.lat.
«W . m...“—

5.?

.w 5“". Ln. , a 141A“ MK.
".2 2,. ..
.39).“? ,, ‘

. flaw
. .y 3.2

.9; .v .1.

{I}... ‘
.. ‘
1.41 313...».“39.

. 3.3.1...

A . 5y 9
1:.
Wait:

1..

1 IL
)5... .3.

~11!

 

 

 

 

s.v..
hi.)

1 . :fi.

, .V

v

 

 

«hum

92...:

u ”Wmmmhmm

.fifi. .

I31. .5;

“mm? Hanan

heavily
.- VIN
f

‘ .2.
«Hit-‘- 1..
lift;

u {.434

[meets .LIBRAri:
'3 Michigan State
£100} University

 

This is to certify that the
dissertation entitled

SPECTROSCOPY OF NEUTRON UNBOUND STATES IN
NEUTRON RICH OXYGEN ISOTOPES

presented by

NATHAN HENRY FRANK

has been accepted towards fulfillment
of the requirements for the

PhD. degree in PHYSICS AND ASTRONOMY

 

V Major Profes'sor’s Signature
/§/20/§5

Date

MSU is an Affinnative Action/Equal Opportunity Institution

~s..-—.-._.---_-—-—-.—-—---—--.-.—-—.—a----o—._

 

PLACE IN RETURN Box to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05 p:/ClRC/DaleDue.indd-p.1

 

 

SPECTROSCOPY OF NEUTRON UNBOUND STATES IN
NEUTRON RICH OXYGEN ISOTOPES

By

Nathan Henry Frank

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

2006

ABSTRACT

SPECTROSCOPY OF NEUTRON UNBOUND STATES IN NEUTRON RICH
OXYGEN ISOTOPES

By

Nathan Henry Frank

The existence of so-called magic nuclei has been well established for nuclei near stabil—
ity; they are well reproduced by the nuclear shell model. Magic nuclei have a certain
number of protons and neutrons. These nuclei are more bound than their respective
neighbors. In the past it was assumed that the magic numbers are fixed throughout
the nuclear chart; there is mounting evidence that this in fact is not the case. Recently
the breakdown of the well known magic neutron number N = 20 and the emergence
of a new magic number of neutrons N = 16 has been proposed for the oxygen iso-
tOpes. Experimental observations of the relative binding energies of nuclei, such as
the one-neutron separation energy as well as shell model calculations suggest that
N = 16 is indeed a new magic number for neutron rich nuclei very far from stability.
Under this assumption, the nucleus 2“O with a magic number of eight protons and
sixteen neutrons would be doubly-magic. Another observable to identify magic nuclei
is a high first excited state energy. Previous experiments to verify this prediction of
the first excited states of 23O and 24O demonstrated that these states are unstable to
neutron emission. The goal of the current work was to observe the neutron unbound
states of 23O and 24O by neutron decay spectrosc0py.

The energy of the neutron unbound first excited states were reconstructed by mea-
suring the momentum vector of the charged fragment and neutron resulting from the
decay. Neutron unbound 230’“ and 24O" were produced using a 26Ne beam impinged
on a beryllium target. The charged particles were bent away from the neutrons using

the recently commissioned Sweeper Magnet and analyzed in charged particle detec-

tors. The neutrons continued at zero degrees to be detected by the Modular Neutron
Array, MONA.

Finally, the observed decay spectra of 22O", 230” and 2“O” were compared to
simulation. The decay of ”O“ is consistent with a thermalized neutron source, while
neutron unbound excited states of 48 :l: 10 keV and 670 :I: 150 keV were observed
in the decay energy spectra for 230 and 2"‘0, respectively. The theoretical prediction
of the first excited state of 230 is consistent with the measurement. The theoretical
predictions considering the first excited state of 24“O are in fairly good agreement.
Comparison of theory to the measurement confirm a change in shell structure around

N = 16 in oxygen isotopes.

To my wife, Holly

iv

ACKNOWLEDGMENTS

First, I would like to thank my advisor Michael Thoennessen. He has been a constant
source of knowledge, advice and encouragement. He helped me stay on track and
I could not have proceeded to this point without him. I thank professors Thomas
Glasmacher, Alex Brown, Stuart Tessmer and \Nayne Repko for being on my guidance
committee and providing assistance along the way.

I must thank the Operations and Support staff at the NSCL for providing the
beam necessary to perform the experiment of this dissertation. I especially would like
to thank those who helped build the mapping mechanism for the Sweeper Magnet.

I would like to thank the National High lVlagnetic Field Laboratory for building
and testing the Sweeper Magnet.

I would like to thank the members of the MONA collaboration for building MONA
and helping perform the experiment. I would especially like to thank Andreas Schiller,
Jean-Luc Lecouey, Thomas Baumann, Bryan Luther, Joe F inck, Ruth Howes, Jim
Brown, and Paul DeYoung for helpful discussion, advice. and dissertation reading.

I would like to thank John Yurkon his help in building and repairing the charged
particle detectors. I would like to thank Daniel Bazin for help in working with the
charged particle detector system as well as a constant source of advice on COSY.

I would like to thank Heiko Scheit for writing the simulation and for helpful advice
and assistance.

I thank my fellow graduate students for your companionship and support through
the long days and nights of graduate school.

I thank my family and friends for constant support, especially my wife Holly for

her patience and support through this entire process.

Contents

1 Introduction 1
2 Theory and Motivation 5
2.1 Indications for Shell Evolution in Oxygen Isotopes ........... 5
2.2 Previous Experimental Result ...................... 9
2.3 2+ Energy Predictions from Theory ................... 11
2.4 Production of 2“O ............................. 12

3 Method 15
3.1 Decay Energy Reconstruction ...................... 15
3.2 Production Mechanism .......................... 18
3.3 Experimental Setup ............................ 18
3.3.1 Beamline Tfacking Detectors ................... 19

3.3.2 Target Chamber ......................... 23

3.3.3 Sweeper Magnet ......................... 23

3.3.4 Charged Particle Detectors .................... 26

3.3.5 MONA ............................... 28

3.4 Electronics and Data Acquisition .................... 28
3.4.1 Charged Particle Electronics ................... 28

3.4.2 MONA Electronics ........................ 31

3.4.3 Trigger Electronics ........................ 33

4 Analysis 34
4.1 Overview .................................. 34
4.2 Secondary Beam Particle Identification ................. 35
4.3 CRDC Calibration ............................ 36
4.4 PPAC Calibration ............................. 44
4.5 Element Identification .......................... 45
4.5.1 Ionization Chamber Calibration ................. 48

4.5.2 dE Scintillator Calibration .................... 48

4.6 Isotopic Identification ........................... 51
4.6.1 TKE Scintillator Calibration ................... 51

4.6.2 Time-of—F light Corrections .................... 57

4.7 Neutron Processing ............................ 68
4.8 Fragment Reconstruction ......................... 72
4.9 Neutron Decay Spectra .......................... 78

vi

5 Discussion 90

5.1 Simulation ................................. 90
5.2 Comparisons to Simulated Spectra ................... 92
5.3 Physics Interpretation .......................... 96
6 Summary and Conclusions 104
Bibliography 107

vii

List of Figures

1.1

1.2
2.1

2.2

2.3

2.4

2.5

2.6

3.1
3.2

3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11

4.1
4.2

4.3
4.4
4.5

4.6

First excited state energy versus atomic number (4) and neutron num-
ber (N) for calcium isotopes ........................
Schematic plot of energy levels in the nuclear shell model. ......

Effective single particle energies (ESPE’s) vs neutron number for oxy-
gen isotopes .................................
First excited state energy versus atomic number (A) or neutron number
(N) for even oxygen isotopes. ......................
Calculated neutron ESPE’s for 308i (a) and 24O (b) starting with the
151/2 sub—shell. ..............................
One neutron separation energy (Sn) versus neutron number (N) for
odd N, even Z (a) and odd N, Odd Z (b). ...............
Measured y-ray energy spectrum from experiment for 2“O (solid line)
and a simulated (dashed) 'y-ray energy peak ...............
Evolution of the 21+ state in oxygen isotopes. .............

Schematic of the 240 decay. .......................
Schematic of the coupled cyclotron facility and the A1900 fragment
separator at the NSCL ...........................
Experimental setup ............................
Charged particle detector layout .....................
Experimental beamline ..........................
Parallel plate avalanche counters .....................
Sweeper Magnet technical drawings ...................
Cathode readout drift chamber .....................
dB and TKE scintillators. ........................
Charged particle electronics .......................
Charged particle trigger .........................

Energy loss (dE) versus RF time. ....................
Energy loss versus the A1900 Fragment Separator focal plane dispersive
position. ..................................
Time-of-Flight secondary beam identification plot ...........
y—position versus :r—position for the mask of CRDC2 ..........
Mean y-position of both CRDCs versus run number for all charged
fragments in coincidence with incoming 26Ne secondary beam. . . . .
Pad width opad for CRDCI (left) and CRDC2 (right) ..........

viii

10

11
13

16

17
20
21
21
22
24
25
27
29
32

37

38
39
40

41
43

4.7
4.8
4.9

4.10

4.11

4.12
4.13

4.14
4.15
4.16
4.17
4.18
4.19

4.20
4.21

4.22

4.23

4.24

4.25
4.26
4.27
4.28
4.29
4.30

4.31
4.32
4.33
4.34
4.35
4.36
4.37

4.38
4.39

Sample width asample for CRDC1 (left) and CRDC2 (right). .....
Integrated charge for CRDC1 (left) and CRDC2 (right). .......
Integrated charge for IppACl (upper-left), yppAm (upper-right), IEPPACQ
(lower-left), yppACQ (lower-right). ....................
Sample width asampze for {EPPACI (upper-left), yppACI (upper-right),
:cppAcg (lower-left), yppAC2 (lower-right). ................
Pad width opad for $ppACl (upper—left), yppAm (upper-right), mppAcg
(lower-left), yppACQ (lower-right). ....................
Ionization chamber pad peaks versus run number. ...........
Energy loss in ionization chamber versus vertical position at the dE
scintillator (ydE). .............................
Down-right PMT integrated charge versus ydE ..............
Down—right PMT integrated charge versus xdE. ............
dE scintillator energy loss ........................
Energy loss (ionization chamber) versus energy loss (dE scintillator).
TKE scintillator energy loss (arbit. units) ................
TOF of down—left PMT versus down—right PMT after travel time cor-
rection ....................................
Average TOF versus 6x without (top) and with (bottom) 6,, correction.
Corrected TOF tTopcom versus constructed dispersive position 33’ un—
corrected (tOp) and corrected (bottom) ..................
Corrected TOF tTopcon-Q versus sis—position at the reaction target uncor-
rected (top) and corrected (bottom). ..................
Corrected TOF tTopcmg versus y-position at the reaction target uncor-
rected (top) and corrected (bottom). ..................
Corrected TOF tTopcoM versus 9,, uncorrected (top) and corrected (bot-
tom) .....................................
Final corrected TOF tfina] .........................
TKE energy versus TOF tfina] .......................
Projection from TKE versus corrected TOF plot .............
Prompt 'y-ray and neutron peaks in the neutron TOF spectrum.
y—position versus :r-position on MONA. .................
A Sweeper Magnet map with positive dispersive position marked at
both the reaction target and CRDC1 ...................
Dispersive position distribution mm at the reaction target ........

Forward—tracked CRDC1 x-position versus measured CRDC1 :r-position.

Forward-tracked CRDC1 :r—angle versus measured CRDC1 zit-angle.

Forward-tracked CRDC1 y-position versus measured CRDC1 y-position.

Forward-tracked CRDC1 y-angle versus measured CRDC1 y-angle.
Backward reconstructed target. x-angle versus measured target x-angle.
Backward reconstructed target y-position versus measured target y-
position ...................................
Backward reconstructed target y-angle versus measured target y-angle.
Backward reconstructed secondary beam energy versus measured sec-
ondary beam energy. ...........................

ix

45

46

47
49

50
52
53
54
55
56

58
59

61

62

65
66
67
68
69
71

76
78
79
79
80
80

81
81

4.40

4.41

4.42

4.43

4.44

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8

6.1

Reconstructed fragment kinetic energy spectrum (left) and neutron
kinetic energy spectrum (right) for 220* (top), 230“ (middle), and 240*
(bottom). ................................. 83
Reconstructed fragment angle spectrum (left) and neutron angle spec—
trum (right) for unbound 22O“ (top), 230* (middle), and 240* (bottom). 84
Opening angle (60pm) between neutron and charged fragment (left)
and reconstructed decay energy spectrum (20 keV / bin) (right) for 220*
(top), 230* (middle), and 240'“ (bottom). ................ 86
Decay energy spectra for correlated (points with error bars) and un-
correlated (histogram) neutron and charged fragment events for 220*

(top) and 230‘ (bottom) .......................... 87
Top: 240* spectrum with scaled 230‘ spectrum used for the subtraction.

Bottom: Subtracted decay energy spectrum of 240* ........... 89
Decay energy spectrum of 220*. ..................... 93
Decay energy spectrum of 23O"‘. ..................... 94
Decay energy spectrum of 240*. ..................... 95
Oxygen isotope production paths .................... 97
Single particle configurations for unbound states in 230 ......... 99
23O decay energy fit and theory comparison. .............. 100
Single particle configuration for the 2+ unbound state in 240 ...... 101
240 decay energy fit and theory comparison. .............. 103
First excited 2+ state for nuclei near Z = 8. .............. 105

List of Tables

2.1 Two—proton knockout cross-sections comparing calculated measured . 14

4.1 Isotope to total ratio from the production in the A1900 fragment sep-

arator without and with the extended focal plane slits. ........ 36
5.1 Beam properties used within the simulation. .............. 90
5.2 Resolutions used in the simulation. ................... 91
5.3 Mass excess, Edam, and resulting excitation energies for observed states

in 230‘ and 240‘. ............................. 98
5.4 Comparison of theoretical calculations of the first neutron unbound

excited 2+ state in 240 ........................... 102

xi

Chapter 1

Introduction

The atomic nucleus is an unique quantum-mechanical many—body system. The nu-
cleus is made up of two kinds of nearly identical mass particles, protons and neutrons.
The protons and neutrons are fermions; they have a spin of 1/ 2. The neutrons have
zero electric charge while the protons have an electric charge equal in magnitude but
opposite in sign to the electron. The protons and neutrons in the nucleus interact
via the strong nuclear force and the electromagnetic (Coulomb) force. The nuclear
force holds the nucleus together and the Coulomb force pushes the protons apart. The
distance between the nucleons is on the order of 10“15 m because the strong force
only attracts over very short distances. Despite the complicated quantum mechan-
ical interactions of nucleons that comprise the nucleus, experiments on nuclei have
Observed distinctive prOperties.

There are about 2500 nuclei for which we have experimental information, but only
about 300 of these are found naturally occurring on earth [1]. This provides a large
amount Of experimental data to study prOperties of nuclei as they evolve with the
number of protons and neutrons. There are certain numbers of neutrons and protons
that Show specific indicators of the structure of nuclei. These “magic” numbers are
experimentally observed for 2, 8, 20, 28, 50, 82, etc. A high lying first excited state for

even proton (Z) and neutron (N) numbers, lower level density, the large number of

16 18 20 22 24 26 28 30 32 34

 

 

 

 

o I I I I I I f I

36 38 4o 42 44 46 48 50 52 54
A

Figure 1.1: First excited state energy versus atomic number (.4) and neutron number
(N) for calcium isotopes. Data points from: 38"‘6’50’5’2Ca [3], “Ca [4], 42Ca. [5]. 44Ca. [6]
and 48Ca [7].
stable nuclei or more tightly bound nuclei, and large two neutron separation energy
(Sgn), one neutron separation energy (Sn), or one proton separation energy (Sp) are
all indicators of magic numbers of neutrons and protons [2]. The separation energy is
the energy necessary to excite a nucleus to the point where it decays via particle or
multi-particle emission. As an example of neutron magic numbers, Figure 1.1 shows
the energy of the first excited state of calcium isotopes as a function of atomic number
(.4). The large energies for “Ca. and 48Ca indicate the existence of the magic numbers
N = 20 and N = 28. respectively.

To be able to describe the observed properties of nuclei is a continuing challenge for
theory. Due to the complicated nature of nuclei, calculations based on the interactions

of individual nucleons is currently only possible up to .4 ~ 12 and will probably

not be possible for much heavier nuclei due to computation limitations [8]. Since a
microscopic approach is not tractable to heavier nuclei, a model based on effective
interactions in a mean field has to be applied. This approach is known as the nuclear
shell model which resembles the shell structure found for electrons in the hydrogen
atom. The difference between the two shell structures are the Coulomb versus nuclear
and Coulomb forces and the relative size of 10'10 m versus 10‘15 m for electrons and
nuclei, respectively. In contrast to the atomic system, where the electrons move in the
central potential of the nucleus, in the nuclear system the potential for the nucleons,
has to be approximately by a mean potential generated by the nucleons themselves.

In addition to the differences in the calculation of energy levels for electrons and
nuclei, protons and neutrons have a stronger spin-orbit coupling force than the atomic
system. The shell model structure shown in Figure 1.2 (adapted from Reference [9])
shows the energy separations for major shells for a spherical potential with a strong
spin-orbit coupling. The number of nuclei summed up to major shell closures corre-
spond to the magic numbers observed in experiments on stable nuclei, which illustrates
the success of the nuclear shell model. There are many approaches to calculate the
many different parameter sets of the nuclear shell model. In general, theories can be
accurate to within a few hundred keV of experimental values [1]

Based on the observed behavior of stable nuclei, a reasonable assumption would
be that magic numbers at stability continue out to the neutron deficient and neutron
rich nuclei at the driplines. The driplines mark the limits of nuclear binding and are
located at nuclei that are unstable to proton decay (proton dripline) or neutron decay
(neutron dripline). The assumption that shell structure does not change away from
stability is not generally correct. For example, the neutron number of N = 14 has been
shown to appear as a. magic number for 22O [10] which has six more neutrons than the
heaviest stable oxygen isotope. The experimental confirmation of new magic numbers
or the disappearance of known magic numbers due to changes in shell structure far

from stability is a current topic of research in nuclear physics.

Angular Spin-Orbit Coupling Number of Magic
Momentum (1/2,3/2,5/2,7/2,...) Nucleons Number
\\ Shell Total
\_ ”15/2 (15,—[IeLj—184
, 3d‘3/2 [120-
—LS——7£--4SI/2 ‘-
2 7y ____.__ .—
, -3d—’<,,/ g 2 Nita—(gi-
Gfgg —29——<\\ 3a»; (61-—
3" . I ~ 29% , (10)—
—-II .(
\\
\ 1 i 13/2 —— (141-41261—126
,--3p‘/2 (21-
-3p‘_‘~--3p3f- (4)-
2f c" 2f5/2 (5)-[ 1
"" ~-.———2f 7/2 (Bl— 100
Sing 1 9 . _
odd I 1’ ‘Ih I2 I10}
_]h._..—r‘
‘\
‘~ 1 1h"/2———-—(]§I-—I32l—-32
— -—----35 I , I“
2: (PE—2:131; — (1.)—
4h u _' ‘ ~ ‘ 2d 5/2 l 6 l- [61d
even ll I9772 FT (8)-
-19——<:
‘\ 199/2 , (‘lOf—lSOl———50
x“ 2p V; 5 (2 F—Iggl
3m {—ZP—txrzp‘h if 12 4- ]gtl 1
odd --lf —-<.\
‘ 1f7/2 IB'l-[ZBJ—ZB
~25—-—~ ,————. id3/ (4i—I201—20
33:; {—1d—gi‘-25'f2 2 (21-4161
~——--id5/2 lei—[11.1
“-1sz (ZI—IBI—B
33;: -1P-— ‘-—Ip3/2 (Al—(61
0 —Is------—Is‘/2 I2)-—[2]———2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.2: Schematic plot of energy levels in the nuclear shell model adapted from
Reference [9]. The first column lists the principle angular momenta levels from the
harmonic oscillator potential, the second column includes the ”spin-orbit potentials,
the third column labels the sub-shell and total occupancy, and the last column rep-
resents the magic numbers.

Chapter 2

Theory and Motivation

2.1 Indications for Shell Evolution in Oxygen Iso-
topes

A change in shell structure has been predicted for neutron-rich oxygen isotOpes. The
two plots shown in Figure 2.1 show the effective single particle energy (ESPE) based
on the “universal SD” (USD) and the Kuo—Brown G—matrix calculations for oxygen
isotopes [11], where the effective single particle energy corresponds to the energy level
for a nucleon in a particular sub-shell by taking into account the forces of the other
nucleons. The USD interaction is based on an empirical fit of known data within the sd
major shell [12,13] and the G-matrix uses an effective mean field potential [14,15]. The
even-neutron isotopes of 22’2“st are marked to emphasize the shell gaps expected
in the calculations. A magic number is interpreted as a large energy gap between
sub-shells. The neutrons in 22QMSO occupy the sd major shell which is made up of
the sub-shells 0d5/2, 151/2 and 0(13/2. A gap between the 151/2 and 0(13/2 sub-shells
for neutrons in the calculations predict 24O to be a doubly-magic nucleus like 160,
which means that both N and Z are magic numbers. The two calculations differ in
the prediction of 22O as a doubly magic nucleus due to a difference in the expected

sub-shell energy gap which would be reflected in the energy of the first excited state

 

 

 

 

 

 

5 T j' I Tj T f I I I T T—I T [if rm l I j T TM Y I [fl I j l T
. USD G matrix -
_ 0d3 28 0d3 -
OJ
.2. - 0 ~
E _ 1s1 24o '
8 . 0d
22
-5 *- 0
_10 r . i I; i L r I i 1 r J J . 1 i
5 10 15 20 5 10 15 20
Neutron number Neutron number

Figure 2.1: Effective single particle energies (ESPE’s) vs neutron number for oxygen
isotopes. Shell model calculations using USD (left) or G-matrix (right) from Reference
[11]. Open circles indicate filled sub-shells for 220, 24O, 280, respectively.

as shown in Figure 2.2. Figure 2.2 shows the high lying excited state supporting the
USD calculations for the doubly magic nature of 22O [10]. Both calculations agree on
the prediction of the new magic number of N = 16 which is the topic of the present
thesis.

Neither magic numbers of N = 14,16 are observed near stability as a result of a
small sub-shell energy gap. The spin-isospin component of the nucleon-nucleon force
has been suggested as the reason for this change in structure far from stability [17].
The nucleon-nucleon interaction used in Reference [17] is a product of isospin (7') and
spin (a) operators. The tensor resulting from this product has large attraction for
protons and neutrons of the same orbital angular momentum (l) and Opposite spin
giving total angular momentum of j> = l + 1/2 and j< = l — 1/2. The overlap of
opposite Spin and isospin wave functions with the potential above yields an angular
momentum independent energy shift, making this overlap a monopole interaction [18].
Figure 2.3 shows the difference between the 0d3/2 orbital for neutrons in 30Si and 24O.

The filling of the 0d5/2 orbital for protons in 308i makes neutrons in the 0d3/2 orbital

 

 

 

o I I I I
14 16 18 20 22 24

A

 

Figure 2.2: First excited state energy versus atomic number (A) or neutron number
(N) for even oxygen isotopes. Data points taken from References [3,16].

Rl

 

CD

 

 

_ (a) }pf shell-— (b) .-

30 . «-—— 24
14SI16 ’x 0d3/2 8016

 

 

 

 

 

 

ESPE (MeV)
.b

O

 

 

 

 

 

 

Figure 2.3: Calculated neutron ESPE’s for 30Si (a) and 24O (b) starting with the 131/2
sub-shell. The change of the 0d3/2 sub-shell is indicated by the dotted line connecting
(a) and (b). The occupation of proton and neutron sub-shells is shown for 308i (c) and
24O (d). The major interaction generating the difference in the sub-shell of 1d3/2 in 30Si
and 24O is represented by the Wiggly line in (c). Figure adapted from Reference [17].
more bound than for 240 where there are no protons in the 0d5/2 orbital. The effect
of even one more proton in the Dds/2 explains why 2SF is bound and 2SO is not. The
monopole effect in this calculation is stronger than the pairing effect because 26O is
neutron unbound. As a result of the monopole interaction, 24O is expected to have
an increase of the energy gap between the 0d3/2 and 131/2 sub—shells for neutrons as
compared to nuclei closer to stability.

The first experimental evidence for a large energy gap between the 0d3/2 and 131/2

sub-shells for neutrons in 24O came from experimental observation of the one-neutron

separation energy. Figure 2.4 is adapted from a study of one-neutron separation energy

(Sn) as it changes across neutron number [19]. Each joined set of points is for one value
of the isospin number (T 2), which moves across many different isotOpes. Decreases in
the one neutron separation energy with an increase of neutron number are a good
indicator for a magic number as the result of a large energy gap between sub-shells.
The N = 8 magic number is indicated on the plot by a vertical line along the Tz = 1/ 2
line of the one neutron separation energy, where the nucleus to the left is 13C and to
the right is 17O. The break for N = 8 is also visible for T 2 = 0 between the nuclei
14N and 18F as well as for Tz = 1 between the nuclei 12B and 16N. Another important
feature for the magic number of N = 8 is that evidence for it disappears for the
T2 = 3/ 2 line between 11Be and 15C. Also to be noted is the break for N = 20 for
many values of T z. The N = 20 magic number disappears for T 3 = 9/2 between
29Ne and 33Mg which is consistent with the result of 32Mg at T2 = 4 [20]. The next
noticeable feature is the unexpected clear break for the one neutron separation energy
for the Tz = 7/2 line at N = 16, between 230 and 27Ne. This new break does not exist
for nuclei near stability and is an indication for the evolution of the shell structure

leading to a new magic number for nuclei near the dripline in this region.

2.2 Previous Experimental Result

The one-neutron separation energy trends and theoretical calculations indicate that
24O has a new closed shell at N = 16 due to an enhanced sub-shell energy gap, which
would make it doubly magic. A cy-ray and charged particle coincidence experiment was
performed to search for the first excited 2+ state of 24O decaying to the 0+ ground
state [21]. The experiment measured 'y-rays in coincidence with 20213233240. The
spectrum shown in Figure 2.5 [show that there is no y-ray in coincidence with 2“O.
The first 2+ excited state is expected to have a configuration with one neutron in both
the 1.91/2 and 0d3/2 sub-shells. Therefore the experiment is consistent with a larger

energy gap between the 151/2 and 0d3/2 neutron sub-shells as compared to nuclei near

 

1%

10

4:;

Sn (MeV)
O N

 

 

 

 

ON-PCM

 

 

 

 

 

 

Figure 2.4: One neutron separation energy (Sn) versus neutron number (N) for odd
N, even Z (a) and odd N, odd Z (b) adapted from Reference [19]. The lines connect
points with the same T; values, which are noted to the side for clarity.

10

 

 

 

340‘
O f E
25 if
E ' iii!
20 .5 it:
:~; 5:5 s
15 a r f 3.
4 r i
‘0 E- . i i =|
" ' '5 . z, I _."1‘
5 I II ::I- iii] 11". {III E.
o . . . AI.“
0 2000 4000
E,(keV)

Figure 2.5: Measured 'y—ray energy spectrum from experiment for 2“O (solid line) and
a. simulated (dashed) 7-ray energy peak [21]. The y-ray peak was simulated with an
energy of 3.7 MeV assuming 20% Of the 24O is produced in the 21+ state. The lower
limit of the production to the 21+ state based on the data was 3%.

stability. It is noted here that the experiment also found that the first excited state

of 23‘0 is neutron unbound. This requires a different experimental method to be used

to confirm the doubly magic nature of 24O since the state is likely to be unbound to

neutron emission.

2.3 2+ Energy Predictions from Theory

There have been several calculations that predict the energy Of the first excited state
for 24O. Figure 2.6 shows a comparison of results from theoretical calculations to
experimentally measured data for the first excited state of 2+ for even oxygen isotopes.
The experimentally known points are for 1820320 [3,16]. The theoretical calculations
cover a wide range of methods. An Antisymmetrized Molecular Dynamics (AMD)

calculation [22] is inconsistent with the data. Somewhat better agreement is achieved

11

by a quasiparticle random phase approximation (QRPA) calculation with Skyrme
and pairing forces in [23]. In general shell model calculations show better agreement
to the measured energies. A Monte-Carlo shell model using the USD and Kuo—Brown
potential [24] and calculations using the Warburton-Becker-Millener-Brown (WBMB)
hamiltonian [25] and USD with continuum [26] are all consistent with the first excited
state energies of the data. Additional calculations performed for 240, a Random Phase
Approximation (RPA) using the Gogny-DlS force [27] and a shell model calculation
using the new USD interaction [28], predict that the excited state is above the one-
neutron separation energy. Though not all theories reproduce the data, they all predict
the 21'" excited state of 2“O to be unbound with respect to one-neutron emission,

consistent with the non-observation of a 'y-ray transition [21].

2.4 Production of 24‘0

To detect neutron—unbound decay, from excited states of 240, the states have to be
populated. The predicted configuration for the excited state are one particle—one hole
(1p - 1h) couplings of a Odin-18172 with states of total angular momentum J = 1*, 2+
or a 0c11,.1,/2-0d‘;)'/12 with states of J = 1+, 4+ [11], where the first two excited states are
expected to be 2+ and 1*, respectively. Possible choices Of populating 24O excited
states are one-proton removal from 25F or two-proton removal from 26Ne. If 24O is
assumed to behave like a doubly-magic nucleus, another proton added to 24O would
be at a high energy. 25F could then be thought of as a 0d5/2 proton coupled to a
24O core. Therefore one-proton stripping of 25F would be expected to populate the
ground state with a much higher cross-section than the excited state in 24O. With an
estimated spectroscopic factor Of 3% [28], the estimated cross-section from the 25F
ground state to the first excited 2+ state of 24O was approximately 0.12(:I:0.018) mb.

In comparison, the cross-section of 26Ne in the ground state to the first excited 2+

state was approximately 0.035 mb (see Table 2.1). The two-proton removal from

12

 

MeV

 

 

 

 

14 16 18 20 22 24 26

Figure 2.6: Evolution of the 21+ state in oxygen isotOpes. The dashed line marks
the one-neutron separation energies for even oxygen isotopes of 16O (15.6637 MeV),
1BO (8.044 MeV), 20O (7.608 MeV), 22O (6.85 MeV), and 240 (3.61 MeV) (from
Reference [29]). The theoretical calculations are A: Obertelli [27], x: Khan [23], D:
Siiskonen [25], I: Volya [26], o: Utsuno [24], +: Brown [28], A: Thiamova [22]. The
experimental points are 0: Firestone [3] and Belleguic [16] where the error bars are
within the closed circles.

Table 2.1: Two-proton knockout cross-sections comparing calculations of two different
models to measured values where applicable. When the final states are not resolved,
“all” is mentioned instead of the level energy.

 

Beam energy Final Level energy 0(“)_2p oexp
(MeV/u) nucleus (MeV/ u) (mb) (mb)
82 28Mg all 1.8 1.5(1)
88 30Mg all 1.3 049(5)
67 34Si all 2.2 0.76(10)
28 9He all 0.7 z 0.35
83 24o 0 0.35904 -
83 24o (4.18) 0.035(5) -

 

“calculated with model from [31].
bnew version including proton correlations [32].

26Ne was chosen because the expected beam rates at the National Superconducting
Cyclotron Laboratory were approximately a factor of 50 larger for 26N e compared to
25F which made up for the difference in calculated cross—sections [30]. The two-proton
cross-section was calculated using a model assuming a direct two-proton stripping
reaction based on Reference [31]. Table 2.1 shows comparisons of calculated two-
proton removal and measured cross-sections which agree within a factor of two. This

provides confidence in the two-proton removal cross—section predicted for the excited

2+ state of 240.

14

Chapter 3

Method

3.1 Decay Energy Reconstruction

The goal of the experiment was to measure the neutron unbound state(s) of 2‘IO. 240
was produced using a two-proton stripping reaction from the secondary beam of 26Ne.
Then the decay products, 230 and a neutron, were measured in coincidence. The neu—
tron was detected in the Modular Neutron Array (MONA) and the fragment’s prOp-
erties were measured using the Sweeper Magnet and charged particle detectors. The
Sweeper Magnet bent the 26Ne beam and charged fragments away from the beamline
direction. The neutrons continued in the direction of the beamline to MONA. Figure
3.1 shows a schematic of the decay. The decay was fully characterized by measuring
the momentum vectors in the lab frame, which were constructed by measuring the
energies and angles of the neutrons and charged fragments.

The decay energy is the energy above the one-neutron separation energy and is
calculated using conservation of energy and momentum. The derivation is performed

in four-vector notation for the charged particle p; and neutron pn:

Pr = (Er, Pi) (3-1)

15

 

 

 

Figure 3.1: Schematic of the 24O decay.

p.n = (Ema) (3.2)

The constant m is calculated using the four-vector product, which is constant
regardless of the inertial frame the particles are in. The square of the invariant mass
mm is calculated from the four-vectors (Eq. 3.3) giving two terms; one that depend on
the masses and a cross-term that depends on the energy (momentum) of the fragment
and neutron as well as the opening angle between them, O, also shown in Figure 3.1.

The square of the sum of the two four-vectors mg, is calculated using:
m?n = (pf + p,,)2 = pf2 + pn2 + 2pfpn = m: + m: + 2(EfEn —- prpn cos O) (3.3)

where rm and mIn are the fragment and neutron mass, respectively. The decay energy
Ed is then the difference of the invariant mass and the sum of the fragment and

neutron masses:

 

Ed = \/m.';’ + mg + 2pm:n —— W, cosO) — (m, + mm) (3.4)

16

.mcfimmu oszoEom E or

95383 m>_m.mam_u/\ _ _ _ _ _ _ _ fl _ , _
.. l .. .. cow

    

898 :8 939.6
cocoa—Ooh

  

 

 

5828
use: com 2

 

cc:
@5338

 

/ oomx

953 .88

«8.8 $0.58 co_

 

~5me

Figure 3.2: Schematic of the coupled cyclotron facility and the .A1900 fragment sep-

arator at the NSCL.

17

3.2 Production Mechanism

The experiment was performed at the National Superconducting Cyclotron Labora-
tory (NSCL). The layout of the facility is shown in Figure 3.2. The primary beam of
40Ar was produced in the ion source, entered the K500 cyclotron, and was accelerated
to an intermediate energy of 12.5 MeV / A. The beam continued to the K1200 cyclotron
where it was stripped Of electrons and accelerated to 140 MeV / A. The primary beam
intensity for data taking was ~1.9 epA (~105 pnA) as measured at the exit of the
Coupled Cyclotrons. The 26N e secondary beam was produced by fragmentation from
the primary beam on a 893 mg/cm2 natural Be production target at the entrance
of the A1900 Fragment Separator [33]. The A1900 uses dispersive dipole magnets to
separate the beam particles by magnetic rigidity Bp, the product of magnetic field
and bending radius which is equal to the momentum—to—charge ratio. The A1900 con-
sists of two mirror symmetric halves with a dispersive focal plane in between. This
dispersive focal plane contains an achromatic degrader of 750 mg/cm2 acrylic and
momentum slits to limit the momentum acceptance. The A1900 was set to different
Bp values for the first and second half of the separator, 4.01930 Tm and 3.58098
Tm, respectively, in order to select the 26N e nucleus. A timing detector located at the
exit of the A1900 was necessary for identifying the 26Ne particles at the experimental
setup. The Bp of the 26Ne after the timing scintillator was 3.56931 Tm. The beam

purity was better than 80%.

3.3 Experimental Setup

The experimental setup is shown in Figure 3.3. It includes the tracking of the incoming
beam particles. The neutrons are detected around zero degrees with the modular
neutron detector array MONA. The experiment performed requires tracking the paths
of particles in front and behind the reaction target. The time-of—flight Of the neutron

is used to obtain its energy, and a position measurement is made to calculate the angle

18

of the neutron assuming a point-like target. The charged particles were deflected by
the Sweeper magnet and detected and identified by a set of position sensitive, energy
loss and energy detectors. The charged particle energy and angle at the reaction target
were reconstructed from the measured angles and positions from the charged particle
detectors using a matrix that calculated the trajectories from the field of the Sweeper
Magnet.

For particle tracking in front of the target, the secondary beam passed through
two parallel plate avalanche counters (PPACs), which measure x,y positions and to-
gether provide direction. The x,y position of PPAC2 and angles of the beam were
used along with the quadrupole triplet transfer matrix to track the x,y positions and
angles forward to the reaction target. For timing Of the incoming particles, a timing
scintillator detector was placed in front of the target, which provided a time reference
right before the reaction target.

The charged particle detectors included two cathode readout drift chambers (CRDCs)
to measure x,y position shown in Figure 3.4. The remaining detectors were used in
obtaining isotOpic separation. The ionization chamber and dE scintillator were used
for element separation and identification by measuring the energy loss Of the charged
particles in each detector. The dE scintillator also generated the charged particle
trigger. The time-of-fiight measurement and energy measured in the TKE scintillator
provided isotopic identification. The time-of—flight was constructed between the dE
scintillator and the timing scintillator in front of the target. The TKE scintillator

stopped the particles and measured the remaining energy.

3.3.1 Beamline Tracking Detectors

The secondary beam traveled down the beamline to the reaction target, shown in
Figure 3.5. The secondary beam first passed through the PPACs, which were filled
with 5 Torr of iso—butane gas, see Figure 3.6. The traversing beam excited the gas

separating the molecules into positively and negatively charged ions. There were three

19

>95
.9923 :3sz

22023
22th 89ch

 

.093 .5389
.2098 9:8:

 

906925 02:23 coEmoa

  

      

  

   

639: 539.5
633 0.8233

    

- I—I

Figure 3.3: Experimental setup

20

Vacuum Box

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CRDC1 Ionization Chamber a
I CRDC2
——>
”3.9.919 ..................................................................
Height
.2... ‘v 1.870 m c <
dE Scintillator g

 

 

 

 

 

I
TKE Scintillator

Figure 3.4: Charged particle detector layout

quadrupole triplet

 

 

 

 

 

 

 

 

 

 

 

 

elements
TA TB TC 0.638 m
PPACs _. fl”?
_ A reaction target
—— 2.718 m —— 2.143 m __ -
3568 m
A1900 timing timing
detector scintillator

Figure 3.5: Experimental beamline

21

anode

.charged particle

electron

 

cathode
strips and

pads

Figure 3.6: Parallel plate avalanche counters

22

parallel plates in each PPAC. The central plate was held at a positive voltage of 580
V to collect the electrons. The charge collected by the central plate induced an image
charge on aluminum strips which were connected to pads placed along both directions.

There were 128 pads spaced on both axis with a pitch Of 1.27 mm.

3.3.2 Target Chamber

The target chamber included a timing scintillator and the reaction target. The reac-
tion target was natural Be with a measured thickness of 721.3 mg/cm2. The scintil-
lator was made of BC-404 material with a thickness of 0.254 mm. The beam passed
through the scintillator producing electron-hole pairs emitting light during recombi-
nation. The light was detected by one photo multiplier tube (PMT) mounted to it.
A PMT converts photons into electrons with a photosensitive layer, called the pho-
1 tocathode. The electrons from the photocathode are multiplied by a multiplication

structure which increases the number of electrons by factors of more than 10 million.

3.3.3 Sweeper Magnet

The superconducting Sweeper Magnet was built by the National High Magnetic Field
Laboratory at Florida State University [34]. It is designed to bend particles up to
4 Tm at a 43 degree bend from the beamline using Niobium-Titanium (Nb-Ti) coils.
The vertical gap of 14 cm provided a large opening for the neutrons produced in the
reaction to pass through. Mechanical diagrams Of the design are shown in Figure 3.7.
There are two resistive coils (trim coils) placed on the outer edge of the magnet on
the opposite side of the return yoke so that one could place magnetically sensitive

detectors next to the magnet.

23

Satellite Cryostat Resistive Coils

I
I.
t
I
l
I
n
I
l
I
I
I
..
I
I
I
I
-
-
-
-
..
u
-

 

Magnet Cryostat Nb-Ti Coils

Figure 3.7: Sweeper Magnet technical drawings

24

frisch grid

 

II

anode

+750V

 

J
/

 

charged particle track /

 

 

~950V

  

F ioniization of the gas

 

electron drift

 

 

 

 

 

 

 

 

    

  

I. lg/é.
I [I /////////////I
I. I///////// // //z
I._ lg/f/f/é
I l7///7// ///////x

l/_/ ///_///////,
I In////// 47/4.
I lz/////_///////
I r//////////////

        

   

   

    
 

     

 

 

girl/Illa

 

l
274

   

 

1»

resistor 4

>
‘>

chain

 

cathode

pads

Figure 3.8: Cathode readout drift chamber

25

3.3.4 Charged Particle Detectors

Cathode Readout Drift Chambers (CRDCS) in the schematic shown in Figure 3.8
were used to detect the position of charged particles. They were filled with 20% iso-
butane and 80% CF 4 at an operating pressure of 50 Torr. The gas mixture enabled
the particles to pass through the detectorliberating charge pairs without creating an
avalanche effect. The pairs were separated by an electric field produced by a plate at
~950 V, which was connected through a resistor chain to a set of aluminum strips. At
the end of this region, the electrons passed through a Frisch grid at -10 V and were
collected by an anode wire held at 750 V. The region near the anode wire produced
a small avalanche that increased the number of electrons available for collection. The
x-direction was determined by using cathode pads to detect the induced charge from
the anode wire. There were 128 pads with a pitch of 2.54 mm. The position in the
y-direction was measured by the drift time, determined by the time difference of the
trigger and the anode wire signal.

The ionization chamber was designed to help determine the particle charge by
measuring the energy loss. The gas used Was P-10, which is composed of 90% argon
and 10% methane at an operating pressure of 150 Torr. The particles passed through
the volume dissociated charge pairs and the electrons were pushed towards the 16
collection plates at the bottom of the chamber with a high negative voltage, approx-
imately -1000 V. The collection plates were held at a positive potential, typically
100 V. The plates were used to reduce the overall noise as compared to using one
large plate for collecting the electrons. Combining the 16 signals gave the energy loss
measurement.

The plastic scintillators were made of BC-404 material with the dE scintillator of
thickness 0.5 cm and the TKE scintillator of thickness 15 cm, shown in Figure 3.9.
Both scintillators had four PMTs to detect the light produced by the scintillator.
The dE scintillator used light guides to direct the light to the PMTs. The PMTs were

operated at a voltage range of 1500-2000 V. The PMTs were labeled according to

26

l
L 0.50 cm

29° up-right (ur)

up-left (ul) \‘3/ /
j

95.00 cm 55.00 cm ® dE scintillator

__L «

 

 

 

 

 

 

 

r—“*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PMT
/ 55.00 cm .
down-left (dl) down-right (dr)
active area
40 x 40 cm
1
15.00 cm J
55.00 cm -
l ’ 7
55.00 cm ® TKE scintillator
~ H v 55.00 cm

 

 

 

Figure 3.9: dB and TKE scintillators where the beam direction is into the page.

27

their position with respect to the beam direction designated up-left (ul), down-left

(d1), up-right (ur), and down-right (dr).

3.3.5 MONA

MONA, the Modular Neutron Array, is designed to detect high-energy neutrons with
high detection efficiency and consists of 144 scintillators arranged in 9 layers of 16
detector modules [35,36]. Each module has dimension of 2 m by 0.1 m by 0.1 m. MONA
was placed at a distance of 817(2) cm from the reaction target. Neutrons scatter off
protons or carbon of the scintillator producing light. The light was collected at the
end of each module with a light guide and a PMT. The energy of the neutrons was
calculated by the time-of-flight from the timing detector in front of the target to a
module. The angle was calculated by measuring the position in MONA. The horizontal
(x) position was reconstructed by measuring the time difference of the signals from
each end of the bar with a position resolution of 7.5 cm. The vertical (y) position and
the position along the beam direction (2) were determined from the location of the

module giving a position uncertainty of :l:5 cm. The time resolution was <1ns.

3.4 Electronics and Data Acquisition

3.4.1 Charged Particle Electronics

Figure 3.10 shows the readout electronics for the beamline and charged particle de-
tectors used in the experiment. The pad signals were digitized with the Front-End-
Electronics (FEE), which samples the pad pulse. The time sampling was 200 ns and
25 ns for the PPACs and the CRDCs, respectively. The readout was controlled with
three programmable logic modules (Xilinx Logic Module, XLM) one module for both
PPACs and one module for each CRDC. The PPAC data were saved in a continuous

sampling mode where the trigger indicated that a valid event had occurred. Upon re-

28

 

 

E 555550" Boo
Tl .5.an 5.530
T 5350 cone”.

:25550 556 555.2 5595

 

 

 

a: cum m: m >550

 

tfiw

993.35%
mvz. Dcm up

 

 

 

 

Emmy 000

VET

 

a: o9
A 5.5m:

 

0.00 OD<

 

VT @Tl

5.8m

 

 

A 08:
A mums 585.

 

.mnEmco c2535.

 

m: com «.50

 

 

Am? l «E

2? 30cm 58%

xN

 

 

 

85551 509.55%
@All

 

 

mono mo
.. a... e 85

 

 

 

 

 

Em t a
m: 2550

 

599 20:95; .6 Eon.—
E 5598 mEEP

 

 

E Q
mc 09.
@t

 

 

E Al
ram 85

 

 

 

58:... Y— 2._x_ lvA HHH T

 

 

 

E @l

 

 

mama 5858 our
”89> XN
mama 2558 mm? O<n_n_
58-x
5555c
use: 8o. 2

 

 

 

 

 

ta VEAllll‘fivl .8 L
tom

 

53E 5555.

Figure 3.10: Charged particle electronics

29

ceiving this signal, the XLM searched for data at a specific time range in the past to
find the particle signal passing through the detector. The continuous sampling mode
was necessary for the PPACs because the anode plate does not provide a quality
stop signal. In contrast, the CRDCs recorded data only when the trigger signal was
received. Upon receiving this signal, the XLM recorded data until it received a stop
signal generated by the anode wire. The data were recorded if the signal was above
the hardware threshold set within the XLM.

The anode wire signal was sent through a preamplifier and shaped by a Time
Filter Amplifier (TFA). The threshold of the Constant Fraction Discriminator (CFD)
was matched to the voltage setting of the anode wire. The CFD internal delay was set
to 200 us. The output of the CFD was split and sent to the Multi—Hit Time-to-Digital
Convertor (TDC) and XLM as the stop signal and into a Scaler. The start for the
TDC and XLM was the master trigger. The time difference between the anode signal
channel and the trigger reference channel was used as a. measure of the y-position.

The logic signal of the timing scintillator detector at the end of the A1900 came
from the A1900 to experimental vault and was sent to a sealer and used as the stop for
the Time—to—Amplitude Convertor (TAC) where the TAC start was the master trigger.
The output amplitude of the TAC was prOportional to the time between the timing
scintillator detector at the end of the A1900 and the master trigger corresponding to
the time of the thin scintillator. The signals were digitized in an Analog-to—Digital
Convertor (ADC). The timing scintillator in front of the reaction target signal was
delayed by approximately 100 ns and sent into a CFD with an internal delay of 3 ns.
This signal was split and used for the stop fed into the TDC and the scaler. The
master trigger was the common start for the TDC.

The ionization Chamber’s anode pad signals were amplified by preamplifiers and
a shaper. The shaper for each channel was set for maximum gain and the shaping
time was 3 us. The shaped signals were delivered to a peak sensing ADC. The signal

amplitudes were proportional to the energy loss of the charged particles as they

30

traversed the distance of the chamber.

The dB and TKE scintillators each had four signals. The integrated signal charge
from the dB and TKE scintillator correspond tO the energy loss of the particles
passing through it. The signals for both were split and one was used as a stOp for a
time measurement of each PMT relative to the master trigger after conversion in a
CFD (internal delay of 3 ns) and the other was used for the charge integration of the
signal.

The start for the time measurement was the master trigger which was generated
using an ’OR’ of the four dE scintillator PMTs. The trigger details will be addressed
below. The charge integration was performed using a Charge—to-Digital Convertor
(QDC) after a delay of 100 ns. This delay was made as small as possible to minimize

the signal attenuation due to cable length.

3.4.2 MONA Electronics

Each MONA PMT was connected to a QDC to integrate the charge of each signal and
a CFD for conversion into logic pulses as an input to a TDC [35, 36,37]. There were
288 individual channels for the QDCs, CFDs, and TDCS. The CFDs also provided an
additional output to be provided to the trigger logic. XLMs were utilized to handle
the complicated trigger logic for MONA. The trigger logic was divided into two parts,
level-1 and level-2. Level-1 handled each of the 9 individual layers providing input to
scalers, QDC module gate generation and checks that at least one detector module had
two PMTs fire. If one detector module had two PMTs fire, the level-2 logic registered
a. MONA trigger which started the process of waiting for a sweeper electronics trigger
for approximately 200 ns. The level-2 logic generated the computer ’GO’, fast clear,

and inhibited the CFDs until the detector was ready for another event.

31

MONA trigger

___, OFF
Fast Clear
From MONA
MONA Coincidence Gate

 

A

. Computer ‘GO’
~50 ns

"200 "3 ~200 ns From MONA

 

To MONA

 

 

Sweeper Gate

M t T' ‘ON’
('OR’ofde PMTs) as er "gger

 

 

 

500 ns delay —> —|7
Common Start -§— XLM Start
Trigger Reference
Gate (10 us) —->-<—

Gate (160 ns) —->-<-—

 

 

 

 

v

-| <—

Sca 3' Multi Hit TDC
XLMs

 

 

 

Figure 3.11: Charged particle trigger

32

3.4.3 Trigger Electronics

The sweeper trigger generated by the ’OR’ Of the four thin scintillator PMTs was sent
to the MONA trigger logic for processing, a scaler, and also generated several gates
and starts, as shown in Figure 3.11. If the MONA level-2 logic received a sweeper
gate within the MONA coincidence gate, the computer ’GO’ and master trigger ’ON’
conditions were set. If no sweeper gate was generated within the coincidence gate a
fast clear was sent to all the QDCs and TDCs of MONA as well as the TDC, QDC, and
ADC of the sweeper electronics. After a fast clear, a data ready state was achieved
within approximately 700 ns. For a valid event, the master trigger ’ON’ was received
after approximately 450 ns. The master trigger was included in an ’AN D’ gate with a
delayed sweeper master gate. This start was then used for all the sweeper XLMs and
the Multi-Hit TDC. The triggering was handled in this way for the Multi-Hit TDC
and XLMS because they had no fast clear capability.

The online analysis was performed with SpecTcl [38] and the data were recorded

on DLT tape for storage and Offline analysis.

33

Chapter 4

Analysis

4. 1 Overview

The data analysis was performed off-line using Physics Analysis \Vorkstation (PAW)
[39] and energy loss and kinematic calculations were performed with LISE++ [40].
Calibration runs before the experiment as well as off-line calibrations were necessary
for the detectors. After calibrations of the charged particle and beamline tracking
detectors, neutron and charged fragment reconstruction, the analysis of the data was
performed.

All TDCs were calibrated with evenly spaced timing pulses from a time calibrator.
Mask runs for the CRDCs and PPACs were performed to determine the x,y positions.
The energy losses from the ionization chamber, dE scintillator, and energy deposited
after the other detectors in the TKE scintillator were calibrated and position corrected
using the position information of the CRDCs. The charged fragment time-of-flight was
corrected using measured positions and angles to provide the isotopic separation. After
these steps were performed, gates on incoming 26Ne secondary beam and different
isotopes were possible.

Cosmic ray data were recorded to calibrate the position along the length of the

bars of MONA. A thick target was used to stop the secondary beam producing y-rays

34

as well as neutrons, which determined the absolute Offset of the time-Of-fiight for all
of MONA.

The Sweeper Magnet’s magnetic field was carefully mapped. Ion-Optical transfer
matrices were calculated for the Sweeper Magnet and the quadrupole triplet with
COSY Infinity [41]. Data runs with discrete Sweeper Magnet settings using secondary
beam were performed to verify the ion-optical transfer matrices.

Finally momentum vectors of the neutrons and charged particles at the reaction
target were reconstructed and isotope gates of 210, 220, and 230 were used to re-
construct the decay 22O“ ——> 210 + n, 230* —-+ 22O + n and 240" ———> 230 + n,

respectively.

4.2 Secondary Beam Particle Identification

Figure 4.1 shows the secondary beam produced from the A1900 Fragment Separator.
The RF time was the cyclotron frequency relative‘to the electronic trigger of the
A1900 data acquisition system. The secondary beam particle of interest was 26Ne,
which was the second highest isotope produced for both the 3% and 1% momentum
acceptance settings. The main contaminants were 29Mg, 27”N a, 24F and lighter parti-
cles produced mainly in the wedge at the dispersive focal plane of the A1900 fragment
separator. To reduce the contaminants, the A1900 extended focal plane slits (XFP)
were placed at i10 mm, shown in Figure 4.2. Table 4.1 shows the change of the rate
of secondary beam contaminants without and with the extended focal plane slits.
The purity for 26N e was increased from approximately 13.5% without extended focal
plane slits to approximately 93.2% with extended focal plane slits.

The secondary beam time-of-flight spectrum was calculated based on the cali-
brated times of the timing detector at the. exit of the A1900 and the timing detector
in front of the reaction target. The time Offset was determined with the knowledge of

the expected central magnetic rigidity (Bp) for 26Ne Of 3.56931 Tm and the distance

35

Table 4.1: Isotope to total ratio from the production in the A1900 fragment separator
without and with the extended focal plane slits.

Isotope no slits slits
27Na 52.9% 0.6%
26Ne 13.5% 93.2%

 

29Mg 10.6% -
28Na 2.0% -
24F 0.8% -

 

between thescintillators (36.68 m, see Figure 3.5). Figure 4.3 shows the calibrated
beam time-of-flight spectrum with the identification of 26Ne and 27Na along with
light fragments. 26Ne was clearly separated and a gate around it was applied before

calibrating any other detector.

4.3 CRDC Calibration

The position calibration Of the CRDC in the dispersive plane (I-pOSlthD) was deter-
mined by the pad pitch 2.54 mm. The position calibration in the non-dispersive plane
(y-position) was determined by sweeping beam across the detector with a mask placed
in front of it with holes drilled at known positions (see Figure 4.4). The masks were 45
mm upstream from each detector, which required an iterative process using the angle
calculated from the CRDCs to calibrate the y-position for each detector. This was
approximately a 3% and less than 1% effect for the slope used for the y-calibration
Of CRDC1 and CRDC2, respectively. In addition, the y-position drift over time (as
shown in Figure 4.5) was taken into account. The y-position drift was approximately
a 3% change to the slope used in the y-calibration for both CRDCs.

The distribution of charge on the pads of the CRDC was used to calculate the
air-position. The pad data were read out every 25 ns. (see Section 3.4.1). The total
charge on each pad was then calculated from the sum Of all time intervals after the

subtraction Of an electronic Offset. All pads were calibrated to the same gain. The

36

 

200

175 '-

150 -

100 -

dE (MeV)

75 -»

50‘;

25 ,4,
r

 

 

40
RF Time (ns)

60

Figure 4.1: Energy loss (dE) versus RF time.

37

 

 

 

200 I l I 1 U r V f ‘l 1 I I 1 f I' 1

175 -

150 .. XFP SIIIS

125 h

 

 

 

50

 

 

 

 

 

0 A 17.;— - 1‘319w . J 1' l J _-_--:-——'--~1
-40 -20 0 20 40
Focal Plane x(mm)

 

Figure 4.2: Energy loss versus the A1900 Fragment Separator focal plane dispersive
position.

38

counts

103- n 26Ne '.

102? ‘:
E 27
. Na

10 _. Light Fragments ‘ . ~ 1

i

: l , (I

1 ll [Ill

 

 

 

 

 

 

 

     

 

240 260 280 300 320 340
TOF (ns)

Figure 4.3: Time-of-Flight (TOF) secondary beam identification plot

39

100

 

 

 

 

 

50 - . -
'
A 9‘ .‘. *4
E ' i
v 0 r t .. 9" '
>‘ 1.» 9 1i- at.
-50 . . .
5
‘109100 ‘ -30 i A 6 7 5‘0 ‘ 160 H 150
x(mm)

Figure 4.4: y-position versus x—position for the mask of CRDC2

40

 

20 V V V I V V V I V V V I V V V l V V V I V V V I V V V r‘r V r

 

 

15 - ' -
o
c: ’ 3 00°
.2 - a .9-
“5 30 0° 0 I
. . . 30.’
“Q . as» "
x ' . J 00& I
. I g .60 .0
E 10 I. 0. o a: anou 'o -
v 0'0 . o
c: , ~
.8 6‘ 0 d) . I
a ° 5.3. .
‘3‘ I
o
.‘
5 r -

CRDC1 : Open circles
CRDC2 : solid circles

 

 

 

 

I I I I I I I l I I J A J l l j l l I I I. I I J

0“ 20 40 60 80 100 120 140' 160
run number

 

 

Figure 4.5: Mean y-position Of both CRDCS versus run number for all charged frag-

ments in coincidence with incoming 26Ne secondary beam. The arbitrary offset is for
display purposes.

41

:c-position was calculated by taking the mean upad of the approximately gaussian

distribution of charge on the 128 pads:

23:) iqi

211:; Qt

Similarly the total charge summed for the same time intervals from different pads

1“de :1 (41)

was also approximately gaussian distributed. Thus distributions along sample (time

interval) or pad number were characterized by calculating a. asampze or apad using:

0 = \/M2 — 11-? (4-2)

where Mg and #1 were calculated using:

22‘ iqu
iq‘L

where q,- is the total charge for a pad or a sample.

 

(4.3)

Cuts placed on trample and apad ensured that the distribution of charge along
pad and sample number were of similar width, event by event. The independent
parameter of total integrated charge was chosen to demonstrate the consistency after
the cuts, where similar events should have similar total charges. The spectra for each
CRDC shown in Figure 4.6 show a peak around a mean of three pads for apad. The
cuts shown in Figure 4.6 were applied to the asample spectra shown in Figure 4.7 for
each CRDC separately. Similarly, the asample spectrum for each CRDC show a peak
around a mean of three samples. Cuts on the 03mph. spectra were applied to the total
integrated charge spectrum for each CRDC shown in Figure 4.8. The distributions for
each CRDC were approximately the same which indicates that the cuts were effective.
The events shown in the total integrated charge spectra shown in Figure 4.8 were used

for the rest of the data analysis.

42

 

 

 

 

 

 

 

 

 

 

104’ V v v v f v v 1

l

103 .

3 l
2
510 r

3 _ 1

10 i

I I M 1

1 l

o 0 25 T 50

Opad

 

Figure 4.6: Pad width opad for CRDC1 (left) and CRDC2 (right). The events between
the lines in each spectrum were accepted for the next cut for each CRDC separately.

 

 

 

 

 

 

 

 

104 ' ' a f :
l 1
3
10 - 1y 1
4 1
‘3 102 r 1’ '1
3
8
10 ' 1F 1
4 i
l - fl ll I Ill 1
o 2.5 ' o 2.5 5
Osample C,sample

Figure 4.7: Sample width awmpze for CRDC1 (left) and CRDC2 (right). The events
to the right of the lines in each spectrum were accepted for each CRDC separately.

43

 

103y

102-

counts

10

 

 

 

 

0 10000 7 0 ' 7 20000
integrated charge integrated charge

Figure 4.8: Integrated charge for CRDC1 (left) and CRDC2 (right).

4.4 PPAC Calibration

The calibrations for the PPACs used the pad pitch of 1.27 mm in both directions.
The distribution of charge on the pads of the PPAC were used to calculate the a:
and y-positions with Equation 4.1. The pad data were digitized with a time sampling
period of 250 us (see Section 3.4.1). The total charge on each pad was then calculated
from the sum of all time intervals after the subtraction of an electronic oflset. The
pads along each direction were calibrated to the same gain.

The same quality parameters for the CRDC pads were constructed for the PPAC
pads. However, the parameters were not as useful because the PPAC is an avalanche
detector which produces a large range of induced charge on the pads. The spectra.
shown in Figure 4.9 show the large integrated charge distributions for each direction
.TppACl, yppACI, :rppAcg, and yppAcg. The spectra in Figures 4.10 and 4.11 show the
quality parameters of asample and am, respectively. Each PPAC direction IEPPAC],
yppAcl, (EppAcg, and yppAcz show wide distributions of asample and 0M. Due to the
wide distributions in the parameters, determining reasonable cuts was difficult. The
one cut that was employed was on oped for values near zero. This cut eliminated events

where only one pad had a. digitized charge value resulting in spikes on the position

44

 

H
O
N
"I

counts

 

 

 

counts

 

       

 

0 I I '2000 0 l '2000‘ L 4000
integrated charge integrated charge

Figure 4.9: Integrated charge for IL'ppACl (upper-left), yppAc1 (upper-right), rcppAcg
(lower-left), yppAcg (lower—right).

spectra.

4.5 Element Identification

Element separation was achieved by using the measured energy loss which depends on
the charge (q) of the nucleus ( [42] pg. 24). Unambiguous element separation required

both properly calibrated ionization chamber and dE scintillator energy losses.

45

 

l--\

O
U.)

"'I

counts

 

#-

COUIIIS

 

 

 

 

 

0 2.5. 0'H2.5“ 5
G (5

sample sample

Figure 4.10: Sample width ammpze for $ppACl (upper-left), yPPACl (upper-right),
xppAcg (lower-left), yppAcg (lower-right).

46

 

 

 

 

 

 

 

 

?

a 'a
C :
:3 .
O u
‘3 1
1.

'5

m 1
{—3 I
G i
:3 .
O u
0 i
I

- II. I a:

 

 

 

0‘ ”2.5' 0‘ l l ‘25., ' 5
C5 C5

pad pad

Figure 4.11: Pad width 0de for IL‘ppACl (upper-left), yppAm (upper-right), .TppACQ
(lower-left), yppAC2 (lower-right).

47

4.5.1 Ionization Chamber Calibration

The calculation and calibration of the energy loss in MeV for the ionization chamber

was performed using:

15

AE(MeV) = Z(qim.~(t) + b.)Em,c(y) (4.4)

i=2

The summation excluded the first and last pads (2') because of incomplete charge
(qi) collection near the upstream and downstream drift foils. The correction factor
variables that contained the gain match and drift over time (ml-(t) and b.) were
determined for each pad (see Figure 4.12). The overall energy calibration for the
detector (Eml) was determined with a secondary beam tune that included 26Ne and
230. The spectrum shown in Figure 4.13 shows the y—direction dependence (ydE),
which was corrected (c(y)) to be used for the final element separation. The y—position
spectrum shown in Figure 4.13 was calculated in the non—dispersive direction at the

dE scintillator.

4.5.2 dE Scintillator Calibration

The corrections necessary to obtain the energy loss'from the dE scintillator were due
to light attenuation in the detector. The PMT raw energy signals were corrected for
drifts of the signals with time. The two left side PMTs digitized charge signals were
gain matched to each other with beam particles interacting at the spatial center of the
scintillator. The left side PMT average charge after gain matching and the down—right
PMT charges were position corrected for light attenuation in the scintillator. The up-
right PMT charge was not used because the PMT did not work. The parameters
for the position dependent correction were calculated at the dE scintillator dispersive
(zdg) and non-dispersive (ydE) directions, from the positions measured by the CRDCs.
The position dependent attenuation was different for each PMT depending on the

mounted position on the scintillator (see Figure 3.9). The left. side PMTs correspond

48

550 .......-..

 

.l
i
.1
d
.l
4

A
A AA AA}. A A
AA“ I AA ‘
A‘A ‘ ‘MPA‘A “ H
‘ A
‘ A‘
AAA‘
500

 

 

 

   

 

 

 

450 - -
7‘?
§ 34“—
s v" W
:- a!
350 -
300 l L . I a . . I . L A L. . . I . . . I I l L I . . A I . . a
O 20 4O 6O 80 100 120 140 160

run number

Figure 4.12: Ionization chamber pad peaks versus run number. The symbols represent
each pad used from the ionization chamber.

49

 

dE (MeV)

 

 

 

 

Figure 4.13: Energy loss in ionization chamber versus vertical position at the dE
scintillator (11.113)-

50

to positive xdg and the right side PMTS to negative xdg. The ydE parameter is positive
for up PMTs and negative for down PMTs. The corrections were performed with
the production data. To show the position dependence, the spectra before and after
correction are shown in Figures 4.14 and 4.15 for the down-right PMT. The position
dependence was corrected for the you; position shown in Figure 4.14 and then the arc“;
position shown in Figure 4.15. The ydE correction was larger than the Ida correction
for the down-right PMT charge because the particles in the experiment were located
at negative :ch position. After correcting for the position dependence, the left side
PMT average and down-right PMT charges were averaged together to generate the
final spectrum shown in Figure 4.16.

The spectrum shown in Figure 4.17 shows the final element separation using the
ionization chamber and dE scintillator energy losses. The cut shown in Figure 4.17

was used to identify the oxygen elements.

4.6 Isotopic Identification

The two parameters that provide isotopic separation are a corrected Time-of—Flight
(TOF) and energy deposited in the TKE scintillator. The ToF was the dominant
parameter to obtain isotopic separation and was corrected for several measured pa-

rameters before and after the Sweeper Magnet.

4.6.1 TKE Scintillator Calibration

The up-right and down-left PMTs of the TKE scintillator worked properly and these
were used to produce the energy deposited spectrum. The PMT spectra were corrected
for drifts over time. The position correction for light attenuation as a function of :rdE
and ydg was performed in two iterations in the same way as the dE scintillator. Figure

4.18 shows the final energy loss plot hinting that. there are two oxygen isotopes.

51

 

integrated charge (arb. units)

 

800

600 -

400 -

integrated charge (arb. units)

 

 

-200 -150 -100 -50 0 50 100 150
yd]; (mm)

 

 

 

Figure 4.14: Down—right PMT integrated charge versus ydE. No position correction
(top) and with position correction (bottom) using the yd}; parameter.

52

 

 

800 ' I ' r ' I ' l ' I ' l ‘ l

600

400

integrated charge (arb. units)

 

 

800 4a4=1 = 4' = : = : 4 e7: : =1i
600 -

400 -{ ,

integrated charge (arb. units)

 

 

 

 

 

-200 -150 -100 -50 O 50 100 150
xdE(mm)

Figure 4.15: Down-right PMT integrated charge versus xdg. No position correction
(top) and with position correction (bottom) using the raw parameter.

53

counts

 

1200 - ' ‘ a

1000 -

800-

 

600 -

400 -

200 -

 

 

 

4L

450

400
dB (arbit. units)

0 i L
300 350

Figure 4.16: dB scintillator energy loss

54

 

 

 

 

 

 

14 - . 1 1 - . .
i 20
12 - .
$0
8
10 - 7
6
A 5
‘5 4
a 8 ~
3
53
2
6 ..
$9
4 - 7 028
g; 0.7
0.6
0.5
2 n J A l . l n 0.4
300 350 400 450 500

dB (arb. units)

Figure 4.17: Energy loss (ionization chamber) versus energy loss (dE scintillator). The
cut for oxygen isotopes is shown by the curve.

55

counts

 

 

     

 

 

 

wo- ljffijfifiv' till -
us. -
mo- -
u- .
w. -
5. -
400 600 l' ‘800‘ ' '1000 1200 1400

E (arb. units)

Figure 4.18: TKE scintillator energy loss (arbit. units)

4.6.2 Time-of-Flight Corrections

The ToF for the charged fragments was constructed as a difference between the cal-
ibrated time signals of the timing detector in front of the reaction target and each
of the dE scintillator PMTs. Three of the PMTs, down-left, down-right and up-left,
were working properly. Down-right was the trigger, resulting in a self triggered spike
in its ToF spectrum. The TOF for a given PMT includes the travel time of the particle
between the timing detector in front of the reaction target and the dE scintillator,
and the light travel time from the position that the particle entered the dE scintillator
to the location of the PMT. Therefore the first correction for the TOF construction
was to correct for the light travel time in the dE scintillator relative to each PMT.

The distance to each PMT (d.) was assumed to be a straight line:

 

(12‘: \/(($dE — :17.)2 + (yarn: - 311)?) (4-5)

where (rcdggdg) are the positions calculated at the dE scintillator. The index 2'
represents each PMT with positions of (why) of (in mm) (1375.275), (137.5,—275), (-
137.5275), and (4375-275), for up-left (ul), down-left (d1), up-right (ur), and down-
right (dr), respectively. The speed of light in BC-404 scintillator with an index of
refraction 1.58 is given by:

1.5

t. = d.—— (4.6)
C

The final TOF for a given PMT used its calibrated time with the light travel time
subtracted from it. The time average of the dr and d1 PMTs used the travel time
subtracted ToFs. The spectrum shown in Figure 4.19 shows the comparison of the
tdr and tdz PMT subtracted ToFs. The events between the two parallel lines were
used for the next set of ToF corrections. The events outside of the parallel lines come
from events where the ToF signal for a given PMT was generated after light reflection

within the scintillator. A straight line light travel time correction from the point of

57

 

tdl (ns)

 

 

80 n n . I . . . I u 1 n
80 82 84 86

tdr (ns)

 

 

 

 

r
oi‘fii....1m

88- 9

Figure 4.19: TOP of down-left PMT versus down-right PMT after travel time correc-
tion.

interaction to the PMT cannot correct for light reflection. so the events outside the
parallel lines are not used for subsequent corrections to the average TOF.

The averaged TOF includes particles that are moving at different velocities over
varying distances. The exact velocity and distance a particle travels from the reac-
tion target to the dE scintillator is determined by the energy, angle, and position
that the particle has when entering the Sweeper Magnet. The Sweeper Magnet bends

and separates particles of different magnetic rigidities. For isotopes with the same

58

 

tavg (ns)

 

tToFco"1(aI'b. units)

 

 

 

 

0x (rad)

Figure 4.20: Average TOF versus 6x without (top) and with (bottom) 6x correction.
The line in the upper spectrum indicates the corrected trend.

magnetic rigidity or momentum, the heavier ones will be slower giving a longer av-
erage TOF. Therefore isotope separation can be achieved by using a parameter that
is prOportional to the magnetic rigidity of the particle. The dispersive position and
angle measured in the CRDCs provide two such parameters. The dispersive angle 0x

was chosen for the first correction to the average TOF as shown in Figure 4.20.

59

The 0,. correction was applied to the average TOF, tavg, using:

tTopcom = tavg(ns) + 6x(rad) 62(ns/rad) (4.7)

where tTopcom is the 6x corrected ToF. After the 6x correction, the isotopic sepa-
ration can be improved with the constructed dispersive position (33’) in the CRDCs,
measured positions 22,8 and yta at the reaction target, and the measured non-dispersive
angle 6,. using the CRDCs.

The spectra shown in Figure 4.21 shows the dependence of the tTopcom on disper-

sive position (1’) calculated using:
$'(mm) = 1:1(mm) — 433(mm) tan(6x) (4.8)

The :c’ dispersive position was chosen at a plane upstream from CRDC1 near the
edge of the Sweeper Magnet’s magnetic field. The plane chosen provided the least
dependence of 23’ on BX after the particle traveled through the magnetic field. The
position as’ is proportional to second order effects of different momenta as well as the
expected parabolic function dependence on different path lengths from the reaction
target to the dE scintillator. The :r’ dispersive position provides the correction to

tToFcorrl USiDgI
tTOFCOUQ = tTopcorrl—(5.0*10’4(ns/mm)2x'(mm)2+6.5*10’3(ns/mm)z'(mm)) (4.9)

where tTopcong is after the 513’ correction.

The TOF dependence on the 517,8 and yta positions at the reaction target are ex-
pected to be linear. The :13“, and yta positions are tracked forward to the reaction
target using the PPACs and matrix generated for the quadrupole triplet. The linear
dependence of tTopwng on 33m position, and tTOch-rg on yta position are shown in the

spectra in Figures 4.22 and 4.23.

60

88 .....

 

   

 

 

 

 

 

86:4.

E I"

5. 84-

p .

5 .

E82-

‘3 I

.1- .
80-
78%;”
86_!

5. 84-

.o -.

5 '.

E82: ~

35’ :
80-
i

78 ..I..

Figure 4.21: Corrected TOF tTopcom versus constructed dispersive position :1:’ uncor-
rected (top) and corrected (bottom). All events to the left the line on the bottom plot
were scattered beam events and rejected.

61

88 -.

I-rvlvvt

L[‘oFcorrZ (arb. umts)

 

 

Lrochz (arb. units)

 

 

 

Figure 4.22: Corrected TOF tTopcmg versus x-position at the reaction target uncor-
rected (top) and corrected (bottom).

62

 

t'1"oFcon'3 (arb' units)

 

 

t'I‘oFcorr3 (arb units)

 

 

 

Figure 4.23: Corrected ToF tToFcon-3 versus y—position at the reaction target uncor-
rected (top) and corrected (bottom).

63

The linear correction of tTopcorrg with mm position was performed using:

tToFcorr3 = tToFcorr? 'i- 0.0595(n,s/m):z:ta(m) (4.10)

where tTOpCO,,3 was then corrected by the linear dependence on yta position using:

tTopcom; = tTopcmg + 0.02495(ns/m)yta(m) (4.11)

The last correction involved the non-dispersive angle (6,) constructed using mea—
sured non-dispersive positions in the CRDCs. The parabolic dependence is shown in

the spectra shown in Figure 4.24 and the correction using:
tfinal = tTopcm-M + 170(ns/rad)26y(rad)2 — 9.732(ns/rad)6y(rad) (4.12)

provided the final ToF, tfina].

The final corrected ToF £5,131 spectrum shown in Figure 4.25 shows the separation
of oxygen isotopes. The FWHM for each isotOpe was approximately 0.8 ns and the
separation between the isotopes were approximately 1.5 ns. The spectrum shown in
Figure 4.26 shows the linear relationship of the TKE to the corrected ToF in the
spectrum. Since the B p acceptance of the Sweeper Magnet and nucleus charge q are
constant, the nucleus mass m and velocity 0 will be inversely proportional to one

another as shown in:

Bp= -—— (4.13)

Therefore, shorter ToF tam] correspond to faster particles which then have to be
higher in mass. This relationship along with the expected dispersive positions and
angles for different oxygen isotopes compared to measured dispersive positions and
angles in coincidence with each group provides our isotOpe identification.

The isotope cuts for 21’220 were two-dimensional as taken from the spectrum shown

64

 

 

 

 

 

3:5 bag meoumoi

 

ASE: 5.8V mucumohu

0.02

-0.02

-0.04

0y (rad)

Figure 4.24: Corrected ToF tTopcom versus 0,, uncorrected (top) and corrected (bot-

tom).

65

500

, 400

counts

300

200

100

 

 

220

 

 

 

 

 

tfinal (arb. units)

Figure 4.25: Final corrected ToF tfina]

66

 

 

1400"""""-,"""T'*'

1200

1000 .

TKE (arb. units)

00
O
O

 

600 -'

 

 

 

400 Lkljgglllgklljljgl

78 80 82 84 86
tfinal (arb. units)

Figure 4.26: TKE energy versus ToF tfiml

in Figure 4.26. The 230 two-dimensional cut would include contamination from the
220 fragment distribution. Since the final decay energy spectrum would have con-
tamination from the 220 fragment, the 230 cut was taken from a projection onto a
diagonal line passing through each isotOpe in the spectrum shown in Figure 4.26. The
tilted box shows the events allowed in the projected spectrum. The cut for 23O frag-
ments is marked on the spectrum shown in Figure 4.27. Based on three Gaussian fits

to the spectrum, the contamination of 220 fragment in the 230 cut is approximately

67

 

 

 

 

500
220
400 -
300 -
‘3
5
8
200 -
100

 

 

65 66 67 68 69 70 71 72

projection (arb. units)

Figure 4.27: Projection from TKE versus corrected ToF plot where the solid lines
represent Gaussian fits of the 2132330 isotopes. The reduced x2 of the nine parameter

fit is 1.257.

20% of the total counts in the cut. The contamination will be subtracted out of the

final decay Spectrum.

4.7 Neutron Processing

The momentum vector of the neutron was calculated based on the TOP and position

information from MONA. The calibrations of the TDCS, x—position, and time offsets

68

 

'j ' 1 ' 'T'fi '

 

73 74

 

 

40- n

 

 

 

30 - -
.3 3O
:3
O
O
20 - Y -
10 - -

 

 

l

 

 

l
J IIIIIII I I III II II

100 200

 

central bar ToF (ns)

Figure 4.28: Prompt y-ray and neutron peaks in the neutron ToF spectrum. The high
yield of prompt '7-rays was produced using a thick reaction target. The upper-right
insert is zoomed in on the prompt 'y-ray peak.
for each bar were performed before the experiment started using cosmic muons and
time calibrator (see Ref. [37] and Section 4.1).

After the time calibrations, the overall time offset of MONA was determined using
the prompt ’y—ray peak in the neutron ToF spectrum, see Figure 4.28. The prompt
ry-ray peak was produced when the incoming beam struck a thick reaction target

which stopped the secondary beam. The time offset was set so that the TOP of the

69

y-ray peak was at 27.75 ns which corresponds to the flight time of the y-rays from
the reaction target to MONA. The :r-position Of the neutrons was calculated from the
calibrated time difference between the left Q and right tR PMTs Of each detector
module:

:1: = (tL — tR)mx(cm/ns) + br(cm) (4.14)

where mx and bar are the calibration coefficients for each detector module. The cosmic
muons were employed to determine the calibration coefficients mac and b;c by locating
the edge of each detector module on the time difference spectrum between the left
and right PMTs. The time-of-flight for the neutron tn was the calibrated time average

Of the left and right PMTs of each detector module:

_tL+tR
' 2

 

25.. (4.15)

The y- and z-positions were determined by the y and z centers of the detector module
the neutron interacted with. The velocity of the neutron 0,, was calculated with the
measured neutron TOF tn, and position of the neutron specified by the 33-,y—, and

z-positions as shown:

 

_ \/:rz-l-yz+z2
_ tn

 

’07,

(4.16)

The velocity on was used to calculate the energy of the neutron and to sort events
with more than one recorded hit in MONA. The first hit chosen for the reconstruction
was the fastest hit after 45 ns to eliminate choosing a y-ray or a velocity that was
not physical. The spectrum shown in Figure 4.29 shows the physical acceptance of
MONA. The horizontal width Of MONA is completely filled and the vertical position
shows a noticeable cut at 21:50 cm. The vertical acceptance is from the Opening of the
downstream end Of the Sweeper Magnet. Neutron events were accepted within the

.1550 cm vertical acceptance.

70

75

 

 

 

 

 

 

10
9
’1 8
7
50 i 6
5 5
25 - a a: 4
A 3
s
e
c: 0 '
8 g .7 e 2
a a :7 ; i:
F 25 l
_ : E
.f E
. .: 1
. — 0.9
'50 g 0.8
— 0.7
-75 i - - 0.5
V t L— 0.4
—100 100

x-position (cm)

Figure 4.29: y-position versus x—position on MONA. The lines are drawn to indicate
the vertical acceptance due to the opening at the end Of the Sweeper Magnet.

71

4.8 Fragment Reconstruction

The Sweeper Magnet’s magnetic field was mapped to produce an ion-optical matrix
using COSY Infinity [41]. The magnetic field was mapped using seven Hall probes
mounted vertically to a movable cart to measure the field across the gap. The cart
moved on top of a plate along arcs of fixed radius through the magnet. A stepper
motor was used to move the cart along the arc and the cart required manual assistance
to move from one are to the next one. There were 45 arcs with a spacing of 2.54 mm
and 568 measurements along an arc with an interval of approximately 2 mm yielding
a total of around 25,000 data points per probe. The mapping was performed with
12 evenly spaced field settings all recorded at the same time. A reference Hall probe
mounted between the top and bottom coils was used for recording the magnet’s field
setting. The Hall probe was used instead of the current readout of the power supply,
because the probe would indicate any hysteresis in the magnet for low currents.
Before mapping, the coordinate systems of both the reaction target and charged
particle detectors were measured on the mapping plate. The error in the magnetic field
measurement due to the Hall probes and electronics was half of the least significant
bit in the electronics or approximately 3 Gauss. Since the Hall probes measurement
uncertainty was so small, a temperature probe was placed next to the Sweeper Magnet
to monitor temperature change. The error for multiple measurements along the same
arc was a maximum Of approximately 30 Gauss, where the uncertainty is dominated
by the position placement uncertainty Of the stepper motor.

The maps were processed by performing individual fits for each measured Hall
probe at each position against the reference Hall probe. The functions calculated by
the fit were the starting point for any magnetic field map calculation. For a given field
setting of the Sweeper Magnet, magnetic field values were calculated for each position
along the arc, radius, and Hall probe vertical position. The central field plane mag—

netic field values were then calculated from fits vertically across several Hall probes.

72

The central field plane or midplane is the where there are only perpendicular field
components to the horizontal direction. The Sweeper Magnet map shown in Figure
4.30 is an example Of a calculated midplane field. A field map of this character was
used by COSY to calculate matrices. To make a matrix with COSY, a specific trajec-
tory Or reference trajectory needs to be specified. The reference trajectory connects
the coordinate system at the reaction target to the charged particle detectors. The ref-
erence trajectory is defined by a magnetic rigidity, length Of the reference trajectory
and the starting position and angle into the magnetic field map. Before calculat-
ing matrices, a consistent coordinate system was determined for the reaction target,
charged particle detectors, and the reference trajectory for the matrix calculation.
The Runge-Kutta method within COSY to track particles through the magnetic field
was employed to compare calculated trajectories with measured trajectories. Based
on the comparisons, a consistent coordinate definition was determined.

Based on the coordinate system definition, the magnetic field measurements of the
Sweeper Magnet were used to produce two types of ion-optical matrices, forward and
inverse. Forward ion-Optical matrices propagated properties Of the charged particles
from the reaction target to the plane Of CRDC1 with matrix terms up to third order.
Inverse ion-Optical matrices propagated properties of the charged fragments from
the plane of CRDC1 to the reaction target, where the inverse matrix is defined as
the inverse of the forward matrix. The parameters needed at the reaction target to
propagate through the forward ion Optical matrix were positions (517w, yta), angles

(6x_ta, firm) and relative energy difference (6“,) which gave positions (:rcrdc, ycrdc) and

73

 

  
 

'200‘ reaction target

mm

-400-

-600- +

_800_ CRDC1

 

 

 

fir I I I I I I I
—200 0 200 400 600 800 1000 1200
mm

Figure 4.30: A Sweeper Magnet map with positive dispersive position marked at both
the reaction target and CRDCl. The beamline and charged particle detector axis are
indicated by lines perpendicular to the arrows. The dashed line represents a possible
trajectory through the field. The two peaks are approximately 4 Tesla.

angles (6x_crdc, Quack) at CRDC1 using:

/ ...\ 7 m

 

 

 

 

0.-.“... 6.-..”

ycrdc = M for 3),, (4.17)
gy-crdc 6%,,

Al ) a... t 5,, j m

where 111m, is the forward transformation matrix. The Al parameter not mentioned
previously is used to calculate path length difference to the reference trajectory length,
but cannot be measured and is therefore not relevant to this work. The positions (33,8,
yta) and angles (6,9,3, (9)....) at the reaction target were calculated by using a forward
ion-optical matrix for the quadrupole triplet propagating parameters from the PPACs
to the reaction target. The energy difference, 6.3, was calculated with the secondary

beam energy using:
__ Ebeam — Ert

6 a
t Ert

(4.18)

where Ebeam is the calculated energy of the incoming beam event-by—event and Er,
is the energy of the reference trajectory for 26Ne for a given magnetic field setting Of
the Sweeper Magnet.

The inverse ion optical matrices calculated from the positions and angles at
CRDC1 and new position to angles, energy difference, and the y-position parameters

at the reaction target using:

( 6mg \ { $crdc \

 

 

 

 

yta 6x-crdc
em = va ya... (4.19)
9.. 9.-....
1 99/ l ...)

out in

K]
O!

 

1750 - a

1500 - ~

 

1250 - '

1000 -

COUIltS

 

750 '-

500 -

250 r

 

 

 

 

 

-20 —10 20

xta (mm)

Figure 4.31: Dispersive position distribution mm at the reaction target.

This is different than the process in COSY for making backward (inverse) ion-Optical
matrices as shown in Reference [43]. COSY assumes that all particles enter the mag-
netic field at the same dispersive target position 32m. However, this assumption is
incorrect for this case as shown in the spectrum shown in Figure 4.31.

Since the dispersive position :rta distribution had a FWHM width Of approxi-
mately 12 mm wide, the at“, position was included in the inverse matrix using a

different process than in COSY. Starting with the forward matrix input and output

76

vectors specified in Equation 4.17, the partial inversion process exchanged specific
pairs of parameters between the input and output vectors. The non-dispersive pa-
rameters were exchanged, 3)... and 193,43 with ycrdc and 6,.-crdc. The dispersive direction
parameters were exchanged by swapping 6H,, with radc and then 6m with 6mm. The
Jim parameter is left in the input vector available for inclusion in the inverse matrix
transformation. With the inverse and forward matrices calculated, the accuracy of
the matrices was tested for three different magnetic field settings. The comparison of
parameters measured and calculated with the matrices characterized the uncertainty
of the matrices beyond the charged particle detector resolutions. Comparisons for
relevant parameters at the reaction target and CRDC1 were made by prOpagating
the secondary 26Ne beam through the forward and inverse matrices.

First a set Of comparisons was performed to check the forward matrix output
at the coordinate system Of CRDC1 (Figures 4.32-4.35) and a second set to check
the inverse matrix output at the reaction target (Figures 4.36-4.39). The reaction
target and CRDC1 dispersive direction parameters (2..., 6H8, 6“,, made, and 6mm)
and non-dispersive direction parameters (yta, 6w.“ ycrdc and Grade) do not mix for
the first-order matrix elements which are the most important, so any inconsistency
in a reconstructed parameter at CRDC1 will be seen as an inconsistency in a recon-
structed parameter at the reaction target in the same direction. The comparisons for
propagated parameters to measured parameters both at the reaction target and at
CRDC1 for the data-taking rigidity setting show good agreement for all parameters.
The high-rigidity setting shows good agreement in all parameters except for 513cm and
6x-ta. This represents a problem in reconstructing to and from very negative dispersive
positions on CRDC 1. The non-dispersive plane reconstruction forward and backward
compare well for both the data and high rigidity settings.

It can be concluded from the comparisons that the matrix calculation works well
for the phase space covered by the 26Ne secondary beam. The error for reconstructing

from negative dispersive positions at CRDC1 has been determined and is included

 

 

 

 

 

 

 

 

100 v I ' 1,:ig ' f I '7 17 V V t

E ' J' ‘ 102

:50 l . h -

U .3 '-

3 ‘ . 10

U

'0 0 . . '

Cu ’ 1
50-50T ‘ ‘ ' A -50 T; ‘ J A -50 0 ‘ 50 A 100

O 50 0 50
CRDC1 x (mm) CRDC1 x (mm) CRDC1 x (mm)

Figure 4.32: Forward-tracked CRDC1 x-position versus measured CRDC1 x-position.
Low Bp setting (left), data-taking Bp setting (center), and high Bp setting (right).

in the experimental resolution. The comparison Of data for the low rigidity setting
does exhibit problems in reconstructing several parameters with both reconstruction
in the dispersive and non-dispersive directions. The most likely issue is that the
matrix elements do not reproduce the trajectory of charged particles that take a path
through the edges of the peaks shown in Figure 4.30. A trajectory Off Of the peaks
passes through a region where the field lines bend particles in the non-dispersive
direction, which results in changes to higher than first order matrix elements that
are not represented well. Since the reconstructed data rigidity setting does not cover
the large positive dispersive position on CRDC1, the inaccuracies of the matrices

presented for the low rigidity setting are not issues for this particular reconstruction.

4.9 Neutron Decay Spectra

Figure 4.40 shows the spectra Of the charged fragment and the neutron kinetic energies
for the unbound decays of 22O", 230", and 240*. The three fragment energy spectra
appear very similar. From a simple reaction mechanism picture one would expect
that all fragments are produced at almost the same velocity, thus leading to a higher

kinetic energy for the heavier oxygen isotopes. However, the detected fragments are

78

 

 

 

 

 

5:? 0.05 ' ‘-
£3;
2 0 025
on , - 5
g :
>< .I
a 0 ' 91" g:
D .
'c -0.025 '
E
.2 -0.05 t "
-0 0

. 5 0 0.05-0.05 0 0.05-0.05 0 0.05
CRDC1 x-angle (rad) CRDC1 x-angle (rad) CRDC1 x-angle (rad)

Figure 4.33: Forward-tracked CRDC1 .r-angle versus measured CRDC1 :r—angle. Low
Bp setting (left), data-taking Bp setting (center), and high Bp setting (right).

 

.5
O

N
o
I

 

forward CRDC1 y (m)
8 o

.L
o

 

 

 

 

6
CRDC1 y (mm)

 

6
CRDC1 y (m)

 

0
CRDC1 y (m)

Figure 4.34: Forward-tracked CRDC1 y-position versus measured CRDC1 y-position.
Low Bp setting (left), data-taking Bp setting (center), and high Bp setting (right).

79

 

 

0.02

 

   

 

 

 

 

 

e
a
go 0.01 -
g 142..
>
U
'U _ .
:a 0.01
E
'44
“om—0.02

0 002 T -0.02 0 0.02
CRDC1 y-angle (rad) CRDC1 y-angle (rad) CRDC1 y-angle (rad)

Figure 4.35: Forward-tracked CRDC1 y-angle versus measured CRDC1 y—angle. Low
Bp setting (left), data-taking Bp setting (center), and high Bp setting (right).

 

 

 

 

 

0.05 . . 3.

A a, V211 ' 2

g - {cl-:2] i I ‘7 _ > 10

i 0.025 -‘ . ‘ ’ , '

00 I" a. l -' ' i) l L;- ,5

5 i. " 21 ' ~23

I; 0 9 .5 ' 9 10

a ;.

° -V'xr .9 . ’ L

a -0025 - _: ' «- '

O _.‘. . ' “

0 " 1
‘0'05-005 0 -0.05 0.05

x-angle (rad)

0 -0. 5 0
x-angle (rad) x-angle (rad)

Figure 4.36: Backward reconstructed target z—angle versus measured target x-angle.
Low Bp setting (left), data-taking Bp Setting (center), and high Bp setting (right).

80

0.05 ----

 

 

 

 

 

I IA . v.1
g , :,.. 10 2
7:1 * 4”” i A": » .1?-
.9. 0.025 ~ i. I" 1' A‘ 3?.
u f ‘ b - i
8 r r 0 - P
8- l 0 '\__
I I 4] £ ' 9' i2“
>~ 0 .. . . . 10
'U o ‘l' u
2 . . .
o , * _ ,2 - _.,
b i f A '; .. . .-r
‘3 -0.025 " ' ' "- . .-' :5 -- 1-5“;- 5 .
8 i ’4? : :‘- l : REA 1
O " . r
l—
-0.054+*‘AJL“4 “-‘A4“‘- *“-‘4k*-
-0.0S . 0 -0.05 _ 0 -0.05 ‘0 0.05
y-posmon (m) y-posmon (m) y-posmon (m)

Figure 4.37: Backward reconstructed target y-position versus measured target y-

position. Low Bp setting (left), data-taking Bp setting (center), and high Bp setting
(right).

 

 

 

 

 

 

0.05 ' ' ' ' ' t ' ' ' ' ' i v v - I v v - v ' - - f f , t j -
6 I I I
E! . . .
I: 0.025 - -r ..
a : : :
SA 0 - - .. 9;.
8 i ,_ o _ , a
g i ': .
a 0.025 - J- .-
0 l . ,
8 l
*- i
ADDS-0.05 A A A 0 4 A A T0054 A A A 0 A A A A-0.05A A A O L J A
y-angle (rad) y-angle (rad) y-angle (rad)

Figure 4.38: Backward reconstructed target y—angle versus measured target y-angle.
Low Bp setting (left), data-taking Bp setting (center), and high Bp setting (right).

81

 

2400 ---.--- -fffi-a- -#-,tfi
I I
I

     

 

 

 

 

a 2300 . J. _' .1. . .9112:
>5 ’ . 0 ‘ AA.‘ _ | f,
99 I 1’ ' .
g ’ ‘l . {A '
E : i: . i: ”fl-{AV A
' . 0 r
g 2100 r .r 'r 1
O r *3" u
2 l 54;? ' a
l At: A A ‘ 4— A L A AA A A ’ A A A 1 A A A '
200(1000 220 2000 2200 2000 2200 2400
energy (MeV) energy (MeV) energy (MeV)

Figure 4.39: Backward reconstructed secondary beam energy versus measured sec-
ondary beam energy. Low B p setting (left), data-taking Bp setting (center), and high
Bp setting (right).

limited to the same momentum acceptance of the Sweeper Magnet which corresponds
to lower energies for the heavier isotopes. The fragment kinetic energy spectrum for
the decay Of 240‘ is broader because of the contamination of fragments from the decay
of 230* which are incorrectly reconstructed as 24O"‘.

The neutron kinetic energies are much more sensitive to the decay of the unbound
excited oxygen isotopes than the resulting fragment energies. Momentum conserva-
tion in the center-Of-mass syStem transforms into much larger velocity (and therefore
energy) differences in the lab-system. While the decay spectra of 240‘“ and 230“ show
fairly narrow peaks, the decay Of ”O" is substantially broader indicating a signifi-
cantly different decay pattern.

Further evidence for differences for the decay of the three oxygen isotopes can be
seen in the angular distributions of the fragments and neutrons as shown in Figure
4.41. Again, the fragment angular distributions only show minor differences, the de—
cays of 240* and 230‘ seem to peak at slightly smaller angles compared to the 220‘
decay. In contrast, the neutron angular distribution of the 230'“ decay peaks at sig-
nificantly smaller angles than 220" or 240‘ which is a first indication of a small decay

energy. 240* seems only slightly more forward-peaked relative to the almost sym-

82

 

 

 

 

 

60. .
1240' f ‘ :9
5 5
O O
U Q

20L ..

200 » ‘7' ‘ =1"L“*""*""1

 

 

 

l00 -

counts
3
o
p
counts
to
o
O

 

 

 

15'

10*

counts
counts

 

 

 

 

 

 

 

0 , , 2000 A 0 200
fragment kinetic energy (MeV) neutron kinetic energy (MeV)

Figure 4.40: Reconstructed fragment kinetic energy spectrum (left) and neutron ki-
netic energy spectrum (right) for 220* (top), 230" (middle), and 240* (bottom).

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

£3 5’
S 5
8 8
200 -
100 -
£3 £9
a a
8 50 8100 '
15 .
8 :9 10 ' a
5 g .
o o l
O U A, i ‘ ‘ i
5 1 T j ,
l 1
[LI J
0 5 0 5 10
fragment angle (deg) neutron angle (deg)

Figure 4.41: Reconstructed fragment angle spectrum (left) and neutron angle spec-
trum (right) for unbound 220* (top), 230’“ (middle), and 240'“ (bottom).
metrically (around 3.5 degrees) 220* angular distribution. The spikes in the neutron
angular distribution spectra are due tO the discrete position of the detector modules
in MONA along the y-direction.

Finally, from the neutron and fragment kinetic energies and angles, the Opening
angle 00W, and decay energy spectra were calculated according to Equation 3.4. The
measured fragment energies had to be corrected for the energy loss in the target.

Because the location of the interaction within the target was unknown it was as-

84

y...)

 

 

 

sumed that the reaction took place in the center of the target and an energy loss
corresponding to half the target thickness was added to the fragment energies.

Figure 4.42 shows the spectra for the Opening angle between the charged fragment
and neutron 60pm and the decay energy spectra. Of 22O", 230'“, and 24O"‘. The opening-
angle Spectra reinforce the evidence seen in the neutron angular distribution. The
decay from 230* is very sharply peaked below one degree, and the 240'“ decay shows
a narrower distribution peaked at smaller angles compared to the 220"“ decay.

The decay energy spectra show a sharp peak for the decay Of 230" at an energy
very close to the threshold. Although not as distinct the decay energy spectrum of
240* is significantly different from the 220* decay energy spectrum. It peaks at smaller
decay energies and is not as broad as the 220* spectrum.

Before comparing the data with simulations it was instructive to create “mixed-
event” spectra. These spectra were created by calculating the decay energy from the
relevant fragment parameters from one event with the neutron parameters from the
previous, thus unrelated event. The analysis will reveal if the observed coincidence
events are truly correlated or not. Figure 4.43 shows a comparison Of the decay energy
spectra of 230'" and 240* with the corresponding spectra created by event mixing.

There is nO difference between the real data and the event—mixed data for the
decay Of 220* indicating that the detected neutrons and fragments were not directly
correlated. This can be understood by the many different possibilities to populate
220'“ from 26Ne and will be described in detail in the next section. In contrast, the
“real and mixed 230" decay energy spectra are significantly different. This is further
strong evidence that the neutrons and fragments are strongly correlated and result
from a discrete state in 230’“. The limited statistics for the 240* decay did not allow
for a. similar analysis.

As mentioned before, the 240‘ data could not be cleanly separated from the very
strong 230* data and thus the decay energy Spectra for 240* contain contributions

from 230*. From the spectrum shown in Figure 4.27 (see Section 4.6.2) it was es-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

40 -
£9 53
S 8
8 8
20 -
400
3
S
0
° 200 i
10
9 3
S 8
8 8
5
5 0 5
decay energy (MeV)

2.5
opening angle (deg)

Figure 4.42: Opening angle (90pm) between neutron and charged fragment (left) and

reconstructed decay energy spectrum (20 keV/ bin) (right) for 220* (top), 230" (mid-
dle), and 240“ (bottom).

86

 

 

 

 

 

 

60 - -
50 ~ -
4O - -l
ll
3 l
30 - -
' I l
20 - '
1. U '1 ll
0 0.5 1 l 5
decay energy (MeV)
500 - -
400 ,- '1
300
.‘9
S:
:3
8
200 -
100

 

 

 

 

decay energy (MeV)

Figure 4.43: Decay energy spectra for correlated (points with error bars) and uncor-

related (histograrn) neutron and charged fragment events for 220’“ (top) and 230"“
(bottom).

87

timated that about 20% of the total events in the charged fragment gate Of 230
(corresponding to the decay Of 240") were 220 (corresponding to the decay Of 23O").
This estimate was based on Gaussian fits of 23O and 22O in the spectrum shown in
Figure 4.27.

The top panel shown in Figure 4.44 shows the decay energy spectrum of 240"
together with the 230* spectrum scaled to 20% of the 240" events. The 230"“ Spectrum
appears broader that the decay energy spectra shown in Figure 4.42 because for the
subtraction the events were reconstructed assuming the decay of 240* and not 230".
The final (subtracted) 2’40" decay energy spectrum is shown in the bottom panel
shown in Figure 4.44. Even though the statistics is limited and the shape of the
spectrum at low energies is uncertain due to the uncertainties Of the contributions Of

230‘ a peak at about 600 keV is clearly evident.

88

 

 

 

 

 

801. ..

     
    

‘
240 total

60

counts

40

20

. . .
23O contamination

 

 

 

 

 

0 44AL14...1.‘..l....l...;l.. . ’4 ‘
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
decay energy (MeV)
_ 60 - 7 .. -
50 - -l -

 

 

r1
1

 

40

E

o 30- -
20- .

 

 

 

contamination-subtracted decay energy (MeV)

Figure 4.44: Top: 2"0" spectrum with scaled 23O" spectrum used for the subtraction.
Bottom: Subtracted decay energy spectrum of 240‘.

89

Chapter 5

Discussion

5. 1 Simulation

To extract the unbound decay energies and widths, the physical acceptances and
efficiencies of the detector setup need to be taken into account in a simulation. A
Monte Carlo code was written that simulated an 86 MeV/ A 26Ne secondary beam
reacting on a 721.3 rng/cm2 thick beryllium target. The beam position, angle and
energy distributions, the position and time resolution of MONA, and the position and
angle resolution of the CRDCs were included as listed in Tables 5.1 and 5.2.

A gaussian distributed uncertainty was used for the charged particle parameters

and the :c-position and time-Of-flight of the neutrons. The y- and z-positions Of the

Table 5.1: Position and angle resolution in the x and y direction of the 26Ne secondary
beam at the target. AB is energy uncertainty.

 

Beam Parameter 0
27,8 5 mm
6“,, 10 mrad
3),, 12 mm
Qy-ta 1.5 mrad
AE 2.6 MeV

 

90

 

Table 5.2: The charged particle and MONA detector resolutions used in the simulation.

Charged Particle a MONA Parameter a

 

Parameter
made 1.3 mm 1‘ 5 cm
6mm 1 mrad y 5 cm“
ycrdc 1.3 mm 2 5 cm‘
6y_c,.dc 1 mrad t, 0.1 ns
xta 0.7 mm

 

*flat distribution of :l:5 cm

neutron were descritized and randomized with a flat probability distribution. The
physical acceptance Of MONA was included in the tracking of the neutrons. Presently
interactions Of the neutrons in MONA are not yet included in the simulations so that
it is not possible to extract cross sections. The neutrons were assumed to stop in the
first layer Of MONA.

A flat probability distribution for the point- Of interaction within the natural beryl—
lium reaction target was assumed. The energy of the outgoing fragment was assumed
to be the same energy per nucleon as the incoming 26Ne. The directions Of the emitted
neutrons and charged particles were assumed to be isotropic and back-tO—back in the
center-of-mass frame. The decay energy distribution was modeled by a Breit-Wigner
lineshape [44]:

do F

_= 5.1 A
dE (E—E,.)2+§F2 ( )

 

where the state is specified by the resonance energy (E) and width (F). In addi-
tion, neutron emission from the continuum at higher excitation energies was simulated

by a thermalized neutron source of the shape [10,45]:

F(E) = x/Ee—E/T (5.2)

91

 

 

 

where T is the nuclear temperature.

The simulation produced positions and angles Of the secondary beam at the reac-
tion target, positions and angles at CRDC1 for the charged fragment, and positions
and time-Of-flight for the neutrons at MONA. The simulation produced event data in
the same format as the actual data so that both could be analyzed with the same

code.

5.2 Comparisons to Simulated Spectra

The spectra in Figures 5.1, 5.2 and 5.3 are comparisons Of the simulated and measured
decay energy spectra for 220*, 230"“ and 240*, respectively.

As mentioned in Section 4.9, the neutron energies and angles as well as the Open-
ing angle between the neutrons and fragments of 220* exhibited different shapes
compared to 230” and 240‘” indicating a different decay pattern. The decay energy
spectrum shows a broad distribution with no clear resonance structure. A simulation
assuming a thermalized neutron source with a temperature of 2 MeV resulted in a.
good description of the data as shown in Figure 5.1.

The measured decay energy spectrum of 230'“ is dominated by a strong narrow
resonance close to the threshold. The data could be well described with a single
resonance located at E, = 45 keV with a width of F = 20 keV. In addition, a. small
contribution from a thermalized neutron source with a temperature Of 1 MeV could
account for the broad background (see Figure 5.2). A reduced X2 search yielded the
best fit for E. = 48 i: 10 keV. The width Of the simulated peak is dominated by
the experimental resolution. Based on the fits, an upper limit for the width Of the
observed state is found to be approximately 30 keV.

The measured decay energy spectrum of 240* shown in Figure 5.3 was fit by a
simulated state with a resonance energy E. = 600 keV and width F = 300 keV. From

a reduced X2 search the resonance energy was determined to be E1. = 670 :l: 150 keV.

 

 

 

 

60 " r
l .
II'
40 - -
CO
E
:3
a |[
30 ' '. 1
l
I|
20 a
ll
ll l
l
10 , [ml : l [ "
. [I
| ' |
l I 'I “IA 1
Ii‘lr'il l f I 1
. . .. .. . . . . . . . . . . L. . l- illlililmillllll'wméii.

 

 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
decay energy (MeV)

Figure 5.1: Decay energy spectrum of 220"“. The histogram corresponds to fit assuming
a thermalized neutron source of nuclear temperature T = 2 MeV.

93

 

 

 

 

 

 

 

 

500 _ 5'00 + .-
[
300
400 -
I 200
100
300 +
‘8
S
O
U
200 -
100 -

 

 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
decay energy (MeV)

Figure 5.2: Decay energy spectrum of 230“. The upper histogram is the result of a
simulation including contributions from a resonant state (E. = 45 keV, F = 20 keV,
middle histogram) and background with a thermalized neutron source (lower his-
togram).

94

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60 - .
.1—
50 - -- -
_-H-
40 i .
§ ::

0 30 -_.l -
20 - -
10 - -

- ,l
0 5

 

decay energy (MeV)

Figure 5.3: Decay energy spectrum Of 240*. The fit assumes a resonance with a reso—
nance energy of E. = 600 keV and a width of F = 300 keV.

95

 

The width of the simulated peak in the spectrum shown in Figure 5.3 is due to the
experimental resolution and the width of the state. The width Of the resonance was
kept constant. It Should be mentioned that the 240* decay energy Spectrum is also
consistent with a thermalized neutron source, but the neutron energy and angle as
well as the Opening angle between the neutrons and the fragments do not support
this conclusion. In addition, in the population of 240"“ from the breakup of 26N e there

are no thermalized neutrons available as will be described in the next section.

5.3 Physics Interpretation

The broad decay energy spectrum of 22O" can be explained with the emission of
neutrons from a continuum of unbound states. 220* can be populated from 26Ne in
several different ways as shown in Figure 5.4. It can be produced directly by 2p2n
(or 0:) knock—out or it can be pOpulated by one- or two-neutron evaporation following
the population Of highly excited states in 230* and 240* via the 2p1n or 2p knock-
out reactions, respectively. In either case, the neutron separation energy of 220* is
very high (6.85 MeV [29]), which also implies a high level density. Thus it is unlikely
to Observe individual resonances in the decay of 220*. Also, 210 has several bound
excited states and the present decay energy measurement cannot distinguish between
decays to the ground state or any of the excited states. Finally, the neutron measured
in coincidence with 210 could also be one Of the evaporated neutrons from highly
excited 230‘“ or 240'“. Thus the overall decay Spectrum can be approximated with the
emission Of a spectrum of thermalized neutrons as described in Section 4.9.

The situation for the decay of 230“ is slightly different. Again 230* can be produced
directly into highly excited continuum states via a 2p1n reaction or by evaporation of
one neutron following the pOpulation Of excited states in 2“0". However, the neutron
separation energy is only 2.74 MeV, so that the spectrum just above the threshold is

still consisting of discrete states and not by a high level density. Thus the present Ob-

96

14

12

1O

 

0 MeV

 

Figure 5.4: Separation energies Of three—, two-, and one-neutron relative to 24O calcu—
lated using Reference [29]. The gray boxes represent a continuum of unbound states,
the dashed lines indicate three. two-, and one-neutron separation energy relative
tO 24O, the thick solid lines represent predicted unbound states, and the thin solid
lines are measured excited states. The arrows indicate possible paths for producing
neutrons with a charged fragment.

97

 

Table 5.3: Mass excess [29], Edecay and resulting excitation energies in keV for Observed
states in 230* and 24O‘". The mass excess values and extracted decay energy uncer-
tainties are rounded to the nearest 10 keV. The excitation uncertainty is rounded up
to the nearest 10 keV.

230: 240*
Parent mass excess 14610 d: 120 19070 i 240
Daughter mass excess 9280 i 60 14610 :1: 120

 

 

 

Edemyl 48 :t 10 670 i 150
E‘ 2788 :1: 140 4280 :i: 310
1this work

servation of a narrow resonance just above threshold is strong evidence for an excited
state in 23’0" just above threshold. The simulation shown in Figure 5.2 including a
narrow resonance and a broad thermal background confirms the observation.

The excitation energy of this state can be calculated with Equation 5.3 and re-
quires the knowledge Of the decay energy (Edecay) as well as the masses of the parent

nucleus (230), the daughter nucleus (”0), and neutron (Mn).

E" = 133...... + M820) + M. — M (230) (5.3)

Table 5.3 shows the masses and the decay energy including the uncertainties. The
resulting excitation energy Of the state in 230’“ is 2788 :l: 140 keV. It can be seen from
Table 5.3 that the main uncertainty of the excitation energy is not determined by the
present decay energy measurement but by the uncertainty of the measured masses.

230’“ does not have any bound excited states [21], thus the measured energy Of
the state in 23O" of 2788 d: 140 keV corresponds to the first excited state of 23O. The
observed unbound state(s) of 23'0 are predicted to have strong single-particle charac—
ter. Based on the theoretical calculations there are two states with low decay energy,
5/2+ and 3/2+ [11]. Figure 5.5 shows the single particle configurations Of the 5/2+
and 3/2+ unbound excited states. The 5/2+ state is expected to be a configuration

with two neutrons in the 1.51/2 shell and a. hole in the Dds/2 shell. The 5/2+ state in

98

 

230* 230*

3/2+ d3” 5/2“
-é— S1/2 H
w (15,2

220
d3/2
0+

802

m
d 5/2

Figure 5.5: Single particle configurations for 5 / 2+ and 3/2+ unbound states in 23O.
The 23O unbound state(s) emits a neutron and populates the 0+ ground state of 22O.
The empty circles with arrows indicate which sub-shell neutrons were promoted. The
solid circles indicate where neutrons are for a given configuration.

230 decays via a second order transition to the 0+ ground state of 22O which would
correspond to a narrow width for the 5/2+ state. The 3/2+ state is expected to be
a configuration with one neutron in the 0d3/2 which decays to the 0+ ground state
Of 22O. The transition involves removing the neutron from the 0d3/2 sub-shell which
would correspond to a wide width for the 3/2+ state.

The Observed unbound state can be assigned the predicted 5/2+ level in 230’“,
which is in good agreement in the excitation energy with shell model calculations
using the USD interaction [11] as shown in the right side Of Figure 5.6. The expected
theoretical width for a decay energy of 48 keV from the 5/2+ state would be ap-
proximately 5 eV according to theory [28]. The experimental resolution of the width
dominates the data and so an upper limit of 30 keV for the width Of the state is

reasonable. The measured state Of 23O" probes the gap between the 0(15/2 and 131/2

99

 

3/2+

 

 

 

 

 

 

 

0d —4 0
-1.0 ——-3.5
A 5/2+ —_3 0
% A2 0 - .. «1- -l—l-1 .. .. - -
a ‘3.0 0d3/2 __2 5
LIJ 41
o_ -4.0 __
U) 13,,2 2.0
LU -5.0 1 5
A60 0d
—— 0.5
-7.0 5'2 0d“
-8 o I 151/2 —— 0 MeV
' A 22 23
USD G-matrix 0 + n 0 Theory

Figure 5.6: Left: Effective Single particle energies of the 5d shell for USD and G-
matrix calculation from Reference [11]. Right: Comparison of the shell model [28] to
the extracted decay energy (solid line) for the first unbound excited state Of 23O. The
dashed line marks the one-neutron separation energy of 2.74 MeV.

shells. The left panel of Figure 5.6 shows the USD and G-matrix calculation of the
Effective Single Particle Energies (ESPES) for 2“Q“ from [11]. Based on the good
agreement to the USD calculation, the sub-shell gap between the 151/2 and 0(15/2 is
well represented. In contrast, the G-matrix calculation predicts a much smaller level
spacing between the 151/2 and Dds/2 sub-Shells. This measurement confirms that the
USD calculations represent the level spacing better than the G-matrix calculations
as presented in Reference [11]. In the future it would be interesting to search for
the second predicted unbound excited state Of 3/2+ which is not observed in the
present data. It should be mentioned that the narrow resonance could in principle
also correspond to a decay from a higher lying state in 230 to a bound excited state
in 220.

The simplest decay of the three Observed isotopes is 240 because it only can be
produced directly by two—proton removal from 26Ne. 24O itself does not have any
bound excited states and the number of levels between the one- and two-neutron
separation energy are predicted to be low. The continuum of states is only expected

to start above the two-neutron separation energy [26]. 230 does not have any bound

100

240*
d3/2 -.—

S1/2 A 2+

230

d 3/2

’l/2+
S1/2 -O—

w
d 5/2

Figure 5.7: Single particle configuration for the 2+ unbound state in 240. The 24O
unbound state emits a neutron and populates the 1/2+ ground state Of 230. The empty
circles with arrows indicate which sub-shell neutrons were promoted. The solid circles
indicate where neutrons are for a given configuration.

excited states either so that any Observed resonance is an unique decay to the ground
state and the ambiguity Of possible excited state to excited state decay possible in
230 is not present in 240.

Similar to 230, the Observed decay energy can be converted to an excitation energy
in 240. The relevant masses and the decay energy listed in Table 5.3 result in an
excitation energy of 4280 i 310 keV. The relatively large uncertainty is equal between
the uncertainty of the present decay energy measurement and the uncertainty of the
mass measurements.

The comparison Of the unbound decay energy for 24O‘“ to theory is shown in
Figure 5.8. The measured resonance decay energy from the first excited state from
2“O" is predicted by shell model calculations to be a 2+ state decaying to the 1/2+
ground state of 230. Figure 5.7 shows the expected configuration of the 2+ state
consisting Of one neutron in the 1.51/2 shell and one neutron in the 0d3/2 shell. The

expected theoretical width for a decay energy of 600 keV from the 2+ state would be

101

Table 5.4: Comparison of theoretical calculations of the first neutron unbound excited
2+ state in 24O.

21" (MeV) Calculation
3.81 Obertelli [27]

 

4.0 Khan [23]
4.18 Siiskonen [25]
4.85 Volya [26]
5.1 Utsuno [24]
5.16 Brown [28]

8.5 Thiamova [22]

 

approximately 46 keV [28]. The extracted width of approximately 300 keV is larger
than that of theory. Table 5.4 shows the theoretical calculations shown in Figure 5.8.
The Obertelli [27], Khan [23], and Siiskonen [25] calculations are in agreement within
the uncertainty Of the measured unbound first excited 2+ state in this work. The
measurement confirms the doubly—magic nature Of 24O which is the first direct input.
to theory for oxygen isotopes measuring the energy gap between the 0d3/2 and 1.91/2

sub-shells.

102

 

__.._ —=a\.—I!-~ —__-- - _d=".. '.' - _. ..-. .. *—

/_ __ 4.0

 

" " _ _ " _ :_3.0
__2.0
__1.0

_ __OMeV

23O+n 240 Theory

Figure 5.8: Comparison of theory to the extracted decay energy (solid line) for the first
unbound excited state Of 240. Theoretical calculations A: Obertelli [27], x: Khan [23],
Cl: Siiskonen [25], I: Volya [26], o: Utsuno [24], +: Brown [28], A: Thiamova [22]. The
dashed line marks the one-neutron separation energy of 3.61 MeV 24O.

103

 

Chapter 6

Summary and Conclusions

Spectroscopy Of neutron-unbound states was employed to measure the first excited
states in 230* and 240*. The recently commissioned Sweeper Magnet, including the
subsequent charged-particle detectors and the Modular Neutron Array, MONA, were
used to detect the charged fragments and neutrons in coincidence. The nuclei were
produced by a 26Ne secondary beam impinged on a beryllium target.

The reconstructed decay energy spectra of 220*, 230*, and 240“ were compared
to simulations. The decay of excited 220*, which was produced through one, two,
and three neutron emission channels could be explained by the emission from the
continuum with a thermal distribution [45,46]. The 230* decay exhibited a strong
peak close to the threshold. The resonance energy of 48 :l: 10 keV corresponds to an
excited state Of 2788 :l: 140 keV which is consistent with the pOpulation of a neutron
in the 0d5/2 sub-shell as predicted by the shell model with the USD interaction [28].
An upper limit for the width of approximately 30 keV for the narrow resonance is
established. The uncertainty of the decay energy is dominated by the uncertainty
of the mass measurements of 230 and 22O. The 240* decay was characterized by
a resonance at 670 j: 150 keV with a width Of 300 keV. This corresponds to an
excited state at 4280 :l: 310 keV and can be attributed to the first 2+ state based

on the shell model calculations. The current measurement in connection with the

104

 

Energy Range

[3 1000-2000 keV
I 2000-4000 keV
A I >4000 keV
El

Known Nucleus

 

8 16
N

 

 

>

Figure 6.1: First excited 2+ state trends for nuclei near Z = 8. The excitation is
marked for some even Z and N isotOpes where the measurement of this work has been
added to the known data from Reference [3]. Z = 8, N = 8, and N = 16 are outlined
with dark black lines.

currently accepted masses of 2“O and 230 rules out several shell-model calculations
which predict a larger gap between the 1.51/2 and the 0d3/2 sub—shells. Figure 6.1
shows the known first 2+ excited states with the measurement from this work Of 2“0
included. The magic numbers Of N = 8 near stability and N = 16 far from stability
are clearly indicated by the high lying first excited state. The high lying excited state
Of 24O confirms the doubly-magic nature Of oxygen for N = 16.

Further investigation Of the neutron-rich oxygen isotopes is necessary to fully char-
acterize the shell structure in this region Of the nuclear chart. The present experiment
Observed the first unbound excited states in 230" and 240'". In order to reduce the
uncertainty Of the comparisons to theory, more accurate mass measurements of 22O,
230, 240 should be performed. New unpublished mass measurements for 230 and 240

have been performed which would reduce the uncertainty in the excitation energy of

105

 

 

24O by approximately 100 keV [47] as well as make the shell model calculations of
Volya [26], Utsuno [24] and Brown [28] agree within the uncertainty Of the Observed
state (see Figure 5.8). In addition, new experiments to populate higher-lying excited
states in these nuclei are needed. For example, a dedicated experiment for 230 should
be able to observe the excited 3/2+ state due to a neutron in the 0d3/2 sub-shell. In
order to test the evolution of the shell model even farther away from stability one
has to cross the dripline and study the decay Of the neutron-unbound ground-state of
250. This experiment, where 250 was populated via the one-proton stripping reaction
from a secondary beam of 26F, has recently been performed and is currently being

analyzed [48].

106

 

 

Bibliography

[1] BA. Brown. The Nuclear Shell Model Towards the Drip Lines. Prog. in Part.
and Nucl. Phys, 472517, 2001.

[2] Bohr, A. and Mottleson, BR. Nuclear Structure Volume I: Single Particle Mo-
tion. World Scientific, 1998.

[3] Firestone, R.B. Table of Isotopes, 8” ed. \Viley—Interscience, New York, 1996.

[4] J.A. Cameron and B. Singh. Nuclear Data Sheets for A = 40. Nucl. Data Sheets,
102:293, 2004.

[5] B. Singh and J.A. Cameron. Nuclear Data Sheets for A = 42. Nucl. Data Sheets,
92:1, 2001.

[6] J .A. Cameron and B. Singh. Nuclear Data Sheets for A = 44. Nucl. Data. Sheets,
882299, 1999.

[7] T.W. Burrows. Nuclear Data Sheets for A = 48. Nucl. Data Sheets, 107:1747,
2006.

[8] P. Navratil, J .P. Vary, and B.R. Barrett. Large-basis ab initio no~core shell model
and its application to 12C. Phys. Rev. C, 62:054311, 2000.

[9] Mayer, M. G. and Jensen, H.D. Elementary Theory of Nuclear Shell Structure.
John Wiley and Sons, Inc., 1955.

[10] Pc. Thirolf, 13v. Pritychenko, B.A. Brown, P.D. Cottle, M. Chromik, T. Glas-
macher, G. Hackman, R.W. Ibbotson, K.W. Kemper, T. Otsuka, L.A. Riley, and
H. Scheit. Spectroscopy of the 21+ state in 220 and shell structure near the
neutron drip line. Phys. Lett. B, 485216, 2000.

[11] BA. Brown. New Magic Nuclei Towards the Drip Lines. Proceedings of the 10“1
International Conference on Nuclear Reaction Mechanisms ( ed. by E. Gadiolil)

Ricerca Scientifica ed Educazione Permanente, Supplemento N. 122:41, June 9-
13, 2003 Varenna, Italy.

[12] T.S.S. Kuo and GE. Brown. Structure of Finite Nuclei and the Free N ucleon-
Nucleon Interaction. Nucl. Phys, 85:40, 1966.

[13] T.S.S. Kuo. State Dependence of Shell-Model Reaction Matrix Elements. Nucl.
Phys. A, 103271, 1966.

107

 

[14]

[15]

[16]

[17]

[18l

{19]

[20]

1211

[22]

[23]

[24l

 

B.H. Wildenthal. Empirical Strengths of Spin Operators in Nuclei. . Prog. in
Part. and Nucl. Phys, 11:3, 1984. A

B.A. Brown and B.H. Wildenthal. Status of the Nuclear Shell Model. Annu.
Rev. of Nucl. Part. Sci, 38:29, 1988. l

M. Belleguic, M.-J. Lopez-Jimenez, M. , Stanoiu, F. Azaiez, M.-G. Saint-Laurent,
O. Sorlin, N .L. Achouri, J .-C. Angelique, C. Bourgeois, C. Borcea, J .-M. Daugas,
C. Donzaud, F. De Oliveira—Santos, J. Duprat, S. Grévy, D. Guillemaud-Mueller,
S. Leenhardt, M. Lewitowicz, Yu.-E. Penionzhkevich, and Yu. Sobolev. In-beam
y-spectroscopy using projectile fragmentation: Structure Of neutron-rich nuclei
around N = 20. Nucl. Phys. A, 682:136c, 2001.

T. Otsuka, R. Fujimoto, Y. Utsuno, B.A. Brown, M. Honma, and T. Mizusaki.
Magic Numbers in Exotic Nuclei and Spin-Isospin Properties of the NN Interac-
tion. Phys. Rev. Lett, 872082502, 2001.

T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe, and Y. Akaishi. Evolution of
Nuclear Shells due to the Tensor Force. Phys. Rev. Lett., 95:232502, 2005.

A. Ozawa, T. Kobayashi, T. Suzuki, K. Yoshida, and I. Tanihata. New Magic
Number, N = 16, near the Neutron Drip Line. Phys. Rev. Lett, 84:5493, 2000.

T. Motobayashi, Y. Ikeda, K. Ieki, M. Inoue, N. Iwasa, T. Kikuchi, M. Kurokawa,
S. Moriya, S. Ogawa, H. Murakami, S. Shimoura, Y. Yanagisawa, T. Nakamura,
Y. Watanabe, M. Ishihara, T. Teranishi, H. Okuno, and RF. Casten. Large defor-
mation Of the very neutron-rich nucleus 32Mg from intermediate-energy Coulomb
excitation. page 9, 1995.

M. Staniou, F. Azaiez, ZS. Dombradi, O. Sorlin, B.A. Brown, M. Belleguic,
D. Sohler, M.G. Saint Laurent, M.J. LOpez-Jiménez, Y.E. Penionzhkevich,
G. Sletten, N.L. Achouri, J.C. Angelique, F. Becker, C. Borcea, C. Bour-
geois, A. Bracco, J.M. Daugas, Z. Dlouhy, C. Donzaud, J. Duprat, Zs. Fiilép,
D. Guillemaud-Mueller, S. Grévy, F. Ibrahim, A. Kerek, A. Krasznahorkay,
M. Lewitowicz, S. Leenhardt, S. Lukyanov, P. Mayet, S. Mandal, H. van der
Marel, W. Mittig, J. Mrazek, F. Negoita, F. De Oliveira—Santos, Zs. POdolyak,
F. Pougheon, M.G. Porquet, P. Roussel-Chomaz, H. Savajols, Y. Sobolev,
C. Stodel, J. T imar, and A. Yamamoto. N = 14 and 16 shell gaps in neutron-rich
oxygen isotopes. Phys. Rev. C, 691034312, 2004.

G. Thiamova, N. Itagaki, and T. Otsuka. Study of the structure of light nuclei
by AMD+GCM method. Czech. JP, 542329, 2004.

E. Khan, N. Sandulescu, M. Grasso, and Nguyen Van Giai. Continuum quasi-
particle random phase approximation and the time-dependent Hartree-Fock-
Bogoliubov approach. Phys. Rev. C, 66:024309, 2002.

Y. Utsuno, T. Otsuka, T. Mizusaki, and M. Honma. Varying shell gap and
deformation in N = 20 unstable nuclei studied by the Monte Carlo shell model.
Phys. Rev. C, 602054315, 1999.

108

 

 

 

 

[25] T. Siiskonen, P.O. Lipas, and J. Rikovska. Shell-model and Hartree-Fock calcu-
lations for even-mass 0, Ne, and Mg nuclei. Phys. Rev. C, 60:034312, 1999.

[26] A. Volya and V. Zelevinsky. Discrete and Continuum Spectra in the Unified
Shell Model Approach. Phys. Rev. Lett, 94:052501, 2005.

[27] A. Obertelli, S. Péru, J.-P. Delaroche, A. Gillibert, M. Girod, and H. Goutte.
N = 16 subshell closure from stability to the neutron drip line. Phys. Rev. C,
712024304, 2005.

[28] B.A. Brown. private communication.

[29] G. Audi, A.H. Wapstra, C. Thibault, J. Blachot, and O. Bersillon. The 2003
AME: (II). Tables, graphs and references. Nucl. Phys. A, 729:337—676, 2003.

[30] J .-L. Lecouey. Is 240 a doubly magic nucleus? Proposal for PA C27.

[31] D. Bazin, B.A. Brown, GM. Campbell, J.A. Church, D.C. Dinca, J. Enders,
A. Gade, T. Glasmacher, P.G. Hansen, INF. Mueller, H. Olliver, B.C. Perry,
B.M. Sherrill, J .R. Terry, and J .A. Tostevin. New Direct Reaction: Two-Proton
Knockout from Neutron-Rich Nuclei. Phys. Rev. Lett, 912012501, 2003.

[32] PG. Hansen and J .F. Tostevin. private communication.

[33] A. Stolz, T. Baumann, T.N. Ginter, D.J. Morrissey, M. Portillo, B.M. Sherrill,
M. Steiner, and J .W. Stetson. Production Of rare isotope beams with the NSCL

fragment separator. Nucl. Instr. and Meth. B: Beam Interactions with Materials
and Atoms, 241 (1-4):858—861, 2005.

[34] MD. Bird, S.J. Kenney, J. Toth, H.W. Weijers, J.C. DeKamp, M. Thoennessen,
and A. Zeller. System Testing and Installation of the NHMFL/ N SCL Sweeper
Magnet. IEEE Trans. Appl. Supercond., 15 (2)21252—1254, 2005.

[35] T. Baumann, J. Boike, J. Brown, M. Bullinger, J.P. Bychoswki, S. Clark,
K. Daum, P.A. DeYoung, J.V. Evans, J. Finck, N. Frank, A. Grant, J. Hin—
nefeld, G.W. Hitt, R.H. Howes, B. Isselhardt, K.W. Kemper, J. Longacre, Y. Lu,
B. Luther, S.T. Marley, D. McCOllum, E. McDonald, U. Onwuemene, P.V.
Pancella, G.F. Peaslee, W.A. Peters, M. Rajabali, J. Robertson, W.F. Rogers,
S.L. Tabor, M. Thoennessen, E. Tryggestad, R.E. Turner, P.J. VanWylen, and
N. Walker. Construction of a modular large-area neutron detector for the N SCL.
Nucl. Instr. and Meth. A, 543:517—527, 2005.

[36] B. Luther, T. Baumann, M. Thoennessen, J. Brown, P. DeYoung, J. Finck,
J. Hinnefeld, R. Howes, K. Kemper, P. Pancella, G. Peaslee, W. Rogers, and
S. Tabor. MONA —— The Modular Neutron Array. Nucl. Instr. and Math. .4,
505233—35, 2003.

[37] W.A. Peters. Ph. D. Thesis. in preparation, Michigan State University, 2006.

109

[38] R. Fox, C. Bolen, K. Orji, and J. Venema. NSCLSpecTcl Meet-
ing the Needs of Preliminary Nuclear Physics Data Analysis.
http: / / www. tcl. tk/ community / tcl2004 / Papers / RonF 023/ for. pd f.

[39] CERN EurOpean Laboratory for Particle Physics. PAW, Physics Analysis Work-
station. http://paw.web.cern.ch/paw/, 2006.

[40] O. Tarasov and D. Bazin. LISE++ 2 design your own spectrometer. Nucl. Phys.
A, 746:411, 2004.

[41] M. Berz and J. Hoefkens. COSY INFINITY Version 8.1 Programming Manual.
Technical Report MSUCL-1196, National Superconducting Laboratory, Michigan
State University, East Lansing, MI 48824, see http://cosy.nscl.msu.edu/, 2001.

[42] Leo, W.R. Techniques for Nuclear and Particle Physics Experiments. Springer—
Verlag, 1994.

[43] M. Berz, K. Joh, J.A. Nolen, B.M. Sherrill, and AF. Zeller. Reconstructive

correction of aberrations in nuclear particle spectrographs. Phys. Rev. C, 47 :537—
544, 1993.

[44] AM. Lane and RC. Thomas. R—Matrix Theory of Nuclear Reactions. Rev. of
Mod. Phys, 30.257, 1958.

[45] F. Deak, A. Kiss, Z. Seres, G. Caskey, A. Galonsky, and B. Remington. Method
for the study of neutron emission from light fragments in intermediate energy
heavy-ion collisions. Nucl. Instr. and Meth. in Phys. Res. A, 258:67—74, 1987.

[46] RA. Kryger, A. Azhari, A. Galonsky, J .H. Kelley, R. Pfafi, E. Ramakrishnan,
D. Sackett, B.M. Sherrill, M. Thoennessen, J .A. Winger, and S. Yokoyama. Neu-
tron decay of 10Li produced by fragmentation. Phys. Rev. C, 472R2439, 1993.

[47] B. Jurado, H. Savajols, W. Mittig, N.A. Orr, P. Roussel—Chomaz, D. Baiborodin,
W. Catford, M. Chartier, CE. Demonchy, Z. Dlouhy, A. Gillibert, L. Giot,
A. Khouaja, A. Lépine—Szily, S.M. Lukyanov, J. Mrazek, Y.E. Penionzhkevich,
S. Pita, M. Rousseau, and A.C.C. Villari. Odd Even Staggering of Binding
Energies and Evolution of the N = 28 Shell Closure far from Stability. in press.

[48] C. Hoffman. Ph. D. Thesis. in preparation, Florida State University.

110

A

lllllllllllllllllll