MEASUREMENT OF 34Ar(α,p)37K USING THE JENSA GAS JET

TARGET

By

Justin Edward Browne

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics — Doctor of Philosophy

2021

MEASUREMENT OF 34Ar(α,p)37K USING THE JENSA GAS JET TARGET

ABSTRACT

By

Justin Edward Browne

X-ray bursts are very luminous thermonuclear explosions that occur in binary star sys-

tems. In these systems, a neutron star accreting matter from a companion star undergoes

a runaway thermonuclear explosion, caused by a breakout from the CNO-cycle into the αp-

process. The αp-process consists of a series of (α,p) and (p,γ) reactions. In this process,

there are “waiting point” nuclei at which the nuclear burning pauses until the stellar condi-

tions change so that the (α,p) reaction rate increases and burning continues. 34Ar is one of
these waiting point nuclei, and sensitivity studies have found that varying the 34Ar(α,p)37K

reaction rate significantly impacts the light curve of x-ray bursts.

Because the 34Ar(α,p)37K cross section had never been directly measured before, the re-

action rates used in simulations are based on Hauser-Feshbach predictions. These predictions

are hypothesized to be inaccurate because the Hauser-Feshbach statistical model requires a

high level density in the compound nucleus and assumes there are no dominant resonances.

This thesis describes an experiment at the National Superconducting Cyclotron Lab-

oratory (NSCL) designed to test Hauser-Feshbach predictions by directly measuring the

34Ar(α,p)37K cross section. A radioactive ion beam of 34Ar15+ with energies of 57.04 MeV
and 54.19 MeV was delivered to a (5–8) × 1018 atoms/cm2 thick He target, created by the Jet
Experiments in Nuclear Structure and Astrophysics (JENSA) gas jet target. The recoils and

beam were detected by the ANASEN position-sensitive ionization chamber, and the ejectiles

were detected by an array of silicon detectors combining SuperORRUBA and SIDAR. The

beam included contamination from the decay products of 34Ar, namely 34Cl and 34S. While

the contribution from 34S(α,p)37Cl could be subtracted because the cross section had be
previously measured, the contributions from 34Cl(α,p)37Ar and 34Ar(α,p)37K could not be

separated, so a combined cross section for the two was derived from the data.

The combined 34Cl(α,p)37Ar and 34Ar(α,p)37K cross sections were determined to be
(70 ± 21) mb at (5.91 ± 0.08) MeV and (52 ± 13) mb at (5.51 ± 0.08) MeV in the center of
mass frame. Comparison with Hauser-Feshbach theory indicates that the experimental cross

sections are lower by 37 % and 20 %, for the two energies, respectively. This suggests that the
hypothesis that the Hauser-Feshbach model overestimates the 34Ar(α,p)37K cross section by

2 orders of magnitude is unlikely to be true at these energies.

TABLE OF CONTENTS

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

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

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 X-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Cross Section and Reaction Rate
. . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Hauser-Feshbach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Measurement of 34Ar(α,p)37K . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.1

Jet Characteristics

Chapter 2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Beam Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 JENSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Silicon Detector Array . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
2.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Trigger Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.1
2.3.2 Position-Sensitive Ionization Chamber

2.3 Detectors

Chapter 3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Beam Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Detector Solid Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Energy Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Silicon Detectors
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ionization Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Ejectiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Recoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.1
3.3.2

Chapter 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

v

vi

1
1
5
8
11

13
13
17
22
28
28
32
33
35

38
38
39
45
46
47
53
56
57
60
65

75
76

78

81

94

LIST OF TABLES

Table 2.1: Typical values measured during a JENSA experiment.

. . . . . . . . . . .

20

Table 2.2: The pressures measured at CCD4 for different catchers with a compressor
. . . . . . . . . . . . . . . . . . .

discharge pressure (Pdisch) of 300 psig.

Table 3.1: The experimental beam energies.

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

Table 3.2: The layers through which the beam passes and loses energy. . . . . . . . .

Table 3.3: The ionization chamber energy calibration values.

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

Table 3.4: The thickness of the dE detectors.

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

Table 4.1: The relative uncertainties of the quantities used to calculate the combined
. . . . . . . . . . . . . . .

34Cl(α,p)37Ar and 34Ar(α,p)37K cross section.

26

39

49

51

60

76

v

LIST OF FIGURES

Figure 1.1: The light curve (luminosity vs. time) of a simulation of an x-ray burst ex-

hibiting a double-peaked structure from [11]. 30S(α,p)33Cl and 34Ar(α,p)37K
were found to be blocking the reaction flow in the simulation. Varying
these reaction rates also affects the shape of the light curve. Reproduced
. . . . . . . . . . . . . . . . . . . . . . . . .
by permission of the AAS.

Figure 1.2: An example of how the cross section (σ(E)) and Maxwell-Boltzmann dis-
tribution (P (E)) combine to form a product which is peaked in one energy
range, known as the Gamow window. The Gamow window is shaded.
.

Figure 1.3: An illustration of the experimental scenario of a beam of particles imping-
ing on a target. The beam travels through an area of Ab with a velocity
of v. The target occupies a volume of thickness xt and area At.
. . . . .

Figure 1.4: Predictions of the 34Ar(α,p)37K cross section [21, 22, 24].

. . . . . . . .

Figure 2.1: The Coupled Cyclotron Facility and the A1900 Fragment Separator.

. .

Figure 2.2: Spectrum showing the identification of beam species using the energy loss
in two sections of the PSIC. The energy loss in the dE section is plotted
against the energy loss in the E section.
. . . . . . . . . . . . . . . . . .

Figure 2.3: Diagram of the JENSA gas system. . . . . . . . . . . . . . . . . . . . . .

Figure 2.4: These diagrams show the setup for measuring the areal density of the jet.
On opposite sides of the jet are a 241Am α-particle source and a Micron
BB15 silicon detector. The difference in energy of the detected α-particles
between runs with and without a jet is used to determine the areal density
of the jet. The detector’s 64 front-side channels allow for the areal density
to be measured in the left-right direction, and the four back-side channels
allow for it to be measured in the up-down direction. (a) shows the setup
from the side, and (b) shows the setup from above.
. . . . . . . . . . . .

Figure 2.5: The nozzle used in this experiment.

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

Figure 2.6: Two pumping configurations tested to decrease the pressure at CCU4. (a)
shows the first approach in which the exhaust of all pumps feed into the
(b) shows the configuration used in the experiment in
main chamber.
which the exhaust from UP4 feeds into the cavity pumped by UP1.
. .

4

7

8

10

14

17

19

23

25

27

vi

Figure 2.7: A diagram of the detectors used in the experiment and the reaction prod-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ucts they detect.

28

Figure 2.8: The relationship between particle energies and the polar angle at which
they are emitted for the reactions that occur in this experiment.
(a)
shows the different reactions together, and (b) shows them separately.
The angular ranges that are covered by detectors are shown. The high
energy (> 30 MeV) lines correspond to the recoils, and the low energy
(< 30 MeV) lines correspond to the ejectiles. For each (α,p) reaction,
there are multiple levels that can be populated in the recoil nucleus, and
for each of these levels, there is a different relationship between energy
and angle. For elastic scattering, this is not the case, so there is only one
line per particle.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.9: The silicon detector array used in this experiment, looking upstream, to-
ward the source of the beam. The detector naming counts up going clock-
wise, starting at the upstream section and repeating for each subsequent
downstream section. Detectors 5 and 12 were removed to accommodate
. . . . . . . . . . . . . . . . . . . . . . .
jet and beam tuning hardware.

Figure 2.10: The silicon detectors used in this experiment are (a) 4 60 µm-thick Micron
BB10s, (b) 12 1 mm-thick Micron BB15s, and (c) 5 60 µm-thick and 5
. . . . . . . . . . . . . . . . . . . . . . . . . .
1 mm-thick Micron YY1s.

Figure 2.11: The positions of the silicon detectors in the experiment. The z-axis is the
beam axis and the y-axis is the jet axis, meaning the reaction location is
at the origin.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.12: A diagram showing the different sections of the ionization chamber. Each
signal is read from a wire or set of grids biased at 150 V. The biased grids
have grounded grids between them. The X and Y sections consist of 32
channels each, which allows for the calculation of the outgoing angles of
the recoils. The dE and E sections consist of 1 channel, which combines
the signal from multiple grids, each.
. . . . . . . . . . . . . . . . . . . .

Figure 2.13: An example showing how the four ASICs motherboard triggers are com-
bined to create the VM-USB trigger. (a) shows two events during normal
operation. (b) shows how a missing complete signal can propagate errors
to subsequent events. (c) shows how the OR of the motherboard triggers
. . .
can be used to prevent this error from propagating to other events.

Figure 3.1: The coordinate systems used to describe BB10s and BB15s (a) and YY1s
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(b).

29

30

31

32

33

37

40

vii

Figure 3.2: The location of detector E1 with an increasing number of transformations
applied until the detector is at the experimental location. The reaction
location is at (cid:104)0, 0, 0(cid:105).
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.3: An example of Monte Carlo results of the solid angle for detector E1.

.

Figure 3.4: Spectra from silicon detector calibrations. (a) shows a normal channel
with a 241Am peak and two pulser peaks. (b) shows a channel with only
one pulser peak. (c) shows a channel with no 241Am. (d) shows a channel
with no pulser peaks.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.5: The hit pattern in the ionization chamber (a) without and (b) with the
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

jet present.

Figure 3.6: The time series data for the pressures measured by CAPic and CAPin.
CAPic measured the pressure in the ionization chamber; for parts of the
experiment, it was not recorded by the EPICS system. Hand measure-
ments were still recorded during this time, but these were not used for the
calibration. CAPin measured the pressure immediately before entering
the nozzle; this was used to determine the areal density of the jet.
. . .

Figure 3.7: The peaks in the ionization chamber were fit in multiple steps. The black
histograms show the experimental data and the teal curves show the fit
curves. First, the E section is fit, as shown in (a) because it is the channel
in which the peaks are most easily distinguished. The peaks are not as
well separated in the remaining channels, so the information from the E
channel is used. (b) shows the elliptic gates around the peaks in the E vs.
dE spectrum and how the separate peaks in the dE channel are fit after
using these gates.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.8: The calibration curve for the E section of the ionization chamber. The
lowest energy group corresponds to 34Ar, the middle 34Cl, and the highest
34S. The 34S points do not agree with the the 34Ar and 34Cl points. This
is likely due to interference from the larger 34Cl peak.
. . . . . . . . . .

Figure 3.9: The time difference between hits in the ionization chamber and the sili-
con detectors. “Ungated” shows this for all hits. “Gated on α-particles”
shows this only for hits in E9 and E13 inside the α-partcle gate shown in
Figure 3.10.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.10: The energy-polar angle relationship in E9 and E13, the detectors without
a thin detector in front of the thick detectors. These detectors can clearly
see the α-particles from elastic scattering. A gate is drawn around these
hits and used as the gate in Figure 3.9.
. . . . . . . . . . . . . . . . . .

43

45

48

49

51

52

53

54

55

viii

Figure 3.11: Diagram showing the incoming and outgoing particles in the reactions of
this experiment in the (a) center of mass reference frame and the (b) lab
reference frame.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Figure 3.12: The energy loss in the dE layer vs. the energy loss in the E layer of the
silicon detector telescopes, corrected for the difference in detector thick-
nesses for the experimental energy E2. (a) shows this plot without gating
on the timing difference described in Section 3.4, and (b) shows the plot
gated on this timing. The separate groups for α-particles and protons can
be seen. The regions used for gating are shown. The intermediate-energy
α-particles are excluded in (b) because the recoils are not detected in the
. . . . . . . . . . . . . . . . . . . .
ionization chamber (see Figure 2.8).

Figure 3.13: The relationship between the energy and the polar angle of the ejectiles
for the experimental energy E2. The gates on the recoil polar angle and
the ejectile energy are able to separate events caused by the reactions of
interest from those caused by random coincidences. (a) and (f) show the
events in sidar, with an ejectile identified as a proton. (b) and (g) show
the events in sidar, with an ejectile identified as an α-particle. (c) and
(h) show the events in sorr_dnt, with an ejectile identified as a proton.
(d) and (i) show the events in sorr_dns (these events are not used to
calculate the cross section). (e) and (j) show the events in sorr_up. (a)–
(e) show events gated only by the timing gate. (f)–(j) show events gated
r < 0.6° gate.
by the timing gate, the Elab
The cleanness of these spectra suggest that the number of background
events is negligible. The two points below the (α,α) line in (b) and (g)
are where α-particles that are only detected in the dE detector would be
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
expected to be seen.
Figure 3.14: The levels in the recoil nuclei 37Cl, 37Ar, and 37K [61], with E − Ein = 0
being the energy of the beam and target system, excluding the kinetic
energy [62]. The dotted red lines show the energy of the system with the
. . . . . . . . . . . . . . . . . . . . .
kinetic energies of this experiment.

e > 500 keV gate, and the θlab

Figure 3.15: The energy deposited in various sections of the ionization chamber by the
recoils. The lines show the energies at which the recoils are expected to be
detected for the three species of recoils. (a) shows the energy deposited
in the dE section vs. the energy deposited in the E section. The sepa-
rate species would be most separated in the E section, but the detection
threshold for that section is too high to be used. (b) shows the sum of the
energy deposited in the X and Y sections vs. the energy deposited in the
dE section. This shows that the energy resolution of these sections is too
low to be useful for particle identification.
. . . . . . . . . . . . . . . . .

59

61

62

64

ix

Figure 3.16: The 34S(α,p0)37Cl cross section data from [63] recreated. The dashed
vertical lines indicate the energies at which this experiment was conducted.
. . . .
The solid line shows the cross section calculated by TALYS [22].

67

Figure 3.17: The detection efficiency as a function of recoil excitation energy for the
34Ar(α,p)37K reaction. The total detection efficiency is an average of the
efficiencies of each level weighted by the relative cross section of the levels. 69

Figure 3.18: An example of a Monte Carlo simulation used to calculate the efficiency
of detecting each reaction. The filled shapes are events that are detected,
and the unfilled shapes are those that are not detected. (a) shows the
ejectile energy vs. the ejectile polar angle. The lines correspond to the
different recoil excitation energies. (b) shows the ejectile azimuthal angle
vs. the ejectile polar angle. The locations of the silicon detectors can be
seen.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.19: The relationship between the target areal density and the pressure mea-
sured at CAPin. The circles are the calibration points, and the crosses
. . . . .
are the experimental values that were calibrated using this fit.

Figure 3.20: The time series data that changes for each run. (a) shows the continuous
data for CAPin throughout the entire experiment. (b) shows the areal
jet density averaged over the time span of each run. (c) shows the total
number of particles delivered to the target for each run.
. . . . . . . . .

Figure 4.1: The experimentally measured 34Cl(α,p)37Ar + 34Ar(α,p)37K cross sec-
tion, with the Hauser-Feshbach predictions, calculated using TALYS-1.8
[22]. The predicted cross sections are weighted averages of the two cross
sections, which are also shown. The weights for the 34Ar(α,p)37K cross
. . . . . . . . . . . . . . . .
section are 67.7 % for E1 and 66.5 % for E2.

70

73

74

77

x

Chapter 1

Introduction

Nuclear physics plays an integral role in the study of astrophysics. Understanding the

nuclear processes in stars sheds light on many astrophysical topics, such as energy genera-

tion or synthesis of the chemical elements. Measurements made in the laboratory are used

to develop astrophysical models that can be compared to observations. Discrepancies be-

tween these models and observations allow us to identify which parts of nuclear physics or

astrophysics need to be further developed.

New rare isotope beam facilities allow us to investigate nuclear reactions involving un-

stable nuclei, which power explosive astrophysical phenomena. This thesis describes a new

technique that was developed to take advantage of reaccelerated radioactive beams available

at the National Superconducting Cyclotron Laboratory (NSCL) in order to study reactions

that are important for understanding an astrophysical phenomenon known as x-ray bursts.

The results of the first experiment using this technique to measure the 34Ar(α,p)37K cross

section are reported.

1.1 X-Ray Bursts

X-ray binaries are a type of binary stellar system in which a neutron star or black hole

accretes matter from a companion star. The energy released by the change in gravitational

energy of the accreted matter makes the system very luminous in x-rays. A subset of these x-

1

ray binaries exhibit bursts in which the luminosity increases by about an order of magnitude,

releasing about 1040 erg. These bursts typically last 10 s to 100 s and occur with recurrence

times of hours to days [1, 2].

As the accreted matter accumulates on the surface of the neutron star, it is compressed

and heated to (106–107) K, which is hot enough for thermonuclear reactions to occur. For

thin shells of gas, such as the accreted layer on the surface of the neutron star, the heat

produced from the nuclear burning is not compensated by the cooling through expansion,

leading to a thermal instability [3]. The partial degeneracy of the electron gas at typical

densities of (105–106) g/cm3 also limits the ability of the layer to expand with rising tem-

perature. Since the nuclear reactions are very sensitive to the temperature, the increase in

the temperature from these nuclear reactions increases the rate at which the reactions occur.

This leads to a thermonuclear runaway.

The details of the burst depend heavily on the parameters of the system, such as the

accretion rate, the composition of the accreted material (especially the amount of hydrogen,

helium, and CNO elements), rotation speed, and heating from deeper parts of the neutron

star. A typical burst scenario involves hydrogen burning via the CNO cycle, helium burning

via the triple-α reaction, breakout of the CNO cycle, helium burning via the αp-process,

then hydrogen burning via the rp-process.

The αp-process is composed of mainly (α,p) and (p,γ) reactions. Although (p,γ) reactions

tend to be much faster than their competing (α,p) reactions, an equilibrium with the inverse

(γ,p) reaction is established, so that overall the (α,p) reaction is more dominant. This

synthesizes nuclei up to around Sc (Z = 21) [2]. Equation (1.1) shows a typical reaction

path for the αp-process. From here, the (p,γ) start to dominate, and the rp-process starts,

which is composed of (p,γ) and β+ reactions. This continues until the hydrogen is exhausted,

2

and is limited by the SnSbTe cycle, the endpoint of the rp-process [4].

14O(α,p)17F(p,γ)18Ne(α,p)21Na(p,γ)22Mg(α,p)25Al(p,γ)26Si(α,p)

(1.1)

29P(p,γ)30S(α,p)33Cl(p,γ)34Ar(α,p)37K(p,γ)38Ca(α,p)41Sc

The exact reaction path depends heavily on the temperature and density. Different

competing reactions dominate at different temperatures. For example, some β-decay rates

for nuclei with short half-lives are comparable to the competing (α,p) or (p,γ) rates, leading

to alternative or parallel reaction paths [2].

The shape of the light curve—how the intensity of light output varies over time—is one

of the main observables used to compare calculations with actual bursts. Some x-ray bursts

exhibit multi-peak structures in the light curve. This was explained as being caused by the

luminosity exceeding the Eddington limit, resulting in the expansion of the neutron star’s

radius. The star then cools, and the frequency of the radiation is pushed outside of the

detection range of the detector [5]. However, in some rare cases, the bolometric luminosity—

the total energy output in all energy ranges—also exhibits double-peaked [6–8] or even

triple-peaked [9, 10] structures. One explanation of this is that there are “waiting points”

where (p,γ)-(γ,p) equlilibrium causes the reaction flow to stall until the temperature increases

enough for the (α,p) reaction rate to allow for the reaction flow to continue. Figure 1.1 from

[11] shows the light curve from a simulation of an x-ray burst exhibiting a double-peaked

structure. The reaction flow was found to be blocked by 30S(α,p)33Cl and 34Ar(α,p)37K,
making 30S and 34Ar waiting points. Varying these reaction rates was also found to affect

the shape of the light curve. Therefore, the rates of (α,p) reactions on these isotopes are of

particular interest.

3

2 × 1038

1.5 × 1038

]
s
/
g
r
e
[

L

1 × 1038

5 × 1037

<unaltered>
100 · 30S(α,p)33Cl
100 · 34Ar(α,p)37K

0
−10

0

t [s]

10

20

Figure 1.1: The light curve (luminosity vs. time) of a simulation of an x-ray burst exhibiting
30S(α,p)33Cl and 34Ar(α,p)37K were found to be
a double-peaked structure from [11].
blocking the reaction flow in the simulation. Varying these reaction rates also affects the
shape of the light curve. Reproduced by permission of the AAS.

4

Sensitivity studies are studies in which many reaction rates are varied to see the effect it

has on burst calculations. Varying the 34Ar(α,p)37K reaction rate has been found to have a

significant impact on the light curve of x-ray bursts [11, 12].

Finally, different conditions, such as temperature, accretion rate, the metallicity of ac-

creted matter, etc. allow for either bursts or stable burning [13, 14]. In steady-state burning,

(α,p) reactions also play an important role in determining the fuel-to-seed ratio for the

rp-process [14].

These considerations motivated the experimental study of the 34Ar(α,p)37K reaction in

this thesis.

1.2 Cross Section and Reaction Rate

Consider a scenario in which particles with velocity v are traveling through a volume

V occupied by another group of particles. The moving group is called the beam and the

stationary group is called the target. The number of beam and target particles are Nb and
Nt, respectively, their number densities are nb and nt, and the current density of the beam
is jb = nbv.

The reaction rate per target nucleus is

λ = σjb.

(1.2)

σ is the reaction cross section, a property of the reaction describing the probability of it

occurring, given in units of area. The number of reactions for a period of time, R, can be

5

expressed as

R = λNt = σnbvntV.

The reaction rate per volume is then given by

r = nbntσv.

(1.3)

(1.4)

In a stellar environment, the reactants are not monoenergetic. To account for this, the

reaction rate must be averaged over the energies of the particles:

(cid:90)

(cid:104)σv(cid:105) =

σ(E)v(E)P (E) dE ,

(1.5)

where P (E) dE is the probability of a particle having an energy between E and E + dE. In

a star, the energies are distributed according to the Maxwell-Boltzmann distribution, which

is given by

P (E) dE =

2√
π

1

(kBT )3/2

√
E exp(−E/kBT ) dE .

(1.6)

Putting this all together, the stellar reaction rate that is typically tabulated is given by

(cid:114) 8

(cid:90) ∞

NA(cid:104)σv(cid:105) =

1

µπ

(kBT )3/2

0

Eσ(E) exp(−E/kBT ) dE .

(1.7)

Even for very high astrophysical temperatures, the maximum of the Maxwell-Boltzmann

distribution is at very low energies. At these low energies, the cross section of reactions that

involve two charged particles is very low because of the Coulomb barrier. Figure 1.2 shows

how the factors of the v(e)σ(E)P (E) product vary over energy, resulting in a peak in the
product. The energy region of this peak, which contributes the most to the integral of (cid:104)σv(cid:105),

6

log(σ(E))
log(v(E)P (E))

σ(E)v(E)P (E)

Center of Mass Energy

Figure 1.2: An example of how the cross section (σ(E)) and Maxwell-Boltzmann distribution
(P (E)) combine to form a product which is peaked in one energy range, known as the Gamow
window. The Gamow window is shaded.

is called the “Gamow window”. To best determine the stellar reaction rate, it is important

to measure the cross section as close to the Gamow window as possible.

To express the cross section in terms of the experimental parameters, we will consider

the situation illustrated in Figure 1.3, in which a beam with velocity v contained within the

bounds of an area Ab impinges upon a target contained in a volume bounded by an area At
and a thickness xt. First, we count the number of reactions (Nr) and multiply the reaction
rate from Equation (1.3) by the duration of observation (t).

Nr = Rt = σnbvntV t

(1.8)

The beam current density can be written as the beam intensity (ib) divided by the beam
area, i.e. jb = ib/Ab, and the target volume can be written as the product of its area and

7

Ab

v

At

xt

Figure 1.3: An illustration of the experimental scenario of a beam of particles impinging on
a target. The beam travels through an area of Ab with a velocity of v. The target occupies
a volume of thickness xt and area At.

thickness, i.e. V = Atxt. This gives us

Nr = σ(ib/Ab)nt(Atxt)t.

(1.9)

However, we must only consider the area in which the beam and target overlap. If the beam

is smaller than the target and Ab completely overlaps At, we can limit V to the volume of
area Ab and thickness xt. This results in the following for the experimental measure of the
cross section:

σ =

Nr

ibntxtt

.

(1.10)

1.2.1 Hauser-Feshbach

For reactions that proceed through an intermediate compound nucleus, the Hauser-

Feshbach statistical model is commonly used to calculate nuclear cross sections. The results

from this model are used for the 34Ar(α,p)37K reaction rate in x-ray burst calculations.

8

In the case of a reaction iµ(j, k)lν, and in which nuclei i and j are in states µ and ν, the

cross sections is expressed as

σµν
jk (Eij) =

1

(2J µ

i + 1)(2Jj + 1)

π2

2µijEij

×(cid:88)

JΠ

T µ
j (E, J, Π , Eµ

i , J µ

k (E, J, Π , Eν

l , J ν

l , Π ν
l )

(2J + 1)

(cid:80)

i )T ν

i , Π µ
m Tm(E, J, Π )

(1.11)

,

i , J µ

i , Π µ

respectively; T µ

j (E, J, Π , Eµ

where Eij is the center of mass energy; µij is the reduced mass of the incoming projectile-
target system; E, J, and Π are the energy, total angular momentum and parity of a state,
i ) is the transmission coefficient between the compound
nucleus in state with the parameters (E, J, Π ) and particle i in state µ, which has the param-
i ) via emission or capture of particle j; and Tm(E, J, Π ) is the transmission
coefficient for the emission of a particle m to all possible final states. The individual trans-
i ) are found by solving the Schrödinger equation

mission coefficients T µ

j (E, J, Π , Eµ

i , J µ

i , Π µ

i , J µ

i , Π µ

eters (Eµ

using an optical model. Tm can be expressed as

Tm(E, J, Π ) =

T λ
m(E, J, Π , Eλ

m, J λ

m, Π λ
m)

ω(cid:88)
(cid:90) E−Sm

λ=0

+

(cid:88)

Eω
m

JmΠm

Tm(E, J, Π , Em, Jm, Πm)ρ(Em, Jm, Πm) dEm ,

(1.12)

where ω is the highest known state in k, Sm is the separation energy, and ρ(Em, Jm, Πm)
is the level density of the compound nucleus. This is split into two parts: a sum over all

known states, and an integral over the level density to account for all remaining states. The

sum in Equation (1.11) implies that, for any incoming energy Eij, resonant states for any
spin J and parity Π can be populated. This requires a sufficiently high level density in the

compound nucleus at the energies of interest [15–20].

9

)
b
(

σ

10−1
10−2
10−3
10−4
10−5
10−6
10−7
10−8
10−9
10−10

2.5

AZURE
TALYS
SMOKER

3

3.5

4

ECM (MeV)

4.5

5

5.5

Figure 1.4: Predictions of the 34Ar(α,p)37K cross section [21, 22, 24].

In the case of 34Ar(α,p)37K, the accuracy of Hauser-Feshbach predictions is in doubt. The

critical level density at which it is appropriate to use the statistical model is estimated to be
(5–10) MeV−1 [21]. In the excitation range of (6–12) MeV for 38Ca—the range populated in
this experiment—the level density is near this threshold; however, the effective level density

is lower when taking into account the fact that only natural parity states can be populated

because the reactants are both even-even nuclei. If the level density is low, resonances from

single levels play a larger role, and the statistical model breaks down.

The particulars of the optical model potentials used to calculate the transmission coef-

ficients also greatly affect the Hauser-Feshbach predictions. Section 1.2.1 show some pre-

dictions of the cross section from the Hauser-Feshbach codes TALYS [22] (using the default

parameters, which uses the α optical model potential from [23]) and SMOKER [21]. This

shows that predictions can vary by orders of magnitude.

Similar reactions have been directly measured and have found that the cross sections was

significantly different than the Hauser-Feshbach predictions. The 23Na(α,p)26Mg reaction

10

was directly measured [25], and it was found that the reaction rate is about a factor of

40 larger than the rate in the REACLIB database [26]. The 22Mg(α,p)25Al reaction was

also directly measured [27]; the cross section was found to be smaller that Hauser-Feshbach

predictions by a factor of about 8, but the astrophysical reaction rate was found to be higher

than rates determined by other indirect experimentally constrained methods by a factor of

103 at 1 GK.

1.3 Measurement of 34Ar(α,p)37K

The 34Ar(α,p)37K reaction has never been directly measured before. There have been

attempts to constrain the cross section using indirect methods; however, they have their

limitations [27]. [28–31] used the 40Ca(p,t)38Ca reaction to determine the excitation energies

in 38Ca, the compound nucleus in the 34Ar(α,p)37K reaction. These levels are important for

determining the resonances of the reaction. Section 1.2.1 shows the cross section obtained

from this level information using the R-matrix code AZURE. The cross section is on average

orders of magnitude lower than the Hauser-Feshbach calculations.

[32, 33] describe the measurement of the 37K(p,α)34Ar reaction, the time-inverse reaction
of 34Ar(α,p)37K. The time-inverse reaction can be used to calculate the forward reaction

using detailed balance [34]. Preliminary results from [32] are an order of magnitude lower

than the NON-SMOKER predictions for the 37K(p,α)34Ar cross section. The astrophysical
reaction rate for 34Ar(α,p)37K reported in [33] differs from Hauser-Feshbach predictions by

1 order of magnitude at 1 GK up to 3 orders of magnitude at 3 GK.

In this thesis, the first direct measurement of the 34Ar(α,p)37K cross section was per-
formed. To perform such a measurement, we must have a beam of either 4He or 34Ar

11

impinging on a target of the other. Because 34Ar is radioactive, it is not feasible to have

a 34Ar target. Therefore, we must perform the experiment in what is called the “inverse

kinematics” frame, in which the heavier reactant is the projectile and the lighter reactant

is the target. This requires a facility that can deliver radioactive beams. An advantage of

conducting the experiment in the inverse kinematics frame is that the heavy recoil escapes

the target and can be detected because the energy in the lab frame is so high. Additionally,

the light ejectiles of the elastic scattering reaction are limited to only forward angles (< 90°),

meaning that only ejectiles from (α,p) reactions are seen at angles > 90°.

12

Chapter 2

Experimental Setup

NSCL experiment E15232 took place at the National Superconducting Cyclotron Labo-

ratory (NSCL) from May 6 to May 19, 2016. It was designed to directly measure the cross

section of 34Ar(α,p)37K.

The NSCL provided a reaccelerated 34Ar radioactive beam. The JENSA system (see

Section 2.2) was used to create a windowless supersonic 4He jet target intersecting with

the beam. This system allows for a high target purity and for the reaction to happen at a

precise location and energy. An ionization chamber was placed downstream of the target to

detect the unreacted beam and the more massive reaction products (recoils). The protons

produced in the reaction (ejectiles) were detected by an array of silicon detectors surrounding

the target.

2.1 Beam Production

The experimental beam was produced via in-flight beam fragmentation, a process in

which intermediate-energy nuclei impinging upon a target are broken up into smaller nuclei

[35]. An 36Ar7+ primary beam was created in the Electron Cyclotron Resonance (ECR)

ion source and sent to the K500 cyclotron. After being accelerated to 13.06 MeV/u in the
K500, the beam impinged upon a 600 µg/cm2 C stripping foil, producing an 36Ar18+ beam.

This beam then was accelerated to 150 MeV/u in the K1200 cyclotron, and impinged on a

13

Figure 2.1: The Coupled Cyclotron Facility and the A1900 Fragment Separator.

1089 mg/cm2 thick 9Be production target, producing a beam of a variety of nuclides.

34Ar18+ was extracted from this mixed beam using the A1900 separator [36]. The first

two dipole magnets were set to select for nuclei with a magnetic rigidity of Bρ = 2.745 T m.

The beam then passed through an energy-degrading wedge with an effective thickness of

148.296 mg/cm2, which changed the magnetic rigidity depending on element number. Fi-

nally, two more dipole magnets selected for nuclei with a magnetic rigidity of 2.617 T m. This
34Ar18+, with an energy of 93 MeV/u and a typical intensity of

resulted in a beam of 55 %
6 × 106 pps.

The 93 MeV/u

34Ar beam is too energetic to be relevant for the astrophysical site of

interest. In order to deliver the beam at astrophysically relevant energies, it was stopped

and re-accelerated to a lower energy. The beam was stopped using a system of two solid

Al degraders and a linear gas cell. The first degrader had an effective thickness of 512 µm

and the second degrader was wedge-shaped with an average effective thickness of 1710 µm.

The use of a wedge degrader is important because it allows particles with different energies,

which are physically separated, to be degraded by different amounts. The degraders are able

14

to be rotated, which changes the effective thickness, i.e. teff = t/ cos(θ), where teff is the
effective thickness, t is the thickness normal to the surface, and θ is the rotation angle. This

allows for the energy degradation to be finely tuned [37–39]. The degraders were rotated by

37.0° and 28.5°. The beam then was stopped in a gas cell filled with 55 Torr of He and was

extracted using a three-stage system of electrostatic fields, propulsion through a supersonic

nozzle, and a radio frequency quadrupole (RFQ) [39, 40]. The entire system is located on a

platform of high voltage, that accelerates the particles to the next stage.

The next stage of re-acceleration is charge-state breeding in the electron-beam ion trap

(EBIT) [41]. The ions are decelerated as they approach the EBIT, which is on a high-voltage

platform of up to 60 kV, injected into the EBIT at energies above the potential barrier, and

then ionized by an electron beam before they can escape. The ions are charge bred for the

selected ionization state and then extracted with an energy of (20–60) keV times the charge

state by changing the potential barrier at the EBIT entrance. This method also causes

the beam to be bunched, which is useful in the experiment for separating different events

[41]. The beam is then accelerated to 600 keV/u in an RFQ. From there, a superconducting

linear accelerator with three quarter-wave resonator cryomodules capable of accelerating

or decelerating the beam to (0.3–6) MeV/u [42] accelerates the beam to the experimental

energy.

The beam delivered to the experiment was 34Ar15+, with a typical intensity of (103–

104) pps at (5.5–5.9) MeV. The charge state of 15+ was chosen due to intensity and purity
considerations. An 34Ar18+ beam would be a good candidate, except that the low extraction

efficiency would result in a beam intensity too low for the experiment; an 34Ar17+ beam

would be contaminated with many low-mass nuclides because Q/A = 1/2; and an 34Ar16+
34Ar15+ had a high extraction
beam would be significantly contaminated with 17O8+.

15

efficiency and was only contaminated by the decay daughters 34Cl15+ and 34S15+.

The ideal energy at which to do the measurement would be in the Gamow window, the

energy range over which most reactions occur for a reaction in an astrophysical environment

and at specific astrophysical conditions (see Section 1.2) [43]. Using

(cid:34)(cid:18) 1

4π
0

E0 =

(cid:19)2(cid:16)π



(cid:17)2(cid:16)

Z0Z1e2(cid:17)2(cid:16)m01

2

(cid:17)

(kBT )2

(cid:35)1/3

(2.1)

from [43], the Gamow peak is located at an energy of E0 = 2.035 MeV for 34Ar(α,p)37K
in a 1 GK x-ray burst. At this energy, however, it would take too long to conduct the

experiment because the cross section is too low. The experimental energies were chosen to

balance measuring as close to the Gamow peak as possible with obtaining a reasonably precise

measurement. Using Hauser-Feshbach predictions for the cross section (see Section 1.2) and

the predicted beam intensities, the center of mass energies of 6.12 MeV and 5.82 MeV were
34Ar(α,p)37K reactions could be detected for each energy using 68 h and

chosen so that 200

103 h of beam time, respectively. These energies correspond to 1.71 MeV/u and 1.625 MeV/u

in the lab frame. The actual beam energies delivered to the target during the experiment

were slightly different, due to a problem with calibration of the beamline dipole magnets.

The actual energies were 1.68 MeV/u and 1.59 MeV/u.

The 34Ar beam delivered to the experiment was contaminated with the daughter and

granddaughter nuclei, 34Cl and 34S. 34Ar decays into 34Cl with a half-life of 843.8 ms. 34Cl,
in two states, decays into 34S with half-lives of 1.5266 s and 31.99 min [44], respectively.

Figure 2.2 shows an example spectrum that is used to identify the constituents of the

beam. The different species can be identified by comparing their energy loss in different

sections of the PSIC (see Section 2.3.2) because they have different stopping powers in

16

)
V
e
k
(
E
d

n
i

s
s
o
L

y
g
r
e
n
E

13500

13000

12500

12000

11500

11000

10500

10000

9500

34Ar

34Cl

16000

17000

19000

18000
Energy Loss in E (keV)

20000

300

250

200

150

s
t
n
u
o
C

100

50

0

34S

21000

22000

Figure 2.2: Spectrum showing the identification of beam species using the energy loss in two
sections of the PSIC. The energy loss in the dE section is plotted against the energy loss in
the E section.

isobutane. Typical fractions of 34Ar, 34Cl, and 34S were approximately 60 %, 30 %, and

10 %, respectively.

2.2 JENSA

The target was produced using the Jet Experiments in Nuclear Structure and Astro-

physics (JENSA) gas jet target [45]. It is designed for studies in nuclear structure and nuclear

astrophysics. For this purpose, JENSA was designed to be a windowless, dense, localized,
recirculating, pure gas target. It is able to achieve an areal density of 9 × 1018 atoms/cm2,
with a typical width of 5 mm and a standard distance between nozzle and catcher of 12 mm.

The fact that there is no window confers some benefits: the energy of the beam is not

significantly affected before reaching the target, allowing for measurements at more precise

energies; the beam experiences less angular straggling; and reactions occurring in a window,

17

which would produce background, are avoided. A dense target allows for more reactions to

occur during the experiment, which allows for a greater sensitivity for lower cross section

measurements. Because the target is localized, the position of the reaction is precisely

known, which allows for more precise measurements of angular distributions. The fact that

it is recirculating means that it saves gas, which is especially important when expensive gases

are used. Target purity is important to avoid background from reactions with other target

constituents or impurities. The gas jet target also has the advantage that there is no target

degradation from the beam.

JENSA creates a supersonic jet by sending high-pressure gas through a nozzle into a

vacuum chamber. The gas is collected in two conically-shaped catchers, which are pumped

by multiple stages of pumps to a compressor. The compressor re-pressurizes the gas before it

is sent to the nozzle again. A diagram of the pumping configuration can be seen in Figure 2.3,

and typical values for the pressure gauges and other instruments can be found in Table 2.1.

The gas is compressed by a PDC-4-100-500 two-stage compressor system. Ballast tanks

stabilize the pressure before, after and between the two compression stages.

The compressor requires at least 1 atm at its inlet to be able to operate. Normally, this

pressure is maintained by the gas flowing through the nozzle, creating the jet target, and

being pumped back to the inlet of the compressor. However, there are times during which

it is either desired or necessary to not produce the jet and send gas through the pumping

system. In order to maintain the required 1 atm in these situations, when the compressor is

isolated from the pumping stages, a path was added for gas to flow directly from the outlet

of the compressor back to the inlet. The amount of gas that flows through this path, which

affects the pressure difference between the inlet and outlet, is controlled by a needle valve,

NVloop.

18

PIRturbo

Shim.

UP4

UP3

UP2

UP1

CAPin∗

Tfm

U5

U4

U3

U2

U1

CCU4

CCU3

CCU2

CCU1

PIR1

PIR2a

7

10

PIR2b

11

12

13

8

9

Vgate

PIR3

Nozzle

Vin

FM

Vbot1

REGbot

CATout

CATin

PIR4

PVley1

Pley

HEley

L1

L2

He

L3

NVvent

PVinlet

REG1

Vreg

Vbot2

Vsub1

NVhm

HM

NVloop

PVloop

Vsub2
Vsub3

CAP5b∗

Compr.

Vcomp_in

Pinlet Pinter Pupstr Pdisch

Vley_out

Vrough

Rough

PVley2

Tley1

Tley2

CAP5a∗

PIRrough

CAP4

Figure 2.3: Diagram of the JENSA gas system.

19

Table 2.1: Typical values measured during a JENSA experiment.

Gauge

PIRturbo

PIRch
CCU1
CCU2
CCU3
CCU4

Pressure
(Torr)

2 × 10−1 i
1 × 10−1 i
1 × 10−4
3 × 10−5
5 × 10−7

– iv

Gauge

Pinlet
Pinter
Pupstr
Pdisch

Pressure
(psig)

0.5
70
320
300

Instrument Measurement

HM
FM
Tley1
Tley2
Tfm
CAPic

iii

– v

29.5 CFM
40 °C
24 °C
32 °C
15 Torr

Gauge

PIR1
PIR2a
PIR2b
PIR3
PIR4
CAP4
Pley

CAP5a
CAP5b
CAPin

Pressure
(Torr)
i

1.2
–iv
> 1.5
> 1.5
> 1.5
30
2 × 102
800
ii
780

i
i
i

1.5 × 104 ii

i These pressures were measured with pirani gauges, the measurements of which are gas-dependent. During the experiment, the pressures measured
were in the range for which pirani gauges provide inaccurate measurements [46]. pirani gauges reading (0.15–5) Torr could be corrected, but those
reading > 5 Torr could only be corrected to > 1.5 Torr.
ii These pressures were measured with MKS Baratron Capacitance Manometers with a full range of (1–25 000) Torr operated by MKS vacuum
4 CAP5a∗.
iii Flow meter measurements depend on pressure, temperature, and specific gravity of the gas. The measurement is corrected for these factors
SG, where

gauge controllers with a full range of (1–20 000) Torr. Because of this, the measurement must be corrected by factor of 5/4, e.g. CAP5a = 5
Measurements with a star (*) represent the uncorrected value, and those without a star indicate a corrected value.

(cid:113) T

(cid:114)

114.7 psi

using FM = FM∗
f1f2f3
SG is the specific gravity. Measurements with a star (*) represent the uncorrected value, and those without a star indicate a corrected value.

, where T is the temperature in K; and f3 =

, where p is the pressure in psi; f2 =

, where f1 =

530 K

√

p

iv These gauges were not functioning properly during the experiment.
v This instrument, a hygrometer, was not used during the experiment.

20

From the compressor, there is a line going to the nozzle, where the pressure, flow, and

temperature are measured by CAPin∗, FM, and Tfm. The gas then flows through a nozzle,
creating a supersonic jet in the experimental chamber, and the jet is caught by two concentric

catchers. The nozzle is threaded and screws into the nozzle receiver, and the catchers sit on

top of larger receivers that connect to the pipes. These designs mean that the nozzle and

catchers can be easily switched out with different designs. The nozzle used in this experiment

was the E design (see Figure 2.5), and the inner and outer catchers had diameters of 20 mm

and 30 mm, respectively. Using this setup, 90 % of the gas was caught in the inner catcher,

9 % was caught in the outer catcher, and 1 % escaped into the chamber.

The gas not collected by the catchers contributes to the ambient pressure of the experi-

mental chamber. This gas is pumped out by a Shimadzu TMP-3203LMC-A1 turbomolecular

pump, which is backed by one RUVAC WSU 501 roots vacuum pump. This is pumped into

the outer catcher (pumping stage 1).

To return the gas to the 1 atm required to operate the compressor, there are multiple

pumping stages between the jet and the compressor. The first stage, composed of one

RUVAC WSU 2001 roots vacuum pump, pumps the gas from the outer receiver. The next

stage, composed of three RUVAC WSU 2001, pumps this gas and also the gas from the inner

receiver, which accounts for all of the gas in the system. Two RUVAC WSU 1001 comprise

the next stage, and, as the final pumping stage, two DRYVAC DV 650, a heat exchanger,

and one more DRYVAC DV 650 return the gas to the compressor.

To prevent gas from escaping into the beamline and contaminating the accelerator, as

well as to prevent energy loss of the projectiles before interacting with the target, the system

contains four stages of differential pumping upstream of the experimental chamber. Brass

apertures were installed to restrict gas flow to the upstream pumping volumes. Between the

21

chamber and the first pumping volume, there was a 6 mm aperture; between the first and

second, there was an 8 mm aperture; and between the third and fourth, there was a 12 mm

aperture. The apertures were kept as small as possible to prevent gas flow to the upstream

pumping volumes as much as possible without blocking the beam. Since the beam is focused

at the target location, the beam diameter is larger when it is further from the target; because

of this, the aperture sizes change with distance along the beamline. The first two volumes

are pumped with a TURBOVAC 1000 C turbomolecular pump back into the chamber; the

third is pumped with a TURBOVAC 600 C into the chamber; and the fourth is pumped

with a TURBOVAC 600 C into the second pumping volume. Finally, the ReA3 beamline is
separated from the JENSA beamline by an interlocked gate valve; if CCU4 > 1 × 10−5 Torr,
the gate valve automatically closes.

See Appendix for JENSA operating instructions.

2.2.1 Jet Characteristics

Ahead of the experiment, some tests were performed to determine the characteristics of

the jet. Areal density, size of the jet, and pressures along the beamline were measured for

different nozzles, receivers, and pumping configurations.

The areal number density of the target, ρA, is an important quantity for calculating the

reaction cross section (see Section 3.6). It is defined as

(cid:90)

ρA(x, y) =

ρ(x, y, z) dz ,

(2.2)

where ρ is the volumetric density, x and y are the coordinates orthogonal to the beam axis,

and z is the coordinate parallel to the beam axis.

22

BB15

64 Channels

241Am

Jet

Nozzle

BB15

s
l
e
n
n
a
h
C
4

Jet

Catcher
(a) Side view

241Am

(b) Above view

Figure 2.4: These diagrams show the setup for measuring the areal density of the jet. On
opposite sides of the jet are a 241Am α-particle source and a Micron BB15 silicon detector.
The difference in energy of the detected α-particles between runs with and without a jet is
used to determine the areal density of the jet. The detector’s 64 front-side channels allow for
the areal density to be measured in the left-right direction, and the four back-side channels
allow for it to be measured in the up-down direction. (a) shows the setup from the side, and
(b) shows the setup from above.

The areal density of the jet was determined by measuring the energy loss of 5.486 MeV α-
particles [47] emitted by an 241Am source. This was done by measuring the energy deposited

by the α-particles in a Micron BB15 silicon detector without a jet being produced and then

measured again with the jet. The setup is shown in Figure 2.4. Energy loss data of He in

He [48] was then used to calculate the areal density of the jet using

ρA = S(E) · ∆E,

(2.3)

where S(E) is the stopping power of α-particles in He gas at energy E and ∆E is the

measured energy loss.

Because of the spatial resolution of the detector (see Section 2.3), the radial distribution

23

of the areal density could be determined. Two strips along the jet axis determined how the

jet expands as it moves away from the nozzle.

These tests also allowed us to see how the distribution changed with different nozzle

designs [49]. The nozzle chosen for this experiment, shown in Figure 2.5, was the nozzle

which produced the most dense jet at the reaction location. The resulting jet had an areal
density of 6 × 1018 atoms/cm2, and a width of 5 mm for Pdisch = 250 psig. These data were
used as the calibration for the relationship between CAPin and the areal density of the jet
during the experiment. See [49], [45], and Section 3.6 for more detailed explanations of

measuring the areal density of the jet.

The gas pressure outside of the jet along the beam axis is important for two main reasons.
The pressure past the last pumping stage must be below 10−5 Torr, so that the gas does not
affect beam transport or disrupt the operation of the reaccelerator. Also, the pressure up to

the target should be as low as possible to minimize the energy loss and energy spread before

the beam reaches the target and to prevent reactions outside of the jet area.

The pressure along the beamline was measured for different sizes of the catchers into which

the jet flowed. The catchers tested were outer catchers with diameters of 20 mm, 25 mm,

and 30 mm and inner catchers with diameters of 10 mm, 15 mm, and 20 mm. Table 2.2

shows the results of these tests. The pressure was measured at CCD4 and at a compressor

discharge pressure (Pdisch) of 300 psig. CCD4 records the pressure in the fourth pumping
stage downstream of the jet. The 30 mm outer catcher and 20 mm inner catcher were used

in the experiment to minimize the pressure outside of the jet.

24

Ø0.63 in
Ø0.38 in

O-RING GROOVE
Ø0.44 in ID
0.063 in WIDE
0.047 in DEEP

THREAD
3/4–16

1.84 in

0.59 in

0.25 in

1.1 mm

0.537 in
30°

6.0°

0.75 in

0.09 in

1.172 in

45°

0.0805 in

0.413 in

MAXIMUM EDGE WIDTH 0.010 in

0.130 in

Figure 2.5: The nozzle used in this experiment.

25

Table 2.2: The pressures measured at CCD4 for different catchers with a compressor dis-
charge pressure (Pdisch) of 300 psig.

Catcher Diameter
Outer
(mm)
20
20
20
25
25
25
30
30
30

Inner
(mm)
10
15
20
10
15
20
10
15
20

Pressure
(µTorr)

23
23
23
9.4
1.5
2.1
> 170
1.6
1.5

i

The pumping configuration of the turbomolecular pumps along the beamline was changed

to minimize the pressure in the fourth differential pumping stage. Two competing factors

were at play. Pumping gas into another pumping stage increases the pressure in that stage;

however, a turbomolecular pump’s pumping efficiency is affected by the pressure at its ex-

haust. Therefore, it is possible that the increase in pumping efficiency outweighs an increase

in pressure at a prior pumping stage along the beamline. These tests led to switching from

Figure 2.6a, in which all pumps exhaust into the main chamber, to Figure 2.6b, in which the

exhaust of UP4 feeds into the cavity pumped by UP2.

i The pressure given is a lower limit because the roots blower pumps overloaded before reaching 300 psig.

26

PIRturbo

Shim.

UP4

UP3

UP2

UP1

U5

U4

U3

U2

U1

CCU4

CCU3

CCU2

CCU1

Nozzle

CATout

CATin

(a)

PIRturbo

UP4

UP3

UP2

UP1

U5

U4

U3

U2

U1

CCU4

CCU3

CCU2

CCU1

Shim.

Nozzle

CATout

CATin

(b)

Figure 2.6: Two pumping configurations tested to decrease the pressure at CCU4. (a) shows
the first approach in which the exhaust of all pumps feed into the main chamber. (b) shows
the configuration used in the experiment in which the exhaust from UP4 feeds into the cavity
pumped by UP1.

27

2.3 Detectors

The detector setup, shown in Figure 2.7, was designed by considering the reactions that

were expected to occur: (α,α) and (α,p) induced by each beam species. An ionization

chamber was placed downstream of the target along the beam axis to detect the heavy

recoils and unreacted beam, which are emitted in a small forward-facing cone. The ionization

chamber is able to handle the high rate of the beam and detect particles in the (30–60) MeV

range. The light ejectiles, however, are emitted in a much wider range of directions, so an

array of silicon detectors was installed surrounding the target. Figure 2.8 shows the energies

and angles at which the particles are emitted and the angular coverage of the detectors.

2.3.1 Silicon Detector Array

The silicon detector array is designed to detect the light ejectiles, α-particles and protons.

As shown in Figure 2.8, only protons are emitted at polar angles of θ > 90°, but at polar

angles of θ < 90°, both α-particles and protons are emitted. In this range where both species

are seen, they are distinguished using particle identification telescopes. These “telescopes”

consist of two detectors each: a thin one in which the particle loses some of its energy and

sorr_up sorr_dn sidar

Ejectile

Beam

Jet

Recoil

Ionization
Chamber

Figure 2.7: A diagram of the detectors used in the experiment and the reaction products
they detect.

28

IC

sidar

sorr_dn

sorr_up

34Ar(α,p)37K
34Cl(α,p)37Ar
34S(α,p)37Cl
(α,α)

60

50

40

30

20

10

)
V
e
M

(

y
g
r
e
n
E
e
l
c
i
t
r
a
P

0

0

20

40

60

80

100

120

140

160

180

Lab Polar Angle (°)

)
V
e
M

(

y
g
r
e
n
E
e
l
c
i
t
r
a
P

50
40
30
20
10
0
50
40
30
20
10
0

(a)

34Ar(α,p)37K

34Cl(α,p)37Ar

34S(α,p)37Cl

(α,α)

0

20 40 60 80 100 120 140 160 0

20 40 60 80 100 120 140 160 180

Lab Polar Angle (°)

(b)

Figure 2.8: The relationship between particle energies and the polar angle at which they are
emitted for the reactions that occur in this experiment. (a) shows the different reactions
together, and (b) shows them separately. The angular ranges that are covered by detectors
are shown. The high energy (> 30 MeV) lines correspond to the recoils, and the low energy
(< 30 MeV) lines correspond to the ejectiles. For each (α,p) reaction, there are multiple
levels that can be populated in the recoil nucleus, and for each of these levels, there is a
different relationship between energy and angle. For elastic scattering, this is not the case,
so there is only one line per particle.

29

E7/bE7

E1/bE1

E14/bE14

E8/bE8

E6/bE6

E2/bE2

E13/bE13

dE14

dE8

E9/bE9

E3/bE3

E4/bE4

dE10
dE11

E10/bE10

E11/bE11

(a) sorr_up

(b) sorr_dn

E15

E16

E19

E18

dE19

dE15

dE18

dE16

dE17
E17

(c) sidar

Figure 2.9: The silicon detector array used in this experiment, looking upstream, toward
the source of the beam. The detector naming counts up going clockwise, starting at the
upstream section and repeating for each subsequent downstream section. Detectors 5 and
12 were removed to accommodate jet and beam tuning hardware.

a thick one in which it loses its remaining energy. Because the stopping power of different

species of charged particles in the detector material is different, the relationship between the

energy loss in the two detectors can be used to determine the species of the ejectile.

The array uses detectors from the Oak Ridge National Laboratory SuperORRUBA [50]

and SIDAR [51] arrays, and consists of three sections: sorr_up, sorr_dn, and sidar.

Figure 2.9 shows the names and positions of the detectors. The detectors numbers count up

clock-wise starting with the upstream detectors (detectors numbered 5 and 12 were removed

before the experiment started). Detectors labeled EN are detectors thick enough for particles

to be stopped in them, and the back-sides of those detectors are labeled bEN. Detectors

labeled dEN are thin detectors in a telescope setup.

30

(a)

(b)

(c)

Figure 2.10: The silicon detectors used in this experiment are (a) 4 60 µm-thick Micron
BB10s, (b) 12 1 mm-thick Micron BB15s, and (c) 5 60 µm-thick and 5 1 mm-thick Micron
YY1s.

The sorr_up section of the array covers lab polar angles 90° to 130°. Because the

detectors are fully upstream of the target, the α-particles from elastic scattering are not

seen in these detectors. Because there is no need to distinguish between (α,α) and (α,p)

and because the energy of the protons are < 6 MeV, only one layer of detectors was used.

Therefore, six 1 mm thick BB15 detectors were used in this section.

The sorr_dn section of the array covers lab polar angles 60° to 90°.

In this polar

angle range, both protons and α-particles are seen. Because of this, telescopes must be

used to distinguish between the two. One part of this section, sorr_dnt, consists of four

telescopes, each with a 60 µm thick Micron BB10 detector in front of a 1 mm thick Micron

BB15 detector. The other part, sorr_dns, consists of two single-layer detectors. This

setup was chosen because detecting the α-particles from elastic scattering would be useful

for beam normalization, but near 90°, where the cross section is highest, the energy is so low

that they would be stopped in the first layer, and the energy deposited would be hard to

distinguish from the noise.

The sidar section of the array covers lab polar angles 10° to 35°. In this polar angle

range, both protons and alphas are seen, so a two-layer setup of 60 µm and 1 mm Micron

31

150

100

50

0

y

−50

−100

−150

100

50
x

0

−50

−100

−100−50 0

50 100 150 200 250

z

Figure 2.11: The positions of the silicon detectors in the experiment. The z-axis is the beam
axis and the y-axis is the jet axis, meaning the reaction location is at the origin.

YY1 detectors were used.

2.3.2 Position-Sensitive Ionization Chamber

The ANASEN position-sensitive ionization chamber (PSIC) [52] was placed at the end

of the beamline to detect the recoils and beam particles. The PSIC consists of a series of

electrode grids stacked along the beam axis, with a separation of 18.3 mm between neigh-

boring grids. The grids alternated between grounded electrodes and electrodes that were

biased at 150 V. These grids were separated into four sections. The first two, X and Y, were

position sensitive; they each consist of 32 channels that read out signals from individual grid

wires separately. The different channels correspond to different left-right positions in the X

section and different up-down positions in the Y section. The following sections, dE and

E, consisted only of one signal each. The dE section combined the signal from two biased

32

X

Y

dE

E

Figure 2.12: A diagram showing the different sections of the ionization chamber. Each signal
is read from a wire or set of grids biased at 150 V. The biased grids have grounded grids
between them. The X and Y sections consist of 32 channels each, which allows for the
calculation of the outgoing angles of the recoils. The dE and E sections consist of 1 channel,
which combines the signal from multiple grids, each.

electrodes, and the E section combined the signal from five biased electrodes. Figure 2.12

illustrates this configuration. The chamber was filled with 15 Torr of isobutane. This was

chosen over carbon tetrafluoride to optimize for energy resolution and separation of different

beam species in the E section.

2.4 Data Acquisition

Multiple data acquisition systems were used in this experiment: the Experimental Physics

and Industrial Control System (EPICS) [53, 54] was set up to record continuous time series

data of pressure gauges and beam currents throughout the experiment, and two separate

NSCLDAQ systems [55, 56] were merged to record the signals from the detectors. The data

can be correlated because the EPICS data is stored with an absolute timestamp for each

point, and the NSCLDAQ data has an absolute timestamp at the start of each run and a

relative timestamp for each event in that run.

33

The EPICS data recorded gauge measurements during the experiment. The most im-

portant measurements were CAPin, and CAPic. CAPin corresponds to the pressure just
before the nozzle, which is important because it is correlated to the density of the jet (see

Section 3.6). CAPic corresponds to the pressure in the ionization chamber, which is impor-
tant because it affects the energy that particles lose while traveling through the ionization

chamber.

Two independent NSCLDAQ data streams were combined to create the final event data

stream for the experiment. The silicon detector data were recorded in the VME stream,

which specializes in recording a large number of channels. The PSIC data were recorded in

the DDAS stream, which specializes in recording signals with high data rates.

The silicon detector array (described in Section 2.3.1) was composed of 12 BB15 (64

front-side and 4 back-side channels each), 4 BB10 (8 front-side channels each), and 10 YY1

detectors (16 front-side channels each). This results in 1008 channels total. To record

so many channels, the detectors were fed into a system of HINP16C application-specific

integrated circuits (ASICs) [57]. Each HINP16C chip consists of 16 channels. Each channel

has a charge sensitive amplifier, which is split and sent to two circuits: one for fast processing

of timing information and one for slow processing of energy information. Two chips were

combined on one chipboard, and up to 10 chipboards were connected to a motherboard.

The energy signals for each motherboard are sent to a JTEC Model XLMXXV module to be

digitized and then sent to a data acquisition computer via a VMEBus. The timing signals

were combined as described in Section 2.4.1 to create signals triggering the readout of the

data acquisition system.

The DDAS system, which was composed of XIA Pixie-16 modules, was used for two

reasons: because 1) the PSIC detected the beam and recoils and 2) there were relatively few

34

channels.

2.4.1 Trigger Logic

Combining two independent NSCLDAQ systems means that care must be taken to ensure

the two systems are synchronized. To do this, a 100 Hz pulser is fed into both systems and

used as a clock. This requires the DDAS system to be configured to accept an external

timestamp and the VME system to be configured to use a scaler module as the timestamp.

In the ASICs system, the motherboards are configured to send a trigger signal when the

front side of a silicon detector receives a signal. When this happens, we want to record

signals from all other channels that also received a signal, whether they were configured to

send a trigger or not. To do this, the logical OR of the motherboard triggers is sent to the

XLMXXV modules to start trigger the processing and recording of the signal. This signal is

vetoed if any of the XLMXXV modules are not ready. In order to not lose data, the VM-USB

must wait until each XLMXXV module has received and processed data for that event before

sending the data to the data acquisition computer. The XLMXXV sends a complete signal

when it finishes processing data, and these are used to create a signal to trigger the VM-USB

module to send the data to the data acquisition computer. The complete signal from each

XLMXXV is sent to its own latch module as the start signal. The VM-USB trigger is the

logical AND of these signals. This signal is sent to the VM-USB module to trigger read-out,

but also is sent to the latch modules as the stop signal. Altogether, this means that once all

motherboard signals have been processed, the data is sent to the data acquisition computer,

and the system is ready for the next event.

A problem can occur if the signals are not grouped properly into events. For example,

if for some reason one complete signal is missing, the latches will be open until the missing

35

complete signal occurs in the next event. This causes an error to occur in the next event,

which propagates to all subsequent events. To prevent this, the OR of the motherboard

triggers is also used to stop the latches. Figure 2.13 shows an illustrated example of how

these signals are combined to create the VM-USB trigger and how the OR of the motherboard

triggers is used to fix errors that can occur with missed signals.

See Appendix A of [58] for a more detailed explanation of the ASICs setup.

36

Trigger A
Trigger B
Trigger C
Trigger D

Trigger OR

Complete A
Complete B
Complete C
Complete D

Latch A
Latch B
Latch C
Latch D

VM-USB Trigger

(a)

(b)

(c)

Figure 2.13: An example showing how the four ASICs motherboard triggers are combined to create the VM-USB trigger. (a)
shows two events during normal operation. (b) shows how a missing complete signal can propagate errors to subsequent events.
(c) shows how the OR of the motherboard triggers can be used to prevent this error from propagating to other events.

37

Chapter 3

Analysis

3.1 Beam Energy

The experiment was conducted at two experimental energies. At the first energy—the
higher of the two—an 34Ar15+ beam with a total kinetic energy of (57.04 ± 0.75) MeV was
delivered to the target. At the second, the 34Ar15+ beam had a total kinetic energy of
(54.19 ± 0.73) MeV.

The reaccelerator accelerates particles to the same velocity. Because E = 1

2 mv2, E/m is
.

the same for each species, and the total kinetic energy for particle x is Ex = mx
m34Ar

E34Ar
While traveling through the target, the beam loses energy. This means that the average

energy at which reactions occur is less than the beam energy. The energy loss of the beam

constituents through 1019 atoms/cm2 of He was calculated using ATIMA [59]. For a thin

target, the average energy of the beam in the target is the incoming energy minus half of

this energy loss. This is not necessarily the average beam energy at which reactions happen

because the cross section may change much within the energy range of the target; this is

particularly true if the cross section exhibits resonances. The various beam energies are

shown in Table 3.1.

38

Table 3.1: The experimental beam energies.

Beam
Species

34S15+
34Cl15+
34Ar15+
34S15+
34Cl15+
34Ar15+

E1

E2

Energy

Before Target

(MeV)

57.02 ± 0.75
57.03 ± 0.75
57.04 ± 0.75
54.17 ± 0.73
54.18 ± 0.73
54.19 ± 0.73

Energy Loss

in Target
(MeV)

1.649 ± 0.007
1.790 ± 0.007
1.932 ± 0.007
1.674 ± 0.007
1.817 ± 0.007
1.960 ± 0.007

Average

Lab

Energy
(MeV)

Average

Center of Mass

Energy
(MeV)

56.20 ± 0.75
56.14 ± 0.75
56.07 ± 0.75
52.50 ± 0.73
52.36 ± 0.73
52.23 ± 0.73

5.924 ± 0.079
5.917 ± 0.079
5.909 ± 0.079
5.534 ± 0.077
5.519 ± 0.077
5.504 ± 0.077

3.2 Detector Solid Angles

Accurately knowing where the detectors were positioned with respect to the target is

important for determining the fraction of reactions that was actually observed during the

experiment. How much solid angle was covered and the angles at which the detectors were

positioned were calculated analytically using a program written for this purpose [60].

The first step is to describe the surface of the detector as a function of two coordinates.

A coordinate system to describe the location of the detector surface, r0(u, v), is chosen for
each individual detector so that one coordinate is constant along each edge of a detector

strip. This condition simplifies integration over the surface. To satisfy this condition, the

CartesianZ coordinate system (Equation (3.1)) was used for the BB10 and BB15 detectors,

and the PolarZ coordinate system (Equation (3.2)) was used for the YY1 detectors. These

coordinate systems are show in Figure 3.1.

CartesianZ:

PolarZ:

r0(u, v) := (cid:104)u, v, 0(cid:105)
r0(u, v) := (cid:104)u cos(v), u sin(v), 0(cid:105)

(3.1)

(3.2)

39

v

v

u

(a) BB10s and BB15s

u

(b) YY1s

Figure 3.1: The coordinate systems used to describe BB10s and BB15s (a) and YY1s (b).

Next, the detector surfaces r0(u, v) described in their individual local coordinate systems
are transformed into surfaces r(u, v) in a common coordinate system that describes the

entire setup. This common coordinate system is one in which: the reaction location is the

origin, the z-axis is the beam axis, the x-axis is the horizontal axis perpendicular to the

beam axis, and the y-axis is the vertical axis perpendicular to the beam axis. Two types of

transformations are used here: translation and rotation. The translation operation has one

parameter: the displacement d, and it is defined as

T(d)r = r + d.

(3.3)

The rotation operator has two parameters: a unit vector ˆu, which—along with the origin—

40

describes the axis of rotation and the angle of rotation θ. It is defined as

R(ˆu, θ)r =

x+(1−u2
u2

x) cos θ

uxuy(1−cos θ)−uz sin θ uxuz(1−cos θ)+uy sin θ
uyuz(1−cos θ)−ux sin θ

y) cos θ

 r.

(3.4)

uxuy(1−cos θ)+uz sin θ
uxuz(1−cos θ)−uy sin θ uyuz(1−cos θ)+ux sin θ

y+(1−u2
u2

z+(1−u2
u2

z) cos θ

The coordinate systems and transformations are supplied as input to the program, so

this may be used for different experimental setups.

For example, the transformations applied to detector E1 are

R1 = R(cid:0)(cid:104)1, 0, 0(cid:105), 90°(cid:1),
T2 = T(cid:0)(cid:104)0, 8.6,−80.2(cid:105) mm(cid:1),
R3 = R(cid:0)(cid:104)0, 0, 1(cid:105), 6.0°(cid:1),
T4 = T(cid:0)(cid:104)0, 95.3, 0(cid:105) mm(cid:1), and
R5 = R(cid:0)(cid:104)0, 0, 1(cid:105), 330.0°(cid:1).

When these are all applied, the position of the detector is

r(u, v) = R5T4R3T2R1(cid:104)u, v, 0(cid:105)

= (cid:104)51.1 + 0.914v, 90.4 − 0.406v,−80.2 + u(cid:105) mm.

(3.5)

A configuration for this setup is shown below:

41

1 {
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27 }

" templates ": {

" BB15 ": {

" coords ": " CartesianZ ",
" u_limits ": [0.0 , 75.0] ,
" v_limits ": [ -20.0 , 20.0]

},
" SORR_UP ": {

" template ": " BB15 ",
" transformations ": [

{" Rotation ": [0 , -90, 0]} ,
{" Rotation ": [0 , 0, 90]} ,
{" Translation ": [0 , 8.636 , -80.2386]} ,
{" Rotation ": [0 , 0, 6.03]} ,
{" Translation ": [0 , 95.25 , 0]}

]

}

},
" detectors ": [

" template ": " SORR_UP ",
" transformations ": [

{" Rotation ": [0 , 0, -30]}

]

{

}

]

The solid angle can be found using the surface area, S, using

du dv and

dS =

dΩ =

× ∂r
∂v

∂r
∂u
r · dS
|r|3 .

(3.6)

(3.7)

Using this coordinate system, arbitrary functions can be minimized with respect to u

and v. The average value can also be found using

favg =

,

(3.8)

(cid:82)(cid:82) f dΩ
(cid:82)(cid:82) dΩ

42

150

100

y

50

0

50

0
1
2
3
4
5

0

x

−50

−100

−100

−50

0

z

100

50

Figure 3.2: The location of detector E1 with an increasing number of transformations applied
until the detector is at the experimental location. The reaction location is at (cid:104)0, 0, 0(cid:105).

where Ω is the solid angle and f is the function of interest. The spherical coordinates, which

are defined as

(cid:113)

r(u, v) =

x(u, v)2 + y(u, v)2 + z(u, v)2,

θ(u, v) = arccos

, and

(cid:19)
(cid:18) z(u, v)
(cid:18) y(u, v)
(cid:19)

r(u, v)

,

x(u, v)

φ(u, v) = arctan

(3.9)

(3.10)

(3.11)

are examples of functions that were averaged using Equation (3.8).

Shadows can be applied to a detector. Shadows are surfaces that block the path from the

origin to the detector. This allows for any obstruction to be described as above, independent

of the coordinate system of the detector itself. For this analysis, shadows that correspond

to the nozzle and receiver were applied to the detectors above and below the target because

43

they partially block those detectors.

The positions and solid angles calculated in this way were used in the efficiency calcula-

tions detailed in Section 3.6. The total solid angle covered by the silicon detector array is
(3.8 ± 0.5) sr.

The input into the calculation of the detector positions are not perfect and have some

measurement uncertainty associated with them, which leads to an uncertainty in the values

calculated. To account for this, a Monte Carlo method is used. The input values are

randomly varied according to a Gaussian distribution described by their mean and standard

deviation. The mean and standard deviation of the results are then calculated from 10 000

runs. Figure 3.3 shows the results from such a calculation. The input values come from

a combination of technical drawings, alignment tools, and hand measurement. The source

of uncertainty is dominated by the hand measurements. For sorr_up and sorr_dn, the

translation uncertainties are 1 mm. For sidar, the distance to the target was inconsistently

recorded; to account for this, the translation uncertainties for the final translation were

20 mm along the beam axis and 3 mm perpendicular to the beam axis.

44

700

600

500

400

300

200

100

s
t
n
u
o
C

0
0.208

0.209

0.21

0.212
0.211
Solid Angle (sr)

0.213

0.214

0.215

Figure 3.3: An example of Monte Carlo results of the solid angle for detector E1.

3.3 Energy Calibrations

Both the ionization chamber and the silicon detectors measure the amount of energy

deposited by a particle traveling through them. The particle causes ionization in the detector

material. The resulting charge is collected and converted to a voltage change, which is then

processed by the electronics and stored as a digitized channel in the data acquisition system.

The signal height is linearly related to the energy deposited in the detector, so the energy

calibration function is

E = aCh + b,

(3.12)

where E is the energy deposited in the detector and Ch is the digitized signal value, referred

to as the “channel”.

45

3.3.1 Silicon Detectors

The energy calibration was done in two steps. First, the channel which corresponds to

zero energy was found. Second, the channel which corresponds to a known energy was found.

Using these two points, a linear relationship between channel and energy was determined.

The zero-energy channel is the same as the zero-voltage channel, which can be found using

two different pulser signals with known voltage ratios, regardless of the absolute voltage input

into each channel. This is important because the pulser signal is split among all channels

sharing the same hardware input (possibly not equally), so the exact voltage is not known.

However, as long as the ratio between the different pulser signals is known, the zero-voltage

channel can be found.

Ch(V2) − Ch(V =0)
Ch(V1) − Ch(V =0)
Ch(V2) − Ch(V =0) =

=

(cid:18) V2

V1

(cid:19)

− 1

Ch(V =0) =

Ch(V =0) =

AV2
AV1
(Ch(V1) − Ch(V =0))
V2
V1
Ch(V1) − Ch(V2)
V2
V1
R Ch(V1) − Ch(V2)

R − 1

(3.13)

After the zero-energy channel is found, the slope of the calibration can be found using the

detection of a particle with a known energy from a radioactive source. In this experiment,

the 5.486 MeV peak from the α-decay of an 241Am source was used.

46

E241Am

− Ch0)

=s(Ch 241Am
E241Am

s =

Ch 241Am

− Ch0

(3.14)

There are some channels that could not be calibrated using this method because some

or all of the peaks necessary for calibration were missing. Figure 3.4 shows some examples

of channels that could not be calibrated. These were not used in the analysis. The BB10

channels had no pulser data to use for the calibration, so a calibration based on the nominal

values of the preamplifier chips was used instead.

3.3.2

Ionization Chamber

The ionization chamber detects beam particles and reaction recoils, both of which have

a much higher energy than the particles emitted from a radioactive source. Because of this,

the ionization chamber could not be calibrated using a radioactive source. Instead, the beam

and recoils were used.

Uncertainty and spread in the energy detected in each section of the ionization chamber

is introduced for each material through which the beam travels before reaching that section.

These sections are shown in Table 3.2. The materials in which energy is lost before the

first detecting section of the ionization chamber are the He target, the Mylar window, and

the non-detecting dead layer of isobutane in the ionization before the first grid. Because of

this, it is ideal to calibrate the ionization chamber using runs that did not have the beam

traveling through the target. This, however, was possible only for the dE and E sections

47

1000

100

10

1000

100

10

s
t
n
u
o
C

s
t
n
u
o
C

0

2 0 0 0

V2

(a)

V1

241Am

(c)

(b)

(d)

6 0 0 0

8 0 0 0

1 4 0 0 0
4 0 0 0
Energy Channel (a.u.)

1 0 0 0 0

1 2 0 0 0

1 6 0 0 0

2 0 0 0

6 0 0 0

8 0 0 0

1 4 0 0 0
4 0 0 0
Energy Channel (a.u.)

1 2 0 0 0

1 0 0 0 0

1 6 0 0 0

Figure 3.4: Spectra from silicon detector calibrations. (a) shows a normal channel with a
241Am peak and two pulser peaks. (b) shows a channel with only one pulser peak. (c) shows
a channel with no 241Am. (d) shows a channel with no pulser peaks.

48

Table 3.2: The layers through which the beam passes and loses energy.

Section

Material

Thickness

target
window
dead layer

X
Y
dE
E

e
r
i
w
Y
C

I

30
25
20
15
10
5
0

He

Mylar

isobutane
isobutane
isobutane
isobutane
isobutane

300

250

200

150

100

s
t
n
u
o
C

50

0

(5–8) × 1018 atoms/cm2

3 µm
2 cm

3.66 cm
3.66 cm
7.32 cm
18.30 cm

e
r
i
w
Y
C

I

30
25
20
15
10
5
0

5000

4000

3000

2000

1000

0

s
t
n
u
o
C

0 5 10 15 20 25 30

IC X wire

0 5 10 15 20 25 30

IC X wire

(a) Without jet

(b) With jet

Figure 3.5: The hit pattern in the ionization chamber (a) without and (b) with the jet
present.

and the central wires of the X and Y sections. The outer wires of the X and Y sections

could not be calibrated using these runs because there was no jet where the beam particles

could scatter off to reach these channels. Instead, these channels were calibrated using the

scattered beam from the experimental runs. Figure 3.5 shows the difference in number of

events in each pixel of the ionization chamber for the runs with and without the jet.

The energy to be used in the calibration was calculated using the energy loss code ATIMA

[59]. The energy loss in each section was calculated by integrating along the path of the

projectile. These energy losses depend on the density of the target and the pressure inside

49

the ionization chamber, which varied throughout the experiment, as is shown in Figure 3.6.

These changes were tracked using the pressure gauges CAPin and CAPic, which were recorded
by EPICS (see Section 2.4), with a sampling frequency of 0.2 Hz.

The pressure inside the ionization chamber was measured by a capacitance gauge CAPic.
There were some gaps in the measurements because an EPICS system restart caused the

gauge to stop being read. This limits the number of runs that could be used for calibration.

The areal density was determined using the pressure of the gas immediately before the

nozzle (see Section 2.2.1). During the experiment, this was measured in CAPin∗. The method
used to determine the relationship between CAPin and the areal density of the jet is detailed
in Section 3.6.

The channels used in the the calibration are the centroids of fits of the peaks in the energy

spectra of the corresponding sections. However, the different beam species (34S, 34Cl, and

34Ar) are hard to distinguish in the one-dimension energy spectra of the X, Y, and dE

sections. In the E section, the beam species are easy to distinguish, so this is used to create

two-dimension spectra with the E section, and gate on the peaks to create a one-dimension

spectrum for each species. Figure 3.7 shows the resulting fits.

Figure 3.8 shows the results of this process. The 34Ar and 34Cl points fit on a line.

However, the 34S peaks systematically deviate; these peaks were consistently fit at a lower

channel than expected. In Figure 3.7, it can be seen that there is overlap between the 34Cl

and 34S peaks, and since there are many more counts in the 34Cl peak, the tail of that peak

can significantly affect the shape of the 34S peak. Because of this, the 34S peaks were not

used for calibration.

50

15.4

15.2

15

14.8

14.6

14000

13000

12000

11000

10000

)

r
r
o
T
(

c
i
P
A
C

)

r
r
o
T
(

i

n
P
A
C

2 0 1 6-0 5-1 0

2 0 1 6-0 5-1 1

2 0 1 6-0 5-1 2

2 0 1 6-0 5-1 3

2 0 1 6-0 5-1 4

2 0 1 6-0 5-1 5

2 0 1 6-0 5-1 6

2 0 1 6-0 5-1 7

2 0 1 6-0 5-1 8

2 0 1 6-0 5-1 9

2 0 1 6-0 5-2 0

Time (YYYY-MM-DD)

Figure 3.6: The time series data for the pressures measured by CAPic and CAPin. CAPic
measured the pressure in the ionization chamber; for parts of the experiment, it was not
recorded by the EPICS system. Hand measurements were still recorded during this time,
but these were not used for the calibration. CAPin measured the pressure immediately before
entering the nozzle; this was used to determine the areal density of the jet.

Table 3.3: The ionization chamber energy calibration values.

Section

Channel
(0-based)

X

Y

dE
E

16
17

0–15, 18–31

15
16

0–14, 17–31

0
0

Slope

Intercept
2126 ± 19
2.903
1892 ± 11
2.903
1951 ± 195
2.903
1482 ± 25
3.411
1485 ± 34
3.411
1483 ± 37
3.411
9.984 −530 ± 73
11 264 ± 88
6.358

51

s
t
n
u
o
C

2E5
0
2E5
0

1800

1600

1400

1200

1000

800

1E5
5E4
0
2E5
0
5E5
0

)
l
e
n
n
a
h
C
(
E
n

i

l
a
n
g
i

S

s
t
n
u
o
C

(1)

(3)

(2)

(4)

800

1200

1600

800

1200

1600

Signal in E (Channel)

(a)

1E4

8E3

6E3

4E3

2E3

0

s
t
n
u
o
C

800

1000

1200

1400

1600

1800

Signal in dE (Channel)

(b)

Figure 3.7: The peaks in the ionization chamber were fit in multiple steps. The black
histograms show the experimental data and the teal curves show the fit curves. First, the
E section is fit, as shown in (a) because it is the channel in which the peaks are most
easily distinguished. The peaks are not as well separated in the remaining channels, so the
information from the E channel is used. (b) shows the elliptic gates around the peaks in the
E vs. dE spectrum and how the separate peaks in the dE channel are fit after using these
gates.

52

22000
21000
20000
19000
18000
17000
400

200

0

-200

)
V
e
k
(

y
g
r
e
n
E

)
V
e
k
(

l
a
u
d
i
s
e
R

900 1000 1100 1200 1300 1400 1500 1600 1700

Signal (Channel)

Figure 3.8: The calibration curve for the E section of the ionization chamber. The lowest
energy group corresponds to 34Ar, the middle 34Cl, and the highest 34S. The 34S points
do not agree with the the 34Ar and 34Cl points. This is likely due to interference from the
larger 34Cl peak.

3.4 Timing

The silicon detectors and the ionization chamber register hits from the same reaction at a

fixed time difference that is determined by the flight times of the particles from the reaction

point as well as electronics delays. In order to separate random coincidences from actual

coincidences, we can gate on the time difference between the two systems.

The time difference between hits in the two systems contains many peaks, as shown in

the “Ungated” plot in Figure 3.9. To determine where to gate for true coincidences, we

need to identify hits that we know originate from the same reaction. We used the elastic

scattering events by gating on the alpha particles detected in the silicon detectors near 90°

in the lab frame. Figure 3.10 shows the relation between the energy detected and polar angle

in detectors E9 and E13. These are the detectors without a thin detector layer in front of

the thick detector. In these detectors, α-particles from elastic scattering can be seen. Gating

53

Ungated
Gated on α-particles

4500

4000

3500

3000

2500

2000

1500

1000

s
t
n
u
o
C

500
0
−5000 −4000 −3000 −2000 −1000

0

1000

2000

3000 4000

5000

tIC − tSi (ns)

Figure 3.9: The time difference between hits in the ionization chamber and the silicon
detectors. “Ungated” shows this for all hits. “Gated on α-particles” shows this only for hits
in E9 and E13 inside the α-partcle gate shown in Figure 3.10.

on this region gives a single peak in time difference, as shown in the “Gated on α-particles”

plot in Figure 3.9.

Fitting a Gaussian curve to this peak, we get the following fit:

(cid:18)
−(x − b)2

(cid:19)

2c2

f (x) = a exp

+ d,

(3.15)

with parameters a = 414 ± 5, b = 1147 ± 1, c = 43 ± 1, and d = 5 ± 1. Using a 3σ (99.7 %)
confidence interval to make a gate, we set the gate at (1016–1278) ns.

54

)
V
e
k
(

y
g
r
e
n
E
e
l
i
t
c
e
j
E

10000

8000

6000

4000

2000

0

0

20

40

100

s
t
n
u
o
C

80

60

40

20

0

140

160

180

80

60
120
Ejectile Polar Angle (°)

100

Figure 3.10: The energy-polar angle relationship in E9 and E13, the detectors without a thin
detector in front of the thick detectors. These detectors can clearly see the α-particles from
elastic scattering. A gate is drawn around these hits and used as the gate in Figure 3.9.

55

3.5 Particle Identification

During this experiment, there were a variety of reactions that occurred. There were three

beam species, and for each of those species, there were two reactions, (α,α) and (α,p). In

order to distinguish between all of these reactions, we must know which particles are being

detected. There are two properties that are used to determine the species of a detected

particle: kinematics and energy loss.

Figure 3.11 shows a kinematics diagram of these reactions. There are a few degrees

of freedom: the polar and azimuthal angles in the center of mass frame (θCM and φCM,

, Elab

, and Elab

. φCM affects φlab

e

r

r

respectively) and the excitation energy of the outgoing recoil (Eex). θCM and Eex affect θlab
. The relationship between θlab and Elab for

θlab
e
each particle can be plotted as a series of lines, as in Figure 2.8. Each line corresponds to a

and φlab

,

e

r

different Eex, and along each of those lines, θCM varies.

The first step of particle identification involves distinguishing particles based on θlab and

Elab. The recoils are only emitted with θlab < 10° and Elab > 30 MeV. This means that

recoils are detected only in the ionization chamber, and because the energy of the ejectiles is

too low to be detected in the ionization chamber, we know that the ionization chamber only

detects recoils and unreacted beam. Because α-particles are limited to θlab < 90°, we know

that any particles detected in sorr_up should be protons. And in sorr_dn and sidar,

protons and α-particles can be distinguished using energy loss, as described below.

In addition, background events may be detected in all detectors by reactions in gas

outside of the jet, beam scattered off of apertures, gas impurities, multiply scattered particles,

electronic noise, etc. However, the cleanness of the spectra after applying the coincidence

gates (shown in Figure 3.13) suggests that this is minimal.

56

recoil

recoil

θCM
r

target

projectile

target

θlab
r

θlab
e

ejectile

(b) Lab Frame

projectile

θCM
e

ejectile

(a) Center of Mass Frame

Figure 3.11: Diagram showing the incoming and outgoing particles in the reactions of this
experiment in the (a) center of mass reference frame and the (b) lab reference frame.

Two different particles that travel through the same material will lose energy at different

rates. This property, the stopping power, depends on the energy of the particle. Therefore,

this is measured with multiple stages of detection: one which measures the energy loss and

another which measures all residual energy.

In the silicon detectors, this involves a thin

detector and a thick detector in a “telescope” configuration. In the ionization chamber, this

involves splitting the detector into multiple sections, which are read out separately.

3.5.1 Ejectiles

The ionization chamber detects a high rate of unreacted beam, which partially overlaps

with the recoils. In order to exclude random coincidences of silicon detector hits with un-

reacted beam, we negatively gate on the central angles of the ionization chamber (< 0.6°).

This excludes only events which would not be detected anyway because of the following

reasons: 1) the ejectile angle is too low or 2) the ejectile energy is low.

The single detectors in sorr_up detect protons at low energies. To distinguish protons

from electronic noise, a gate was made to reject signals with E < 500 keV.

The silicon detector telescopes consist of two detector layers: a 60 µm thick detector in

57

front of a 1 mm thick detector. These are called the dE and E layers, respectively. Figure 3.12

shows the relationship between the energy loss in the dE layer. Figure 3.12b is gated on

the timing gate described in Section 3.4, and Figure 3.12a is not. There are many more

α-particles that are not detected in coincidence with an ionization chamber hit. This is

because many of the scattered recoils are emitted at an angle larger than that covered by the

ionization chamber. This can be seen in Figure 2.8. This is only the case for the (α,α) recoils;

the (α,p) recoils are all emitted at angles less than the acceptance angle of the ionization

chamber.

The actual thicknesses of the detectors are not exactly the nominal thickness; they deviate

from this nominal value by up to 23 % from detector to detector (but not within a detector).

This affects the energy deposited in that detector. In order to merge events from different

detectors, the energy losses were normalized to a dE detector thickness of 60 µm. The

correction assumes energy loss is proportional to thickness, resulting in normalized energy

loss values of

dE 60 =

60 µm

t

dE

E60 = E + (dE − dE 60),

(3.16)

where t is the actual thickness of the dE detector, dE and E are the energies detected in the

dE and E detectors, respectively, and dE 60 and E60 are the normalized energies.

The range of a 9 MeV α-particle in silicon is 60 µm, which means that α-particles with an

energy below 9 MeV are stopped in the dE detectors and are not detected in the E detectors.

The energy of scattered α-particles decreases as the scattering angle approaches 90°. The

9 MeV threshold is crossed in the sorr_dn section, and there are two parts of this section:

sorr_dnt comprises four telescopes, and sorr_dns comprises two single detectors with

no dE layers. sorr_dns detects α-particles throughout the whole angular range, but is

58

p
p gate
α
α gate

12000

10000

8000

6000

4000

2000

)
V
e
k
(

0
6
E
d

0

0

5000

15000

20000

10000

E60 (keV)

(a)

p
p gate
α
α gate

12000

10000

8000

6000

4000

2000

)
V
e
k
(

0
6
E
d

0

0

5000

15000

20000

10000

E60 (keV)

(b)

100

s
t
n
u
o
C

80

60

40

20

0

100

s
t
n
u
o
C

80

60

40

20

0

Figure 3.12: The energy loss in the dE layer vs. the energy loss in the E layer of the silicon
detector telescopes, corrected for the difference in detector thicknesses for the experimental
energy E2. (a) shows this plot without gating on the timing difference described in Sec-
tion 3.4, and (b) shows the plot gated on this timing. The separate groups for α-particles
and protons can be seen. The regions used for gating are shown. The intermediate-energy
α-particles are excluded in (b) because the recoils are not detected in the ionization chamber
(see Figure 2.8).

59

Table 3.4: The thickness of the dE detectors.

Detector Thickness (µm)

dE8
dE10
dE11
dE14
dE15
dE16
dE17
dE18
dE19

63
65
60
63
60
67
67
74
59

not capable of particle identification based on energy loss. sorr_dnt detects α-particles in

only the most downstream strips.

Ejectiles are thus identified as hits in the silicon detectors; with an energy greater than

500 keV; within the timing gate of a hit in the outer wires of the ionization chamber; and if

the hit occurred in sorr_dnt or sidar, have dE 60 and E60 within the proton or α-particle
gates. Figure 3.13 shows the effect of these gates.

3.5.2 Recoils

There are three categories of particles detected in the ionization chamber: unreacted

beam, (α,α) recoils, and (α,p) recoils. For each category, there are three species. The
unreacted beam and (α,α) recoils are 34S, 34Cl, and 34Ar. The three (α,p) recoils are 37Cl,
37Ar, and 37K.

The unreacted beam is limited to a polar angle of < 0.6°, so anything with a larger angle

is known to be a recoil. The other two can be distinguished by using the information on the

ejectile as described in Section 3.5.1.

There are two degrees of freedom in these reactions—center of mass polar angle and

60

)
V
e
M

(

y
g
r
e
n
E
e
l
i
t
c
e
j
E

20
15
10
5
0
20
15
10
5
0
20
15
10
5
0
20
15
10
5
0
20
15
10
5
0

0

30

60

90

(a)

(b)

(c)

(d)

(e)

120 150
60
Ejectile Polar Angle (°)

30

0

(f)

(g)

(h)

(i)

(j)

90

120 150

34Ar(α,p)37K
34Cl(α,p)37Ar

34S(α,p)37Cl
(α,α)

Figure 3.13: The relationship between the energy and the polar angle of the ejectiles for
the experimental energy E2. The gates on the recoil polar angle and the ejectile energy are
able to separate events caused by the reactions of interest from those caused by random
coincidences. (a) and (f) show the events in sidar, with an ejectile identified as a proton.
(b) and (g) show the events in sidar, with an ejectile identified as an α-particle. (c) and
(h) show the events in sorr_dnt, with an ejectile identified as a proton. (d) and (i) show
the events in sorr_dns (these events are not used to calculate the cross section). (e) and
(j) show the events in sorr_up. (a)–(e) show events gated only by the timing gate. (f)–(j)
show events gated by the timing gate, the Elab
r < 0.6° gate. The
cleanness of these spectra suggest that the number of background events is negligible. The
two points below the (α,α) line in (b) and (g) are where α-particles that are only detected
in the dE detector would be expected to be seen.

e > 500 keV gate, and the θlab

61

i

n
E
−
E

7

6

5

4

3

2

1

0
−1
−2

37Cl

37Ar

37K

Figure 3.14: The levels in the recoil nuclei 37Cl, 37Ar, and 37K [61], with E − Ein = 0 being
the energy of the beam and target system, excluding the kinetic energy [62]. The dotted red
lines show the energy of the system with the kinetic energies of this experiment.

excitation energy. They can be determined using the ejectile information. With that infor-

mation, the energy and angle of the recoil can be predicted. We can then compare these

predictions to our measurements and determine which particle identification is most likely.

To do this, the probability that an event is an occurrence of X reaction is

(cid:32)(cid:80)

S

WX =

WX(cid:80)

PX =

(cid:0)ES − ES,X (θCM, Eex)(cid:1)2

X WX

sys + σ2
σ2

stat

(cid:33)−1

(3.17)

(3.18)

where WX is the weight for X, S is a section of the ionization chamber, ES is the experi-
mentally measured energy deposited in S, and ES,X (θCM, Eex) is the energy predicted to be
deposited in S if X occurred with a center of mass polar angle of θCM and a recoil excitation
energy of Eex.

The different species are most separated in the section of the ionization chamber where

they are stopped—the E section. Figure 3.15a shows the energy loss in the dE section vs.

62

the E section, with the lines showing the energies that the recoils are expected to deposit

in those sections. The energy detection threshold for the E section was about 13 MeV (see

Section 3.3.2), which is higher than the energy of the recoils. This occurred because the

settings for the ionization chamber electronics were optimized using the unreacted beam,

and did not account for the fact that the recoils would have less energy. This means the

data most useful for determining the identity of the recoils is not available.

The recoil species might be able to be identified using the other sections of the ionization

chamber. Figure 3.15b shows the sum of the energy deposited in the X and Y sections vs.

energy deposited in the dE section. This is the most promising combination of ionization

chamber sections, but the energy resolution is not precise enough to be able to assign a

species. There is a parallel analysis looking to overcome this, but this work instead presents

a combined cross section of the 34Cl(α,p)37Ar, and 34Ar(α,p)37K reactions (see Section 3.6).

This is still useful for accomplishing the main goal of the experiment: testing the Hauser-

Feshbach theory.

63

(a)

0

5

10

E (MeV)

15

20

(b)

13

12

11

10

9

8

7

6

18

16

14

12

10

)
V
e
M

(
E
d

)
V
e
M

(
Y
+
X

8

6

7

8

9
10
dE (MeV)

11

12

13

34Ar(α,p)37K

34Cl(α,p)37Ar

34S(α,p)37Cl

Figure 3.15: The energy deposited in various sections of the ionization chamber by the recoils.
The lines show the energies at which the recoils are expected to be detected for the three
species of recoils. (a) shows the energy deposited in the dE section vs. the energy deposited
in the E section. The separate species would be most separated in the E section, but the
detection threshold for that section is too high to be used. (b) shows the sum of the energy
deposited in the X and Y sections vs. the energy deposited in the dE section. This shows
that the energy resolution of these sections is too low to be useful for particle identification.

64

3.6 Cross Section

The number of reactions detected is related to the differential cross section, dσ
dΩ

(cid:90)(cid:90)

N =

ε(Ω)fliveI(t)ρA(t)

dσ
dΩ

dt dΩ ,

, through

(3.19)

where I(t) is the beam intensity, ρA(t) is the areal number density, t is time, ε(Ω) is the
detection efficiency, flive is the live time fraction, and Ω is the solid angle. An overall

detection efficiency, ε, is introduced, such that

(cid:90)

ε(Ω)

dσ
dΩ

dΩ = εσ.

Using Equations (3.19) and (3.20), an equation for the cross section can be found:

ε(cid:82) fliveI(t)ρA(t) dt

N

.

σ =

(3.20)

(3.21)

To determine the cross section, we need the number of reactions (N), efficiency (ε), beam

intensity (I), target areal density (ρA), and live time fraction (flive). I, ρA, and flive vary
from run to run, while ε does not.

N is measured simply by counting up the number of events that satisfy the criteria in

Section 3.5. Specifically, that means:

• the event must contain an ejectile hit in the silicon detectors that either:

– occurs in a telescope pair of detectors and have dE60 and E60 signals that fall

within the proton gate described in Section 3.5.1 or

– occurs in sorr_up and has an energy of > 500 keV

65

• the event must contain a recoil hit in the ionization chamber that has a polar angle of

> 0.6°, and

• the timing difference between the recoil and the ejectile hits falls within the gate

described in Section 3.4.

Because of the inability to distinguish between the recoils, the number of reactions mea-
sured is that of all three reactions. However, the cross section of the 34S(α,p0)37Cl reaction
has been previously measured [63], and that can be used to separate the contribution of

34S(α,p)37Cl from that of 34Cl(α,p)37Ar and 34Ar(α,p)37K. The 34S(α,p)37Cl cross sec-
tions at the energies measured in this experiment were (23.7 ± 0.8) mb for the higher energy
and (25.7 ± 0.8) mb for the lower energy. At the experimental energies, there is only one ex-
cited state of 37Cl that can be populated energetically. According to TALYS-1.8 simulations

[22], the cross section of 34S(α,p)37Cl into this excited state is 0 mb at the experimental

energies, so the cross section into the ground state is used as the total cross section. Since
Hauser-Feshbach overestimates 34S(α,p0)37Cl, as shown in Figure 3.16, it probably over-
estimates 34S(α,p1)37Cl as well.
34Cl(α,p)37Ar and 34Ar(α,p)37K are then treated as a
single reaction, and so the end result is a cross section of 34Cl(α,p)37Ar and 34Ar(α,p)37K

combined.

In the following discussion, 34S(α,p)37Cl, 34Cl(α,p)37Ar, and 34Ar(α,p)37K are referred
to as reactions a, b, and c, respectively. The total reactions (Nabc)—which is what is directly
measured—can be split up into the reactions from a and the reactions from b and c:

Nabc = Na + Nbc

= εafliveσa

(cid:90)

(cid:90)

Ibc(t)ρA(t) dt .

(3.22)

(3.23)

Ia(t)ρA(t) dt + εbcfliveσbc

66

100

10

)
b
m

(

n
o
i
t
c
e
S

s
s
o
r
C

5

5.5

6.5

6
7.5
Center of Mass Energy (MeV)

7

8

8.5

Figure 3.16: The 34S(α,p0)37Cl cross section data from [63] recreated. The dashed vertical
lines indicate the energies at which this experiment was conducted. The solid line shows the
cross section calculated by TALYS [22].

Solving for the combined cross section for b and c:

(cid:82) fliveIbc(t)ρA(t) dt
Nabc − Na
(cid:90)

, where

σbc =

εbc

Na = εaσa

fliveIa(t)ρA(t) dt ,

(3.24)

(3.25)

εbc is a combined efficiency for b and c, and Ibc is the sum of the beam intensities of b and
c, i.e. Ibc = Ib + Ic.

The efficiency accounts for all reasons that reactions that occur might not be detected.

This includes the intrinsic detector efficiencies, angular coverage, and energy thresholds of the

detectors. The intrinsic efficiency of both the silicon detectors and the ionization chamber are

assumed to be 100 %. Some detector channels did not function properly; these dead channels

were identified using the calibration runs, and they were excluded from the analysis. This

effect was accounted for in the efficiency. The angular coverage is calculated as described in

67

Section 3.2. The angular distribution of the cross section is assumed to be isotropic in the

center of mass. In the laboratory reference frame, the reaction is “forward-shifted” because

of the reference frame shift; this means the ejectiles are more likely to be detected at angles

closer to 0°. The 500 keV energy threshold (described in Section 3.5) affects the ability to

detect ejectiles that are emitted closer to 180° and reactions in which the recoil is highly

excited.

The efficiency was calculated using a Monte Carlo calculation in which the polar and

azimuthal angles and the excitation energy of the recoil are randomized. The angles were

chosen isotropically in the center of mass, and the excitation energies were weighted based

on Hauser-Feshbach calculations by TALYS-1.8 [22]. Figure 3.17 shows how the efficiency

of detecting 34Ar(α,p)37K reactions changes with respect to the excited state that the 37K

populates. The efficiency increases as excitation energy increases because the ejectiles become

more forward-focused, where the detector coverage is greater;

it rapidly increases when

the ejectiles become fully forward-focused (i.e. all ejectiles are emitted at > 90°); and it

goes to zero when the ejectiles are so forward-focused that they are not even detected in

sidar, the most downstream detector section. The calculations were done using the default

TALYS parameters in the forward-kinematics frame, meaning the projectiles were α-particles

with energies of 6.383 MeV and 6.719 MeV. 2, 88, and 94 recoil excited states were used
in the calculations for 34S(α,p)37Cl, 34Cl(α,p)37Ar, and 34Ar(α,p)37K, respectively; this

accounts for every excited state below the incident energy threshold as reported in [62]

(see Figure 3.14). The separate reactions were simulated separately, and with 1 million

iterations each, the efficiencies for 34S(α,p)37Cl, 34Cl(α,p)37Ar, and 34Ar(α,p)37K were
calculated to be (30.42 ± 0.06) %, (29.25 ± 0.05) %, and (29.23 ± 0.05) %, respectively, with
the uncertainties being the statistical uncertainties from the Monte Carlo sampling only.

68

0.6

0.5

0.4

0.3

0.2

0.1

y
c
n
e
i
c
ffi
E
n
o
i
t
c
e
t
e
D

0

0

1

2

3

Excitiation Energy (MeV)

4

5

6

7

8

Figure 3.17: The detection efficiency as a function of recoil excitation energy for the
34Ar(α,p)37K reaction. The total detection efficiency is an average of the efficiencies of
each level weighted by the relative cross section of the levels.

Since a combined efficiency is needed for 34Cl(α,p)37Ar and 34Ar(α,p)37K, the average is
taken: εbc = (29.24 ± 0.07) %. The true efficiency will depend on the ratio of reactions
occurring. However, as the two efficiency values agree within uncertainty, the error of the

average efficiency encompasses all possibilities.

The uncertainty of the efficiency comes from three sources: 1) the statistical uncertainty

from the number of particles that are detected in the Monte Carlo calculation (see above),

2) the weighting of the excited levels, which depends on the Hauser-Feshbach model, and 3)

the solid angle. The uncertainty from 2) is estimated from the difference between the overall

detection efficiency and the detection efficiency of the ground state, which is 28.5 %. The

uncertainty from 3) is taken from the Monte Carlo calculation in Section 3.2 propagated to

the efficiency using σε

ε =

σΩ
Ω = 0.141.

The integral of the product of the areal density of the jet and the intensity of beam x

69

)
°
(

e
l
g
n
A
r
a
l
o
P
e
l
i
t
c
e
j
E

16

14

12

10

8

6

4

2

0

)
°
(

e
l
g
n
A

l
a
h
t
u
m
i
z
A
e
l
i
t
c
e
j
E

350

300

250

200

150

100

50

0

0

20

40

0

20

40

(a)

140

160

180

(b)

140

160

180

80

60
Ejectile Polar Angle (°)

100

120

80

60
Ejectile Polar Angle (°)

100

120

34Ar(α,p)37K

34Cl(α,p)37Ar

34S(α,p)37Cl

Figure 3.18: An example of a Monte Carlo simulation used to calculate the efficiency of
detecting each reaction. The filled shapes are events that are detected, and the unfilled
shapes are those that are not detected. (a) shows the ejectile energy vs. the ejectile polar
angle. The lines correspond to the different recoil excitation energies. (b) shows the ejectile
azimuthal angle vs. the ejectile polar angle. The locations of the silicon detectors can be
seen.

70

will be referred to as Sx, i.e.

(cid:90)

Sx =

fliveρA(t)Ix(t) dt .

(3.26)

Since the areal density and the beam intensity vary throughout the experiment but vary

little throughout a single run, Sx can be expressed as

(cid:88)

Sx =

(cid:104)ρA(cid:105)inx,i,

(3.27)

i

where (cid:104)ρA(cid:105)i is the average areal density for run i and nx,i is the number of beam particles of
species x delivered to the experiment for run i (this quantity takes into account the factor

of flive because this quantity is measured by a scaler that is vetoed if the DAQ system is

unable to read). This means the final equation used to calculated the combined cross section

of 34Cl(α,p)37Ar and 34Ar(α,p)37K is

σbc =

Nabc − Na
εbcSbc

Na = εaσaSa

(3.28)

The areal density of the target is measured using the pressure of the gas after the com-

pressor and right before entering the nozzle (CAPin, shown in Figure 2.3). Prior to the
experiment, the relationship between CAPin and ρA was measured, as described in Sec-
tion 2.2.1.

An 241Am α-particle source was positioned facing the jet with a Micron BB15 detector

on the other side of the jet to detect the α-particles. The α-particles lost energy in the target

proportional to the areal density of the target. By measuring the difference between the

71

energy of the α-particles traveling through the jet at a given pressure and the energy of the

α-particles traveling through no jet, a CAPin–ρA relationship was determined.

Three tests were done with the nozzle used in the experiment, varying the amount of

gas in the system. The pressure measured at Pdisch for each was (150, 250, and 350) psig.
The average measurements for CAPin for these runs were (6.18, 9.52, and 13.4) × 103 Torr,
and the areal density through the jet at the height of the beam axis were (4.4, 6.3, and
7.9) × 1018 atoms/cm2 [64].

Figure 3.19 shows the data from this calibration, the calibration function, and the data

from the experimental runs to which the calibration is being applied. The calibration function

is

ρA = a(CAPin − CAPin,0) + b,

(3.29)

where a and b are the adjustable parameters of the fit function and CAPin,0 is a constant.
The values for these were CAPin,0 = 12.5 × 103 Torr, a = 4.99 × 1014 (atoms/cm
2
)/Torr,
and b = 7.60 × 1018 atoms/cm2. CAPin was averaged for each run, and this calibration was
used to calculate the average areal density for each run.

The time integral(cid:82) I dt is the number of beam particles delivered to the target. The beam

intensity depends on which reaction is being considered. For the 34S(α,p)37Cl cross section,

is used, for the combined 34Cl(α,p)37Ar and 34Ar(α,p)37K cross section, I34Cl

+ I34Ar
I34S
is used. The total number of beam particles delivered to the target (ntot) is the number

of triggers during the run in the dE section of the ionization chamber, counted by a scaler

module in the DAQ. The individual values are calculated by nX = fX ntot, where X is the
beam species of interest, and fX is the fraction of the total beam that is species X. The
values of fX are taken as the counts within the gates shown in Figure 3.7b. The values of

72

)
2
m
c
/
s
m
o
t
a
(

A
ρ

8.5 × 1018
8 × 1018
7.5 × 1018
7 × 1018
6.5 × 1018
6 × 1018
5.5 × 1018
5 × 1018
4.5 × 1018
4 × 1018

6000

7000

8000

Calibration Fit
Calibration Data
Experiment Data

9000

10000 11000 12000 13000 14000

CAPin (Torr)

Figure 3.19: The relationship between the target areal density and the pressure measured at
CAPin. The circles are the calibration points, and the crosses are the experimental values
that were calibrated using this fit.

fX vary by run.

73

)

r
r
o
T
(

i

n
P
A
C

14000
13000
12000
11000
10000

8e+18

(a)

(b)

(c)

)
2
m
c
/
s
m
o
t
a
(

(cid:105)
A
ρ
(cid:104)

t
o
t
n

7.5e+18

7e+18

3e+07

2e+07

1e+07

0

2 0 1 6-0 5-1 0

2 0 1 6-0 5-1 1

2 0 1 6-0 5-1 2

2 0 1 6-0 5-1 3

2 0 1 6-0 5-1 4

2 0 1 6-0 5-1 5

2 0 1 6-0 5-1 6

2 0 1 6-0 5-1 7

2 0 1 6-0 5-1 8

2 0 1 6-0 5-1 9

2 0 1 6-0 5-2 0

Time (YYYY-MM-DD)

Figure 3.20: The time series data that changes for each run. (a) shows the continuous data
for CAPin throughout the entire experiment. (b) shows the areal jet density averaged over
the time span of each run. (c) shows the total number of particles delivered to the target for
each run.

74

Chapter 4

Results

Equations (3.24) to (3.26) are the equations used to calculated the combined cross section

of 34Cl(α,p)37Ar and 34Ar(α,p)37K.

The two experimental energies are (5.91 ± 0.08) MeV and (5.51 ± 0.08) MeV in the center
of mass frame (see Section 3.1). They are referred to as E1 and E2, respectively. For E1, 67

total reactions were detected, leading to a statistical uncertainty of 8 for the cross section
determination; 1.6 ± 0.1 of these were attributed to 34S(α,p)37Cl. The beam weighting ratios
were Sb/Sbc = 32.3 % and Sc/Sbc = 67.7 %, where Sx is given in Equation (3.26), b refers
to 34Cl(α,p)37Ar, c refers to 34Ar(α,p)37K, and bc refers to the combination of the two.
The resulting combined cross section for 34Cl(α,p)37Ar and 34Ar(α,p)37K is (70 ± 21) mb,
where the uncertainty of 21 mb is composed of a 9 mb statistical uncertainty and a 12 mb

systematic uncertainty.

For E2, 216 total reactions were detected, leading to a statistical uncertainty of 15 for the
cross section determination; 4.4 ± 0.3 of these were attributed to 34S(α,p)37Cl. The beam
weighting ratios were Sb/Sbc = 33.5 % and Sc/Sbc = 66.5 %. The resulting combined cross
section for 34Cl(α,p)37Ar and 34Ar(α,p)37K is (52 ± 13) mb, where the uncertainty of 13 mb
is composed of a 4 mb statistical uncertainty and a 9 mb systematic uncertainty.

The relative uncertainties of the inputs of Equation (3.24) are shown in Table 4.1. The

largest source of uncertainty in this experiment is the systematic uncertainty of the efficiency,

75

Table 4.1: The relative uncertainties of the quantities used to calculate the combined
34Cl(α,p)37Ar and 34Ar(α,p)37K cross section.

Statistical

Systematic

E1

E2

Nabc
σa
εx
Sx
Nabc
σa
εx
Sx

12 %

–

0.2 %
0.3 %

7 %
–

0.2 %
0.2 %

–
6 %
17 %
3 %
–
7 %
17 %
4 %

which comes from the uncertainty in the solid angle (see Section 3.2).

4.1 Discussion

To compare to the predictions of Hauser-Feshbach theory, Hauser-Feshbach predictions

of the cross sections were calculated using TALYS-1.8 [22] with the default α optical model
potential from [23]. The cross section for 34Cl(α,p)37Ar was calculated to be 142.8 mb and
89.8 mb at E1 and E2, respectively, and the corresponding values for 34Ar(α,p)37K were

95.0 mb and 52.2 mb. To compare these Hauser-Feshbach predictions to the combined cross

section that we determined in this experiment, a weighted average of the two was calculated:

σbc =

Sb
Sbc

σb +

Sc
Sbc

σc.

(4.1)

These weights, Sx/Sbc, factor in how much beam and target are interacting in each exper-
imental run. This gives a prediction of 110.4 mb for E1 and 64.8 mb for E2. A comparison

of these predictions with the experimental results is shown in Figure 4.1.

76

100

)
b
m

(

σ

34Cl(α,p)37Ar, TALYS
34Ar(α,p)37K, TALYS
Combined, TALYS
Combined, This Work

10

4.5

5

5.5

ECM (MeV)

6

6.5

7

Figure 4.1: The experimentally measured 34Cl(α,p)37Ar + 34Ar(α,p)37K cross section, with
the Hauser-Feshbach predictions, calculated using TALYS-1.8 [22]. The predicted cross
sections are weighted averages of the two cross sections, which are also shown. The weights
for the 34Ar(α,p)37K cross section are 67.7 % for E1 and 66.5 % for E2.

77

Chapter 5

Conclusions

The JENSA gas jet target setup at the NSCL was completed and optimized. The gas

target was characterized, and determined to be able to achieve an areal density of up to
9 × 1018 atoms/cm2. Using the SuperORRUBA and SIDAR Si detector arrays and the
ANASEN ionization chamber with JENSA, a new method was developed to measure (α,p)

cross sections with radioactive beams at low, astrophysically relevant energies. The first ap-

plication of this method was the first direct measurement of the 34Ar(α,p)37K cross section

at 5.5 MeV and 5.9 MeV in the center of mass frame, with the goal of testing Hauser-Feshbach

reaction rate calculations and resolving discrepancies with indirect measurements which in-

dicate that these calculations overpredict the reaction rates.

Because of the contamination of the 34Ar beam with the daughter and grand-daughter

34Cl and 34S nuclides and the inability to distinguish between the recoils of the three (α,p)
reactions in the ionization chamber, an individual measurement of the 34Ar(α,p)37K re-
action was not possible. However, the contribution from 34S(α,p)37Cl could be isolated
because it had been previously measured, and a combined cross section for 34Cl(α,p)37Ar
and 34Ar(α,p)37K was determined.

With this combined cross section the main goal of this thesis can still be accomplished:

to test Hauser-Feshbach model predictions. The experimental combined cross sections are a

factor of 1.58 and 1.25 lower than Hauser-Feshbach predictions at E1 and E2, respectively.

78

This can be considered reasonable agreement, given typical uncertainties of the Hauser-

Feshbach method of factors 2–3, especially for unstable nuclei.

Previous measurements have been conducted to indirectly inform the astrophysical re-
action rate. [30] and [31] report NA(cid:104)σv(cid:105) to be approximately a factor of 25–50 lower than
Hauser-Feshbach predictions; however, a rate with artificially enhanced α-spectroscopic fac-

tors, to account for α-clustering, is on the same order of magnitude as the predictions.

Preliminary results from [32], which have not been published in a refereed journal, show

the rate of the inverse reaction, 37K(p,α)34Ar, to be about an order of magnitude lower

than Hauser-Feshbach predictions. The results from this work show that the hypothesis that

Hauser-Feshbach overestimates the reaction rate by orders of magnitude is unlikely to be true

at these energies in the 34Cl–34Ar region, indicating the possibility that α-clustering enhance-
ments compensate for the low level density. Because the contributions from 34Cl(α,p)37Ar
and 34Ar(α,p)37K cannot be distinguished, it is, in principle, possible that one reaction

is overestimated by Hauser-Feshbach and the other is underestimated. However, because

Hauser-Feshbach typically overpredicts reaction rates, this seems unlikely.

A similar story has played out for 22Mg(α,p)25Al. Indirect measurement had suggested

that the astrophysical rate would be much lower than predicted by Hauser-Feshbach [65]. The

direct measurement reports a cross section that, while still lower than the Hauser-Feshbach

prediction, is much closer than indirect measurements would suggest [27]. However, unlike

in this work, the discrepancy is still a factor of 8, much larger than our factor of 1.25–1.58.

This may indicate that Hauser-Feshbach calculations for (α,p) reactions in the upper mass
region of the αp-process (A ∼ 34) are more reliable than in lower mass regions.

Because the results are close to the Hauser-Feshbach predictions, it is recommended to

continue using Hauser-Feshbach rates, but reduced by a factor of 1.25–1.58. More data, espe-

79

cially at energies in or closer to the Gamow window, are needed to see if this overprediction

is systematic, and if so, how large it is at the astrophysically relevant energies.

With the method developed here, JENSA should be used to further study 34Ar(α,p)37K
30S(α,p)33Cl would be interesting

and other (α,p) reactions on waiting point nuclides.

because it has been identified as a waiting point nuclide [11]. It has a mass between that

of 22Mg and 34Ar, so its (α,p) rate could answer questions about the mass range in which

Hauser-Feshbach predictions are accurate. These reaction cross sections can be measured at

lower energies by increasing the beam intensity or the density of the target. The new Facility

for Rare Isotope Beams will be able to provide more intense beams, and the jet could be made

more dense by cooling the gas before it is sent through the nozzle. A more dense jet would also

increase the energy spread of the beam, which would be useful for covering a larger energy

range with fewer changes to the experimental energy. For 34Ar(α,p)37K specifically, future

experiments could improve upon this method by taking care that the ionization chamber is

configured properly to measure the energy with enough precision to differentiate the different

recoil species. This would allow for the different (α,p) reactions to be identified, and the
reaction rate for each could be measured. Alternatively, the 34Cl(α,p)37Ar cross section

could be measured separately, which would allow for the contribution from that reaction to

be subtracted in the same way that the contribution from 34S(α,p)37Cl is subtracted in this

work.

80

APPENDIX

81

Appendix

JENSA Manual

Vacuum System Startup

This is the procedure to evacuate the chamber side of the system. It assumes that the

pumps are turned off and the system is either filled with gas or being held at a static vacuum.

This does not evacuate the compressor (See Compressor Startup).

1. Seal the main chamber.

2. Close Vin and Vcomp_in, isolating the compressor from the chamber.

3. Turn on cooling water.

(a) Open return valve.

(b) Open intake valve.

(c) Close loop valve.

(d) Check flow meters under the compressor to ensure cooling water is flowing. If the

flow does not increase, make sure the cooling water valves under the compressor

are open.

(e) Check flow meters next to the turbo pumps to ensure cooling water is flowing. If

the flow does not increase, make sure the cooling water valves next to the turbo

pumps are open.

82

4. Start the Roughing Pump.

5. Slowly open Vrough.

6. Turn on the Leybold Control Panel.

7. Slowly open Vley_out. Gas will enter the Roughing Pump and it will start working
harder. To prevent damage to the Roughing Pump, limit the flow of gas into it by

opening Vley_out only a little.

8. Open Vgate.

9. Wait until PIRch ≤ 100 Torr.

10. Turn on Pump L1–Pump L3 with the "Start System" button on the Leybold Control

Panel.

11. Press Reset Button on the Leybold Control Panel to override faulty valve Vley1.

12. Turn on the Motor Control Panel panel by pulling the silver button.

13. Turn on Pump 8–Pump 9, waiting 10 s after each. Check that they each spin up. If

the noise enclosure is closed, it may be difficult to notice.

14. Turn on Pump 11–Pump 13, waiting 10 s after each. Check that they each spin up.

15. Turn on Pump 10. Check that it is spinning up.

16. Turn on Pump 7. Check that it is spinning up. Wait until PIRch ≤ 1 × 10−1 Torr.

17. Turn on Shimadzu. Wait until the pump speed is > 5 % and PIRturbo ≤ 5 × 10−2 Torr.

83

18. Turn on UP1–UP4 and (if attached) DN1–DN4. Start with UP1 and DN1 and incre-

ment to UP4 and DN4, waiting 20 s after each start.

19. Turn on pressure sensors CCU1–CCU4 and (if attached) CCD1–CCD4.

84

Compressor Evacuation

This procedure is for removing the gas from the compressor. This must be done before

filling the compressor with the desired gas. If the desired gas is already in the compressor

or it is already evacuated, it is not necessary to do this.

This assumes the compressor is isolated from the main chamber and pumps (Vin and

Vcomp_in are closed) and that the Roughing Pump is on.

1. If the main chamber and pumps are not evacuated,

(a) Close Vley_out, isolating them from the Roughing Pump.
(b) Wait until PIRrough ≤ 100 Torr.

2. Close V104_man and Vair1, and open Vair2. This will open the internal valves, making
the compressor one connected vessel that can be evacuated all at once. It is normal to

hear compressed air being loudly vented.

3. Close Vgauge. This ensures that the 3 psi gauge stays within its range. Going outside

of its range could damage the spring, affecting its calibration.

4. Slowly open Vcomp_in. Gas from the compressor will enter the Roughing Pump and
it will start working harder. To prevent damage to the Roughing Pump, limit the flow

of gas into it by opening Vcomp_in only a little.

5. Wait until Pinter, Pinter, Pupstr, and Pdisch all ≈ 0 psig.

6. Close Vcomp_in.

7. Close Vair2, and open V104_man and Vair1.

85

Compressor Startup

This procedure is for starting the compressor and creating a loop of gas going from the

compressor outlet, through NVloop, and into the compressor inlet.

It assumes the compressor is either evacuated or filled with the target gas. If this is not

the case, see Compressor Evacuation.

It also assumes the compressor is isolated from the main chamber and pumps. This

means Vin and Vcomp_in must be closed.

V104_man and Vair1 must be open, and Vair2 must be closed. The compressed air lines
should not be making noise. This is the normal operating setup. If the compressor shuts

off after the 30 s interlock stage and there is enough gas in the system, it may be because

V104_man is closed.

1. Turn on the Compressor Control Panel.

2. Open PVloop using the EPICS control panel.

3. Open NVloop completely.

4. Close NVhm completely.

5. Close Vgauge. This ensures that the 3 psi gauge stays within its range. Going outside

of its range could damage the spring, affecting its calibration.

6. Close REGbot completely by turning the dial counter-clockwise.

7. Open Vbot1.

8. Adjust REGbot to 30 psi downstream.

86

9. Increase Pinlet to 15 psig by opening valve Vbot2. Close Vbot2 when 15 psig is reached.

10. Start the compressor by pressing the green start button on the Compressor Control

Panel.

11. After about 30 s, the interlock stage will end, and the second stage of the compressor

will open. Pdisch will increase, and Pinlet will decrease.

12. Add gas (see Adjusting Compressor Pressures) so that 4 psig ≤ Pinlet ≤ 5 psig and

150 psig ≤ Pdisch ≤ 200 psig.

87

Adjusting Compressor Pressures

The density of the jet can be changed by changing Pdisch. This can be done by adjusting
NVloop, which affects the ratio of gas going through the nozzle to gas going through the
bypass loop. This also affects Pinlet, so amount of gas in the system must be adjusted to
assure that the compressor is able to run.

It is important to note that NVloop affects Pinlet and Pdisch non-linearly. When NVloop
is closed, small changes affect the pressures significantly, but when NVloop is open, it must
be opened or closed a lot in order to affect the pressures.

This assumes Vbot1 is open and REGbot is set to allow gas to flow into the system.

Increasing Pdisch, Decreasing Pinlet

1. Close NVloop while Pinlet ≥ 0.5 psig. This will redirect gas from the bypass loop to

the nozzle, increasing Pdisch and decreasing Pinlet.

2. Open Vbot2 while Pinlet ≤ 1.0 psig. This will add gas to the system, increasing Pdisch

and Pinlet.

3. Repeat from step 1, maintaining 0.5 psig ≤ Pinlet ≤ 1 psig, until Pdisch is at the desired

setting.

Decreasing Pdisch, Increasing Pinlet

1. Open NVloop while Pinlet ≤ 1.0 psig. This will redirect gas from the nozzle to the

bypass loop, decreasing Pdisch and increasing Pinlet.

2. Open NVvent while Pinlet ≥ 0.5 psig. This will remove gas to the system, decreasing

88

Pdisch and Pinlet.

3. Repeat from step 1, maintaining 0.5 psig ≤ Pinlet ≤ 1 psig, until Pdisch is at the desired

setting.

89

Jet Startup

This procedure will start a jet in the main chamber. This assumes that the vacuum

system is running and the compressor is on (see Vacuum System Startup and Compressor

Startup) and that the main chamber and pumps are separated from the compressor.

This assumes Vrough and PVinlet are open. It also assumes Vbot1 is open and REGbot

is set to allow gas to flow into the system.

1. Close D1483 using the EPICS control panel. This ensures that if there is a failure that

leads to gas filling the chamber, the beamline and accelerator are not affected.

2. Open Vbot2 to add gas to the system until 4 psig ≤ Pinlet ≤ 5 psig.

3. Close Vrough.

4. Slowly open Vcomp_in and maintain 0.5 psig ≤ Pinlet ≤ 1 psig (see Adjusting Compres-
sor Pressures). This will cause gas to enter the pumps and main chamber and Pinlet
to decrease. Because of this, adding gas will be necessary.

5. Slowly open Vin and maintain 0.5 psig ≤ Pinlet ≤ 1 psig (see Adjusting Compressor

Pressures). Pump loads will increase.

6. After adjustments, open valve Vgauge to observe Pinlet pressure more precisely on the

3 psig gauge.

7. Close Vbot2.

90

Shutdown

This procedure is for turning off the jet and turning off all of the pumps in the system.

This leaves the system in a state that requires no oversight.

This assumes all the pumps are on and the jet is flowing, i.e. the compressor is on and

Vin and PVinlet are open.

1. Reduce the gas by adjusting Pdisch to (150–200) psig (see Adjusting Compressor Pres-

sures).

2. Turn off CCU1 – CCU4 and (if attached) CCD1 – CCD4.

3. Isolate the compressor from the main chamber and pumps by closing Vin and Vcomp_in.

4. Slowly open Vrough.

5. Turn off the compressor by pressing red button on the Compressor Control Panel.

6. Turn off UP1 – UP4 and (if attached) DN1 – DN4. Start with UP4 and DN4 and

decrement to UP1 and DN1. Wait 10 s after each stop.

7. Turn off Shimadzu.

8. Turn off Pump 7.

9. Wait 10 s

10. Turn off Leybold WSU2001 pumps in the following order and wait 10 s after each:

switches 10, 13, 12, 11.

11. Turn off Pump 9 and Pump 8 and wait 10 s after each.

91

12. Turn off Pump L1 – Pump L3 with the “System Stop” button on the Leybold Control

Panel.

13. Wait for pumps to spin down.

14. Close Vrough.

15. Turn off the Roughing Pump.

16. Turn off the Motor Control Panel.

17. Turn off the Leybold Control Panel.

18. To vent the chamber with air, slowly open NVvent2.

92

Emergency Shutdown

This procedure is for when there is a failure in any part of the system, such as the

compressor shutting off or one of the roots blowers shutting off. Such circumstances, if left

unresolved, could lead to damaging the pumps or experimental equipment. The remedy is to

isolate the compressor from the main chamber and pumps and to evacuate the main chamber

and pumps.

1. Close Vin.

2. Close Vcomp_in.

3. Open Vrough.

93

BIBLIOGRAPHY

94

BIBLIOGRAPHY

[1] C. Iliadis, Nuclear Physics of Stars (Wiley-VCH, 2015), pp. 31–33.

[2] H. Schatz and K. E. Rehm, Nucl. Phys. A 777, 601 (2006) doi: 10.1016/j.nuclphysa.

2005.05.200.

[3] C. J. Hansen and H. M. van Horn, Astrophys. J. 195, 735 (1975) doi: 10.1086/153375.

[4] H. Schatz et al., Phys. Rev. Lett. 86, 3471 (2001) doi: 10.1103/physrevlett.86.

3471.

[5] B. Paczynski, Astrophys. J. 267, 315 (1983) doi: 10.1086/160870.

[6] M. Sztajno et al., Astrophys. J. 299, 487 (1985) doi: 10.1086/163715.

[7] W. Penninx et al., Astron. Astrophys. 208, 146 (1989), https://ui.adsabs.harvard.

edu/abs/1989A&A...208..146P.

[8] E. Kuulkers et al., Astron. Astrophys. 382, 947 (2002) doi: 10.1051/0004- 6361:

20011656.

[9] J. van Paradijs et al., Mon. Not. R. Astron. Soc. 221, 617 (1986) doi: 10.1093/mnras/

221.3.617.

[10] G. Zhang et al., Mon. Not. R. Astron. Soc. 398, 368 (2009) doi: 10.1111/j.1365-

2966.2009.15148.x.

[11] J. L. Fisker, F.-K. Thielemann, and M. Wiescher, Astrophys. J. 608, L61 (2004) doi:

10.1086/422215.

[12] R. H. Cyburt et al., Astrophys. J. 830, 55 (2016) doi: 10.3847/0004-637x/830/2/55.

[13] L. Bildsten, in AIP conference proceedings (2000), doi: 10.1063/1.1291736.

[14] H. Schatz et al., Astrophys. J. 524, 1014 (1999) doi: 10.1086/307837.

[15] W. Hauser and H. Feshbach, Phys. Rev. 87, 366 (1952) doi: 10.1103/physrev.87.366.

[16] J. J. Cowan, F.-K. Thielemann, and J. W. Truran, Phys. Rep. 208, 267 (1991) doi:

10.1016/0370-1573(91)90070-3.

95

[17] T. Rauscher, F.-K. Thielemann, and K.-L. Kratz, Nucl. Phys. A 621, 331 (1997) doi:

10.1016/s0375-9474(97)00266-2.

[18] H. Schatz et al., Phys. Rep. 294, 167 (1998) doi: 10.1016/s0370-1573(97)00048-3.

[19] C. Iliadis, Nuclear Physics of Stars (Wiley-VCH, 2015), pp. 133–137.

[20] A. Koning, S. Hilaire, and S. Goriely, TALYS-1.8: A nuclear reaction program – User

Manual (Dec. 2015), pp. 83–92.

[21] T. Rauscher and F.-K. Thielemann, At. Data Nucl. Data Tables 75, 1 (2000) doi:

10.1006/adnd.2000.0834.

[22] A. J. Koning, S. Hilaire, and M. C. Duijvestijn, in ND2007 (2007), doi: 10.1051/

ndata:07767.

[23] V. Avrigeanu, M. Avrigeanu, and C. Mănăilescu, Phys. Rev. C 90, 044612 (2014) doi:

10.1103/physrevc.90.044612.

[24] A. M. Long, Private communication, 2016.

[25] S. Almaraz-Calderon et al., Phys. Rev. Lett. 112, doi: 10.1103/physrevlett.112.

152701 (2014) doi: 10.1103/physrevlett.112.152701.

[26] R. H. Cyburt et al., Astrophys. J. Suppl. Ser. 189, 240 (2010) doi: 10.1088/0067-

0049/189/1/240.

[27] J. S. Randhawa et al., Phys. Rev. Lett. 125, 202701 (2020) doi: 10.1103/physrevlett.

125.202701.

[28] S. O’Brien et al., in AIP conference proceedings (2009), doi: 10.1063/1.3087029.

[29] S. P. O’Brien, “Exploring the αp-process with high precision (p,t) reactions”, PhD thesis

(University of Notre Dame, 2010), https://curate.nd.edu/show/rj430289f1w.

[30] A. M. Long, “An Indirect Study of the Astrophysical 34Ar(α,p)37K Reaction and its
Influence on Type-1 X-ray Burst Light Curves”, PhD thesis (University of Notre Dame,
2016), https://curate.nd.edu/show/rx913n22m9v.

[31] A. M. Long et al., Phys. Rev. C 95, doi: 10.1103/physrevc.95.055803 (2017) doi:

10.1103/physrevc.95.055803.

[32] C. Deibel et al., in Proceedings of XII international symposium on nuclei in the cosmos

— PoS(NIC XII) (Apr. 2013), doi: 10.22323/1.146.0044.

96

[33] A. C. Lauer, “Studying the Reaction 34Ar(α,p)37K and its Impact on XRB Nucle-
osynthesis and Observables”, PhD thesis (Louisiana State University at Baton Rouge,
2017), https://digitalcommons.lsu.edu/gradschool_dissertations/4118.

[34] C. Iliadis, Nuclear Physics of Stars (Wiley-VCH, 2015), pp. 75–77.

[35] D. J. Morrissey and B. M. Sherrill, in The Euroschool Lectures on Physics with Ex-
otic Beams, Vol. I, edited by J. S. Al-Khalili and E. Roeckl (Springer-Verlag Berlin
Heidelberg, 2004), pp. 113–135.

[36] D. J. Morrissey et al., Nucl. Instrum. Methods Phys. Res. B 204, 90 (2003) doi:

10.1016/s0168-583x(02)01895-5.

[37] H. Geissel et al., Nucl. Instrum. Methods Phys. Res. A 282, 247 (1989) doi: 10.1016/

0168-9002(89)90148-4.

[38] L. Weissman et al., Nucl. Phys. A 746, 655 (2004) doi: 10.1016/j.nuclphysa.2004.

09.045.

[39] L. Weissman et al., Nucl. Instrum. Methods Phys. Res. A 540, 245 (2005) doi: 10.

1016/j.nima.2004.11.048.

[40] K. Cooper et al., Nucl. Instrum. Methods Phys. Res. A 763, 543 (2014) doi: 10.1016/

j.nima.2014.06.075.

[41] A. Lapierre et al., J. Instrum. 5, c07001 (2010) doi: 10.1088/1748- 0221/5/07/

c07001.

[42] O. Kester et al., Proceedings of the SRF2009, Berlin, Germany, 57 (2009).

[43] C. Iliadis, Nuclear Physics of Stars (Wiley-VCH, 2015), pp. 163–167.

[44] N. Nica and B. Singh, Nucl. Data Sheets 113, 1563 (2012) doi: 10.1016/j.nds.2012.

06.001.

[45] K. A. Chipps et al., Nucl. Instrum. Methods Phys. Res. A 763, 553 (2014) doi: 10.

1016/j.nima.2014.06.042.

[46] The Vacuum Technology Book, Volume II (Pfeiffer Vacuum GmbH, 2013), https :

//www.pfeiffer-vacuum.com/en/know-how/.

[47] M. S. Basunia, Nucl. Data Sheets 107, 2323 (2006) doi: 10.1016/j.nds.2006.07.001.

[48] C. Hanke and J. Laursen, Nucl. Instrum. Methods 151, 253 (1978) doi: 10.1016/0029-

554x(78)90497-4.

97

[49] K. Schmidt et al., Nucl. Instrum. Methods Phys. Res. A 911, 1 (2018) doi: 10.1016/

j.nima.2018.09.052.

[50] D. W. Bardayan et al., Nucl. Instrum. Methods Phys. Res. A 711, 160 (2013) doi:

10.1016/j.nima.2013.01.035.

[51] D. W. Bardayan et al., Phys. Rev. C 63, 065802 (2001) doi: 10.1103/physrevc.63.

065802.

[52] J. Lai et al., Nucl. Instrum. Methods Phys. Res. A 890, 119 (2018) doi: 10.1016/j.

nima.2018.01.010.

[53] https://epics-controls.org.

[54] L. R. Dalesio, A. J. Kozubal, and M. R. Kraimer, International conference on acceler-
ator and large experimental physics control systems (1991), https://www.osti.gov/
biblio/6110347.

[55] http://docs.nscl.msu.edu/daq/.

[56] R. Fox, R. Au, and A. V. Molen, IEEE Transactions on Nuclear Science 36, 1562 (1989)

doi: 10.1109/23.41102.

[57] G. L. Engel et al., Nucl. Instrum. Methods Phys. Res. A 573, 418 (2007) doi: 10.

1016/j.nima.2006.12.052.

[58] S. Ahn, “The study of nuclear structure of neutron-rich 81Ge and its contribution in
the r-process via the neutron transfer reaction 80Ge(d,p)”, PhD thesis (University of
Tennessee, 2013), http://trace.tennessee.edu/utk_graddiss/2392.

[59] P. Malzacher, N. Iwasa, and H. Weick, https://web-docs.gsi.de/~weick/atima/.

[60] https://www.github.com/j-browne/raumlehre.

[61] J. Cameron et al., Nucl. Data Sheets 113, 365 (2012) doi: 10.1016/j.nds.2012.02.

001.

[62] M. Wang et al., Chin. Phys. C 41, 030003 (2017) doi: 10.1088/1674-1137/41/3/

030003.

[63] A. F. Scott et al., Nucl. Phys. A 552, 363 (1993) doi: 10.1016/0375-9474(93)90499-

n.

[64] K. Schmidt, Private communication, 2017.

98

[65] A. Matic et al., Phys. Rev. C 84, 025801 (2011) doi: 10.1103/physrevc.84.025801.

99