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dissertation entitled

11

The Electromagnetic Excitation of Li

presented by

Donald w. Sackett

has been accepted towards fulfillment
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_.m..____——__._—

THE ELECTROMAGNETIC EXCITATION
OF 11Li

By

Donald W. Sackett

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

1992

ABSTRACT

ELECTROMAGNETIC EXCITATION OF uLi

By

Donald W. Sackett

Abstract

A kinematically complete measurement of the Coulomb dissociation of a 28 MeV / nucleon
beam of 11Li into 9Li and two neutrons by a Pb target has been performed. From
the energies and angles of the emitted neutrons and of 9Li , the excitation energy
E of 11Li was determined on an event-by-event basis, and the Coulomb dissociation
cross section as a function of excitation energy was constructed. The dipole strength
function dB(E 1) / (IE and the photonuclear spectrum, 031(E), were determined from
the Coulomb dissociation spectrum. The photonuclear spectrum 031(E) has a peak
at E=1.0 MeV and a width 1‘ = 0.8 MeV. These parameters are consistent with the
picture of a soft dipole resonance but a significant post-breakup Coulomb acceleration

of 9Li suggests a direct breakup.

The complete kinematical measurement also allowed neutron and 9Li momentum
distributions to be constructed in the rest frame of the 11Li . The momentum distri-
butions were fitted with Gaussian functions, yielding width parameters of 09 = 18 i4
MeV/c and 0,. = 13 :i: 3 MeV/c. A more general feature of the breakup mechanism
of 11Li could be deduced from these measurements. It was found that the 9Li and
neutron momentum distributions, and the neutron-neutron relative momentum dis-

tributions, could be reproduced if the 11Li excitation energy was partitioned between

the 9Li and the neutrons by a 3-body phase space distribution. This indicates there

is no directional correlation between the halo neutrons.

To my parents, who always wondered when I would finish school

iii

ACKNOWLEDGEMENTS

First, I would like to thank my thesis advisor, Dr. Aaron Galonsky, for his pa-
tience, support and humor through my entire career as a graduate student. He
managed to teach a very inexperienced student, one who did not even have an un-
dergraduate degree in physics, a great deal about experimental nuclear physics in a
short period of time. I credit his great concern for the welfare and development of

his students for much of this achievement.

I would like to thank Dr. Kazuo Ieki, a visiting professor from Rikkyo University,
for all of his work on the data analysis of the 11Li and the 7Li(p,n) experiments.
Without his co-analysis of the data, and particularily his work with the cross-talk
analysis, this thesis would have been delayed at least another six months, perhaps
longer. I also would like to thank the many collaborators for helping to make the
experiments a success. In particular, I should single out Adam Kiss, Ference Deak,
Zoltan Seres and Akos Horvath to thank them for their extensive help with many
features of the experiments, and for their wonderful hospitality during my one but
very memorable visit to Hungary. I would like to thank my committee for their
careful reading of my thesis and helpful suggestions. I also thank the A1200 people

for providing a stable and ”intense” 11Li beam.

N o acknowlegement would be complete without mentioning the help received from
fellow students. I would like to thank my office-mates Jim Clayton, Mike Mohar and
Matts Cronqvist for their lessons in electronics and data acquisition, and for rarely
telling me to look it up in the #$#%# manual. I would also like to thank their
replacements, Mathias Steiner, Brian Young and Raman Pfaff, for keeping things
lively in the office during the bleak months of data analysis, although their humor,

political discourse and fear of daylight probably prolonged my stay at the N SCL by

iv

at least a couple months. I would also like to thank Raman for letting me stay at
his apartment (the landfill) for two months while I put the finishing touches on this
thesis. I thank John Winfield for answering my many questions about SARA and
Ron Fox for teaching me all about data acquisition, interval training and Sushi. I
should in general thank all of the cyclotron staff members for their help in making the
11Li experiment a successful one, and I thank the N SCL for their generous financial

support during the course of my graduate studies.

Finally, I would like to thank my wife Lisa, who provided the support and en-
couragement so necessary during the occasional difficult times of the last 5 years.
Whether I was studying for exams, setting up an experiment, hurriedly putting to-
gether a seminar for a job interview or preparing for the thesis defense, she could
always find time to pitch in and make things easier, even though she was also in the
midst of a difficult Ph.D. program. Without her companionship during these years,

I might well have given up on this whole endeavor. I will always be grateful to her.

Contents

LIST OF TABLES
LIST OF FIGURES
1 Introduction

2 Experimental Setup

2.1 The 11Li Beam ............
2.1.1 The Fragment Detectors . . .
2.1.2 The Neutron detectors . . . .

2.1.3 Cross-Talk ...........
3 Telescope Data
4 One-neutron 9Li Coincidence Results

5 Two-Neutron-9Li Coincidence Results
5.1 The Decay Energy Spectrum . . . .

5.2 dB(E1)/dE and 031(E) .......

5.3 Post-breakup Coulomb Acceleration

vi

OOOOOOOOOOOOOOOOOO

OOOOOOOOOOOOOOOOOO

viii

ix

10

11

13

21

29

36

43

5.4 Momentum Distributions ........................ 54

6 Summary 59
Appendices ‘ 62
Appendix A: Energy Calibrations of Telescope Detectors 62
I. The Silicon Detectors . : .......................... 62
II. The CsI(Tl) Detector ............................ 65
Appendix B: Calculation of the Decay Energy 70
Appendix C: Correction for Post-Breakup Coulomb Acceleration 78
Appendix D: Results from the 7Li(p,n) Experiment 83
Appendix E: The Virtual Photon Spectrum 90
Appendix F: Electronics and Data Acquisition 95
I. Neutron Detectors .............................. 95
II. Fragment Detectors ............................. 101
III. Beam Detectors ............................... 104
IV. Data Acquisition .............................. 104
LIST OF REFERENCES 106

vii

List of Tables

3.1 Compilation of cross sections from the telescope data, the 1n-9Li data,
and the 2n-9Li data. The total two-neutron removal cross section is

. given by 02,, and 01,, is the total neutron cross section from the inte-
grated neutron angular distribution. The cross sections for Coulomb

and nuclear dissociation are denoted by ac and mm, respectively. B(El)

is the total strength and 051 is the photonuclear cross section, deter-
mined from the two-neutron 9Li coincidence data. The quantity “June

was calculated in ref. [40] and "ac was determined from the difference

between 02,, and “0mm. .......................... 28

A.1 Ions and their energies present in the calibration beams . . . . . . . 69

viii

List of Figures

1.1

2.1

2.2

2.3

2.4

3.1

Coulomb excitation of a 11Li projectile. The Pb target acts as a source
of virtual photons. An excitation to the continuum followed by decay

to 9Li and two neutrons, with decay energy Ed is also shown ......

The detector setup. The detector telescope is located at zero degrees
inside the target chamber, 15 cm downstream from the target. The

neutron detectors are mounted in two styrofoam blocks. .......

(a) A Time-of-flight spectrum for 9Li /7-ray coincidence events. (b)

Time-of-fiight spectrum for 9Li -neutron coincidence events. .....

A n-n relative momentum spectrum due to cross-talk events only, using

the 7Li(p,n) reaction to produce neutrons at 27 MeV ..........

A n-n relative momentum spectrum from the 11Li data. (A) before
subtracting the cross-talk background measured from the 7Li(p,n) ex-
periment. (b) After subtracting the cross-talk contamination. The his-
togram is the prediction of a 3-body phase space simulation discussed

in Section 5.4 ...............................

(a) Two dimensional AE-E plot for the fragment singles events. Only
the region around the 9Li and 11Li is shown. (b) A similar plot, but

requiring at least one neutron in coincidence with the 9Li fragment. .

ix

14

18

20

22

3.2

4.1

4.2

5.1

5.2

5.3

5.4

(a) A one-dimensional particle identification spectrum for target-in
data (solid histogram) and target-out data (dashed histogram). (b)
The subtracted result. The 9Li peak is near PID=880. The under-
subtraction and over-subtraction have been downscaled by a factor of

ten for plotting purposes. ........................

Neutron energy distributions for target-in (solid points) and target-
out (open points) data are shown in (a). The low energy portion is
due to 11Li dissociation in the Csl. The subtracted result, showing the

neutron energy distribution due to the Pb only, is shown in (b).

Measured angular distribution for 11Li + Au at 29 MeV/ nucleon taken
from [32] is shown with the open diamonds. The solid points represent
the angular distribution for 11Li + Pb at 28 MeV/A (this work). The
dotted lines are fits using narrow and broad gaussians. The dashed

line is the sum of both components ....................

Decay energy spectrum for (a) target in, (b) target out, and (c) the
subtracted result. The target out data result from 11Li dissociation in

the silicon detectors and the Csl detector. ...............
Decay energy spectrum gated on impact parameter, for b> 15 fm. . .
Detection efficiency as a function of decay energy. ...........

Experimental resolution for decay energies of 0.1 MeV, 0.5 MeV and 1.0
MeV is shown in a-c, respectively. The width (see text for definition)

as a function of decay energy is shown in (d). .............

24

30

32

38

40

42

45

5.5

5.6

5.7

5.8

The decay energy spectrum. (a) The solid line is the product of a
Breit-Wigner function with E0 = 0.7 MeV and F = 0.8 MeV and the
photon spectrum, after being filtered through the detector system. (b)
The solid line is the photonuclear spectrum corresponding to the Breit-
Wigner parameters determined from the data. (c) The solid line is the
dipole strength function determined from the data. The dashed line is
a calculation using a cluster model and the dotted line comes from a

correlated 3-body calculation. ......................

Spectrum for the magnitude of the velocity difference V9 - V2“, where
V2,, is the average velocity of the two detected neutrons, is shown in
(a). The histogram is the result of a simulation using an initial distri-
bution with the velocity difference peaked at zero. Spectrum for the
z-component of the center of mass velocity before breakup subtracted
from the center of mass velocity after breakup is shown in (b). The
near-zero centroid reflects overall momentum conservation. The width
of the peak, about 0.008c FWHM, represents the overall velocity res-

olution of the system ............................

Schematic view of a 11Li breakup. The average impact parameter is
b=20 fm, the distance from the lead nucleus where the'breakup occurs
is denoted by r, V is the beam velocity and 1' is the meanlife of the

resonance. .................................

(a) 9Li momentum distibution determined in the 11Li rest frame. The
histogram is the result of a simulation of 11Li breakup with the decay
energy partitioned by a 3-body phase space distribution. (b) Neutron
momentum distribution in the 11Li rest frame. The histogram is the

result from the simulation. .......................

47

50

52

A.1

A.2

A.3

8.1

8.2

R3

Side view of target and fragment telescope setup. The telescope con-
sisted of a 300 pm strip detector, a 300 pm silicon detector, and 1.2
cm thick CsI(Tl) detector. The front view of the strip detector shows
the pixel structure defined by the horizontal and vertical strips, used

to determine the 9Li angle .........................

(a) Energy spectrum for horizontal strip 7 using a 228Th source for
calibration. The energies of the a-particles are given in the text. (b)
Calibration for horizontal strip 7. The six calibration points were fitted

with a straight line .............................

Calibration data for the CsI(Tl) detector. The isotopes and energies
are listed in Table 2. The solid diamonds are Li isotopes, the solid
squares are Be isotopes, the solid circles are B isotopes and the stars

are C isotopes. ..............................

11Li breakup into 9Li and two neutrons. Momentum conservation re-
quires the 9Li and the two-neutron center of mass to have equal and
opposite momenta. In the rest frame of the two-neutron center of mass,

each neutron has equal and opposite momenta ..............

Contributions to the response function for 100 keV decay energies due
to neutron timing resolution, neutron angular resolution, multiple scat-
tering in the target, energy loss in the target, and the 9Li angular res-

olution. The total resolution function is shown in (f). .........

Contributions to the response function for 500 keV decay energies due
to neutron timing resolution, neutron angular resolution, multiple scat-
tering in the target, energy loss in the target, and the 9Li angular res-

olution. The total resolution function is shown in (f). .........

' xii

63

66

68

72

75

76

C.1

C.2

D.1

D.2

D.3

D.4

E.1

E.2

(a) Longitudinal (2) component of 9Li and average neutron relative
velocity for each event. (b) Relative velocity difference after correcting

9Li for post-breakup Coulomb acceleration ................

(a) Decay energy spectrum before correcting for post-breakup Coulomb

acceleration. (b) Decay energy spectrum after the correction ......

(a) Sketch of a typical cross talk event, which yields false neutron-

neutron coincidence events. (b) True coincidence event .........

AEn spectrum constructed from the pure cross talk events from the
7Li(p,n) reaction. The dashed vertical lines indicates the gate used for

cross talk rejection in the AF." spectrum from the 11Li data .....

(a)AE,, spectrum from the 7Li(p,n) reaction for cross-talk between
detectors in the same detector array. (b) Similar spectrum, but for

cross-talk events between detectors in different arrays ..........

AF.“ spectrum from the 11Li data. Here, the events are a mixture of
cross-talk and true coincidences. The vertical dashed lines indicate the

gate used for rejecting cross-talk events. ................

Three different calculations are shown for the equivalent photon spec-
trum. (a) The solid line uses the expression valid for all beam projectile
energies, the dotted line is the result of an approximation for interme-
diate energies [50] and the dashed line is the result of a relativistic

approximation ...............................

Calculation of the equivalent photon spectrum using the relativistic
approximation for hm," = 9 fm (dotted line), bm,n = 10 fm (solid line),

and bmgn = 11 fm ( dashed line). . i ....................

xiii

81

82

84

85

87

88

92

94

F.1 Electronics setup for the neutron detector signal processing. The mod-

ule abbreviations are defined in the text. ................ 96

F2 Schematic of the timing for the leading and delayed neutron. Each
signal has a separately timed gate for the QM, signal. Both the gate
and the analog signal are put into the Linear Gate module. The Qto,

gate is used in the ADC modules for both the QM and QM; signal. . 98

F.3 Electronics processing for the fragment and beam detector signals. The

module abbreviations are defined in the text ............... 102

xiv

Chapter 1

Introduction

The increasing availablility of radioactive nuclear beams has led to the discovery
of several unique properties of light, neutron-rich nuclei. The 11Li nucleus, with 3
protons and 8 neutrons has probably received the most attention, both theoretically
and experimentally, due to its rather unique structure. In the first experiments to
use a 11Li beam, Tanihata et al. [1] measured the total interaction cross section for
11Li and determined the matter radius from the interaction cross section. They also
determined the interaction cross sections and matter radii for 6Li, 7Li, 8Li and 9Li,
and found that 11Li has a larger matter radius than would be expected from the
systematics of the matter radii of the less neutron-rich lithium isotopes. This large
matter radius implies a long tail in the 11Li density distribution. In a subsequent
experiment, Kobayashi et al. [2] found that the transverse momentum distribution
of 9Li from the fragmentation of 11Li nuclei has a much narrower width than that
expected from the Goldhaber model[3] of projectile fragmentation. The narrow width
was interpreted to mean that the density distribution of 11Li has a large spatial extent
and the two valence neutrons form a neutron halo around the 11Li nucleus [2, 4, 5].
This halo structure arises from the long tail of the wave function of the valence
neutrons due to their small binding energy (82,, = 0.34 MeV [6]). Hence, the halo is

expected to be a common feature of nuclei along the neutron drip line.

1

It was also found that the two-neutron removal cross section of 11Li increased
with the atomic number of the target and became extremely large for high-Z targets
such as Pb. To explain the target charge dependence, it was suggested that the
Coulomb excitation cross section for 11Li is large. Thus a high-Z target would act as
a source of photons that bombard the 11Li projectile as it passes [7]. Since llLi has
no bound excited states, 10Li is unbound to neutron decay, and 9Li is particle stable
up to 4.06 MeV [8], Coulomb excitation of 11Li up to 4.4 MeV leads only to Coulomb
dissociation into a 9Li and two neutrons. To explain the large Coulomb dissociation
cross section, a new type of collective excitation was proposed [4, 9, 10]. In this
excitation mode, called a soft dipole resonance (SDR), the 9Li core oscillates against
the halo neutrons in the 11Li nucleus. This resonance is therefore fundamentally
different from the giant dipole resonance (GDR), where all the neutrons oscillate
against all the protons. For the SDR, the restoring force of the oscillation is weak
because of the low density of the halo, hence the excitation energy of the resonance is
expected to be low, near 1 MeV [4, 10], in contrast to the GDR, where the excitation
energy would be about 23 MeV [11]. There have been several theoretical studies of
the excitation of the SDR [4, 12, 13, 14, 15], but little experimental work has been
reported so far because it is necessary to measure the angle and energy of the 9Li and
of both neutrons in order to deduce the excitation energy and shape of the SDR.
The complete kinematical measurement also allows us to investigate the correlations
between the two neutrons. Because 10Li is unbound, the pairing interaction between
the two halo neutrons must be crucial to the formation of a bound 11Li system and
should play a key role in the halo structure. It has been suggested that the interaction
between the halo neutrons may be strong enough to form a dineutron, and that the
1‘Li structure may consist of a dineutron bound to a 9Li core [4]. The goals of this

work were to use the information from a complete kinematic measurement to search

for the soft dipole resonance and to better understand the interaction between halo
neutrons as well as their interaction with the 9Li core. We present a A brief review
of the formalism of Coulomb excitation theory is presented followed by a detailed
description of the experiment. Next results from. the 9Li singles data and the one-
neutron-gLi coincidence (1n-9Li ) data are presented. Finally, several results from the
two-neutron/9Li coincidence (2n-9Li ) events are presented. Some of the results have

been presented in an earlier publication [16].

The basic phenomenon of Coulomb excitation is depicted in Figure 1.1. In the
rest frame of the 11Li projectile, there appears to be a projectile with a large atomic
number passing by. The 11Li nucleus ”sees” a rapidly changing electric and magnetic
field due to this projectile. The time-dependent fields can be viewed as a source of
virtual photons of various multipolarities that interact with the 11Li nucleus. Photons
with energies E greater than the neutron separation energy of 11Li may be absorbed
and either be re-emitted or induce dissociation into a 9Li and two neutrons. For
photon energies greater than 4.4 MeV, other channels are also possible, such as dis-
sociation into a 8Li and three neutrons. The bottom half of Figure 1.1 portrays a
case where a photon was absorbed at a specific energy in the 11Li continuum. The
energy difference Ed=E-Szn is referred to as the decay energy, and it is distributed
between the emitted 9Li and neutrons. The soft dipole resonance is predicted to lie in
this continuum, near E=1 MeV, hence E; z 0.7 MeV since 32,, = 0.34 MeV [6]. The
measurement of the angles and energies of the 9Li and neutrons yielded the value of
Ed on an event-by-event basis, which allows the Coulomb dissociation cross section
to be determined as a function of excitation energy. The terms Coulomb excitation
and Coulomb dissociation will be used interchangeably in the remainder of this work
since Coulomb excitation of 11Li up to 4.4 MeV is equivalent to Coulomb dissociation

of 11Li into a 9Li and two neutrons.

 

It.

2n

 
  

Virtual
Photons

“Li beam at 28 MeV/nucleon

Pb

Figure 1.1: Coulomb excitation of a 11Li projectile. The Pb target acts as a source
of virtual photons. An excitation to the continuum followed by decay to 9Li and two
neutrons, with decay energy E; is also shown.

The cross section (120/ dEdQ for electromagnetic excitation of a projectile in the
Coulomb field of a target was derived in first order perturbation theory by Alder and
Winther [17]. Specializing to electric dipole excitation, A = l, and following Ref. [18]
find:

dado _ deU'lfl) 0191(5)) (11)
«113.10 ' d0 E .

 

 

Here, E is the excitation energy delivered to the projectile and (IQ is the element of
solid angle into which the projectile deflects. The photonuclear cross section 031(E)

is related to the dipole strength function dB(E 1) /dE by:

167r3 E dB(E1)

 

 

 

mm) = 97w dE (1'2)
The quantity dN51(E,Q)/dfl is given by [18]:

dN E,Q Z20 c _, 52-1 , . ‘

gr) = figwe‘sze ‘[ [Mao]? + [1.45012] (1.3)

Here, Z1 is the target charge, a is the fine structure constant, v is the relative velocity,
a is half the distance of closest approach for a head on collision in a strictly Coulomb
potential, 7 is the Lorentz boost for the relative velocity v, 5 = Ea/h'yv and 6 is
the Coulomb deflection angle of the projectile. The angular dependence in Eq. 1.3
is given in terms of 5, the eccentricity of the Coulomb orbit, which is related to the
Rutherford scattering angle by a = 1/ sin(0/2). The function K5455) is a modified
Bessel function of imaginary argument, and 1655(5) is the derivative of K with respect
to the argument. Eq. 1.1 can be integrated over all pure Coulomb orbits to yield the

cross section as a function of the excitation energy:

is: - NEKE)
dE - E

 

051(E) (1.4)

N 3103) , referred to as the equivalent photon spectrum, is a dimensionless function

of the projectile energy and the excitation energy E. N 51(E) represents the number

of virtual photons at energy E available to the projectile from the Coulomb field of
the target. The quantity 031(E) reflects the probability that the nucleus will absorb
an E1 photon of energy E. Thus, the cross section for E1 excitation to energy E
is a product of the number of El photons available at an energy E multiplied by
the nuclear strength for absorbing such a photon. This formulation of the Coulomb
excitation cross section is known as the equivalent photon method [18]. It has a
long history of success in predicting the excitation of low-lying collective states in
stable projectiles [17], so it is natural to extend the method to a search for low-
lying El states in neutron-rich nuclei such as 11Li . 1 One of the appealing features
of the method is that the measurable quantity in the laboratory, doc/dE, is related
in a straightforward manner to the quantities of theoretical interest, dB(E 1) / dE' or

031(5)), by the photon spectrum. Thus a measurement of doc/dE and a calculation

of N31(E) will yield dB(E1)/dE and 031(E) directly.

Contributions from other multipoles, specifically M1 and E2, were estimated to
be negligible. The expression for N 31(E), valid for all projectile energies, is given
in [18]. An approximate expression for relativistic projectile energies is also given
in [18]. For a 11Li beam at 28 MeV/nucleon, the relativistic approximation agreed
with the exact calculation to within 2%. Both the M1 and the E2 photon spectra,
NM1(E) and N 52(E), were calculated in the relativistic approximation as well [18].
The M1 spectrum was several orders of magnitude less than the El spectrum, but
the E2 spectrum was about 400 times greater than the E1 spectrum in our energy

range [18]. However, it has been shown for several models of the 11Li nucleus that

052(E) < III-5031(E) [19]. Hence, NE2(E)0E2(E) < 0H004N31(E)0'E1(E)

Chapter 2

Experimental Setup

2.1 The 11Li Beam

The 11Li beam striking the lead target had an average energy of 30 MeV/nucleon.
This beam energy was used because the neutron cross-talk problem (see below)
becomes more tractable if lower energy neutrons are present and because the El
Coulomb excitation cross section is inversely proportional to the beam energy. Of
course, an even lower beam energy could have been chosen to further exploit these
effects. However, the 11Li beam was produced via projectile fragmentation of an 18O
beam at 80 MeV/ nucleon, and both the intensity and quality of the 11Li beam suffer

as either the 18O beam energy or the 11Li beam energy are lowered.

A 0.7 g/cm2 9Be production target was bombarded with an 80 MeV / nucleon 1806"”
primary beam produced by the K1200 cyclotron at Michigan State University. The
primary beam current was 1.2 x 1011 particles/s. The 11Li exiting the production
target had an average energy of 61 MeV/ nucleon. The 11Li was separated from most
other reaction products by the A1200 Fragment Separator [20]. After exiting the frag-
ment separator, the 11Li beam traversed two dipole magnets and several quadrupole
magnets and was further degraded to 30 MeV/nucleon before reaching the experi-

mental vault and 0.60 g/cm2 Pb target. A 7 cm thick plastic scintillator (called Sl)

on a phototube was placed after the first dipole magnet to reduce the beam energy.
The dipole magnet produced a dispersion in the beam, hence 81 was machined into
a wedge-like shape to match the predicted dispersion, thereby minimizing the energy
spread induced in the 11Li beam by 81. After 81, the beam traversed the second
dipole (a 14 ° bend) and entered the experimental area. The experimental area was
shielded from the beamline containing 81 by a concrete wall 1.4 m thick. Because
of the 14 ° bend in the beamline and the concrete wall, few neutrons produced by
reactions in 81 reached the neutron detector array. The time of flight (TOP) of each
beam particle was measured across a 15.45 meter flight path between 31 and the first
AE detector in the fragment telescope (described in the next section). The average
energy of the final beam striking the Pb target was 30 MeV/ nucleon, with a spread of
:i: 2.5 MeV/ nucleon. Energy loss in the tartet was 4.0 MeV/nucleon. An average of
400 11Li ’s/ second reached the Pb target, and the beam was approximately 80% 11Li .
The four most prevalent contaminants were 12% 8H8 at 25 MeV/ nucleon, 6% tritons
at 45 MeV/ nucleon, 1% 9Li at 45 MeV/ nucleon and 0.02% 14Be at 33 MeV/ nucleon.
Although it was possible for these contaminants to react with Pb and produce a 9Li ,
only MBe would have produced 9Li at high enough energies to be included in the
gated 9Li spectrum from 11Li dissociation. The energy of 9Li from 11Li dissociation
in the Pb target was 28 :l: 2 MeV/ nucleon. The possible contribution from the 14Be

was neglected because of the small percentage present in the beam.

The detector set-up is shown in figure 2.1. The beam spot size at the lead target
was large, about 2.5 cm x 2.5 cm, and the average angular spread of the incident beam
was 0.5 ° , so it was also necessary to measure the incident angle and target position
of each 11Li particle to accurately determine the angle of the emitted 9Li fragment.
This was done with two position-sensitive parallel plate avalanche counters (P PACs)

separated by 1.09 m. With the position information from the PPACs, the incident

Neutron Detectors
(64 total)

Charged-Particle
Veto Paddle

   

; fl
,, ~ 2 , ” .]
%N g/ sue-rm)

xx Telescope
/ \‘\I \‘~
L \ ‘\

“~\ ‘~. Lead

‘\ “s
\ ‘~, Target
\ \\\\“‘

' PPACe (x, Y)

 

 

 

 

 

Figure 2.1: The detector setup. The detector telescope is located at zero degrees
inside the target chamber, 15 cm downstream from the target. The neutron detectors
are mounted in two styrofoam blocks.

10

angle and target position of the 11Li particle could be calculated. The PPACs were
filled with isooctane gas at a pressure of 5 Torr. The signals in the PPACs were
resistively divided into up, down, left and right signals. From these pulse heights,
the particle position in each PPAC was calculated with a resolution of 1.5 mm. The

PPAC detection efficiency for 11Li was greater than 99.7%.

2.1.1 The Fragment Detectors

The 11Li and 9Li fragments were detected and identified with a silicon/CsI(Tl) tele-
scope centered at 0° . The telescope consisted of two silicon AE detectors and a
CsI(Tl) E detector. The first AE detector was a MICRON position sensitive silicon
strip detector 5 cm x 5 cm x 300 pm, consisting of 16 horizontal strips on one side
and 16 vertical strips on the other [21]. Each strip was 3.125 mm wide, the detector
was 14.6 cm from the target and it subtended a half-angle of 9 ° . The group of 16
horizontal and 16 vertical strips could be thought of as forming a grid consisting of
256 square pixels with sides of length 3.125 mm. The angle of the 9Li was determined
by the pixel that the particle traversed and that pixel was identified by the AE signals
from the horizontal and vertical strips that were struck. A fast signal was also picked
off of the AE pulse coming from the struck horizontal strip. The fast signal provided
a stop for the neutron TOF measurement and a start for the incident 11Li TOF mea-
surement. Three of the horizontal strips (#8,#15 and #16) did not work during the
experiment. The second silicon AE detector was placed behind the strip detector to
increase the ratio of energy loss to straggling. This detector was a MICRON 5cm x

5cm x 300 pm silicon detector.

The remaining energy was measured with a rectangular 6 cm x 6 cm x 1.2
cm thick CsI(Tl) crystal, the light being read-out with four Hamamatsu S3204 pin
diodes attached to the back of the CsI(Tl) crystal. The Csl(Tl) was calibrated with

11

9Li beams of energies of 34.0 MeV / nucleon and 45.0 MeV/ nucleon. The calibration
beams were also produced by the fragmentation of 18O on a 9Be target and separated
by the A1200 Fragment Separator. Although in general the light output from CsI(Tl)
is not proportional to the deposited energy, for high energy particles over a limited
energy range, the response is quite linear [22]. Therefore two calibration points for
9Li were sufficient. The 9Li energy spread was limited to 0.6% full width at half

maximum (FWHM). Both 81 and the Pb target were removed during the calibration.

One disadvantage of CsI(Tl) crystals is that their light output response may de-
pend upon where the particle strikes the crystal due to non-uniformity of the thallium
doping [23]. Using the grid defined by the silicon strip detector, the CsI(Tl) crystal
could also be considered a grid of 256 square pixels. For each calibration beam, the
light output from each pixel was determined separately. The light output varied by
as much as 25% over the area of the crystal. Therefore, a separate calibration was
made for each pixel region. Using this technique, the energy resolution was about
2% F WHM, or 6 MeV for the lower energy calibration beam, and the problem of
the non-uniformity of the crystal response was eliminated. In general, the light out-
put from a CsI(Tl) crystal depends not only on the incident energy, but also on the
charge Z and mass number A of the impinging particle [24, 25]. In addition to 9Li ,
the calibration beam contained small quantities of several other isotopes. Calibration
points for 7Li, 8Li, 9Be, 10Be, 11Be, 12Be, 11B, 12B, 13B, 1“B, 14C, 15C and 16C were
also available. The calibration procedure was repeated for these particles and found

a Z-dependence for all the calibrations, but a neglibible A-dependence.

2.1.2 The Neutron detectors

The neutrons were detected with an array of 54 cylindrical detectors, each about

7.4 cm thick and 12.5 cm in diameter filled with either Bicron 501 or NE 213 liquid

12

scintillator. As shown in Figure 2.1, the detectors were arranged in two layers about
5 and 6 m from the target. There were 25 detectors in the first array, and 29 in
the second. In each array the detectors were inserted into holes cut in a block of
styrofoam 20 cm thick and 1.22 m on a side. Because the dominant reaction channel
was expected to be low energy Coulomb excitation of 11Li followed by decay to a
9Li and two neutrons, the neutrons were expected to be concentrated in the forward
direction. Therefore all the detectors were placed at forward angles. The detector
arrays were centered at 0 ° and subtended a half-angle of 5 ° . The neutron energies
were measured via the time-of-flight method using the fast signal from the neutron
detector as a start and the fragment signal in AEI as the stop. The timing resolution
was 1.2 ns. A veto paddle was placed just outside the target chamber to reject any

charged particles that might reach the neutron detectors.

The 7-rays from fragment / 7-ray coincidence measurements provided the calibra-
tion for the neutron TOF measurement. Although the neutrons were predominately
in the forward direction, the 7-rays were produced much more isotropically, and al-
most all of them missed the neutron detectors. In order to produce a substantial
7-ray peak‘in the TOF spectrum of each neutron detector, each detector array was
placed 1 / 2 m from the target instead of the five or six meter distance used during the
rest of the experiment. This increased the solid angle coverage by a factor of 100 and
144 for the array at five or six meters, respectively. Also, during the calibration, the
lead target was removed and the 1.2 cm thick Csl(Tl) detector was used as a target
instead. Since the Pb and the Csl were separated by 16 cm, 7-ray peaks separated by
1.65 us would have been produced in the TOF spectrum. These 7-ray peaks might
not have been resolvable and therefore could have produced a systematic error in the

neutron TOF calibration.

The 7-ray background was determined via pulse-shape discrimination [26]. The

13

number of 7-ray/9 Li coincidences was about 10% of the number of ln—9Li coincidences.
For a neutron detector at 1.7 ° the TOF spectrum for both neutrons and 7-rays is
shown in Figure 2.2. Except for the peak at 17 ns representing the target y—rays,
(these are the target 7-rays detected when the detector arrays are at five and six me-
ters, not the target 7-rays from the TOF calibration) the 7-ray TOF spectrum is well
correlated with the neutron TOF spectrum. It is suspected that 7-rays with TOF’s
similar to the neutron TOF’s resulted from neutron reactions with the liquid scintilla-
tor or surrounding detector material in which a 7-ray was produced and made a pulse
in the same detector or a neighboring detector. The number of detected 7-rays from
such neutron reactions was estimated. Using the cross sections for 7-ray-producing
neutron reactions with the carbon in the scintillator, the carbon, oxygen and nitro-
gen in the light pipe, the silicon and oxygen in the glass cell holding the scintillator
and the aluminum in the detector housing, and considering the 7-ray efficiency of
the neutron detectors, the estimated the number ofy-ray /9Li coincidences is about
8% of the number of neutron-9Li coincidences. This is in good agreement with the
measured value of 10% and supports the hypothesis regarding the source of most of

the 7-rays.

To measure neutron background from scattering in the target chamber or sur-
rounding areas in the vault, some data were taken with a shadow bar placed just
after the target chamber, in place of the veto paddle (Figure 2.1) to block neutrons

coming directly from the target. This contribution was found to be <2%.

2.1.3 Cross-Talk

The measured triple coincidence events (9Li plus two neutrons) contain a mixture
of true neutron-neutron (n-n) events and cross-talk events. Cross-talk occurs when

one neutron makes a signal in a detector and scatters into another detector, making

l4

 

IIIT IIIIIITII'IIJIIIIII

150
(a)

100

IllllIlIIlIl

50

jIIlIIIIIIIIIIII

[III

150

(b)

100

’8

C

L0.

0

\

(l)

J.» P

C (I‘d-WW
D

O

B

_O .
__.|

(D

H

>—

IIIfiIIIIIIII

50

 

 

 

lllllllllLIlllIJl

IIIII

   

O0 50 100 150 200 250
Time-oF-Fliqht (ns)

Figure 2.2: (a) A Time-of-flight spectrum for 9Li /7-ray coincidence events. (b)
Time-of-flight spectrum for 9Li -neutron coincidence events.

15

a signal there too. Cross-talk events are most prolific for detectors that are close
together because of the large solid angle available to the scattered neutron from the
neighboring detectors. The cross talk contribution is not necessarily negligible, in
fact it can be quite large [27, 28]. Therefore some care must be taken to subtract this

contribution from the data.

The kinematics of each event were examined and those events that could have
been cross-talk were rejected. The average neutron energy was about 27 MeV. At
this energy, the most probable reactions in the neutron detector scintillator that also

yield a neutron as one of the reaction products are:

n+p—>n+p (2.1)
n+C—+n+C (2.2)
n+C—in+3a—7.6MeV , (2.3)

If a neutron is not one of the reaction products, then there is no chance of a cross-
talk event. Using a neutron detector threshold above about 1 MeV electron energy
restricts the detected events to those resulting from n-p elastic scattering because the
a—particles and carbon only create a small amount of light in the scintillator. For a
true coincidence event, the TOF of each neutron and the recoil energies of the protons
in the scintillators are measured. For a cross-talk event, the TOF of one of the target
neutrons, the time required for the same neutron to traverse the distance to the next
detector and the recoil proton energies are determined. An energy spectrum, defined
as counts per MeV versus AEn, where AEn = En-E,-Ep, was made from all the triple
coincidence events. For the cross-talk events, En is the energy of a target neutron, E,

is the energy of the recoil proton scattered by this neutron, and E, is the energy of

16

this neutron after it has scattered from the proton in the scintillator. For the cross-
talk events, AEn should be zero by energy conservation, but for true coincidences,
AEn is completely random since the energy E, is a meaningless quantity. Therefore,
a AEn spectrum will consist of a peak at AB“ = 0 for the cross-talk events and a

broad distribution from the true coincidences, which is what was observed.

A gate was drawn around the peak at AEn =0 and events within this gate were
rejected as cross-talk. The width of the gate was determined in a separate experiment
in which the 7Li(p,n) reaction was used to generate neutrons at 27 MeV and send
them into a neutron detector array of similar geometry. In this case, all n-n coinci-
dence events were cross-talk, so the AEn spectrum consisted of only a peak around
AEfl =0. The width of the gate required to reject cross-talk was taken from this spec-
trum. The width of the gate also represents the overall cross talk resolution of the
neutron detector system. Of course, in the 11Li experiment the coincidence events are
a mixture of true coincidences and cross-talk. Because the true coincidences yielded
an arbitrary value for AEn, some true coincidence events were within the AEn gate
and therefore rejected as cross-talk. Using the cross-talk rejection procedure, 20% of
the total true-plus-cross-talk events in the 11Li data were rejected during the anal-
ysis. The remaining events, called the true events, were used in the remainder of
this work. The Monte Carlo studies revealed that 13% of the events rejected could
have been true coincidences and that the set of true events contained at most a 10%
contamination by cross-talk events. The Monte Carlo study of the neutron events was
developed using the cross section data of Cecil et al. citeCecil. The n-n coincidences
from the 7Li(p,n) reaction were composed entirely of cross-talk events and were used

to test the Monte Carlo calculation.

The small cross-talk contamination in the true events were further studied to

determine if any bias was induced in specific spectra. The spectrum doc/(IE will

17

yield the photonuclear cross section as a function of excitation energy, which in turn
may reveal the shape and peak location of the soft dipole resonance. Therefore, it
is important to have a measurement of doc/dE that is reasonably free of bias from
cross-talk contamination. The spectrum for doc/dE was studied four ways. The
spectrum was constructed from all the 2n-9Li events and from only the true events.
A simulated spectrum for doc/dE was produced from the Monte Carlo simulation
with and without cross-talk rejection. For all these cases the shape of the spectrum
was equivalent within statisitcal uncertainties. Therefore it was concluded that the
10% cross-talk contamination present in the true events does not affect the shape of

the spectrum for doc/(IE.

A measurement of the n-n relative momentum spectrum might provide some in-
sight into the halo neutron interaction. For example, a narrow peak at low relative
momenta may reveal a dineutron structure for the halo neutrons, or at least indicate
the presence of a strong correlation. However, because cross-talk events are more
likely to occur between neighboring detectors, cross-talk contamination can generate
a spurious peak at low relative momentum and lead to an incorrect conclusion about
the halo neutron structure. Therefore, great care must be taken to be sure that any

peak at low relative momentum is not produced by unrejected cross-talk events.

Although the crosstalk rejection used in this work was sufficient for determining
doc/(IE, an additional analysis procedure using the results from the 7Li(p,n) reaction
was required for determining a n-n relative momentum spectrum. Because all the 2n
events from the 7Li(p,n) reaction are the result of cross-talk, a n-n relative momentum
spectrum could be made from these data consisting of only cross-talk events. The rel-
ative momentum is defined as q= % | [1'1 - 15': I. This spectrum, shown in Figure 2.3 for
the 7Li(p,n) data, has a sharp peak at 3.5 MeV/c. It is expected that the cross-talk

events from nLi breakup would also produce a peak at low q. The n-n relative mo-

18

 

 

 

4000— IIIIIIIIrrIrlrInI[IIIIITI ..]

I . I

”<7: - -
t: 30007 —-
r: _
D ’- -i
.ci - -
L- 2000— -
8 - O -+
g : 0 I
- e -1

3 1000—- . _.
‘o I 5. :

IILLLLILIII 1L1

 

(3?...

51015 20 25 30

q (MeV/c)

Figure 2.3: A n-n relative momentum spectrum due to cross-talk events only, using
the 7Li(p,n) reaction to produce neutrons at 27 MeV.

19

mentum spectrum for 11Li breakup is shown in Figure 2.4a. There is an enhancement
near q=5 MeV/c, corresponding to a relative energy of 30 keV. It is not clear if the
enhancement at q=5 MeV/c should be attributed to the nature of the halo neutron
interaction or if it is due to unrejected cross-talk events. Unrejected cross-talk events
between neighboring detectors would appear near q=5 MeV/c because the distance

between neighboring detectors was greater for the 11Li experiment.

The effect of cross-talk contamination was further evaluated by using the data from
the 7Li(p,n) reaction. The n-n relative momentum spectrum from the 7'Li(p,n) data,
which was composed entirely of cross-talk events, was subjected to the same cross-
talk rejection procedure as the data from the 11Li experiment. This spectrum was
then normalized to the corresponding llLi data by the total number of In events, and
then subtracted from the 11Li spectrum. The neutron detector thresholds were also
increased to 3 MeV electron energy. This corrected spectrum is shown in Figure 2.4b.
The enhancement at q=5 MeV/c has been eliminated and the resulting spectrum
varies smoothly as a function of the relative momentum. The implications of this
result on the halo neutron correlation will be discussed in a later section (Momentum
Distributions), but it can be concluded here that the enhancement observed at low
q in this work was due to cross-talk contamination that could not be rejected by
the kinematical procedure presented in the beginning of this section. It should be
noted this procedure using the 7Li(p,n) reaction data was used to construct the n-n

correlation function presented in a previous article [16].

20

 

IIITIIIIIrIITIIIIIIrIIIIIIIIT

_

150

(a)
100

50

t—.—t

llllIllllIllllI

0-0-1
.37
O
O

'IIIIIIIIIIITII

 

100

IlllIllll

1b)
75

do/dq (orb. units)

 

01
O

IIIIIIIIFTIIIIIIII

IllllIllllI

f _

is

S

l\.)
0']

O 0
With
.—

 

 

I.
11

l s .

 

llllllIIIIIIIII_IIIIIIIIILIII-l

51015 20 25 3O

qiMeV/c)

Figure 2.4: A n-n relative momentum spectrum from the 11Li data. (A) before sub-
tracting the cross-talk background measured from the 7Li(p,n) experiment. (b) After
subtracting the cross-talk contamination. The histogram is the prediction of a 3-body
phase space simulation discussed in Section 5.4

Chapter 3

Telescope Data

Before proceeding to the main focus of this work, the 2n-9Li even-ts, results from the
fragment singles measurement are presented in this section and results from the In-
9Li measurements are discussed in the next section. The telescope counted the total
numbers of both 9Li nuclei produced and 11Li nuclei which did not react. In addi-
tion, the number of incident 11Li was determined from the beam TOF measurement.
From this information, the two-neutron removal cross section 02,, (“Li —v 9Li + 2n)
and the total reaction cross section am for 11Li + Pb at 28 MeV / nucleon were deter-
mined. Before presenting the results and comparing to other work, a description of

the analysis technique is presented.

A AE-E plot for 11Li and 9Li is shown in Figure 3.1a. The distinction between
11Li and 9Li is blurred due to 11Li dissociation that occurs in the C31. When disso-
ciation occurs in the Csl, the energy signal is a sum of the 11Li energy loss before
dissociation and the remaining 9Li energy after dissociation, since the neutrons in
general do not deposit any energy. Therefore, the energy signal is greater than that
of a 9Li nucleus that enters the C31, but less than that of a non-dissociating uLi .
11Li may also dissociate in one of the silicon AE detectors (2x300 pm thick). For
these events, the resulting 9Li signal appears in the same location on the AE-E plot

as 9Li dissociations that occurred in the lead target. Dissociation in the detector thus

21

22

 

AE (MeV)

 

 

 

 

AE (MeV)

 

L . l l L

 

I . f |(;Va

 

L

 

ISO 230 280 330
E tot (MeV)

380

Figure 3.1: (a) Two dimensional AE—E plot for the fragment singles events. Only the
region around the 9Li and 11Li is shown. (b) A similar plot, but requiring at least
one neutron in coincidence with the 9Li fragment.

23

makes particle identification ambiguous and generates some 9Li events that appear

to come from reactions with the target.

In order to accurately subtract the contribution due to reactions in the telescope,
data was also taken with the target removed and‘the beam energy lowered to com-
pensate for energy loss in the target. The llLi beam energy was reduced by inserting
an aluminum degrader to 81. The energy loss of the aluminum degrader was identical
to that of the target, so the 11Li energy striking the detector was the same as in the
target-in runs. For any spectrum, a subtraction of target-out data from target-in
data yields data representing 11Li reactions in the target. From the AE-E spectrum
shown in Figure 3.1a, a linearized two-dimensional spectrum of particle identification
number (PID) versus EC“ was made using the relation PID = £325,795 — E535. Here,
Em is the sum of the Si and Csl energy signals in MeV and EC“ is the energy de-
posited in the Csl detector alone. Projecting onto the PID axis, a one-dimensional
PID spectrum was made for both target-in and target-out data. These projections
are shown in Figure 3.2a. The peak around channel 1000 is from the 11Li beam. The
spectrum for the target-out runs has been normalized to the target-in runs for the
same number of incident 11Li . Figure 3.2b shows the result of the subtraction of
the two spectra in Figure 3.2a. The 9Li peak appears at PID=880, although with
a considerable asymmetry. An over-subtraction and an under-subtraction occur for
the 11Li data between PID=950 and 1150. It is important to be sure that both the
asymmetry in the 9Li peak as well as the over-subtraction and under-subtraction in

the 11Li region are not due to a flaw in the subtraction procedure.

The over-subtraction and under-subtraction between PID=950 and 1150 is most
likely caused by differences in the beam energy distributions, although the average
beam energies were equal. The energy loss in the aluminum degrader used in the

target-out runs was equal to that in the lead target, but the Al degrader was used

24

 

106 IIDIIIIIIITIIIITITIITIIIIIIII

 

105 (a)

104
If? 103 ‘
C :
D 1
O ..
93 102
t, 1000
33
H
>—

500

Willllllll

llllIllLJIi

   

 

-500

P
—
-
-
_

 

 

i-lllllllll

-1000 llLliltililLtlLLLIILlllIlll
700 800 900 1000 1100

 

PID Number

Figure 3.2: (a) A one-dimensional particle identification spectrum for target-in data
(solid histogram) and target-out data (dashed histogram). (b) The subtracted result.
The 9Li peak is near PID=880. The under-subtraction and over-subtraction have
been downscaled by a factor of ten for plotting purposes.

25

before a final dipole magnet. The rigidity of the 11 Li beam for the target-out data was
modified by the Al degrader, so a different beam energy distribution was produced
at the telescope due to the acceptance of the final dipole magnet. One verification
that the subtraction procedure was correct comes from examining the 11Li region
shown in Figure 3.2a. The amount of 11Li in the peak region for the target-in data,
N 11(in), represents the number of 11Li nuclei that are transmitted through the target
and telescope without reacting. For the target-out data, the number of 11Li in the
peak region, N 11(out), represents the number of 11Li nuclei transmitted through the
telescope without reacting. Because more flux is removed by the target-plus-telescope
than the telescope only, N11(in) < N11(out) , and the difference N=N11(in) —N11(out)
should be negative. Figure 3.2 shows clearly that N is negative. This is one indication
that the subtraction procedure is valid, even though the beam energy distributions
for the target-in and target-out data sets were slightly different. The number N was
determined by integrating the PID spectrum shown in Figure 3.2b from PID=930 up
1200. The result is N =-118,000, and the magnitude of N amounts to 1.7% of the
total incident 11Li . The absolute value of N is the amount of incident 11Li removed

by the Pb target.

The tail on the 9Li peak was assumed to be caused by reactions between 11Li and
Pb other than the two-neutron removal channel. For example, the reaction 11Li —i
8Li + 3n would appear at about PID=790. A more complex reaction yielding an
a-particle plus 6He, both hitting the CsI(Tl) detector, would appear near PID=850.
These reaction products and events from other fragmentation reactions with similar

PID values would not be subtracted by the target-out data.

From the subtracted PID spectrum in Figure 3.2b, both the two-neutron removal
cross section 02,, and the total interaction cross section 0,0, for 11Li on Pb can be deter-

mined at 28 MeV/ nucleon. Fitting the 9Li peak with a Gaussian gives 02,, = 5.1 :1: 0.3

26

barns. The error arises from extracting a symmetrical peak from the asymmetric
peak-plus-tail region. The measurement can be compared with the result of Anne et
al. [32]. They found 02,, =5.0:l:0.8 barns for the dissociation of 11Li projectiles on
a Au target at 29 MeV/ A. They used a silicon telescope for particle identification
and also performed a subtraction of target-out data from target-in data. Assuming
mostly Coulomb dissociation, their result can be scaled by 1.08 to account for the
slight difference in target and beam energy. The 1.08 scaling factor was estimated
based on the measured target charge (ZT) dependence of Coulomb excitation, 2%“
[9], and an the inverse beam energy dependence of the Coulomb dissociation cross
section [18]. The scaled cross section is 02,, =5.4:l:0.9 barns, in good agreement with
the result from this work. The agreement is an indication that the 9Li peak has been

correctly extracted from the asymmetric 9Li tail-plus-peak region.

The total reaction cross section for 11Li + Pb was also determined. The number
of 11Li that traversed the Pb target without reacting, IN I, was measured from by the
Si/Csi(Tl) telescope. A total of 1.7% of the incident 11Li beam was removed by the
Pb target, yielding a total reaction cross section 0,0, =9.7 :t 0.7 barns. The principal
source of the uncertainty arises from a difficulty in determining No. The beam TOF
measurement that yielded No required a start signal in the first AE detector of the
telescope. However, there were some reactions between the 11Li and the Pb target
that produced fragments at angles greater that 9 ° , and theseifragments missed the
telescope. For events where a fragment did not strike the telescope, the beam TOF
could not be determined and therefore the incident 11Li particles could not be counted

for these events.

Our result for 0,0, can be compared to the results from Villari et al. [30]. They have
measured the total reaction cross sections for several neutron-rich nuclei on silicon,

including 11Li + Si at 25.5 MeV/ nucleon and have provided a parameterization of 0,0,

27

fitted over an energy range of 30-200 MeV / nucleon, a projectile nucleus range of A=l
to 40, and a target nucleus range of A=9 to 209. Using their parameterization yields
a total nuclear reaction cross section of 5.7 :i: 0.7 b. This cross section represents
the total reaction cross section less the Coulomb dissociation cross section, since
the parameterization given in ref. [30] does not include a scaling term for Coulomb
excitation. Adding an extracted Coulomb dissociation cross section of 3.8 :1: 0.8 b
[40] yields a total reaction cross section 0,0, = 9.5 :t 1.1 b, in good agreement with
our result. A somewhat less quantitative comparison can also be made to a result
of Blank et al. [31], which yielded 7.23 :l: 0.78 barns for 11Li + Pb at an average
11Li energy of 70 MeV / nucleon. Because the Coulomb dissociation component of 0,0,
is expected to increase by a factor of 70/28 (= 2.5) at our beam energy [18], the two
measurements are probably in agreement. Thus it is reasonable to conclude that the
target-in and target-out subtraction procedure for the telescope data yields reliable
results for both 027, and 0,0,. The results for 02,, and 0,0,, as well as cross sections

determined from the coincidence measurements, are summarized in Table 3.1.

28

Table 3.1: Compilation of cross sections from the telescope data, the 1n-9Li data,
and the 2n-9Li data. The total two-neutron removal cross section is given by 02,,
and 01,, is the total neutron cross section from the integrated neutron angular distri-
bution. The cross sections for Coulomb and nuclear dissociation are denoted by 0c
and 0",“, respectively. B(E1) is the total strength and 031 is the photonuclear cross
section, determined from the two-neutron 9Li coincidence data. The quantity “0mm
was calculated in ref. [40] and (’0, was determined from the difference between 02n
and “0mm.

 

 

 

 

 

 

Data set Quantity Value
Telescope data 02,, 5.1 :l: 0.3 b
a“ 97i07b
1n-9Li data 01,, 8.3 :1: 0.5 b
0c 3.2 :l: 0.6 b
0mm 1.9 i 0.7 b
2n-9Li data ac 3.6 :f: 0.4 b
B(El) 1.00 :l: 0.11 e'zfm2
total 031 4.1 :1: 0.5 mb
“anuc 1.2 b
'0, 3.9 :1: 0.3 b

 

 

 

 

Chapter 4

One-neutron 9Li Coincidence
Results

In this section a measurement of the neutron energy and angular distributions is pre-
sented and the results are discussed in light of previous measurements of the neutron

angular distribution and 9Li transverse momentum distribution from 11Li breakup.

The AE-E spectrum for fragment-neutron coincidence events is shown in Fig-
ure 3.1b. The coincidence requirement eliminated the unreacted 11Li from the spec-
trum. The events shown are due to 11Li breakup in the target, silicon AE detectors
and Csl. It is not possible to draw a gate that eliminates events where dissociation
occured in the detector but preserves events where dissociation occured in the target.
Therefore, all coincidence events were used, and, as with the fragment singles data,

a target-in, target-out subtraction was performed.

The neutron energy distributions for target-in and target-out are shown in F ig-
ure 4.1a. The target-out data have been normalized to the target-in data by the total
number of incident llLi nuclei. The lower-energy neutrons were produced by neutrons
coming from llLi projectiles that lost energy in thesilicon and Csl before dissociating.
The result of the subtraction is shown in Figure 4.1b. A surprising feature is that the

mean energy of the neutrons, 26.9 :1: 0.3 MeV, is lower than both the mean 9Li energy

29

30

 

 

 

I-III IIIIIIFFI Fr] I‘ll I I VII I-l

10000 _—- 5 —‘

I .' e I

8000 E— ' . (a) %

.. O . _

I e I

6000 __— —;

l- . . ..

: 0 :

A 4000 :— 3 ° —;
> - . e . a
0 : ' :
a 2000 :--o ‘. . 1
3 ' . e . 1
5 0 WW
8 ’ I
v - e'e -4
g 6000 :— ' 1
.2 - e (b) .
>" I 0 ° 2
4000 _—- . fi

I ' 0 I

2000 :— e . '1

I- . u

: °' :

 

O I
I
LllLllllLIlLLLIllLIIlllL

0 10 20 30 40 ‘ 50

Neutron Energy (MeV) '

Figure 4.1: Neutron energy distributions for target-in (solid points) and target-out
(open points) data are shown in (a). The low energy portion is due to llLi dissociation
in the C31. The subtracted result, showing the neutron energy distribution due to the
Pb only, is shown in (b).

31

and the incident beam energy, 28.3 :i: 0.4 MeV / nucleon and 28.0 :1: 0.4 MeV / nucleon,
respectively, after correcting for the energy loss in the target. This effect will be

discussed in more detail in the section on post breakup Coulomb acceleration.

The neutron angular distribution could be constructed for angles between 0.5 ° and
4.8 ° . The spectrum was corrected for neutron detector efficiency and for attenuation
of neutrons by half the lead target thickness, the silicon-Csl telescope, three mm of
aluminum at the back of the target chamber, a 6 mm plastic veto paddle, and several
meters of air. The angular distribution is given by the solid points in Figure 4.2. The
open diamonds in Figure 4.2 are data taken from Anne et al.[32] for 11Li + Au at 29

MeV/nucleon and scaled to our conditions by a factor of 1.08.

This forward-peaked angular distribution was produced by the projectile fragmen-
tation of 11Li into 9Li and two halo neutrons by the Coulomb and nuclear field of the
target. The momentum distribution of fragments of mass A from the fragmentation
of stable projectiles is well described by a Gaussian function (130/er3 o< fig/2°34
in the rest frame of the projectile. The width 04 has been parameterized with a
single parameter, 00 z 70 — 90 MeV/c, in the Goldhaber model [3] for many different
projectile and fragment combinations. However, 9Li transverse momentum distri-
butions have been measured [2, 9] and very narrow distributions, corresponding to
00 = 16 MeV/c, were required to reproduce the data. Similar results for the narrow
component for 9Li parallel momentum distributions have also recently been reported
[34]. The narrow width is understood to originate from the removal of the weakly:
bound halo neutrons, which gives a small recoil to the 9Li fragment. The narrowness
of the 9Li transverse momentum distribution reflects the small spread in the Fermi

momentum of the halo neutrons.

The neutron angular distribution was also fitted by the Gaussian distribution in

the Goldhaber model. In the laboratory reference frame, in terms of perpendicular

32

 

103 lrol'lilll'TllIIIIIIIIIIIFI'

I llllll

.-

I I IIIIIIr
I lllllllI

102

I I TIIIIII
1 I 111111]

don/d0 (barn/8r)
5..

100 .
\
x
\.
\

I I rIIIIII
I J lllIllI

 

 

 

10"], JlLlIJILLIIEJLIILLllljlthLlll
0 51015 20 25 30

Neutron Angle [Degrees]

Figure 4.2: Measured angular distribution for 11Li + Au at 29 MeV/nucleon taken
from [32] is shown with the open diamonds. The solid points represent the angular
distribution for 11Li + Pb at 28 MeV/ A (this work). The dotted lines are fits using
narrow and broad gaussians. The dashed line is the sum of both components.

33

(p L) and parallel (I’ll) momentum components, the momentum distribution becomes:

9‘:
dpi‘

Here, N is a normalization factor, p0 is the average projectile momentum per nucleon,

= N exp-(Pi +(pn-Po121/2034) (4.1)

0,4 is the width parameter and 0 is the laboratory angle of the neutrons. Using

p" = pcoso, p l = pain 0, and dp3 = p’dpdfl, the angular distribution is given by:

3% = N exp-pgm'o/zaf, Amp: exp-(p-roco-O)’/30?. dp (4.2)
z N C0820 exp-pacin’O/Zai (4.3)

The normalization factor N and the width parameter 0 are fitting parameters. To
reproduce the neutron angular distribution, a sum of a narrow (0,4 = 0“,) and a
broad (0'4 = 0b,) component were used, with each component given by Eqn. 4.3.
The combination of our data and the data from [32] was used for the fitting. The
results of the fitting are shown in Figure 4.2. The dotted curves are for the narrow
and broad components and the dashed line is the sum of the two components. The
width parameters are 0,“, =11.8 :i: 0.8 MeV/c and 0;, =28 :1: 1 MeV/c. The errors
were determined by the change in the value of each parameter required to. increase
x3 by one, with all other parameters fixed at their optimum values [35]. Both and,
and 05, must be corrected for Coulomb deflection of the 11Li projectile. For Coulomb
dissociation, assuming an average impact parameter of 20 fm [36] and assuming the
breakup occurs at the distance of closest approach between target and projectile,
20.6 fm, the Coulomb deflection angle is 1.6 ° , yielding a width of 0”"; = 6.6 MeV/c.
Subtracting this width (in quadrature) from 0“, above yields 0,”, corrected for

Coulomb deflection of the 11Li projectile, 0“, =9.8 :l:0.1 MeV/c.

The integrated neutron angular distribution yielded a total neutron cross section

of 01,,=8.3 :1: 0.5 barns. The integrated cross section can be interpreted in terms

34

of nuclear and electromagnetic effects and compared to recent calculations of the
Coulomb and nuclear dissociation cross sections. Since the equivalent photon spec-
trum decreases sharply with energy [18], both neutrons, when liberated via Coulomb
excitation, will have little excess energy and will tend to be emitted at forward an-
gles in the laboratory. Hence the multiplicity resulting from Coulomb dissociation,
mc, should be mc =2. There will also be nuclear dissociations that produce 9Li and
two neutrons where either halo neutron in llLi may be scattered or absorbed in the
Pb target. The absorption mechanism for the halo neutrons can be thought of in
terms of the Serber model [37], where for 11Li , a halo neutron may be absorbed by
the Pb target. The projectile remnant, 1°Li , is unbound and decays to a 9Li plus a.
neutron. Because of the low decay energy of 10Li , 150 keV [38] or 800 keV [39], the
neutron from 1°Li decay would appear at forward angles. Another possibility is the
scattering of a halo neutron by the Pb target, also leaving a 10Li fragment. Thus for
the combined absorption and scattering mechanisms, if scattering produces a broad
angular distribution of neutrons, the nuclear dissociation mechanism would produce
both a broad and a narrow neutron angular distribution of neutrons. Because the
neutron angular distribution only covers the forward 20 ° , much of the broad angular
distribution would be unobserved. Therefore, the observed neutron multipliciy for

nuclear dissociation would be m,,,,,, zl.

Using the integrated cross section from the neutron angular distribution, 01,, =
8.3 i 0.5 barns, which can be considered a multiplicity-weighted sum of Coulomb
and nuclear dissociation, and the two-neutron removal cross section 02,, from the
fragment singles measurement, 02,, =5.1 :i: 0.3 barns, the Coulomb (0c ) and nuclear
(0,,“ ) dissociation cross sections for 11Li —v 9Li +2n were estimated by the following

relations:

0'27; = cc ‘1' antic (44)

35

air: = me”: 'i" mnucanuc (4.5)

The solution of these equations, with m, =2 and mm“, =1, yields 0c =3.2:l: 0.6 barns
and 0mm =1.9:l: 0.7 barns. These results are listed in Table l. The cross section 0,,”
has been calculated for 30 MeV/ nucleon 11Li + An using a diffractive eikonal model
[40]. The result, 0,,“ =1.2 barns, is expected to increase slightly for a lead target
and agrees with our result of 0, = 1.9 :l: 0.7 b. Subtracting the calculated 0",“, =1.2
b from 02,, yields 0c =3.9 :i:0.3 b, in agreement with 0, = 3.2 :1: 0.6 determined here.
Also, a recent calculation for 11Li plus Au at 29 MeV/nucleon found that Coulomb
dissociation accounts for up to 80% of the total two-neutron removal cross section
[41]. The cross sections for 06 and 0,,“ from Eqns. 4.4 and 4.5 indicate that 63 :l: 16%
of the two-neutron removal cross section is due to Coulomb dissociation, in agreement

with the calculation.

Chapter 5

Two-Neutron—9Li Coincidence
Results

The primary goals of this experiment were to measure the dipole strength distribu-
tion dB(E1)/dE and the photonuclear cross section 031(E), and to determine the
9Li momentum distributions in the 11Li rest frame in order to better understand the
structure of 11Li . The spectra for dB(E1)/dE and 031(E) may provide the best
evidence for the predicted soft dipole resonance. The momentum distributions will
yield information on how the excitation energy is distributed between the 9Li and
the neutrons, which may provide information about the degree of correlation between
the halo neutrons and possibly evidence for a dineutron structure. In Section 5.1 the
technique used to determine the 11Li excitation energy event-by—event is discussed
and in Section 5.2 the results for dB(E1)/dE and 031(E) and Comparisons to some
calculations are presented. In Section 5.3 9Li and neutron velocity distributions are
displayed. The impact of these velocity distributions on the interpretation of the soft
dipole resonance will be discussed. Finally, in Section 5.4, 9Li and neutron momen-
tum distributions, determined in the 11Li rest frame, are given. The structure of the

11Li nucleus will be discussed in light of these distributions.

36

37

5.1 The Decay Energy Spectrum

The excitation energy E was determined by measuring the 11Li decay energy, E, .
The excitation energy is related to the decay energy by E=Ed +S2,,, where S2,, is the
two-neutron separation energy of 11Li . In the rest frame of the excited 11Li , the

decay energy can be expressed as:

 

1 1 ..
Ed = '2'Pli722n—s + §#2V.f.n (5-1)
. _ m9(2mn) _ mu
thh p, — m9+(2m,,) and #2 - —2 (5.2)

Here, I72..-9 is the relative velocity between the 9Li and the two neutron center of mass,
17"..“ is the relative velocity between the two neutrons in the rest frame of the two-
neutron center of mass, m9 is the 9Li mass and m,, is the neutron mass. The relative
velocities are measured in the laboratory reference 'frame and Lorentz transformed
to the 11Li rest frame. For our beam energy, the relative velocities are nearly frame
invariant, so the Lorentz transform alters the relative velocities <2%. The decay
energy was calculated and the decay energy spectrum was constructed from the 2n-
9Li events. Figure 5.1a,b displays the measured decay energy spectrum for target-in
and target-out runs. Approximately 50% of the events are due to dissociation in the
Si / Csl telesc0pe. The peak at low decay energies for the target-in data indicates
the abundance of events arising from Coulomb dissociation in the Pb target. The
subtracted spectrum, representing 11Li decay events in the Pb target, is displayed in

Figure 5.1c.

Because both electromagnetic and nuclear interactions may contribute to the de-
cay energy spectrum shown in Figure 5.1c, it is important to understand the mag-

nitude of the nuclear contribution in order to accurately calculate the E1 strength

38

 

  
 

 

 

 

  
  
 

  
  

:lfilIlITIII'IIIIrIIII:
6000 Egg Target In —:
E g (a)
4000 :0 a j
: ‘1’ :
2000 1 -J
g r-
g 0
(b)
3 6000
5 Target Out
8 4000 (Normalized)
B
a) 2000 g
H ; ,
6008
to)
4000 ’ I
2000 r
0

 

 

lllllLLLlIllLlLlLLL

0.0 0.5 1.0 1.5 2.0 1
11L1 Decay Energy (MeV)
Figure 5.1: Decay energy spectrum for (a) target in, (b) target out, and (c) the

subtracted result. The target out data result from uLi dissociation in the silicon
detectors and the Csl detector.

39

function. Recent theoretical calculations show that electromagnetic effects contribute
up to 80% of the total dissociation cross section for high Z targets[41] and projectiles
near 30 MeV / nucleon, in agreement with the Coulomb and nuclear cross sections
determined from the 1n-9Li events, 0c = 3.2 :l: 0.6 barns and 0,,” = 1.9 :i: 0.7
barns. For nuclear dissociation mechanisms like those described in the previous sec-
tion, requiring two neutrons to be detected at less than 5 ' would further enhance the

number of events from electromagnetic dissociation relative to nuclear dissociation.

An investigation of the contribution from nuclear dissociation was performed.
Coulomb excitation is largely a peripheral process, occurring at impact parameters
b>b,,,,-,,, and at an average impact parameter of about 20 fm [36]. Here b,,,,-,, is the
impact parameter corresponding to the grazing angle. Using a matter radius of 3.3
fm [1] for 11Li and a Pb radius of 7.1 fm yields b,,,,-,, = 10.1 fm. Nuclear dissocia-
tion, where the halo neutrons are scattered or absorbed by the Pb target, occurs for
impact parameters bz b,,,,-,,. Because of the complete kinematic measurement, an
approximate impact parameter could be determined for each event. A decay-energy
spectrum was constructed consisting only of events with b) 15 fm. In this case the
decay energy spectrum is expected to be free of contamination from nuclear disso-
ciations. The impact parameter was determined for each event from the change in
the velocity vector of the center of mass before and after breakup, since the Coulomb
deflection alters the center of mass velocity. The center of mass velocity after breakup
was determined from the measured momenta of the 9Li and two neutrons. The inci-
dent uLi velocity was measured by TOF and the PPAC’s. The recoil of the Pb was
neglected in this analysis. The decay energy spectrum, gated on events for b) 15,
is shown in Figure 5.2. The decay energy spectrum for all events (no gating) was
shown in Figure 5.1c. Although the magnitude of the gated spectrum is reduced by

25%, the shape of the two spectra agree within statistical uncertainties. Also, it is

40

 

IIEI[IIII]IIII]III

4000

t—O—t
t—fl“
$35
fi"“*
#53“

2000

Yield (Counts/MeV)

 

 

  

O
erllkbqllllllllI

 

 

111.1 Decay Energy (MeV)

Figure 5.2: Decay energy spectrum gated on impact parameter, for b) 15 fm.

41

not known how many of the events with b5 15 fm were the result of Coulomb dis-
sociation. Disentangling Coulomb and nuclear effects is difficult for bz b,,,,-,, because
the Coulomb dissociation cross section increases considerably as b decreases, due to
the increasing intensity of the equivalent photon spectrum [18]. It is quite possible
that many of these events originated from Coulomb dissociation. Therefore, the data
from the ungated decay energy spectrum was used, with the knowledge that events
from nuclear dissociation were not numerous enough to affect the shape of the spec-
trum, but that the integrated spectrum may overestimate the number of events from
Coulomb dissociation and hence the magnitude of the Coulomb dissociation cross

section 0,.

The decay energy spectrum was also corrected for the efficiency of the detection
system. The efficiency for several decay energies was determined by a Monte Carlo
calculation. An empirical fit to the calculated efficiency is show in Figure 5.3. The
efficiency is mainly determined by the product of the geometric efficiency for both
neutrons striking scintillator, and the intrinsic neutron detector efficiency, which is
about 18% for each neutron, using a theshold corresponding to 3 MeV neutrons. The
geometric efficiency is strongly decay-energy dependent, since large decay energies
yield neutrons with higher transverse momenta, and these neutrons are more likely

to miss the detector array.

Using the calculated efficiency, the 11Li flux and the target thickness, the abso-
lute Coulomb dissociation spectrum d0c/dE was determined from the spectrum in
Figure 5.10. Integrating over energy yielded the total cross section, 0, = 3.6 i 0.4
barns. This value is also listed in Table 3.1. The magnitude of 0., determined here
is consistent with 0, determined from the 1n-9Li data (06 =3.2:1:0.6 b) and from 0,,
determined from the difference 0,, =02,, -— 0,,” = 3.9 :l: 0.3 b, where 02,, =5.1:l:0.3

b was measured with the telescope, and 0,,“ =1.2 b from a calculation [40]. The

42

 

Ifirrllfll Illlllll

2.00

t"
o
o

.0
or
o

Efficiency (%

 

 

 

 

Decay Energy (MeV)

Figure 5.3: Detection efficiency as a function of decay energy.

43

statistical accuracy of the decay energy spectrum shown in Figure 5.1c is quite low
for E4 > 0.7 MeV, and the spectrum is consistent with zero for E, > 1 MeV. These
features are reflected in the detector efficiency in Figure 5.3, where the efficiency de-
creases by an order of magnitude for E4 between 0.1 and 1.0 MeV. However, because
06 determined from the decay energy spectrum is consistent with the values obtained
from the fragment singles and from the ln-9Li data, it is unlikely that a significant
portion of the decay energy spectrum was not observed due to low statistical accur-
racy or a cutoff imposed by the detector apparatus. This will also be important when
the strength function and photonuclear cross section are calculated and presented in

the next section.

5.2 dB(E1)/dE and 0.2.00)

The measured decay energy spectrum d0M/dEd, shown in Figure 5.1c, is related to

the true spectrum d0/dEd by the following:

d0c

713:.

dd“

737(5).) =

(El) 5(53. Ed) 43.1 (5-3)

The function 5(EQ, E4) represents the response of the detector system and dictates
how much the true decay energy spectrum is distorted by detector induced biases.
Often, s(E,',,Ed) is a complicated function and unfolding such a response function,
equivalent to performing the inverse transform of Eqn. 5.3, is quite difficult. The
response function of the detection system was studied as a function of decay energy.
Computer-generated events at a specific decay energy were fed through a simulated
detector system to determine the resolution response. Neutron detector timing and
angular resolutions (1 ns and 0.7 ' ), 9Li energy and angular resolutions (3 MeV and
0.6' ), energy losses in the Pb target, and multiple scattering effects in the target
were all considered. The results for decay energies of 100 keV, 500 keV and 1 MeV

44

are shown in Figure 5.4a-c, respectively. The width of the response function is shown
in Figure 5.4d. Because of the tails in the response functions, FWHM is not an
appropriate measure of width. Instmd, starting from the centroid, the peak was
integrated up to a distance :1: s away from the centroid until the area equaled 76%
of the total area of the peak. A width was then defined as 28. For a Gaussian

distribution 2s would be equivalent to FWHM.

Because of the complicated shape of the response function, it was not feasible
to unfold the response from d0M/dEd directly. Therefore, model predictions were
chosen for d0c/dE'd, filtered through a simulated detection system using a MOnte
Carlo program and compared to the measured decay energy spectrum. The filtering
process folds in the effect of the response function 5(Eg, Ed) on the true spectrum.
A search was performed for a model of the true spectrum that best reproduced the
measured decay energy spectrum. As shown in Eqn. 1.4, d0c/dEd is a product of
the photon spectrum N51(E) and a photonuclear spectrum. Therefore, constructing
model distributions of d0c/dE4 requires a function for 031(E) to be chosen, since the

photon spectrum is calculable.

An empirical model, in which 031(E) was parameterized with a Breit-Wigner
function, provided the best reproduction of the data. The Breit-Wigner function is

given by:

 

 

0,,,F and r _ r(E,)T(E,)

051(34) = (Ed-E0)” + (172): '" T (3°)

(5.4)

The function is written in terms of the decay energy E, and the excitation energy
E = 13., + S2,,, with S2,,=0.34 MeV. The centroid and width are denoted by E0
and I‘, respectively, and 0,,, is a normalization constant. The Breit-Wigner function
included a transmission coefficient, denoted by T(E), with the energy dependence of

s-wave neutrons. The transmission coefficient forces the Breit-Wigner shape to zero at

45

 

 

fiIIIIIIIIIIIIIIIIIIIIILIITLIIIII[IIII]IIII_ _<

4— —: 4 SP.

’- Q
- -1

3 —: (c) 3 ‘2,

. r1

3 8

2 —: 2 3’.

4 Q

- t—D

1 '1 1 O

_. X-

—. (D

‘ S

 

Yield (103 Counts/10 keV)
O

(AaN) 1139111

‘IIIIIIIIITIIITIIIIII IIIIIIIIIIIIIIIIIIIIII

  

 

 

 

llllIllIlIlLLJ’llllIlllIILIIIJIIIIIIIIIIIIII

4 ;- 0.8
3 :— (a) . 0,5
2: 0'. 04
E e " '
1E— . ' 0.2

 

lllIlLLLILlllILL llLlILLlIILlllLllLL 0.0
%.0 0.2 0.4 0.6 0.8 0.0 0.5 1.0 1.5 2.0

11L1 Decay Energy

Figure 5.4: Experimental resolution for decay energies of 0.1 MeV, 0.5 MeV and 1.0
MeV is shown in a-c, respectively. The width (see text for definition) as a function
of decay energy is shown in (d).

46

E4 = 0. The measured decay energy spectrum, shown in Figure 5.1, is shown again in
Figure 5.5a, after summing some channels. The solid line represents the Breit-Wigner
model with resonance parameters Bo = 0.7 Mev and l" = 0.8 MeV. The good fit of
this function after being folded with the response function means that, to within our

experimental errors, Eq. 5.4 represents our measured photonuclear spectrum.

Figures 5.5b,c show the measured photonuclear spectrum and dipole strength
function, as determined from the fit to the data in Figure 5.5a. The strength function
is determined from 031(E) according to Eqn. 1.2. The integrated photonuclear cross
section and dipole strength function is 4.1 d: 0.5 mb and 1.00 :1: 0.11 e2 fm’. These
values are listed in Table 3.1. It is important to emphasize that the distributions in
Figure 5.5b,c were deduced from the true decay energy spectrum and therefore can

be compared directly to theoretical calculations.

The narrow peak in the spectrum for 031( E) (I‘ = 0.8 MeV) and the location of the
peak (E0 = 0.7 MeV) are suggestive of a soft dipole resonance for 11Li and in good
agreement with the predictions of several calculations. Broadly speaking, the models
of 11Li excitation can be grouped into two categories. The first group assumes a direct
breakup into 9Li and two neutrons, while the second group considers the existence of
a continuum resonant state in uLi that can be populated by El excitation, followed
by breakup into a 9Li and two neutrons. In the direct breakup picture, the absorbed
photon induces a displacement of the 9Li core relative to the halo and the restoring
force provided by the halo is too weak to keep the 11Li nucleus from dissociating into
a 9Li and two neutrons. Alternatively, in the resonant state picture, the restoring
force is strong enough such that E1 excitation populates a vibrational mode between
the 9Li core and the halo neutrons. Using a direct breakup scheme, the resonance
was originally predicted to exist at a mean decay energy of E4 =0.7 MeV [4]. Another

direct breakup calculation, the cluster model [15], found the dipole strength function

47

 

 
  

 

 

 

 

 

IIIIIIIIIIFIFIIIII
A '- ..
3" 100
g (a) ‘2
.d 50 fi
1.. -
3 ~ _
h, I;

s 57 ‘1
cu - -1
1_tili]iifi]iliflifi‘rq
4; .:
y- ..
3 : E
.8. 33‘ 1
a I- :1
w: 2__ _‘
a - .
a 3 4
1. d
1g.:::]::::]::::]::::‘
A e _ ' fl
a wax «
I ”w ‘
c? :1: .\ (c) 7
”he 1.0% .'.\ _"
0’ hi: '.\ d
V i-

' '--\. I
g _i: x.

. \'. ‘
> 0.5 g- --
0.0 J \‘. -1
El '4 ........ .
s ~-~~.

'111'1111I1111i1111

 

0.0
0.0 0.5 1.0 1.5 2.0
Decay Energy 8,, (MeV)

Figure 5.5: The decay energy spectrum. (a) The solid line is the product of a Breit-
Wigner function with E0 = 0.7 MeV and l" = 0.8 MeV and the photon spectrum,
after being filtered through the detector system. (b) The solid line is the photonuclear
spectrum corresponding to the Breit-Wigner parameters determined from the data.
(c) The solid line is the dipole strength function determined from the data. The
dashed line is a calculation using a cluster model and the dotted line comes from a

correlated 3-body calculation.

48

is sharply peaked near E4=0.2 MeV. The dipole strength function predicted by this
model is shown in Figure 5.5c by the dashed line. The total strength predicted by the
cluster model is B(E1)= 1.34 e’fm’, close to the measured value of 1.00 :1: 0.11 ezfm2
but the strength function peaks at a considerably lower energy. For the resonant state
models, a correlated three body calculation [l4] predicts a peak in the dipole strength
function near E4 = 0.2 MeV also. The predited dipole strength function from this
model is shown in Figure 5.5c by the dotted line. A model of the resonant state as a
vibration between the halo neutrons and the 9Li core predicted peaks at energies of
E0 = 0.5 MeV and EM”, = 2.5 MeV [10]. A calculation that modeled the SDR as a
collective vibrational mode and was constrained to reproduce the measured Coulomb
dissociation cross section found E0 = 0.7 MeV and 1‘ = 0.7 MeV [9]. However, It
was shown in a previous report [16] that the lifetime of a collective state with these
parameters would only be 1/ 5 of an oscillation period. It is difficult to accept the

concept of a collective vibrational state with this constraint.

It can be concluded that the photonuclear spectrum has a peak near a decay
energy of 0.7 MeV and width of 0.8 MeV, but it is not possible, based solely on these
data, to determine whether the breakup occurs directly or passes through a resonant
state. The question of the nature of the breakup mechanism will be addressed in the

following section.

5.3 Post-breakup Coulomb Acceleration

Some 9Li and neutron velocity distributions provide the means to discriminate be-
tween a direct breakup and a resonant state picture for the excitation of 11Li . Fig-
ure 5.6a shows the magnitude of the velocity difference AV = Vg — 16,, where V9

is the magnitude of the 9Li velocity and V2,, is the magnitude of the average neutron

49

velocity for each 2n-9Li event. The centroid of the distribution appears at 0.0090c :1:

0.0003c, indicating the 9Li is, on the average, more energetic than the neutrons.

Before interpreting the velocity difference, it is important to be sure that the result
is not produced by detector biases or systematic errors in the energy and angle mea-
surements. The former was investigated via Monte Carlo calculations. Computer-
generated events with AV distributed about zero were fed through the simulated
detector array. The result of the simulation, shown by the histogram in Figure 5.6a
is peaked around zero, indicating instrumental biases are not causing the shift ob-
served in the data. To check for systematic errors, overall momentum conservation
could be verified since the complete kinematics were measured. Figure 5.6b displays
the spectrum of counts versus the z-component of the center of mass velocity after
breakup minus the z-component of the center of mass velocity before breakup. After
breakup, the center of mass velocity is determined from the measured velocities of the
9Li and both neutrons. Before breakup, the center of mass velocity is given by the
measured energy and direction of the incident llLi . The z-components of velocity
were used because the contribution from the Pb nucleus, which recoils close to 90 ° ,
was negligible in this case. The near-zero centroid of the distribution, -0.0010c :I:
0.0001c, showed momentum conservation is quite well enforced and provided a good
check that the shift in the z—component of AV was not due to systematic error. The
width of the distribution in Figure 5.6b yields the overall velocity resolution of the
detection system, 0.008c FWHM.

It appears that the difference between the 9Li velocity and average neutron ve-
locity is a real effect, and it can be interpreted in terms of the breakup mechanism.
Coulomb excitation is more likely to occur when the 11Li projectile is close to the
lead nucleus, due to the greater intensity of the photon spectrum [18]. If the breakup

occurs soon after excitation, the 9Li will be re-accelerated by the Coulomb field of

50

 

  
 
  

 

 

 

 

 

       
  

C I'fI I I I r I I I IéIfr I I l T I j
200 E —:
E l: :
~ 5 150 —— -—
. o '- .1
U I i
3 100:— fig-S
0 - ..
'>‘-' : i
50 L" f]
: e 2
O '1‘ I l l L l I 1 LI 1 Ll I l
-0.04 -0.02 0.00 0.02 0.04
(Vs " valve
800 r I T I I I I I I I I I T I I I I
A .. f
s i l
3
53, 400
3
.9. 200
>-'

 

LllllLllllllLLILLL

-0.04 -0.02 0.00 0.02 0.04

V... after breakup - Va. incident

Figure 5.6: Spectrum for the magnitude of the velocity difference V9 - V2,,, where V2,,
is the average velocity of the two detected neutrons, is shown in (a). The histogram
is the result of a simulation using an initial distribution with the velocity difference
peaked at zero. Spectrum for the z-component of the center of mass velocity before
breakup subtracted from the center of mass velocity after breakup is shown in (b).
The near-zero centroid reflects overall momentum conservation. The width of the
peak, about 0.008c FWHM, represents the overall velocity resolution of the system.

51

the lead nucleus, thus yielding events in which the ”Li velocity is greater than the
neutron velocity. Because the breakup is occuring close to the Pb nucleus, either the
E1 excitation is populating a resonant state with a short lifetime or the breakup is

direct.

In the case of a resonant state, the meanlife 1' of the resonance can be roughly
estimated from the difference in the z-components of the ”Li velocity and the average
velocity of the two neutrons. The z-direction is the direction along the beamline. For
the z-components of velocity, the centroid of the relative velocity distribution was
0.0080c :1: 0.0003c. Figure 5.7 is a schematic view of a 11Li dissociation. A straight
line trajectory is assumed, since the 11Li is only deflected by a few degrees. It is also
assumed that the excitation occurs at the distance of closest approach, because the
electric field is the most intense at that point [18]. The beam velocity is denoted by V,
and 1' is the meanlife of the resonance. The distance from the Pb nucleus where the
breakup occurs is denoted by r. After breakup, the ”Li regains the Coulomb energy
U = ZL,‘ZP5€2 / r. The equation of motion for the velocity of ”Li after breakup is:

at? _ ZuZpbc” f

7f- - mgr2 r

and 1": bi: + Vti (5.5)

For the z-component, integrating from t = r to t = 00 yields the result:

__ ZLIZPbez 1

v..(oo)-v..(r)- m, we +1142 (5.6)

The velocity V2400) is calculated from the measured ”Li energy. The velocity 162(1)
at the point of 11Li breakup is unknown, but because the decay energy is only about
0.6 MeV, it can be assumed to be equal to the average neutron velocity V2,,,(r) at
that point. Because the neutron velocities are not affected by the Coulomb force,
V2,,,(1') = V2,,,(oo), where V2,,,(oo) is the average neutron velocity determined from

the TOF measurment of the two emitted neutrons. Therefore, V9,,(1') = V2,,,(oo),

52

Pb Target

 

11
Li

/ W/

photon absorbed Break-up occurs
here here

Figure 5.7: Schematic view of a 11Li breakup. The average impact parameter is b=20
fm, the distance from the lead nucleus where the breakup occurs is denoted by r, V
is the beam velocity and r is the meanlife of the resonance.

53

and the centroid of the relative velocity spectrum shown in Figure 5.6a, and given by

(AV) = (V9,(oo) - V2,,,(oo)), is related to the meanlife of the resonant state as:

. 82
(AV) = (V9400) - V2nz(°°)) = @3— TEE—7;“- (5-7)

Using an average impact parameter of b = 20 fm [36] and the centroid of the relative
velocity distribution, (AV) = 0.0080c :l: 0.0003c, the meanlife of a resonant state is
r = 50 :1: 7 fm/c. This meanlife yields a width F = 4.0 :f: 0.5 MeV. Therefore, a
resonant state would require a width of approximately 4 MeV to be consistent with
the measured velocity difference between the neutrons and the ”Li . It must be re-
emphasized that this is only intended to be a rough estimate of the width. However,
the photonuclear cross section yielded a width of only 0.8 MeV, a factor of four too
low. If the breakup mechanism proceeded via a resonant state, the width of the
resonance from the photonuclear cross section would be consistent with the width
determined from the ”Li -neutron energy differences. It is this contradiction between
the width determined from the photonuclear cross section and the width implied
by neutron-”Li velocity differences that rules out a resonant state and indicates the

breakup mechanism must be direct.

It should not be surprising that the presence of a peak in the strength function or
photonuclear spectrum does not guarantee the existence of a resonant state. A peak
was predicted by the by the cluster model [15]. Recent calculations [33] have shown
that, in general, loosely bound systems will have a peak in the strength function near
threshold, and that the peak appears because of the large spatial extent of the loosely
bound nucleons. A more general argument comes from the fact that the photonuclear
spectrum will be zero at threshold, rise with increasing phase space, and eventually
become zero at high excitations because the integrated cross section must be finite,

thus producing a peak in the spectrum.

54

5.4 Momentum Distributions

Much of the study of 11Li has been dedicated to measuring the momentum distribu-
tions of the ”Li and neutrons resulting from the breakup of 11Li on both high-Z and
low-Z targets [2, 6, 43, 34]. A recent measurement of parallel momentum distributions
of ”Li following breakup on a tantalum target yielded 09 ~ 17 MeV/c, and the width
deduced from a measurement of a neutron angular distribution in this work and in
refs. [43, 6] was 0,, ~ 10 MeV/c. Because a kinematically complete measurement
was performed for this work, the ”Li and the neutron momentum distributions could
be constructed in the rest frame of the 11Li . The measured ”Li and neutron momen-
tum distributions are shown in Figure 5.8a,b. The momentum distributions in the
11Li rest frame were parameterized by a Gaussian function d30/dp3 or exp(—p2/20,-”),
with 0,- = 09 or 0,,. An integration over solid angle yielded the function (Maxwellian)
used for the fitting: d0/dp = p”exp(—p”/203). For the ”Li and neutron momentum
distributions, the best fits yielded 09 = 18 :1: 4 MeV/c, in agreement with ref. [34]
and 0,, = 13 :l: 3 MeV/c, in agreement with refs. [43, 6]. These width parameters

have been corrected for detector acceptances and resolution.

The narrow widths of the ”Li and the neutron momentum distributions have been
interpreted as evidence for a neutron halo [6, 43], and as an indication of the internal
momentum distribution of the 11Li nucleus [34]. Recently, the measured values of
09 and 0,, were also used to show that the halo neutrons possess a high degree of
directional correlation [44], indicating they tend to move in the same direction. A
strong momentum correlation such as this would indicate that the halo neutrons
are not in close proximity to each other. Also, a comparison of the widths of the
distributions may also provide some insight into the degree of correlation of the halo

neutrons. For example, for no correlation, the width of the neutron momentum

55

 

 

 

 

 

 

 

 

 

 

 

L.IIIIIIITIIIIIIIIIIIIIITIIIIEI‘:
150i.— I (a) ”Li _.
- .,| _
: , l ' :
100;— ] -=
- '1’ I] :
50}- 4
g: E f a
c: 0 "
: IIIIIIIIIIIILIIIIIIIIIIIIlll7
.3 0 10 20 30 40 50 60'
3
m _IITr IIII IIIr IIIr.
Q 300' I I I ‘
z - (b) Neutrons—-
“U - ..
2001— -:
I I
100;- '—
0..
lellILJl IILI IIELIII
0 10 20 30 40

Momentum (MeV/c)

Figure 5.8: (a) ”Li momentum distibution determined in the 11Li rest frame. The
histogram is the result of a simulation of 11Li breakup with the decay energy parti-
tioned by a 3-body phase space distribution. (b) Neutron momentum distribution in
the 11Li rest frame. The histogram is the result from the simulation.

56

distribution is expected to be \/2 smaller than the width of the ”Li distribution,
as suggested by Hansen [45]. Alternatively, if a strong directional correlation exists
between the neutrons, then the width 0,, = 1 / 2 09 since both neutrons recoil against
the ”Li .

A different interpretation is that the widths 0,, and 09 may reflect the breakup
mechanism of 11Li and the distribution of excitation energy absorbed by the 11Li nucleus.
Because of evidence presented earlier that the breakup of 11Li into ”Li and two neu-
trons following excitation is direct, it is natural to assume the excitation energy
is partitioned between the ”Li and neutrons via a 3-body phase space distribution.
Therefore, a Monte Carlo simulation of the 11Li breakup was developed that used the
product of the measured photonuclear spectrum and the equivalent photon spectrum
as the input excitation energy distribution. This product represents the 11Li breakup
probability as a function of excitation energy. The 11Li decay energy was distributed
between the two neutrons and the ”Li based on a 3-body phase space distribution, and
the angular distributions were chosen to be isotropic in the 11Li rest frame. The simu-
lation also included the detector acceptances. The predictions for the ”Li and neutron
momentum distributions are shown by the histograms in Figure 5.8 a,b respectively.
The good agreement between the histograms and the data supports the interpretation
that the ”Li and neutron momentum distributions at least partially result from the
distribution of excitation energies and the manner in which the excitation energy is

partitioned between the three particles.

The 3-body phase space formulation also yields information about the degree of
correlation between the halo neutrons. The kinetic energy distributions and average

kinetic energies for each of the three particles are given by:

 

m2+m3
m1+m2+m3

N(T,) dT, -.-.- fi,(r,m — T1) dT, and T1,... =

 

E4 (5.8)

57
Time: 2
(T1) = _2— and (P1) = mlTlmoz (5.9)

The average angle between the halo neutrons can be calculated from:
(151 - P3)

and 203'. - P.) ='<P:> — (P3) — (P3) (5.10)
«Pm/(Pa)

(cos 012) =
Here, the subscripts 1 and 2 refer to the neutrons and 3 to the ”Li . Substituting
in the expressions for the average of the squares of the momenta yields (cos 012) =
—m,,/(m,, + m9) = —0.10. The phase space distribution thus predicts a large
opening angle, about 96 ° , between the halo neutrons in the 11Li rest frame. The fact
that the 3-body phase space formulation, which assumes the system is uncorrelated,
reproduces both the ”Li and the neutron momentum distributions is evidence that
there is no correlation between the halo neutrons. This result contradicts a recent
calculation of Tanihata et al. [44], where (cos 012) was calculated from the widths of
the momentum distribution by the relationship (P?) '= 30?. Using 09 = 21 i3 MeV/c
from [2] and 0,, = 10 d: 1 MeV/c from [43, 6], their result was (cos 012) = 1.2 i 0.3,
consistent with 012 = 0 ° , indicating the presence of a strong directional correlation

between the halo neutrons.

Although it is difficult to reconcile these two contradictory results, some addi-
tional data, the neutron-neutron relative momentum spectrum, can also be shown to
agree with the 3—body space formulation of the 11Li breakup. The neutron-neutron
relative momentum spectrum was shown in Figure 2.4. A fit using the Gaussian dis-
tribution described above yielded a width 0,,,, = 10 :l: 2 MeV/c, in agreement with
the result expected from two uncorrelated neutrons each with 0,, = 13 MeV/c and an
opening angle of 96 ' . The histogram is a prediction from the Monte Carlo simulation
discussed above. The simulation is in reasonable agreement with the data, although

the data are somewhat over-predicted at low relative momenta. It is expected that

58

a strong directional correlation between the halo neutrons, like that predicted in ref.
[44], would produce a peak at low relative momenta, a peak that is not present.
However, both the peak and the width of the neutron-neutron relative momentum
spectrum, 10.5 MeV/c and 13 MeV/c respectively, are consistent with an average
opening angle of 96 ° between the halo neutrons in the 11Li rest frame. Therefore, all
of our results, when compared to the predictions of a 3-body phase space formulation,

suggest that there is no correlation between the halo neutrons.

Finally, one caveat regarding this analysis should be mentioned. Our conclusions
are based on the success of a 3-body phase space formulation in reproducing the mea-
sured momentum distributions. It is reasonable to suppose that more sophisticated
models that explicitly include correlations between the halo neutrons could also re-
produce the measured distributions. For example, a correlated soft dipole model [14]
predicts an opening angle between the neutrons of 110 ° , although this result is for
the neutron kinetic energies fixed at 100 keV rather than integrated over the complete
distribution. It would be desirable to compare the predictions of more sophisticated
models such as that of ref. [14] to our data in order to further understand the nature

of the interaction between the halo neutrons.

Chapter 6

Summary

Both fragment singles events and coincidence events from the dissociation of 11 Li nuclei
at 28 MeV / nucleon on a Pb target have been measured. The results from the fragment
singles and 1n-”Li are consistent with measurements from several other experiments
[6, 32, 43, 31] and new results from the 2n-”Li coincident data are presented. From the
”Li fragment singles data, a total two-neutron removal cross section of 02,, = 5.1 :1:0.3
b was measured. Also, from the number of 11Li nuclei transmitted through the target,

a total reaction cross section of 0,0, = 9.7 :1: 0.7 b was determined.

The angular distribution for 1n-”Li events was constructed between 0 ° and 5 ° .
The angular distribution agreed very well with a previous measurement of the neutron
angular distribution for a 29 MeV/ nucleon 11Li beam on a Au target [32]. The data
from this measurement were combined with the data from ref. [32] and fitted with
the sum of a narrow and a broad Gaussian. The fitting yielded a width of 0,, =
9.8 MeV/c for the neutron momentum distribution. From the combined neutron
angular distribution, an integrated neutron cross section of 01,, = 8.3 :1: 0.5 b was
determined. This cross section could be considered to be a sum of the multiplicity-
weighted contributions from Coulomb and nuclear dissociations. For multiplicities m,
=2 and m,,,,,, =1 and 02,, =5.1 b, 02,, = 0,, + 0mm, Coulomb and nuclear dissociation

cross sections of 0c = 3.2 :1: 0.6 b and 04,“, = 1.9 d: 0.7 b were calculated. The values

59

60

of the multiplicities were chosen based on a possible reaction mechanism for nuclear
dissociation, namely absorption of a halo neutron by the Pb or scattering of a halo
neutron by the lead into a broad angular range, and the fact that the combined
angular distribution was limited to a maximum angle of 20 °. The results for 0,
and 0,,” were in reasonable agreement with two different theoretical estimates of the

magnitudes of the Coulomb and nuclear dissociation cross sections [40, 41].

This work focused mainly on the data resulting from the complete kinematical
measurement of the 2n-”Li events. That measurement allowed the 11Li decay energy,
and hence the excitation energy, to be determined on an event-by-event basis. From
the decay energy spectrum, an excitation-energy-dependent Coulomb dissociation
cross section could be constructed. Dividing out the equivalent photon spectrum then
yielded the photonuclear spectrum 031(E) and dipole strength function dB(E1)/dE.
The photonuclear spectrum was fitted with a Breit-Wigner resonance shape, yielding
a resonance energy of E=1.0 MeV and a width F. = 0.8 MeV. These parameters
are in very good agreement with the location and width of the predicted soft dipole
resonance predicted by a variety of models [4, 6, 12, 14, 42]. However, although there
is little dispute that a low-energy E1 enhancement exists in 11Li due to the large
Coulomb dissociation cross section of 3.6 :1: 0.4b, the exact nature of the enhancement
is not known. Specifically, there is considerable debate about whether the excited
11Li nucleus breaks up immediately, as in a direct breakup model, or if it populates a
collective mode of the type discussed in refs. [9, 10]. The nature of the enhancement

cannot be ascertained merely from the measurement of the photonuclear spectrum.

However, from a ”Li -neutron relative velocity spectrum, the lifetime of the reso-
nance was estimated to be r = 50 fm/c, which yields a width of 1" = 4 MeV, a factor
of five greater than the width of the photonuclear spectrum. This contradiction be-

tween the width from the photonuclear spectrum and the width estimated from a

61

relative velocity spectrum indicates that the photonuclear cross section does not de-
scribe a resonant state, and therefore, the breakup is direct. Thus our measurement is
evidence against the existence of a soft dipole resonance, i.e., a vibrational resonance

between the halo neutrons and the ”Li core.

Also, from the complete kinematical measurement, ”Li and neutron momentum
distributions could be reconstruced in the rest frame of the 11Li nucleus. The distri-
butions were fitted with Gaussian functions and yielded widths of 09 = 18 21:4 MeV/c
and 0,, = 13 :1: 3 MeV/c, in good agreement with previous measurements [2, 6, 34].
It should be noted that this determination of 0,, is independent of, but in agreement
with, the value of 0,, from the 1n-”Li events. Perhaps the most interesting feature
of these momentum distributions was that they could be reproduced by a simulation
that used the measured 11Li excitation energy distribution, assuming the excitation
energy was partitioned amongst the ”Li and the neutrons according to a 3-body phase
space distribution. This was interpreted as evidence that the excitation energy distri-
bution and the nature of the breakup mechanism largely determine the shape of the
momentum distributions. Also, this is evidence that there is no correlation between
the halo neutrons, although comparisons of the data with other models are necessary

to confirm this hypothesis.

APPENDICES

 

Apppendix A: Calibration of
FYagment Detectors

I: The Silicon Detectors

Figure A.1 shows a sketch of a side view of the target and fragment detectors and a
schematic representation of the pixel-like quality of the strip detector due to the 16
horizontal and 16 vertical strips. The first AE detector, a MICRON silicon strip detec-
tor, was located 15 cm from the Pb target. The distance was chosen to be close enough
for complete solid angle coverage for the resulting forward focused ”Li fragments, but
still be far enough away to achieve sufficient angular resolution of the ”Li . The
3.125 mm wide strips provide square pixels that are 3.125 mm on a side, yielding a
”Li angular resolution of 1.2 ° . The second AE detector, a MICRON silicon detector
of the same thickness, was used to increase the ratio of energy loss to straggling.
The second silicon detector yielded an energy loss similar to that of the strip detec-
tor. The total energy loss is about doubled, but the energy loss straggling, which
is proportional to the square root of the thickness of the medium, only increases by

40%.

Energy signals were readout from each of the 32 strips, although the magnitudes
of the energy signals from the back set of strips are equivalent to those of the front
set of strips. One energy signal was also readout from the second AE detector. Fast

signals were picked-off of the energy signals coming from the front (horizontal) strips

62

63

Side View

 

 

 

 

“Li beam -
~, I u
I ll:
Pb target
Silicon strip det. CsI(Tl)
Silicon det. detector

Front View of Strip Det.

 

Figure A.1: Side view of target and fragment telescope setup. The telescope consisted
of a 300 pm strip detector, a 300 pm silicon detector, and 1.2 cm thick CsI(Tl)
detector. The front view of the strip detector shows the pixel structure defined by
the horizontal and vertical strips, used to determine the ”Li angle.

64

by a Berkeley 21X742 timing preamplifier/pick-off unit. The fast signals were fed
through a constant fraction discriminator, which generated a logic signal (NIM) as a
stop for the neutron tof measurement. The energy signals from both silicon detectors
went through preamplifiers and amplifiers before being digitized by Ortec AD811
Amplitude-to-Digital Converters (ADC’s).

Two problems were discovered with the strip detectors. First, there was a great
deal of cross talk between strips. Here, cross talk means that the pulse of electrons
liberated by a charged particle striking a strip would induce smaller pulses in neigh-
boring strips. Therefore, for almost every event, several strips yielded signals. The
induced signals were in all cases about two orders of magnitude lower than the sig-
nal caused directly by the charged particle, so in the analysis only the strip which
yielded the maximum signal was used to determine charged particle energy and angle
information. The second problem involved the pulse shape of the signal. The recom-
mended bias for the strip detector was V=17 Volts to reach full depletion. The pulse
rise time, t,, is given by t, = dz/pV, where d=300 pm is the thickness of the silicon,
p=1200 emf/volts is the electron mobility in silicon and V=30 Volts is the voltage
applied to the detector. Substituting these values into the equation yields a rise time
of 44 ns. The ”Li fragments, on average, deposited about 11 MeV into a strip. The
size of this signal, coupled with the rise time, produced a signal whose amplitude
was too low to trigger the time pick-off units. Therefore, fast signals required for the
neutron tof measurement could not be obtained from the strip detector under these
conditions. In order to obtained the required fast output signal, the strip detector was
biased up to V=60 Volts. At this voltage, t, = 12 ns, and a fast signal was obtained
from the time pick-off units. The leakage current was monitored for the duration of

the experiment to check for damage caused by the excessive voltage.

The silicon strip detector and the second AE detector were each calibrated sep-

65

arately using a thin 228Th source. 22”Th and subsequent daughter nuclei emit 0-
particles at eight energies: 5.34 MeV, 5.42 MeV, 5.69 MeV, 6.05 MeV, 6.09 MeV,
6.29 MeV, 6.78 MeV and 8.78 MeV [46]. All of these a-particles stop in less than
300 pm of silicon. The peak at 5.34 MeV was not strong enough to be used as a
calibration point and the a-particles at 6.05 MeV and 6.09 MeV were not resolvable
due to the resolution of the detectors, about 200 keV FWHM. For the oz-particles at
6.05 MeV and 6.09 MeV, an average energy of 6.07 MeV was used instead. Therefore
six different calibration points were available. Each strip of the strip detector was
calibrated separately. The spectrum for horizontal strip 7 is shown in Figure A.2a.
In Figure A.2b a plot of a-particle energy versus channel number is shown. The solid

line is the calibration, determined from a least squares fit to the six points.

II: The CsI(Tl) Detector

The light produced by charged particles stopping in the CsI(Tl) detector was read
out by four PIN diodes attached to the back surface of the CsI(Tl). The voltage
applied across the four diodes was +400 V. The diodes were connected in series, so
the voltage across each diode was +100 Volts. The leakage current was typically 100
nA. The signals from the diodes were first processed by a preamplifier [24] and then
by a standard spectroscopy amplifier before being digitized by an Ortec AD811 ADC
module. Because of the low power dissipation of the preamplifier, 0.5 W [24], the
preamplifier could be placed in the target chamber, hence under vacuum, without

overheating the diode.

Unlike silicon detectors, where the magnitude of the energy signal depends only
on the energy loss of the particle, the light output of CsI(Tl) depends not only on

the energy loss of the incident particle, but on the atomic number Z and often on

 

66

 

100IIITIIIIIII’TTI.IITI]IIII

IIII

' 80 (a)
60

40

Counts/channel

20

 

llllllilLIllllelLlI

 

 

 

 

 

 

y.-

 

Iq—
}
.1-
-
l

(b)

or-partlcle Energy (MeV)

IIIIIITIIIIITI'IIIIIII IIIIIIIIITIIIIIIIIIIIIT

lllllllllllllLIlllLll

 

 

5 LLJILLIIIIHIIILLILLI
500 600 700 800 900 1000

Channel Number
Figure A.2: (a) Energy spectrum for horizontal strip 7 using a 228Th source for

calibration. The energies of the a-particles are given in the text. (b) Calibration for
horizontal strip 7. The six calibration points were fitted with a straight line.

67

the atomic mass A of the particle as well [24, 25, 47, 22]. Furthermore, for a given A
and Z, often the energy dependence is non-linear over a large energy range. There—
fore, instead of a simple calibration using an a-particle source such as 228Th, the
CsI(Tl) must be calibrated with the same ion or ions that are to be measured in the

experiment, and in the same energy range.

The calibration of the CsI(Tl) was performed using ”Li beams at 34 MeV / nucleon
and 45 MeV/ nucleon. The calibration beams were produced by the fragmentation of
an 180 primary beam on a ”Be target. The energy spread of the ”Li beams was limited
to 0.6% FWHM by the A1200. The Pb target and the thick degrader scintillator were
removed from the beamline, so the ”Li beam only traversed the silicon AE detectors
before stopping in the CsI(Tl) detector. The calibration beam consisted primarily of
”Li but contained small percentages of other Li isotopes as well as tritons and He,
Be, B and C isotopes. A list of the isotopes and their energies is given in Table
A.1. The energies represent the ion energy after traversing both silicon AE detectors.
The tritons and He isotopes are not included because they punched through the
CsI(Tl) detector. From the known momentum of the ”Li beam, the Bp value could
be calculated for the last dipole magnet in the beamline, where Bp = p/q and B
is the magnetic field strength, p is the bending radius, p is the momentum of the
beam particle and q is the charge. The other particles could then be identified from
the AE signal and the value of Bp, since AB 0: q2/v2 o< m”/(Bp)”, with v the
velocity of the beam particle. The total energy of each particle was calculated from
the energy loss in the silicon. The result of the calibration for the CsI(Tl) is shown
in Figure A.3. The CsI(Tl) response was linear in this energy range, possessed the

expected Z-dependence, but displayed very little A—dependence.

68

 

800

—
.1
ufi
«.4

——<
q
-
.1
—q
_
-
-
u—q

——
-

700

600

400

300

EnergyiMeV)

01

O

o
IFIIIIIIIIIIIIIIIIIIIIIIIIIII

O

I

I
llllIlLllIllllIllllIllllIllll

p
P
I'—
p-
-
h
P
p

-

 

 

 

200 l I l I l
200 300 400 500

Channel Number

Figure A.3: Calibration data for the CsI(Tl) detector. The isotopes and energies
are listed in Table 2. The solid diamonds are Li isotopes, the solid squares are Be
isotopes, the solid circles are B isotopes and the stars are C isotopes.

69

Table A.1: Ions and their energies present in the calibration beams

 

 

 

 

 

Ion Energy (MeV)
7Li 376.3
8Li 327.1
8Li 434.5
9Li 287.5
”Li 384.9
”Be 516.0
10Be 461.7
10Be 614.0
llBe 415.3
11 Be 556.3
12Be 507.1
11B 654.3
”B 595.9
133 544.9
14C 729.9
15C 674.9
1”C 625.4

 

 

 

 

Appendix 2: Decay Energy
Calculation

It would not be possible to determine the 11Li excitation energy with sufficient res-
olution by only measuring the energies of the incident and final particles. For ex-
ample, energy conservation for the excitation and decay of 11Li requires the equation
E11 + E — S2,, = E9 + E1 + E2 + Em, to be satisfied for each 11Li that breaks up via
Coulomb dissociation. In this equation, E9 is the ”Li kinetic energy, E, and E2 are
neutron kinetic energies, pr is the energy of the recoiling Pb nucleus, E is the ex-
citation energy (the energy of the absorbed photon), Eu is the incident 11Li kinetic
energy and S2,, is the neutron separation energy of 11Li , by convention a positive
number here. In principle, a measurement of the incident llLi energy and a measure-
ment of the energies of the emitted ”Li , the two neutrons and the Pb nucleus would
yield the excitation energy. However, in addition to the difficulty of measuring the
small Pb recoil (about 0.7 MeV), for reasonable neutron and ”Li energy resolutions
of 6E2 = 6E2 = 1 MeV and 6E9 = 3 MeV (representing 1% energy resolution for a
30 MeV/nucleon ”Li nucleus), and a 0.2% energy resolution for a 30 MeV/nucleon
incident nLi beam, the best resolution available from the A1200, the excitation en-
ergy resolution would be 6 E = 3.4 MeV. Because the soft dipole resonance of 11Li is

predicted to exist near E = 1 MeV, a technique with superior resolution is necessary.

Fortunately, a technique that does provide sufficient energy resolution is available

that does not require the Pb recoil energy to be measured. Energy conservation in

70

71
the rest frame of the “Li can be expressed as follows:

1 l 1
Ed = Ems V9,2 '1’ 2m" V10 + Ema V2,2 (3.1)

The neutron and ”Li masses are denoted by m,, and mg and the primed velocities
are the ”Li and neutron velocities in the rest frame of the decaying llLi . The decay
energy E4 of 11Li is related to the excitation energy by E = E4 + 52“. A schematic
picture of a 11Li breakup into a ”Li and two neutrons is shown in Figure RI. The
velocity 179’ is the ”Li velocity in the 11Li rest frame, 2’“ is the velocity of the two-
neutron center of mass in the 11Li rest frame, 25,, = (171’ + 172’)/2, V,’ and 171’ are the
neutron velocities in the 11Li rest frame and V,” and V,” are the neutron velocities in
the rest frame of the two-neutron center of mass. Two relative velocity vectors can

be defined as follows:

as=s—a (M)
17.11.. = i7.” - V." (3.3)
From momentum conservation, I7,” = --V,” and Vg’ = —2m,,l72’n/m9. Substituting

these relationships and eqns. 2.2 and 2.3 into eqn. 3.1 yields the decay energy in

terms of the relative velocities:

 

1 .. l ..
Ed = ‘z'l‘lvz’vi—s + §#2V.I'3.. (B-4)
. m9(2mn) m.
t = z: —— .
w h in mg + mm") and 1:2 2 (B 5)

A measurement of the energy and angle of both neutrons and the ”Li allows the
laboratory velocity vectors of each particle to be calculated. Then the relative velocity

vector between the ”Li and two-neutron center of mass, as well as the neutron-neutron

72

 

/
\ ‘ 9
V211 wk

11L1

Figure B.1: llLi breakup into ”Li and two neutrons. Momentum conservation requires
the ”Li and the two-neutron center of mass to have equal and opposite momenta. In
the rest frame of the two—neutron center of mass, each neutron has equal and opposite
momenta.

73

relative velocity vector, can be calculated in the laboratory frame. The relative
velocity components can then be Lorentz transformed to the 11Li rest frame and
the two-neutron center of mass frame in order to calculate the decay energy with
eqn. 3.4. For example, the longitudinal and transverse components of the relative
velocity between the ”Li and the two-neutron center of mass in the 11Li rest frame is
calculated from the Lorentz transformation as follows:

V9 - Vo Van - V0
V2”: ‘ ‘9' 2'" 1- vov... 1- vov... (3'6)

I = V, — I = Ifg; — ‘6”;
2n-9L 9* 2'“ 7(1 — Vol/01) 7(1 - Vovznr)

 

 

(13.7)

All velocities are in units of c. The longitudinal direction is labelled the z—direction
which is also the direction along the beamline. The transverse components are thus
the x and y components. The 179 and 172,, are laboratory velocities, and the velocity
Va is the velocity of the laboratory frame, which can be calculated from the average
llLi beam energy of 28 MeV/ nucleon. The angularlspread in the 11Li beam is only
about 0.5 ° and the average Rutherford deflection for all the events is 1.6 ° hence the
velocity V}, z V02. For a 11Li beam energy of 28 MeV/nucleon, assuming the
relative velocities are frame invariant only induces about an 11% error in the decay
energy. As will shown later, this error is much less than the decay energy resolution.
Therefore, the relative velocities were considered to be frame invariant, and the decay
energy for each event was calculated from the relative velocities determined in the
laboratory reference frame. The decay energy expressed in terms of the laboratory

relative velocities is then:

1 "0 1 -o .. .. _.
E4 = 541%... + 5pm.”... and V2» = (V1+V2)/2 (3-8)

An advantage of this expression is that the 11Li velocity Va is not required. With the

approximation that the relative velocities are frame invariant, the decay energy of

74

each event was calulated from the laboratory ”Li and neutron velocity components,
and the decay energy spectrum was constructed. Finally, it should be noted that this
technique of using relative velocities to determine the decay energy of unbound states
in excited nuclei has been successfully applied to several neutron-unbound states in
excited 13C and 1”B nuclei [48]. In this case, the excited nuclei decayed into a 12C
plus a neutron or 11B plus a neutron, respectively. A detailed discussion is given in

ref. [48].

The principle motivation for using the relative velocities to calculate the decay en-
ergy was the relatively good decay energy resolution obtainable with this technique.
The resolution response of the detection system as a function of decay energy was dis-
cussed in Chapter 5. The separate contribution to the response from neutron timing
and neutron angular resolutions, energy losses in the Pb target, ”Li angular resolu-
tion, and multiple scattering in the target were also investigated and are presented
here. A plot of each of these contributions for a 100 keV decay are shown in F ig-
ure B.2a—e and the total resolution for a 100 keV decay is shown in Figure B.2f. The
response functions due to the uncertainty in the neutron timing and angle represent
the net effect from both neutrons. The response due to the ”Li energy measurement
represents the combined uncertainty of the energy resolution of the silicon detectors,
the CsI(Tl) detector, and energy losses in the target. Figure 3.3 shows the separate

response functions and the total response function for 500 keV decays.

The correction for energy losses in the target is the largest source of uncertainty
in determining the 11Li decay energy. Because it is not known where in the target
the reaction occurs, it must be assumed that the reaction happens in the center of
the target. In the data analysis, to compensate for energy loss in the target, the
measured energy of each ”Li is increased by the amount of energy the ”Li would lose

in half the thickness of the Pb target. For the average ”Li energy in this experiment

 

 

75

 

 

 

 
 
  

 

   

 

   
 
   

 

 

 

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1000:— -i g E

   

 

 

 

 

(0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4

Decay Energy (MeV)

Figure 8.2: Contributions to the response function for 100 keV decay energies due
to neutron timing resolution, neutron angular resolution, multiple scattering in the
target, energy loss in the target, and the ”Li angular resolution. The total resolution
function is shown in (f).

76

 

 

 

 

 

 

 

 

 

10000 [It]ltttlrrrr]rtrr[llt IIIIIIIIIIIIIIIIIIIII 710000
(a) (d)
8000 Neutron ”L1 8000
5000 “F nergy 5000
4000 4000
% 2000 2000
0 — ‘ 3 E ‘ -— 2 0
2; 10000 10000
._. (0) 1°)
3 8000 Neutron ”L1 8000
E) 5000 “"91. “91' 5000
D
o 4000
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3 2000 2000
(D Q E E] .- n I O
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c) (F) I
8000 Multiple Total '1 3000
5000 Seat. 5
-; 2000
4000 I
0

5.0 0.2 0.40.6 0.8 0.0 0.2 0.4 0.6 0.8 ‘

Decay Energy (MeV)

Figure 3.3: Contributions to the response function for 500 keV decay energies due
to neutron timing resolution, neutron angular resolution, multiple scattering in the
target, energy loss in the target, and the ”Li angular resolution. The total resolution
function is shown in (f).

77

with a 0.598 g/cm2 Pb target, the average ”Li energy loss in half the target thickness
was 22 MeV. In the extreme cases, ”Li could have been formed in the front or the
back of the target, so adding on 22 MeV to the measured ”Li energy could cause a

maximum error in the ”Li energy of :1: 22 MeV.

 

 

Appendix C: Correction for
Post-Breakup Coulomb
Acceleration

Because of post-breakup Coulomb acceleration, the measured velocity of the ”Li is
somewhat higher than the velocity of the ”Li immediately after the breakup of 11Li .
Therefore, the measured relative velocity 179-2", and hence the calculated decay en-
ergy, are not quite correct. In the following, a method for correcting the error in the

decay energy due to post-breakup Coulomb acceleration is presented.

The starting point for the method is the breakup scenario shown in Figure 5.7
in Chapter 5 and the application of the classical equations of motion for a charged
particle moving in an electromagnetic field. The incident 11Li particle is assumed to
follow a straight line trajectory at an impact parameter b with a velocity V. It is
also assumed that the photon is absorbed at the distance of closest approach. Now
suppose the breakup occurs at a distance r from the Pb nucleus. If the relative
velocities could be measured at the breakup point, no correction would be necessary
for the decay energy. However, for ”Li only its re-accelerated velocity is measurable.
Therefore, the change in the ”Li velocity due to the Coulomb field of the Pb nucleus
must be calculated and subtracted from the measured ”Li velocity components. Of
course, the velocities of the neutrons are not altered by the Coulomb field of the Pb,

so the measured neutron velocities are equal to the neutron velocities at the point of

78

79

breakup. For the ”Li particle, the equation of motion is:

. 3 “
11179 _ ZL.ZP58 _:_ and i-‘=b:t+V9t2 (C-I)

Tit— - 771972
The non-relativistic formulation (7 = 1.0) has been used.because 7 = 1.03 for a 28
MeV / nucleon llLi beam. The lifetime of the excited 11Li is denoted by 1'. The photon
is absorbed at t=0, r=b, and the 11Li breaks up at t=tau, at a distance r from the Pb
nucleus. Making the additional assumption that the change in the velocity of ”Li is
small, and hence replacing V9 with the average beam velocity V in the expression
for 1'" allows the equation of motion to be integrated directly. Integrating from t = 1'
to t = co yields the change in the longitudinal and transverse velocity of ”Li . The

z-direction (beam diretion) is taken as the longitudinal direction.

_ 213213st2 1

AV. E V0400) - V9.('r) - m9V \/b’ + V214 (C.2)

AV; E V9J_(OO) - V9_L(T) = ——2 — — ——I (0.3)

The changes in the x and y velocity components are taken as AV, = AV, = AV‘L/fi.
Although straight line trajectories were assumed, transverse accelerations were still
calculated. The convenient approximation of a straight line trajectory merely allows

the integrations to be done analytically.

Calculating the impact parameter for each event as described in Chapter 5, Sec-
tion 1, and using the average lifetime 1' = 50 fm/c that was determined in Chapter
5, Section 3, the values of AV,” AV, and AV, were determined on an event-by-event
basis. These values were then subtracted from the measured ”Li velocity components
to yield corrected ”Li velocity components, defined here as V4,, V”, and V“. The

corrected ”Li velocity components and the measured neutron velocities were used to

80

calculate the relative velocities and hence the corrected decay energy spectrum. Fig-
ure C.1a shows the distribution for the z-component of the relative velocity between
the 9Li velocity and the average neutron velocity V2,, calculated for each event before
any corrections were applied. These data were also presented previously, in Figure 5.6.
The distribution for the relative velocity using the corrected 9Li velocities is shown
in Figure C.1b. This velocity spectrum is centered about zero, indicating the validity

of the correction procedure.

It is also interesting to examine the decay energy spectrum that results with and
without the correction for post-breakup Coulomb acceleration. Figure C.2a shows
the decay energy spectrum that results if no correction is made to the 9Li velocity.
In Figure C.2b, the decay energy spectrum that uses the corrected 9Li velocities is
shown. This spectrum was also shown previously, in Figure 5.1c. Comparing the
two spectra, it can be seen that the post-breakup acceleration causes a significant
broadening, about 200 keV, of the decay energy spectrum and a shift in the centroid

to higher decay energies.

81

 

 

 

 

 

 

 

 

 

250%IIIIIIIIITETIITTTI:
2005— (a) §§+é g —3
150}- fifi :

E f: g E

A 100:" H1
.9. E ,3 5
8 50_— Q ‘1
Q ; o :
3 -031111 111L 111! Llllg
g EIlI—T ITIF TIII III]:
v 200:— l++ -:
:5 5 (b) Hi ; 3
S3 150:— § lfi -:
10°;- éfé +l “:

5 i H 1

50:— 6 f —:

C 0 1 :
-0p.11 1111 lLtL 111%

 

 

 

 

-0.04 -0.02 0.00 0.02 0.04

(Vs, " V2n,)/C

Figure C.l: (a) Longitudinal (z) component of 9Li and average neutron relative veloc-
ity for each event. (b) Relative velocity difference after correcting 9Li for post-breakup
Coulomb acceleration.

82

 

T

lrlllrlllllllllllll

(a)
% Uncorrected

4000

3000

2000

LJLlllllllLlllllllll

 

    

 

 

H

O

O

O
l'll.H!1lI|llll Illrl

Yleld (Counts/MeV)

g (b)
40004 + Corrected

El it
2000’;- lg:

0 ll 1 I fill L
0.0 0.5 1.0 1.5 2.0

 

 

 

 

11L1 Decay Energy (MeV)

Figure C.2: (a) Decay energy spectrum before correcting for post-breakup Coulomb
acceleration. (b) Decay energy spectrum after the correction.

Appendix D: Results from the
7Li(p,n) Experiment

The problem of cross talk was discussed in Chapter 2. The purpose of this appendix
is to display some additional data from the 7Li(p,n) experiment that was relevant to
the cross-talk rejection procedure described earlier. First the basic strategy of the

cross-talk rejection will be reviewed.

The cross-talk rejection procedure consisted of calculating the quantity AEn=En-
13,-E, for a two-neutron 9Li coincidence event. The quantites E“, E, and E, were
defined earlier and are shown in Figure D.1 for a typical cross-talk event. For a cross-
talk event, AEn=0 by energy conservation. Figure D.1 also depicts a true neutron-
neutron coincidence event. For the true events, the quantity E. is determined from the
time difference between the arrival of the two neutrons at their respective detectors.
However, since this is not a cross-talk event, B, does not represent the energy of a
scattered neutron. Hence the quantity AEn takes on arbitrary values for the true

coincidences.

The spectrum for AE,. for the n-n events from the 7Li(p,n) data is shown in
Figure D.2. This spectrum consists entirely of cross-talk events. Although there is
a peak at AEn =0, there is also a non-negligible shoulder on the peak at AR" > 0.
This shoulder originates from events when reactions other than n-p elastic scattering

produced the pulse height. For example, for the reaction n+C—r n + 30: -7.6 MeV, a

83

84

Cross-Talk Event

 

Recoil proton Ep

True Coincidence Event

Figure D.1: (a) Sketch of a typical cross talk event, which yields false neutron-neutron
coincidence events. (b) True coincidence event.

85

 

 

 

 

_1 I 1 I l I 1 III I III II r111:
400:— : : —:
i I I I I
Z — | I .
\ 300— I l “:
‘0 I I -
4.)
c _’_ I I :
D ._...
o 20C>:"' ' ' .
L) _ l | _,
‘-’ I. | -I
E 1003- ' ' —
a) - I l j «-
._. g l I j
>' - I I .
0r- . | ‘
1 111L1 ILII l 11111l41 1 -
-40 '20 0 20 40
AEnlMeV)

Figure D.2: A8,. spectrum constructed from the pure cross talk events from the
7Li(p,n) reaction. The dashed vertical lines indicates the gate used for cross talk
rejection in the AER spectrum from the 11Li data

86

measured pulse height in the scintillator would correspond to a much higher energy
a-particle than a proton. Attributing the pulse to a proton then yields too low a value
for P3,, and hence Ali}fl > 0. The negative Q-value of the reaction also causes AEn > 0.
The vertical dashed lines indicate the width of the gate used in the AE,, spectrum for
the 11Li data to reject cross-talk events. As shown in Figure D.2, most of the cross-
talk events from reactions other than n-p scattering were not eliminated by the gating
procedure. The existence of this type of events was one of the primary motivations
for developing a Monte Carlo simulation that could reproduce the 7Li(p,n) data and
evaluate the amount of cross-talk contamination remaining in the 11Li data before

and after cross-talk rejection.

Another motivation for developing a Monte Carlo simulation was the realization
that cross-talk events occuring between neighboring detectors would be more difficult
to eliminate than cross-talk events occuring between detectors separated by greater
distances. A good illustration of this was found in'the 7Li(p,n) data. Figure D.3a
depicts the AE,, spectrum from cross-talk events from detectors in the same array,
which primarily come from neighboring detectors. Although still peaked at AEfl =0,
the spectrum is broader than the AEn spectrum constructed from cross-talk events
that occurred in detectors in different arrays, as shown in Figure D.3b. Because
neighboring detectors are in such close proximity to each other, the finite size of the
detectors makes the actual flight path of the scattered neutron less well defined, which
caused a. spread in the calculated energy E. of the scattered neutrons. For cross-talk
events from detectors in different arrays, the distance between detectors was at least
1 m, hence the flight path of the scattered neutron, and thus the energy, was better
defined. As shown in Figure D.3b, the cross-talk rejection procedure for these events

was more effective.

The AEfl spectrum for the 11Li data is shown in Figure D.4. These events consist

 

 

87

 

    

 

 

 

 

 

 

 

 

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300— | l —-
S _ (a) ' :
(D
E ~_- Same : -
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100— —
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—4
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0" I
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150— —
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“D h- -
fl _
o -
H I— -I
)- I.
O I I
I-llLilllllllllLllllllr

 

-40 -20 0 20 40

AEnIMeVJ

Figure D.3: (a)AE,. spectrum from the 7Li(p,n) reaction for cross-talk between de-
tectors in the same detector array. (b) Similar spectrum, but for cross-talk events
between detectors in different arrays.

 

88

 

ISOT—v—r—I—l—TII

100 -

 

 

 

 

 

 

Yleld (Counts/MeV)

 

 

 

 

AEntMeV)

Figure D4: A3,. spectrum from the 11Li data. Here, the events are a mixture of
cross-talk and true coincidences. The vertical dashed lines indicate the gate used for
rejecting cross-talk events.

 

89

of both cross-talk and true coincidences. The gate used to reject cross talk, which
was determined from the 7Li(p,n) data and the Monte Carlo simulation, is depicted
by the dashed lines. This spectrum is very broad because the true coincidence events
produce a very flat ABn spectrum. In fact, the lack of a strong peak at AB“ =0
indicates the cross-talk contamination was not too severe. This statement is also
supported by the Monte Carlo simulation of the nLi data, which indicated that only

about 15% of the events were cross-talk events.

Appendix E: The Virtual Photon
Spectrum

The equivalent photon method is a very useful technique for extracting information
about the electromagnetic excitation of radioactive nuclei, provided a reliable calcula-
tion of the photon spectrum is available. The expression for the El photon spectrum
as a function of solid angle, given below and also in eqn. 1.3, is valid for all beam

energies:
dN31(E) _ Z%a 62

do “ 4,2 —l [In-{(5012 + [K£¢(e£)]’] (13.1)

6

 

(5)“ are-"I

Here, Z; is the target charge, a is the fine structure constant, v is the projectile
velocity, 6 = Ea/h'yv, a is half the distance of closest approach for a head on
collision in a strictly Coulomb potential, E is the excitation energy delivered to the
projectile, (10 is the element of solid angle into which the projectile deflects and s is
the eccentricity of the Coulomb orbit, which is related to the Rutherford scattering
angle by 6 = 1/ sin(0/2). The function K;£(e£) is a modified Bessel function with
an imaginary index, and K:{(e) is the derivative of K with respect to the argument.
These Bessel functions are not tabulated, and must be calculated numerically from

the integral [49]:

K;¢(s£) = [000 6‘5““ c0851: dz (E.2)

90

91

Equation 5.1 was integrated over all pure Coulomb orbits to obtain the spectrum as
a function of excitation energy. The integrated expression, N31(E), was used to de-
termine the photonuclear cross section from the measured Coulomb dissociation cross
section (eqn. 1.4). Although a closed form expression exists for N51(E) [50], it is a
complicated function of bessel functions of complex arguments and imaginary indices,
and their derivatives. Therefore, it was easier to perform a numerical integration of
eqn. E.l over solid angle. The integration is performed over (if! = 21r sin 0119 from
0 = 0 up to 0 = 0,, where 0, is the grazing angle. To calculate the grazing angle
the sum of the radii of Pb and 11Li is required. The llLi radius was taken to be 3.2
fm from ref. [1]. It will be shown later that the integrated photon spectrum is fairly
insensitive to the value chosen for the 11Li radius. For each value of excitation energy
E, eqn. E.1 was integrated over solid angle. The result of the calculation, N 51(5))

versus E, is shown in Figure E] by the solid line.

Because of the large amount of computer time necessary to perform this calcu-
lation, some approximations were also investigated. Hussein et al. [50] has given
an approximation for the photon spectrum versus excitation energy that is expected
to be valid in the regime of intermediate energy projectiles (z 30 MeV/nucleon -
100 MeV/nucleon). The dotted line in Figure E.1 shows the result of this approx-
imation for a 11Li beam at 28 MeV/nucleon. The curves agree to better than 2%.
Another approximation, the relativistic approximation, yields the simplest form for
the photon spectrum. In the relativistic approximation straight line trajectories are
assumed, hence the integration of eqn. E.l over d0 is replaced by an integration over
211' b db. The expression, introduced initially by Fermi [51] and further developed by
Weizsacker and Williams [52], is given by:

2

NEIIE) = ;Z%a(§)'IzKo(z>Kl(z> —§(§)222(K3(x)—K3(z»1 (E3)

92

 

 

 

 

 

2500 I I I I [ I I I I I I I r I I I I I I—:

Q 3
z 2000 _ —
L I I
g — a
E 1500 :— —_
D - -
Z I 2
C 1000 — -
o : '
P _ I
.8 L ‘
0- 500: _
O - 1 1 l l 1 l I l l l L l J l I l l l L -

0.5 1.0 1.5 2.0

.0
o

Photon Energy (MeV)

Figure E.l: Three different calculations are shown for the equivalent photon spectrum.
(a) The solid line uses the expression valid for all beam projectile energies, the dotted
line is the result of an approximation for‘intermediate energies [50] and the dashed
line is the result of a relativistic approximation

93

In this expression, K0 and K1 are modified Bessel functions of the argument 3, with
:1: = Ebmgn/h'yv. A calculation of the photon spectrum for bmgn=10.3 fm is shown
in Figure E.l by the dashed line. This value of b,,,,-,, corresponds to the sum of
the nuclear radii of Pb and nLi , using 3.2 fm for the 11Li radius. The relativistic
approximation also agrees to better than 2% with the exact calculation. Therefore,
the relativistic approximation can be used to calculate the virtual photon spectrum

to high accuracy even for beam energies as low as 28 MeV/nucleon.

In order to calculate the photon spectrum with any of the above expressions, the
sum of the nuclear radii of Pb and 11Li must be known to calculate bmgu. Although
the radius of Pb is easily calculated from the empirical expression 1.2/1V3, it is not
so obvious what value to use for 11Li because of the neutron halo. In this work,
the matter radius of 3.2 fm was used, based on the measurement by Tanihata et al.
[1], which yielded hm,“ = 10 fm. To investigate the sensitivity of NEI(E) to bmgn,
the photon spectrum was calculated for values of hm,“ =9, 10, and 11 fm using the
relativistic approximation. The result of the calculations are shown in Figure E.2 by
the dotted, solid, and dashed line for minimum impact parameters of 9, 10, and 11 fm,
respectively. The shapes of the spectra are similar, but not the same. For example,
for an excitation energy of 1 MeV, the photon spectrum increases by 12% between
b=9 and b=ll fm. However, because there is little variation in the shape of the
spectra, only the energy-integrated photonuclear cross section 0'51 will be affected by
the uncertainty in bmgn. More importantly, the shape of the photonuclear spectrum

and the extraction of the Breit-Wigner parameters will be unaffected by the sensitivity

of N‘s-1(3) to b,,,,-,,.

 

 

94

 

 

fl 2500 " —:
g s
Z .I
2000 —
(— '- .1
(D ' I
.0 a _
E 1500 —
D —
Z I
c I.
o 1000 _
p .—
2 I ..
0. 500 C— :
F- l l l I LI 1 L I L l L I I l l L _

 

 

 

530
01-

0.5 1.0 1.5 2.0

Photon Energy (MeV)

Figure E.2: Calculation of the equivalent photon spectrum using the relativistic ap-
proximation for bmgn = 9 fm (dotted line), hm," = 10 fm (solid line), and hm,-n = 11
fm ( dashed line).

 

 

Appendix F: Electronics and Data
Acquisition

The basic flow of the electronics will be described in the following appendix. First
the processing of the neutron signals will be detailed, followed by a description of
the processing for the telescope signals. A description of the logic used for fragment
singles events, neutron-fragment coincidence events, and the main features of the data

acquisition scheme will be given.

I: Neutron Detectors

As shown in Figure F.1, signals from the neutron detectors were first split by an
N SCL-built 4-way splitter (4W8) into three output signals. One of the output signals
was integrated by a Lecroy 2249W ADC module to determine the area of the entire
signal (QM). Another signal from the splitter was used to determine the area under
the tail of the pulse (QM-g). A two—dimensional plot of QM versus QM; was used
during off-line analysis for neutron / 7-ray discrimination. The signal for QM; was put
into a Phillips 7145 Linear Gate (LG) module. The third output from the splitter
was sent to a Tennelec 455 Constant Fraction Discriminator (CFD). The N IM output
signal from the discriminator was input to an N SCL Quad Gate Generator (GG),
which in turn generated a 300 ns wide gate. This gate was also sent to the linear gate

module, being delayed to arrive approximately 30 us after the peak of the signal Qua.

95

 

 

96

3010
.00. n
E
W
’9‘ menu MW

 

soruonoolg 10199190 uonnoN

 

 

 

 

 

 

Figure F.1: Electronics setup for the neutron detector signal processing. The module
abbreviations are defined in the text.

 

97

The output of the linear gate module was an analog signal representing only the tail
portion of the signal from the neutron detector. The signal was also integrated by a

Lecroy 2249W ADC module.

This method of obtaining the Qt,“ signal, i.e. using a LG, is quite different from
the technique used in previous experiments such as 88020 and 86006, but it was
necessary when coincidence events between a fragment and t_wg neutrons were being
measured. For Qua, the gate must be timed to begin approximately 30 ns later than
when the analog signal peaks. The only constraint on the gate for the QM signal is
that it arrives before the QM signal. For events where only one neutron is detected,
the signal from the detector can be split as shown in Figure F.1 and one of the
outputs used to generate gates for QM and Q34“ that are sent directly to the ADC
modules. However, for events where two neutrons are detected, the arrival time of the
QM and QM; signals for the second neutron will have no correlation with the gates
generated by the first neutron because of the different neutron flight times. Therefore
the signals for the second neutron will not be properly gated by the ADC and good

neutron/y-ray discrimination will not be possible.

For the QM signal, this problem is easily overcome by using a wide gate (660 ns
for this experiment) and making the QM signal of the leading neutron arrive about
halfway through the gate, as shown in Figure F2. The 660 ns gate was wide enough
to still encompass the signal from a second neutron under either of the following

extreme conditions:

1. The second neutron has an energy near the minimum value that is expected to
be measured in the experiment, and it strikes the detector that is the furthest

distance from the target, yielding a very large tof relative to the leading neutron.

2. The second neutron has an energy near the maximum value expected and strikes

 

 

98

Leading Neutron

30ns-)I I(- I Q-tail gate 300 ns

 

Delayed Neutron

30ns-)I If- . I Q-tail gate 300 ns

/.

—I [— Q-tot gate

660 ns

>

Figure F2: Schematic of the timing for the leading and delayed neutron. Each signal
has a separately timed gate for the Qt.“ signal. Both the gate and the analog signal
are put into the Linear Gate module. The QM gate is used in the ADC modules for
both the Qtof and Qtail signal.

 

 

time (118)

 

 

99

a detector that is closest to the target, yielding a very short tof relative to the

leading neutron.

For the Qt,“ signal, the problem is more difficult because of the more precise
timing required for the gate relative to the analog signal. The method used in this
experiment was to generate a separate gate from the analog signal from each detector
that yielded a signal. These gates were timed to begin 30 ns later than the time of
the peak of the analog signal, as shown in Figure F2. The gates were all 300 ns wide.
The analog signal and it’s 300 ns gate were put into a linear gate module. A separate
linear gate input was available for each neutron detector. The output (analog) of
the linear gate was the portion of the Qt.“ signal that was inside the input gate.
This signal was sent to a Lecroy 2249W ADC for integration. The gate for the ADC

module is the 660 ns QM gate described above and shown in Figure F2

The remaining signal processing for the neutron detectors will be described next.
Another of the CG outputs was further delayed (100 ns), sent through a leading
edge discriminator (LED), and into a Lecroy 2228A TDC as a stop signal from the
neutron detector. The LED was used to produce a well defined N IM signal from the
gate whose shape was mildly distorted by the 100 ns cable delay. Because the neutron
detector signals start all the TDCs, the TDC value determined from the neutron stop
signal is only related to the cable delay and processing time of the various electronic

modules. However, this value is necessary to calculate the neutron time-of-flights.

The third output from the CG from each detector was sent to a series of N SCL
logic Fan-In (FI) modules. The Fan-In modules acted as a 54-fold OR operation.
The output of the Fan-In modules was sent to an N SCL Fan-Out (F0) module, and
fanned out to several areas. One of the outputs was sent to a gate generator to form

a 315 ns gate labeled the coincidence gate in Figure F.1. A N IM signal from the

 

 

100

fragment telescope electronics was required to arrive within this 315 ns gate for an
event to be classified as a coincidence event and a Master Gate signal to be generated.
Other outputs from the Fan-Out served to start all the TD modules, increment the
neutron sealers, generate the 660 ns ADC gates and strobe the neutron bit registers.

The function of the bit registers will be discussed in section IV.

The 315 ns coincidence gate was also delayed and used in an AND operation with
a NOT from the Master Gate coincidence unit. A NOT Master Gate indicated there
was no fragment that arrived within the 315 ns coincidence gate. For this case, a
neutron signal but no fragment signal, a N IM output from the AND between the
coincidence gate and NOT Master Gate was used to fast-clear the TDC and 2249W
ADC modules. The fast-clear was necessary because the neutron TDCs and ADCs
were started before it was determined electronically that there was a fragment signal
also present. Because neutron singles events would be dominated by cosmic ray
events (2400/ 3), they were not written to tape, and thus it was necessary to clear the
neutron TDC and ADC modules in the case of a neutron singles event. Of course, an
alternative method would have been to delay the neutron signals by several hundred
ns to be sure there was a neutron-fragment coincidence, thus eliminating the need
for a fast-clear, but this technique would have required many more delay boxes and

leading edge discriminators.

Finally, because the clear inputs on the TDC and ADC modules were used by the
fast-clear input, for a good events the modules were cleared internally by the data
acquisition software. Also, as shown in Figure F.1, veto detector signals were sent to
a CFD and a GG. For veto signals in coincidence with neutron detector signals, bit-64
in the neutron register was flagged by a N IM signal. This concludes the description
of the electronic processing of the neutron detector signals. The fragment and beam

particle signal processing will be described next.

 

 

101

II: Fragment Detectors

The electronic processing for the fragment and beam detectors is shown in Figure F.3.
An energy signal was taken from each of the 16 horizontal and 16 vertical strips from
the silicon strip detector. The energy signals from the horizontal (front) strips were
put into LBL 21X742 time pick-off units (TPOs). The time pick-offs provided both
a fast output and an output to be further processed by pre-amplifiers and amplifiers.
The fast outputs were first amplified by N SCL-built fast amplifiers and then were
sent to CFDs. One of the CFD outputs was delayed by 400 ns, reshaped by an LED,
and put into TDC modules as the stop signal for the neutron tof measurement. The
LED output was also sent to the N IM-to—ECL converters, and the ECL output from
the converter was put into the fragment bit registers, which required ECL-type logic
signals. The NIM output from the converters served to increment the fragment sealers.
The other outputs from the time pick-off units, which yielded signals for determining
the energy deposited in the detectors, were processed by N SCL-built pre—amplifiers

and Tennelec 2413 amplifiers, and then sent to Ortec AD811 peak—sensing ADCs.

In order to classify a fragment event as a good event, it was required that signals
from a horizontal strip, a vertical strip, AE2 and the Csl detector be present. The
Tennelec 2418 amplifiers used for the fragment detectors provided a fast output as
well as an output for the ADCs. For the vertical strips, AE2, and the CsI detector, the
fast outputs were sent to CFDs and the N IM output from the CFDs, were subjected
to a 4—fold AND operation. For the front strips, the NIM signals from the CFD
following the fast amplifier were used in the AND operation. If all detectors fired, the
4-fold coincidence unit issued a N IM output that was used for an AND operation with
the coincidence gate generated by the neutron detectors. If the AND was satisfied,

a Master Gate signal was generated. This Master Gate signal was fanned-out as a

 

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102

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Figure F.3: Electronics processing for the fragment and beam detector signals. The

module abbreviations are defined in the text.

103

computer start signal, as a flag indicating a coincidence event is present, as strobes
for the event and fragment registers and was also sent to a gate generator to produce

the 5 ps gates for the Ortec ADC modules.

In addition to the coincidence events, it was also necessary to record the number of
unreacted uLi particles striking the telescope in order to determine cross sections and
to normalize spectra from target-out measurements before subtracting from spectra
recorded during target-in measurements. Also, it was desirable to record the number
of 9Li fragments detected so a 2-neutron removal cross section could be determined
independently from the coincidence data. Therefore, a fragment singles bypass was
also used in order to write fragment singles events to tape. Provided a good fragment
event was present, determined by the 4-fold AND operation mentioned previously,
the resulting N IM signal was also sent through a downscaler. Because only about
10% of the incident 11Li particles dissociate into 9Li and two neutrons in the target
and detectors, and because the neutron detection efficiency is about 10%, the data
being put to tape would consist predominately of fragment singles events. Thus the
fragment singles events were downscaled by a factor of 10. The bypass circuit is
depicted in Figure F.3. The NIM output from the downscaler is subjected to an
AND operation with a NOT Master gate signal. If the AND is satisfied, it indicates
there was no Master gate signal present, hence this event was not a coincidence event
since there was not a signal from the neutron detectors. After verifying the computer
was free, this NIM signal was then sent to the event register to flag the event as a
fragment singles event. Also, it was sent to the fragment scalers, and then it was

fanned-out to strobe the registers and start the computer and to strobe the Ortec

ADC modules.

104

III: Beam Detectors

The beam detectors consisted of two PPAC detectors and a scintillator which was
labelled $1 in Chapter 2. Each PPAC produced four signals, resistively divided
into up, down, left and right signals. These signals were sent to an MSU-built pre-
amplifiear (same type as used for the silicon detectors), to quad shaping amplifiers
(labelled QSH in Figure F.3), and finally to an Ortec AD811 ADC module. This ADC
was strobed by the same 5 ps gates as the ADC modules dedicated to the fragment
telescope signals. A signal in the PPACs was not required to define a valid fragment
event because the detection efficiency of the PPAC was suspected to be less than

100%.

The signal from SI was used as a stop signal for the beam time-of-flight measure-
ment. The signal was sent to a CFD, delayed 600 ns, reshaped in an LED, and sent

to a TDC and scaler input.

IV: Data Acquisition

The data acquisition system at the N SCL is well documented in the manual NSCL
Data Acquisition System Reference Guide by Ron Fox and John Winfield. In this
section, the basic strategy of the data acquisition related to the layout of the input
and output bit registers was briefly discussed. The layout of the input bit registers

were shown in Figure F.3.

Separate registers were used for the neutrons detectors, the fragment registers and
the event classification registers. The electronics for each of the 54 neutron detectors
was wired to a separate bit in the 64 bit neutron register. A Lecroy 4448 48-bit ECL
coincidence register plus an SEC 16 bit register was used. The registers required

strobe inputs as well as clear signals. The origin of the strobe input was described in

105

the section on neutron detector electronics. The clear signal was taken from a Bi Ra
3251 N IM output register that generates a N IM signal when the front-end computer
finishes processing an event. Provided the coincidence bit in the event register is
flagged, the data acquisition code scans the neutron register to see which hits were
flagged. For the flagged hits, the ADC and TDC channels corresponding to those

detectors were read and then cleared.

Each of the 32 strips from the strip detector was also wired into a Lecroy 4448
ECL coincidence register. For either a coincidence or a fragment singles event, as
determined by the event register, the data acquisition code scans the fragment register
for all flagged bits. For any of the first 16 bits that are flagged, the ADC and TDC
channels corresponding to those horizontal strips are read and cleared. Also read
are the ADC values from AE2, the Csl detector, the PPAC ADC module and the
TDC channel of 31. For any of the bits 17-32 that are flagged, the ADC values
corresponding to those vertical strips are read and cleared. Finally, LAM time-out
flags are issued by the software and generated by the Bi Ba 3251 NIM output register.
These signals were sent to a scaler to check for the presence of LAM time-outs during

the experiment.

BIBLIOGRAPHY

 

 

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