It should also be noted that if you want to display a color scale on the side of
your histogram, you can replace "col" with "colz" in the command above. You may
be a bit confused by the unfilled set of "" in the command. These are being used as
“placeholders” for the gate argument, which is described in Section B6. The results

of the command above can be seen in Figure B.2(a).

 

.. ILJJ

.Illllll Ill

 

Inn-llll I!

Illllljll

     
 

 

 

 

 

 

 

 

 

 

 

 

(a) Example two-dimensional ROOT histogram (b) Example of a TCanvas divided into three
displaying b1p0Ekin vs. b2p0Ekin, with user de- pads in the x—direction and two pads in the y-
fined binning of 300 bins between 400 and 800 direction.

on the x-axis and 300 bins between 2960 and

3070 on the y-axis.

Figure B.2: Example 2d ROOT Histogram (left panel) and Divided Canvas (right
panel).

Once you have drawn a histogram using the Draw() command, it is saved into
memory. You can access it later using the command, histname->Draw0 ;, which will

re-draw the histogram named histname in the current window.

86

B.5 TCanvases

As you should have noticed, using the t->Draw() command creates a new graphical
window in which the histogram is drawn. This window is called a TCanvas. You can

also create a TCanvas manually, using the following command:
TCanvas * c2 = new TCanvas();

Here c2 is the “name” of the Tcanvas, and as with histogram or tree names it
could be anything you want. You can have multiple canvases Open during a ROOT
session, but only one of the canvases is active at a given time; the active canvas
will have a yellow outline around its edges indicating that it is the active one. The
command to switch between canvases is canvasname->cd() ; e.g. if I want to switch

to the canvas called c1, then I would use:
c1—>cd();

It is also possible to divide a canvas up into “pads” or sections, allowing you to
draw multiple histograms on one canvas. This is done using the Divide() command.
For example if I want to divide c1 so that it has three pads in the x—direction and

two pads in the y-direction, then I would use:
Cl->Divide (3 , 2);

Figure B.2(b) shows a 3 x 2 divided canvas, with an example histogram drawn in
each subpad.

Another useful feature is the ability to look at histograms with axes on a log scale.
The command to do this in ROOT is SetLog*(), where * is the name of the axis (x,
y, or z) in lowercase. The SetLog command only operates on the canvas or pad that
is currently selected. As an example, if I have a one dimensional histogram and want

to view the y-axis on a log scale, I would use:

gPad->SetLogy();

87

 

For a two dimensional histogram for which I want the z-axis on log scale, I would

type:
gPad->SetLogz();

To go back to linear scale, the command is SetLog* (0), e.g. if I wanted to change

the y-axis back to linear, I would type:
gPad->SetLogy(O);

It is possible to modify histograms and other graphical objects using the built in
GUI. To make use of this, go to the View menu on your canvas and select the Editor
option. You will see a new window appear in the left edge of your canvas. Use of the
editor is fairly intuitive. Note that if you click on different parts of the canvas, the
object being edited (and thus the options available in the editor) change.

As a final note, you will probably want to save pictures of your canvas to file. The

command to do this is:
c1->Print("filename.*")

where * is the file extension. ROOT will automatically set the type of file being
written based on the extension you select. ROOT can save canvases to many different
file types, including .pdf, .ps, .eps, .svg, .png and . jpg. You can also save your
canvas using the File->Save As menu, or you can send it directly to a printer using
File->Print. Histograms points can also be written out to an ASCII file, using the

command:
hstname->Print("all"); > outputfilename.txt

This will write out the points of the histogram into a text file called
outputfilename.txt. The formatting of the output file is a bit clumsy; there is a
way to write out histograms into a plain two column format, but it requires the use

of custom commands; hence it will be explained later on.

88

B.6 Gates

The ability to set “gates” (logical restrictions) on parameters is needed to do any sort
of nuclear physics analysis. Gates in ROOT are treated as logical C++ statements.
Some of the more commonly used logical statements are: “greater than” (>), “less
than” (<), “equal to” (==), “not equal to” ( !=), AND (ML), and OR (I I). Any com-
bination of these logical statements can be used. The gate command is the second
argument of the Draw() command and is surrounded by " ". As an example, if I
want to view a histogram of the parameter b7p0x, with the restriction that another

parameter, b7p0tx, is greater than zero, I would use the following command:
t-$Draw("b7p0x","b7p0tx > 0");

As a more complicated example, if I wanted to see a histogram of b7p0x subject

to the following conditions:

~b7p0tx greater than 0.
—b1p0Ekin less than 3000.
—b7p0Ekin not equal to zero,

then I would type the following:
t->Draw("b7p0x","b7p0tx > 0 && b1p0Ekin < 3000 && b7p0Ekin != 0");

In additional to one dimensional gates, ROOT can also create two dimensional
gates which constrain the values of two parameters to lie within a certain shape.
Two dimensional gates are given a name, and can be used just like any other logical
statement. For example, if I want to apply a 2d gate called “my2dgate” to a histogram

containing the parameter b1p0x, I would do:
t->Draw("b1p0x","my2dgate");

Two dimensional gates can be combined with other logical statements as well,
so if I wanted to draw b1p0x subject to both “my2dgate” and the requirement that

b1p0tx be greater than zero, then I would do:

89

 

t->Draw("b1p0x","my2dgate && b1p0tx > O");

The easiest way to set a 2d gate is to make use of the TCanvas GUI. The steps to

do this are outlined below:
1. Draw the 2d histogram.
2. In the TCanvas containing the new histogram, select View—>Toolbar.

3. In the toolbar, click on the cut tool. It has a picture of scissors on it and is the

farthest right tool on the toolbar.

4. Go onto the histogram and start drawing your gate. Single clicking sets a new

point in the contour, and double clicking closes the gate.

5. Move the mouse cursor over the gate (the cursor will turn into a hand with
a pointing index finger when you are in the right place), and right click. Then
select the SetName option, and type your desired name of the gate in the pop-up

window.

6. If you would like to modify your gate, you can do so by left clicking on one of

the gate points and moving it around.

Figure B.3 shows an example of a 2d gate created using the procedure outlined
above. Unlike in SpecTcl, your 2d gate will not automatically be drawn every time
that you re-draw a histogram, but the gate is still stored into memory until you quit

the program. To re—draw a gate the command is:
mygate->Draw();

You will likely find yourself typing the same gate conditions over and over, which
can get tedious. You can store these logical statements in a TCut object, and when
you do so, the gate conditions can be accessed just by invoking the name of the TCut.

The syntax to create a TCut is explained with an example: if I wanted to create a

90

 

b7-I o :h7-IEkln b7-IEldn>0

  

 

 

 

 

(a) Spectrum showing a parameter with the (b) Example of a two dimensional gate. The
gate drawn in panel (b) applied to it. events outlined in black are included within the
gate.

Figure B.3: Example 2d Gate (right panel) and histogram with the gate applied to it
(left panel).

TCut, named mycut, which requires that b7p0Ekin and b13p1Ekin both be greater

than zero, I would type the following:
TCut mycut = "b7p0Ekin > 0 && b13p1Ekin > 0" ;
The TCut can then be used like a normal logical statement, e.g.

t—>Draw( "b7p0x" ,mycut) ;

Note that in the above command there are no " " around mycut. This is because
the needed " " are contained in the definition of mycut. TCuts can also be combined

with “ordinary” gates or other TCuts as follows:

t->Draw("b7p0x",mycut 8:8: “b13p1x>0"); //\ combine a TCut with a "normal" gate.

t—>Draw("b7p0x",mycut as mycut2); //\ combine two TCuts.

B.7 Creating Pseudo Parameters

Quite often one wants to look at mathematical combinations of the parameters stored
in a ROOT file. The simplest way to do this is to simply include the mathemati-
cal statements in the argument of the Draw() command. For example, if I want to

look at the velocity of a particle, which for the purposes of this example is equal to

V2 - b7p0Ekin/ 10, then I would type the following:

91

t—>Draw("sqrt(2 * b7p0Ekin / 10)");

Any valid C++ math operator can be used; some of the more common examples

are listed below

— add, subtract, multiply, divide: +, —, *, /

— square root of m: sqrt(x)

— raise a: to the power 72.: pow(x,n)

— sin, cos, tan of at: sin(x) , cos(x) , tan(x)

— arcsin, arccos, arctan of as: asin(x) , acos(x) , atan(x)
— absolute value of x: abs(x)

As in the case of gates, you often do not want to type long mathematical expres—
sions over and over again. Fortunately, ROOT allows you to store your mathematical
expression in an object called an “alias.” For example, if I want to store the velocity

expression shown above as an alias called b7p0ve1, I would do:
t->SetAlias("b7p0vel","sqrt(2 * b7p0Ekin / 10)");

Now to draw the velocity I just have to type:
t—>Draw("b7p0ve1")

Aliases can also be included in the definition of other aliases; for example, if I

want to create an alias of 2*velocity, called b7p0velx2, then I could do:
t->SetAlias("b7p0ve1x2","2*b7p0ve1");

Aliases can be used just like any “real” ROOT parameter, e. g. you can draw them,

place gates on them (1d and 2d), and so on.

B.8 Using Macros

If you haven’t noticed by now, using ROOT involves a lot of typing of commands, and

you probably don’t want to repeat a bunch of commands over and over again. ROOT

92

 

allows you to save series of commands in a macro file; invoking a macro file has the
same effect as typing each one of the commands on the command line individually.
ROOT macro files should always have the extension .0, and all of the commands
must be enclosed in a set of curly brackets. The command to run a macro (called e.g.

mymacro.C)ia
.x mymacro.C

As a simple example consider the following macro, called examplemacro.C; it is
located in the /pro j ects/pro j 1/MoNA/RO0T/ directory, and the code is reproduced
here. Comments in the code are set off by // (the comment symbol in C++), and

should explain to you what each line is doing.

{

//Macro File examplemacro.C

TFile *_file0 = new TFile("/projects/proj1/MoNA/RO0T/examp1e1.C");
//Load the file example1.C into memory

TCut posenergy = "b7p0Ekin > 0 && b13p1Ekin > 0" ;
//Create a TCut

t->Draw("b7p0tx>>hst(100,-.1,.1)",posenergy);
//draw a histogram of b7p0tx, subject to the conditions of posenergy

}

You can also invoke other macros from within a macro; for example, if I want to

call a macrofile called macro2 .C from within another macro, I would add the line:
gRDOT->ProcessLine(".x macro2.C");

You can also load in a macro file when you start up ROOT, by typing the name
of the macro after the root . exe command. For example, if I want to automatically

load the file examplemacro .C at startup, then the syntax is:

93

> root.exe .x examplemacro.C

There is a useful “startup” macro file located in /projects/proj1/MoNA/RO0T/;
it is called root_logon.C It does a few formatting tasks like setting to default color
palette to the nice looking RGB one. It also loads up a custom function that allows
you to write out a histogram to a two column ASCII file. If you have loaded up

root_logon.C, then the syntax to write a histogram to file is:
hstname->WriteSpec("filename.txt",xlo, xhi);

where xlo and xhi are lower and upper limits of the histogram.

B.9 Various Odds and Ends

This section contains a brief overview of some more useful commands that don’t really
fit anywhere else. They are listed with a brief description of what the command does
followed by the command syntax.

0 Draw a histogram using data points:
t->Draw("7p0x>>hst(100,-.1,.1)","","p");
This would draw hst with the default point size, which is very small; to change it do:

hst->SetMarkerStyle(20); //sets a reasonable point size

hst->Draw("p"); // redraws "hst" using points

0 Draw a histogram with error bars (calculated as the square root of the number

of counts):

t->Draw("7p0x>>hstnew(100,-.1,.1)","","e“); //new histogram

hstold->Draw("e"); //existing histogram

0 Change the color of the lines or points of a histogram already in memory:

94

 

hst->SetLineColor(4); //Lines

hst->SetMarkerColor(4); //Points

Colors in ROOT are assigned a number, so here I am setting the histograms to be
“color 4” (which is blue). To see a list of all available colors and their corresponding
numbers, select View->Colors from the TCanvas menu.

0 Scale a histogram (by the number x):
hst->Sca1e(x);

0 Draw an existing histogram on the same canvas, without erasing the one already

there:
hst->Draw("same");
0 You can also combine arguments like p and same, e.g.
hst->Draw("psame"); //Draw hst on the same canvas, using points.
0 Clear your current canvas:
c1->C1ear();
0 Write 2D gates into a text file:

ofstream out;

out.open("my2dgates.txt");
gate1->SavePrimitive(out);
gate2->SavePrimitive(out);
gate3->SavePrimitive(out);

out.close();

The text file my2dgates . txt will now contain C++ code describing the 2D gates
gatel, gate2, and gate3. This code can be copied and pasted into a macro file, to

allow the user to load the gates into memory in future ROOT sessions.

95

0 Convert a SpecTcl filter file into a ROOT file:

—Run the executable f1t2root . sh located in /pro j ects/pro j 1/MoNA/RO0T/

This will prompt you for the name of the input filter file and the name of the output
root file. It must be run from a 32—bit spice machine. The new root file will contain a
TTree called h1 that contains all of the parameters written in the filter file. Any dots
in the parameter names will be converted into underscores (e. g. sweeper. fp . crdc1.x
becomes sweeper_fp_crdc1_x), and any uppercase letters past the first letter of the
name will be made lowercase (ToF_hit_1 becomes Tof_hit_1). Also, since ROOT
needs to assign a value to every parameter for every event, any “not valid” events in
the filter file will be given a value of exactly zero in the ROOT file. Finally, there is
a limitation on both the size of the filter files and the number of parameters allowed
per file, which the author of this manual has not yet determined. This limit is fairly
large, however, and can be worked around by making judicious use of Friend Trees
and TChains.

If you are interested in using the more advanced functionality of ROOT, there
are many resources on the web. A good place to start is the official ROOT manual

located at:
http://root.cern.ch

There is also an online bulletin board (“Root Talk”) dedicated to helping users learn

to use ROOT located at:

http://root.cern.ch/phpBB2/

96

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