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LIBRARY 7
Michigan State
University

 

 

This is to certify that the

dissertation entitled

Observation of Initial and Final-State Effects

in the Systems (6He+n), (8He+n), and (9Li+n)

presented by
Luke Chen

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Phys iCS

 

 

Major professor

P.G. Hansen

Date 4/4/2000

 

MS U is an Affirmative Action/Equal Opportunity Institution 0- 12771

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

 

DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIRC/DateDuepss-sz

OBSERVATION OF IDéITIAL AND8FINAL-STATE FFECTS
IN THE SYSTEMS ( HE+N), ( HE+N), AND ( LI+N)

By

Luke Chen

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

2000

ABSTRACT

OBSERVATION OF INITIAL AND FINAL-STATE EFFECTS IN THE SYSTEMS
(6HE+N), (8HE+N), AND (9LI+N)

By
Luke Chen

An experiment was performed at the NSCL to study the unbound nuclei 10Li
and 7’9He produced in breakup of 30 MeV/u 12'11'10Be nuclei on a 9Be target. The
observed relative velocity distribution of the neutron relative to the fragment Shows
that the initial states have significant influence on the observed final-state interactions.
A value of 440i16 keV has been obtained for the 133/2 resonance energy in 7He.
The experiment confirms the existence of a low-lying [=0 state for the 10Li isotope,
corresponding to a scattering length a, <-10 fm. The (8He+n) data are limited by
counting statistics but seem to offer the first evidence for an 1:0, [=1 inversion, in

this case characterized by a numerically large scattering length as g —10 fm.

For my family and friends

iii

ACKNOWLEDGMENTS

First and foremost, I would like to thank Gregers Hansen for being a terrific
role-model as well as my thesis advisor. It was a joy working for someone who
is knowlegeable, patient, insightful, and humorous. I Sincerely appreciated all the
support and encouragement I’ve received during these years working on this research
project. I will miss working with him. I want to thank Michael Thoennessen for
providing me with a chance to work with him and all the help with data analysis.
In addition, I would like to thank Walt Benenson, Aaron Galonsky, Scott Pratt, Jon
Pumplin and Jack Baldwin for serving on my guidance committee.

Much gratitude goes to the collaborators on the thesis experiment: Aaron Galosky,
the group from Rikkyo University (K. Ieki, Y. Iwata, Y. Higurashi, S. Takeuchi) ,
and the group from Hungary (F. Deak, A. Horvath, A. Kiss, and Z. Seres).

I would like to thank all of the NSCL faculty, graduate students, and staff for
making this such a friendly place to work. I will not forget the time I have spent here

in Michigan.

iv

CONTENTS

LIST OF TABLES vii
LIST OF FIGURES x
1 Introduction 1
1.1 Overview .................................. 1
1.2 Spectroscopic Techniques for Bound and Unbound Nuclei ....... 2
1.3 Previous Use of Final-State Interactions ................ 7

1.4 Studies of Unbound Nuclei with FSI .................. 8

1.5 The Objectives of This Work ...................... 9
1.6 Outline ................................... 13

2 Experiment 97017 14
2.1 Radioactive Beam ............................. 15
2.2 NSCL Neutron Walls . .. ......................... 18
2.3 Plastic Scintillator Array ......................... 20
2.4 Silicon Strip Detector ........................... 20
2.5 Sweeping Magnet ............................. 21
2.6 Electronics Setup ............................. 21

3 Data Analysis 23
3.1 Velocity Difference Analysis ....................... 23
3.2 Silicon Strip Detectors .......................... 31
3.3 Plastic Scintillators ............................ 33
3.3.1 Energy Calibration ........................ 33

3.3.2 Fragment Identification ...................... 36

3.3.3 Multiple Fragment Hits ...................... 36

3.3.4 Fragment Velocity Measurement ................. 36

3.3.5 Fragment Velocity Resolution .................. 39

3.4 NSCL Neutron Walls ........................... 42
3.4.1 Neutron Identification ...................... 43

3.4.2 Multiple Neutron Hits ...................... 43

3.4.3 Position Calibration and Resolution ............... 44

3.4.4 Time Calibration and Resolution ................ 50

3.4.5 Neutron Velocity Measurement ................. 51

3.4.6 Neutron Velocity Resolution ................... 52

3.5 Particle Tracking Issues .......................... 53
3.6 The Fitting of the Velocity Difference Data ............... 55
4 Model of the Reaction of the Final-State Interaction 58
4.1 Fragmentation Mechanism for Breakup ................. 58
4.2 Model for Calculation of Final-State Interaction ............ 65
4.3 Parameterization of the Continuum States ............... 67
4.4 Computing Energy Distributions .................... 68
5 6He+n 73
5.1 Introduction ................................ 73
5.2 Results ................................... 73
6 9Li+n 82
6.1 Introduction ................................ 82
6.2 Results ................................... 83
7 8He+n 92
7.1 Introduction ................................ 92
7.2 Results ................................... 93
8 Summary 99
A Data 101
LIST OF REFERENCES 111

vi

LIST OF TABLES

3.1
3.2

3.3

3.4

3.5

3.6

Kinetic energy of the 0 particles for the decay of 228Th .........
‘Cocktail’ beam calibration summary. Summarized here are the con-
tents in the ‘cocktail’ beams with different Bp settings and the de-
tectors which were able to be calibrated. Detector 1 represents the
detector with most deflection, and detector 16 is nearest to the beam
axis. ....................................
The trajectories of various charged fragments as they pass through the
sweeping magnet. The fragments are assumed to be at zero degrees rel-
ative to the beam direction, passing through the center of the magnet
gap. The calculations are done based on the work by [34], which uses
a measured field map of the magnet to integrate the trajectories of the
fragment. Detector 1 is the detector farthest from the beam axis, and
the detector 16 is the nearest. Values between X and X +1 correspond
to a fragment predicted to hit bar X + 1 (such that 13.9 means the por-
tion of bar 14 closer to the beam axis). At energies close to 30 MeV/u,
the 8He fragments take a trajectory that strikes the plastic scintilla-
tors nearest the beam direction. A higher beam energy would have
improved the resolution of the experiment, but the reaction fragments
would have been insufficiently deflected by the sweeping magnet. . . .
Fraction of neutron-fragment coincidence events as a function of num-
ber of bars which detected a fragment. For the neutron-fragment coin-
cidence events, 90.5% are detected by one plastic scintillator. Events
with multiple scintillator hits are not used for analysis. ........
Stopping power parameters for beryllium, lithium, and helium nuclei
passing through 9Be target. Tabulated here are the parameters Co
and CI for a fit to a form of S (T) = COTCI, where T is the kinetic
energy per nucleon of the nucleus. The unit of the stopping power is
MeV/(mg/cmz). Total energy loss can be estimated by multiplying
the target thickness (in units of mg/cmz), with the mid-target energy.
Resolution of momentum and velocity measurement of the plastic scin-
tillators with incident l2Be beam. Listed here are the contributions
from target energy-loss, momentum spread in the 12Be beam, and en-
ergy resolution from the plastic scintillators. ..............

vii

32

38

38

40

42

3.7 Resolution of momentum and velocity measurement of the plastic scin-
tillators with incident 11Be beam. Listed here are the contributions
from target energy-loss, momentum spread in the 11Be beam, and en-
ergy resolution from the plastic scintillators. ..............

3.8 Fraction of neutron coincidence events as a function of number of
bars which detected a fragment. For the neutron-fragment coincidence
events, over 90% are detected by only one neutron wall cell. .....

3.9 Resolution of momentum and velocity measurement of neutron wall
detectors with an incident 12Be beam. Shown are the contributions
from resolution from the fragment velocity resolution, time resolution,
and position resolution effects .......................

3.10 Resolution of momentum and velocity measurement of neutron wall
detectors with an incident 11Be beam. Shown are the contributions
from resolution from the fragment velocity resolution, time resolution,
and position resolution effects .......................

4.1 Goldhaber 00 parameters extracted from incident 11Be projectile. All
values tabulated are in units of MeV/c and are expressed in terms
of standard deviation 0. Shown tabulated here are the extracted 00,
the estimated contribution from the momentum resolution, and the
measured momentum spread of the fragment. Since the halo neutron
in 11Be is so loosely bound, it means that it would not contribute
much Fermi momentum to the system. Consequently it might be more
correct to use A = 10 for the incident 11Be. The extracted 00 parameter
from the use of both of these assumptions are shown. .........
4.2 Goldhaber 00 parameters extracted from incident 12Be projectile. All
values tabulated are in units of MeV/c and are expressed in terms of
standard deviation 0. Shown tabulated here are the extracted 00, the

42

44

52

53

61

momentum resolution, the measured momentum spread of the fragment. 61

4.3 Production cross sections of 7’S’He, and 10Li ...............
4.4 Spectroscopic Factor for (llBe,1°Be) and (1°Be,9Li) obtained from [43]
4.5 The lowest known excited energy for 6'SHe and 9Li taken from [51].

4.6 Effective binding energies of neutrons in 12’ll'mBe nucleus. ......

5.1 Approximate occupation of the available neutron orbitals in the reac-
tion 9Be(AZ,7He)X. ............................

6.1 Approximate occupation of the available neutron orbitals in the reac-
tion 9Be(”Z,1°Li)X. The available neutron orbitals are the same for
9Be(AZ,9He)X since the two unbound systems have the same number
of neutrons. ................................

A.1 6He+n relative velocity distribution. Shown are the total number of
events that satisfy the 5—degree angular cut binned in 0.2 cm/ns in-
crements. The velocity difference distribution Vf — Vn for each of the
12'll’mBe projectiles is shown. ......................

viii

64

64

66

89

102

 

A2

A3

A4

A5

A6

A.7

A8

A9

9Li+n velocity difference distribution. Shown are the total number

of events that satisfy the 5—degree angular cut binned in 0.2 cm/ns
increments. The velocity difference distribution V, - Vn for each of the
12’11’10Be projectiles is shown. ...................... 103
8He+n velocity difference distribution. Shown are the total number

of events that satisfy the 10—degree angular cut binned in 0.2 cm/ns
increments. The velocity difference distribution V, — V" for each of the
12’11'10Be projectiles is shown. ...................... 104
Neutron and fragment velocity distributions from the 9Be(12Be,6He+n)X
reaction. Shown here are the velocity distributions of the 6He frag-
ments and the neutrons from coincidence events. Only events with
single neutron wall and single fragment bar hits are shown here. . . . 105
Neutron and fragment velocity distributions from the 9Be(“Be,6He+n)X
reaction. Shown here are the velocity distributions of the 6He frag-
ments and the neutrons from coincidence events. Only events with
single neutron wall and single fragment bar hits are shown here. . . . 106
Neutron and fragment velocity distributions from the 9Be(1°Be,6He+n)X
reaction. Shown here are the velocity distributions of the 6He frag-
ments and the neutrons from coincidence events. Only events with
single neutron wall and single fragment bar hits are shown here. . . . 107
Neutron and fragment velocity distributions from the 9Be(12Be,9Li+n)X
reaction. Shown here are the velocity distributions of the 9Li fragments

and the neutrons from coincidence events. Only events with single neu-

tron wall and single fragment bar hits are shown here .......... 108
Neutron and fragment velocity distributions from the 9Be( 11Be,9Li+n)X
reaction. Shown here are the velocity distributions of the 9Li fragments

and the neutrons from coincidence events. Only events with single neu-

tron wall and single fragment bar hits are shown here .......... 109
Neutron and fragment velocity distributions from the 9Be(“Be,8He+n)X
reaction. Shown here are the velocity distributions of the 8He frag-
ments and the neutrons from coincidence events. Only events with
single neutron wall and single fragment bar hits are shown here. . . . 110

ix

 

LIST OF FIGURES

1.1

1.2

1.3

Chart of nuclides for bound nuclear systems. Bound nuclear systems
are shown here as a function of their proton number Z and neutron
number N. The black squares represents the stable nuclei in nature,
and these collectively are usually referred to as the “valley of stability”.
Nuclear binding weakens for nuclei away from stability, and eventually
becomes too weak to permit a bound system. The regions where this
occurs are referred to as the neutron and proton driplines. Also shown
are the known magic numbers for the stable nuclei. ..........
Chart of light nuclides. Shown here are the light nuclear systems.
The stable systems are shown in gray and particle-stable systems are
shown in white. Nuclei unstable to a proton-decay are shown in red,
and nuclei unstable to neutron decay are shown in violet. This work
is focused on the unbound systems of 7'S’He, and 10Li. .........
Data from Seth et al. and Bohlen et al.. The upper panel shows the
missing-mass spectrum result of a 9Be(7r‘,7r-+—)9He reaction at 194 MeV
from [13]. The authors reported states at 0, 1.2, 3.8, and 7.0 MeV,
using a scale where the energies are measured in reference to the low-
est observed state, which has a neutron separation energy of -1.13
:l: 0.10 MeV. The figure in the lower panel shows the results of a
9Be(13C,13O)9He reaction at 380 MeV, where the authors reported a
sharp peak for the ground state 1.83 MeV unbound against neutron
decay [14]. Our work suggests that the 9He ground state actually is at
-1 to 1.2 MeV on the scale shown here. .................

 

1.4

1.5

1.6

2.1

2.2
2.3
2.4
2.5
2.6

3.1

Shown here is the systematics of the level crossing in the N27 isotones.
In the y-axis is the eigenvalue energy of the { and {L states, which
is the difference between the energy of the state(E‘) and the neutron
separation energy (3"). Shown in the insets are the wave functions
x(r) = rR(r) of corresponding single particle states calculated with a
Woods-Saxon potential. The 15O is very tightly bound, while the 11Be
is very loosely bound (as evident by the long tail in the wave function),
and the unbound 10Li is characterized by a scattering wave. The nuclei
10Li and 9He are studied in the present work, which suggests 3 states
at S 50 and S 200 keV, respectively. The p state shown for 10Li is
that discussed in the works of Caggiano et al. [12]. The state near 1.1
MeV in 9He has been observed in the double charge exchange reaction
and in multinucleon transfer ........................ 10
Data from Kryger et al. [27]. The relative velocity of the 9Li+n sys-
tem is fitted with an estimated background and a simulated velocity
difference distribution from a computer simulation which included the
experimental resolution, acceptance, and efficiencies. The fit shown
is for a resonance with E, = 50 keV and I‘ = 100 keV. The authors
concluded that the state was either a 10Li ground state or an excited
state with El. z 2.7 MeV. ........................ 11
Data from Thoennessen et al. [28]. Shown here are the computer simu-
lation results (solid), which include contributions from an s-wave with
a, = —30 fm (dot-dashed), p-wave with E, = 538 keV (dashed), and
estimated background (dotted). The essential feature of this data is
the pronounced peak at zero relative velocity, which is interpreted as
a low-lying s-state with an a, < —20 fm. ................ 12

Schematic of the NSCL. The primary beam from the K1200 cyclotron
reacts with a production target in the A1200 fragment separator, which
then produces the radioactive beam used in this experiment. The sec-
ondary beam is directed to the N4 vault by the magnets in the N4

vault ..................................... 15
Experimental setup at the N4 vault of the NSCL. ........... 16
Photograph of N4 Vault ......................... 17

The A1200 Fragment Separator. (Figure courtesy of NSCL design group) 18
NSCL Neutron Wall detectors. (Figure courtesy of NSCL design group) 19
Bending Magnet and Fragment Detector Array ............. 22

Kinematic diagram of the core+n two-body system. V, V“, Vf denotes
respectively (in the lab frame), the velocity of the fragment+n system,
neutron, and fragment velocities. VnCM and VmM denotes (in the

center-of-mass frame) the neutron and fragment velocities. For small
0, V”, = V, — Vn ............................. 24

xi

 

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

Detection probability of decay of a two-body system with the mass
parameters of 7He with a sharp energy distribution E, = 440 keV.
Shown is the detection probability as a function of angular cut for

the fragment-neutron coincidence event. For comparison, an :r-axis
containing the energy scale is also shown this relative velocity distri-
bution. The calculations here include acceptance effects (including the
shadowing of the magnet) as well as resolution effects. As the angu-

lar acceptance increases, the resolution deteriorates as the two peaks
eventually merge together. Ideally, there should be no intensity in the
region of V, — V, = 0, but as the angular cut expands to much beyond

5°, the contribution in that region becomes significant due to poorer
resolution. ................................. 26
Detection probability of decay of a two-body system with the mass
parameters of 7He with sharp energy distributions. Shown is the de-
tection probability as function of decay energy, and in all cases, the
angular cut is fixed at 5°. This calculation includes all acceptance and
resolution effects of the experimental apparatus. The method of us-

ing velocity difference is very efficient for low energy events and the
efficiency decreases for higher energy. At around E, = 0.2 MeV, it
becomes possible to resolve two separate peaks from the velocity dif—
ference spectra. .............................. 27
Detection probability of a 9Li+n system breaking up isotropically after
being formed from 11Be. Shown here are calculated velocity distribu-

tions for a, = 0, —5, -10, —20, —40 fm for a 5° angular cut ....... 28
Detection probability of a 9Li+n system breaking up isotropically after
being formed from 12Be. Shown here are calculated velocity distribu-

tions for a, = 0,—5,—10,—20,—30,—40 fm for a 5° angular cut. . . . 29
Total detection probability of a 9Li-l-n system breaking up isotropi-

cally after being formed from 11Be. Shown here are curves for a, =

0, —5, —10, —-20, -40 fm as a function of angular cut for neutron-fragment
coincidence events. ............................ 29
Total detection probability of a 9Li+n system breaking up isotropi-

cally after being formed from 12Be. Shown here are curves for a, =

0, —5, -10, —20, —40 fm as a function of angular cut for neutron-fragment
coincidence events. ............................ 30
Detection probability of a 8He+n system breaking up isotropically after
being formed from 11Be. Shown here are calculated velocity distribu-

tions for a, = 0, —5, —10, —20, —40 fm for a 10° angular cut. ..... 30
Total detection probability of a 8He+n system breaking up isotropi-

cally after being formed from 11Be. Shown here are curves for a, =

0, —5, -10, —20, -40 fm as a function of angular cut for neutron-fragment
coincidence events. ............................ 31

3.10 Silicon strip Energy calibration spectra with 228Th source. ...... 32

xii

3.11

3.12

3.13

3.14

3.15
3.16

Typical AE vs. beamline time spectrum from a typical ‘cocktail’ beam
calibration run. The start signal comes from the plastic scintillators
and the stop signal comes from the beamline timer, so that a short
time-of-fiight (TOF) represents slower particles. For a fixed Bp, beams
with the same A/Z ratio have the same TOF. .............
A typical energy calibration spectrum for the plastic scintillator. The
energy from cocktail beam runs is plotted against the light output
from the plastic scintillator. Shown here is the energy calibration for
detector 13. ................................
Particle identification for two different fragment detectors. The array
of sixteen plastic scintillators measures the total energy, and the differ-
ent positions of the plastic scintillators help with isotope separation.
The energy loss was measured by an array of silicon strip detectors po-
sitioned downstream from the target. The figure on the left shows an
energy-loss vs total energy spectrum of the 12‘” scintillator bar, which
was farther away from the beam axis than the 16‘” bar. The energy
scale used in the two figures is correct for the helium isotopes. Since
the light output of the plastic scintillators decreases when the charge
of the particle increases, a scale factor of approximately 1.4 is needed
to obtain the correct energy for 9Li. While bar 12 detects mostly 6He
and 9Li, bar 16 detects only 6"‘He, and very little 9Li. Even though 9Li
and 6He have the same A/Z ratio, the 6He fragment will have a wider
momentum spread than 9Li from the fragmentation reaction, where

the spread is characterized by a = 00‘/ W, where A is the mass
for the incident nucleus and AF is the mass of the reaction fragment.
Consequently, there was an appreciable amount of 6He measured, but
not 9Li. ..................................
Neutron identification in this experiment was achieved through pulse—
shape discrimination. Shown here is the fast (QFAST) portion of the
neutron wall signal plotted versus the total pulse size (QTOTAL).
There are three distinct bands in the spectra. The top band rep-
resents y-rays, while there are two bands corresponding to neutron
events. One of these bands comes from the reaction with the proton in
the liquid scintillator, and the other comes from interactions with the
carbon ....................................
Neutron distribution on cell 9 without shadowbar ...........
Hypothetical neutron distribution on cell 9 in presence of shadowbar,
where perfect resolution is assumed ....................

3.17 Neutron Wall cell 9 shadowbar spectra. Shown are the fits using

FWHM=0.2, 0.12, and 0.03 meters, with background parameter H =
6. The best-fit uses FWHM=0.12 m (a = 5.1) for neutron response
function, and the H = 6 corresponds to a 5 % contribution to back-
ground. ..................................

xiii

34

45
47

48

 

3.18

3.19
3.20

4.1

4.2

4.3

4.4

4.5

4.6
4.7

4.8

4.9

Neutron Wall cell 13 shadowbar spectra. Shown are the fits using
FWHM=0.2, 0.12, and 0.03 meters, with background parameter H =
6. The best-fit uses FWHM=0.12 m corresponds to a a = 5.1 m and
H = 10 corresponds to a 9 % contribution to background. ......
TDC calibration spectrum ........................
6°Co 7-ray TOF spectrum. The peak shown has a FWHM of 5 ns. . .

6He Momentum distribution measured in neutron coincidence. The
distribution from incident ”Be is shifted by +500 MeV/c and is nor-
malized to the same area as (“Be,°He+n) spectrum for the purpose of
comparison. Also shown is a distribution of the total momentum res-
olution calculated at mid-target energy of approximately 27.7 MeV/ u,
corresponding to a total momentum of 1370 MeV/c. The curve has
been shifted down for display purposes ..................
8He Momentum distribution measured in neutron coincidence. The
distribution from incident ”Be is shifted by +500 MeV/c and is nor-
malized to the same area as (“Be,8He+n) spectrum for the purpose
of comparison. Also shown is a distribution of the total momentum
resolution calculated at mid-target energy of 27.7 MeV/ u, correspond-
ing to a total momentum of 1840 MeV/c. This curve has been shifted
down for display purposes. ........................
9Li Momentum distribution measured in neutron coincidence. The
distribution from incident 12Be is shifted by +500 MeV/c and is nor-
malized to the same area as (“Be,9Li+n) spectrum for the purpose of
comparison. A calculated momentum distribution of 9Li using single
neutron knock-out from a 11Be and then rescaled by 9/10 is shown
(dashed line). Also shown is a distribution of the total momentum
resolution calculated at mid-target energy of 27 .7 MeV/ u, correspond-
ing to a total momentum of 2060 MeV/c. This curve has been shifted
down for display purposes. ........................
The systematics of 00 as a function of projectile bombarding energy
[45]. It is clear that there is a trend of increasing 00 with increasing
beam energy in the region between 10 to 100 MeV per nucleon. The
reactions corresponding to these data points can be found in [45]. . .
Radial wave function Xo(7‘) of the s-state in 11”Be. The long tail in

49
50
51

62

62

63

64

the neutron wave function of 11Be is a result of the low binding energy. 69

Radial wave function X00") of the p—state in 11'”Be. ..........
Energy Distribution of 6He+n system at Ed: 450 keV calculated using
the potential scattering model using initial 11’”Be nucleus. ......
Energy Distribution of 9Li+n expanded using a l(“’Be s-state and the
unbound states of 9Li. Shown are the energy distributions correspond-
ing to various scattering lengths ......................
Energy Distribution of 9Li+n expanded using a llBe s-state and the
unbound states of 9Li. Shown are the energy distributions correspond-
ing to various scattering lengths ......................

xiv

70

71

71

72

15'

 

4.10 Energy Distribution of 8He+n expanded using a 11Be s—state and the

5.1

5.2

5.3

5.4

5.5

5.6

unbound states of 8He. Shown are the energy distributions correspond-
ing to various scattering lengths ......................

Velocity difference spectra of 6He-l-n scaled to the number of incoming
beam particles. The scale has not been corrected for geometrical accep-
tance and detector efficiency. The uncertainties are purely statistical.
Depending on the initial nucleus, the velocity difference spectrum can
have a very different appearance even though it is the same resonance
being probed. In the case of the incident 11Be, the enhancement near
zero relative velocity comes from the loosely-bound neutrons in the
s-state, which do not interact in a 6He+n system. ...........
Velocity difference spectrum of the 9Be(”Be,°He+n)X system. Shown
are the experimental data with statistical error bars, the computer
simulation of a p—wave resonance at 450 keV, a d-wave resonance with
5 MeV of effective binding energy, and an event-mixed background.
The best fit consists of: event-mixed background: 36%, p-wave: 62%,
and d-wave: 2%. .............................
Velocity difference spectrum of the 9Be(“Be,°He+n)X system. Shown
are the experimental data with statistical error bars, the computer
simulation of a p-wave resonance at 450 keV, a s-wave (a,=0 fm) scat-
tering, and an event-mixed background. The best fit consists of: the
background: 39%, p-wave: 44%, and s-wave: 17%. The contribution
of the non-interacting scattering of the loosely-bound neutron in the

11Be describes the essential difference between the 11Be and ”Be data.

Velocity difference spectrum of the 9Be(1°Be,6He+n)X system. Shown
are the experimental data with statistical error bars, the computer
simulation of a p-wave resonance at 420 keV and an event-mixed back-
ground. The best fit consists of: the background: 26%, and p-wave:
74% ....................................
Error estimate of p-resonance in the 9Be(”Be,°He+n)X. The shaded
region represents the theoretical fits for the region 400 < E, < 500
keV, and the solid line represents the E, = 450 keV fit, which is the
minimum x2 fit ...............................
Error estimate of p-resonance in the 9Be(“Be,°He+n)X. The shaded
region represents the theoretical fits for the regions between 400 <
E, < 500 keV, and the solid line represents the E, = 450 keV fit,
which is the minimum X2 fit. ......................

XV

72

75

76

76

77

78

 

5.7 Reduced-x2 of fits to 9Be(”’11'1°Be,°He+n)X data as a function of the
decay energy of the p-state. For the ”’“Be reaction, the minimum x2
uses three separate components in the fit. The minimization procedure
uses the 22 data points between -2.1 cm/ns and 2.1 cm/ns. The four
free parameters used in the fitting are the 1) total intensity (taken to
be the same as the total number of events), 2) systematic shift in the
computer-simulated relative velocity spectra (Section 3.6), and 3) the
relative intensities amongst three different components requires two
free parameters for fitting. This yields 18 degrees of freedom. In the
case of 10Be, there is a total of 19 degrees of freedom because there
is only a two—component fit in the spectrum. The curves shown cor-
respond to a second-order fit for the reduced-X2, and the dashed lines
represent the reduced-X2 value that corresponds to a 95% confidence
level. Using this as a guide, the typical uncertainty is on the order of
20 keV. .................................. 79

6.1 Data from Zinser et al. [44]. Shown are the radial momentum distribu-
tions of the select fragments detected with neutron coincidence from
an incident 11Be. The most important feature of this data is the nar-
row momentum distribution of the observed 9Li, compare to that of
7Li. The solid curves through the lithium data are momentum dis-
tributions calculated using a potential scattering model similar to the
one used in this work. The curve through the 7Li data is a distribution
corresponding to an s-wave scattering with a, = 0 fm, while the curve
through the 9Li data is calculated using a, = —20 frn. In both cases,
there is a component of a p—wave resonance at 0.42 MeV. ....... 84
6.2 Velocity difference spectra of 9Li+n with three different initial nuclei
scaled to the number incident beam particles. Because of the loosely-
bound s-state of the 11Be, the peak near zero velocity is narrower than
that from ”Be. Note that the l°Be projectile cannot break up into 9Li
and a fast neutron, so the absence of counts in this channel shows that
the discrimination against neutrons from the target is satisfactory. . . 86
6.3 Velocity difference spectrum of the 9Be(”Be,9Li+n)X system. Shown
are the experimental data with statistical error bars, the computer
simulation of a p-wave resonance at 538 keV, a a, =-25 frn s-wave scat-
tering, a d—wave scattering with an effective binding energy of 5 MeV,
and an event-mixed background. The best fit consists of: the back-
ground: 48.%, p-wave: 7%, d-wave: 6%, and s-wave (a,=-25 fm): 39%. 87
6.4 Velocity difference spectrum for the reaction 9Be(”Be,9Li+n)X data
with best-fits using scattering lengths a,=0, -5, and -20 fm ....... 87

 

xvi

 

6.5

6.6

6.7

7.1

7.2

7.3

Reduced-X2 of fits to 9Be(”’11Be,°Li+n)X data as a function of the
scattering length a, of the s-state. For an incident ”Be nucleus, the
minimum x2 analysis uses four separate components in the fit. The
minimization procedure uses the 22 data points between -2.1 cm/ns
and 2.1 cm/ns. The five free parameters used in the fitting are the 1)
total intensity (taken to be the same as the total number of events),
2) systematic shift in the computer-simulated relative velocity spectra
(Section 3.6), and 3) relative intensities amongst four different compo-
nents requires three free parameters for fitting. This yields 17 degrees
of freedom. In the case of 11Be, there is a total of 18 degrees of free—
dom because there is only a three-component fit in the spectrum. The
dashed lines represent the reduced-x2 value that corresponds to a 95%
confidence level ...............................
Velocity difference spectrum of the 9Be(11Be,°Li+n)X system. Shown
are the experimental data with statistical error bars, the computer
simulation of a p-wave resonance at 538 keV, a a,=-25 fm s-wave scat-
tering, and an event-mixed background. The best fit consists of: the
background: 47%, p-wave: 5%, and s-wave (a,=-25 frn): 48%.

Velocity difference spectrum for the reaction 9Be(11Be,9Li+n)X data
with fits using scattering lengths a,=0, -5, and -20 fm. ........

Data from von Oertzen et a1. [32]. Shown are the observed excited
states using a 9Be(1“C,1“O)9He reaction. The energies are shown with
reference to the lowest observed state ...................
9Be(“Be,8He+n)X data compared with event-mixed background at the
same total intensity (dashes) and best fit using a, = 0 fm (solid). The
important feature here is to observe that simple event-mixing cannot
explain the data. In the best fit using a combination of an a, = 0 fm
distribution and an event-mixed background, the fit failed to describe
the narrow, central peak of the data. In that case, the best fit here

88

90

93

obtained uses 100% s-wave component and 0% event-mixed background. 94

9Be(11Be,°He)X data with a fit using two components (solid): a3:-
10 fm (short dashes) and an event-mixed background (dots). The best
fit here obtained uses 71% s-wave component and 29% event-mixed
background. Also shown for the purpose of comparison is the best fit
using only a combination of a, = 0 fin and an event-mixed background
(long dashes). ...............................

xvii

95

 

7.4

7.5

Reduced—x2 of fits to 9Be(“Be,8He+n)X data as a function of the scat-
tering length a, of the s-state. The minimum x2 analysis uses three
separate components in the fit. The minimization procedure uses the
12 data points between -1.1 cm/ns and 1.1 cm/ns. The 3 free parame-
ters used in the fitting are the 1) total intensity (taken to be the same
as the total number of events), 2) systematic shift in the computer-
simulated relative velocity spectrum (Section 3.6), and 3) the relative
intensities amongst two different components requires just one free pa-
rameters for fitting. This yields 9 degrees of freedom. The dashed line
represent the reduced-x2 value that corresponds to a 95% confidence
level, showing that a scattering length numerically larger than -10 fm
best fits the data ..............................
Proposed level scheme for 9He. Shown here are two shell-model calcu-
lations using the Warburton-Brown model (WBP and WBT) and the
data from the two experiments (Seth et al. (KKS) [13] and von Oertzen
et al. (WVO)[32]) that are used for the current tabulated value for the
9He mass in Audi and Wapstra [31]. Also shown is the low lying s-state
observed in this work (LC). Two separate energy scales are shown. On
the left is the energy scale measured with respect to the ground-state
energy, and the energy scale on the right uses neutron separation en-
ergy as a reference. ............................

xviii

96

98

 

Chapter 1

Introduction

1. 1 Overview

There has been much interest in the study of the exotic nuclei far from stability in re-
cent years, and much of that focus has been on the light neutron-rich isotopes. Figure
1.1 is a chart illustrating the known bound nuclear systems, and Figure 1.2 is a similar
chart for the light nuclear systems. In nature, there are under 300 stable nuclei, and
the region they occupy in the chart is known as the “valley of stability”. Generally,
as nuclei approach the driplines, they become increasingly unstable. Nuclei beyond
the dripline region are unstable with respect to nucleon emission, and experimentally
difficult to study. The objective of this work is to explore a technique for the study
of such unbound systems through the use of final-state interactions. In some cases,
the products emerging from the reaction interact strongly with each other, and this
phenomenon is known as final-state interaction. By modeling the interactions in the
final-states, it permits the deduction of the nature of the interactions in the unbound
systems. This technique, as we will show, permits the probing of various neutron-rich
unbound nuclei, and offers new insight into their structure. In this work, details of

this technique will be discussed, and the results of the unbound 7’S’He and 10Li be

presented.

1.2 Spectroscopic Techniques for Bound and Un-

bound Nuclei

In a conventional nuclear physics experiment, the nucleus of interest is produced
in a stable target, which is probed by a nuclear beam delivered by an accelerator.
Thus, the accelerator is a physicist’s microscope to examine the details of nuclear
interaction. However, targets cannot be made to produce neutron-rich nuclei near
the dripline because these nuclei are very short-lived. This problem is solved by the
use of radioactive beams. Using a radioactive beam to interact with a stable target
has exactly the same physics as using a stable beam probing a radioactive target
(if such target were available). Because the measurement is made with respect to
the projectile’s frame instead of the target’s, this technique is commonly referred to
as “inverse kinematics”. The radioactive beam is a very powerful tool for studying
bound and unbound systems near and beyond the dripline. The primary methods of
spectroscopy with radioactive beams include: (1) Coulomb excitation, (2) Breakup
reactions, and (3) Transfer reactions.

Using radioactive beams in conjunction with Coulomb excitation techniques pro-
vides a method to study reduced transition probabilities for the lowest excited states
in a model independent—way [1, 2, 3]. With this technique, the incident nucleus is
excited by the Coulomb field of the target, and the 'y-ray from the de.excitation of
the incident nucleus is then detected.

Breakup reactions have also provided many important results in this field. They
can be used to measure interaction cross sections, and it was with this technique

that the large interaction radius of 11Li was first discovered [4]. In addition, momen—

proton number Z

  
  

Neutron Dripline
Stable Nuclei

—’
neutron number N

Figure 1.1: Chart of nuclides for bound nuclear systems. Bound nuclear systems are
shown here as a function of their proton number Z and neutron number N. The
black squares represents the stable nuclei in nature, and these collectively are usually
referred to as the “valley of stability”. Nuclear binding weakens for nuclei away from
stability, and eventually becomes too weak to permit a bound system. The regions
where this occurs are referred to as the neutron and proton driplines. Also shown are
the known magic numbers for the stable nuclei.

 

 

 

Protons
~23]

 

 

 

 

 

7Be 8Be {’Be 10Be 11Be 12Be 1“Be
‘15 8Li 9Li llLi
“if. 6He 8He
..., 5 3H
n
Neutrons 7

Figure 1.2: Chart of light nuclides. Shown here are the light nuclear systems. The
stable systems are shown in gray and particle—stable systems are shown in white.
Nuclei unstable to a proton-decay are shown in red, and nuclei unstable to neutron
decay are shown in violet. This work is focused on the unbound systems of 7”He, and

mm

tum measurements from breakups have provided important information on nuclear
structure. A primary example is in the study of the halo nuclei, where the narrow
momentum distribution of the fragment after neutron removal suggests the existence
of a diffuse neutron “halo” [5, 6, 7]. More recent experimental work in breakup re-
actions has been done by [8, 9], where both the 7—ray and momentum distributions
of the fragment after a single-nucleon knockout is measured. In this technique, it is
possible to identify both the spin and parity of the nucleus.

Transfer reactions can be used to measure masses of both bound and unbound
systems. Usually in such experiments, some reaction A(B,C)D is selected, where the

masses of A, B, and C are known. Since
Q=Tf_7,i='ma+mb_mc—md, (1.1)

an accurate measurement of the Q-value in conjunction with using reaction partic-
ipants of well—known masses permits determination of the mass and excited states
of the unknown nucleus, assuming that a precise measurement of the momentum is
made. The energy at the reaction needs to be very accurately determined, which
means that the target needs to be very thin, on order of 1 mg/cm2 (a 0.4 mg/cm2
target was used in the 7He experiment [10]). This reaction can involve the exchange
of a pion, as in the single charge-exchange reaction 7'Li(t,3He)7He used by Stokes and
Young [10], or the double charge-exchange reaction of 9Be(7r‘,1r+ )9He used by Seth
et al. [13] to study 9He. In addition, these reactions can involve actual transfer of
nucleons from one nucleus to another, as in the case of the ”Li studies by [11, 12].
Figure 1.3 shows data from a study of the unbound 9He nucleus from the works of
[13, 14].

Of spectroscopy techniques mentioned, only the transfer reaction can be applied
to study unbound systems. This is because the techniques of Coulomb excitation

and breakup reaction both require a beam of the nucleus of interest be produced in a

5

 

 

ITITTTFIlrllll

   

 

20 r 9Betn-.n+)°He (a) .]
180MeVJS°
- KJtSeflwetaL -
10— 4
:2 ” ' 1
c I
3 0 n I V
8 fil; : 3|8 2’
l.- 9Bel’3C,’30)9He ' (bl _.
380MeV,2.L°
gs.

.2 1 ’ “
0" Jill. Jllllllfll... .

-10 0 10
E,[MeVl

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.3: Data from Seth et al. and Bohlen et al.. The upper panel shows the
missing-mass spectrum result of a 9Be(7r‘,7r+)9He reaction at 194 MeV from [13].
The authors reported states at 0, 1.2, 3.8, and 7.0 MeV, using a scale where the
energies are measured in reference to the lowest observed state, which has a neutron
separation energy of -1.13 :l: 0.10 MeV. The figure in the lower panel shows the results
of a 9Be(”C,”O)9He reaction at 380 MeV, where the authors reported a sharp peak
for the ground state 1.83 MeV unbound against neutron decay [14]. Our work suggests
that the 9He ground state actually is at -1 to 1.2 MeV on the scale shown here.

 

laboratory. In the case of unbound systems such as 7He, the lifetime is on the order of
10‘21 second or less, which implies that an unbound nucleus would travel roughly 30
times the nuclear radius after being formed from a reaction. Instead of using transfer
reactions, this work approaches the problem of unbound systems through the use of
final-state interactions. A beam of a well-understood nucleus fragments at the target
and then populates states of various unbound systems. The interactions of the post-
reaction fragments are simulated by a potential scattering model, and the nature of

the interaction of the unbound nucleus is deduced.

1.3 Previous Use of Final-State Interactions

F inal-state interactions have played an important role in the study of the neutron-
neutron interaction [15, 16, 17, 18]. A convenient way to describe the neutron-neutron
interaction in a low energy scattering process involves the quantity scattering length,
which describes the range of an interaction. More on scattering length will be given
in Chapter 4. At the beginning, it was understood that accurate determination of
the neutron-neutron scattering length along with the proton-proton scattering length
will help to determine the charge dependence of the strong nuclear force. Today,
the charge symmetry of the strong forces is well-documented [19], and the quantity
An = am, — app is a direct measure of charge-symmetry—breaking [20]. This is the
reason why experiments are still being performed today trying to further ascertain
the value of am, even though the first measurement was made over forty years ago.
While the nature of the proton-proton interaction can be deduced by a direct
nucleon-nucleon scattering process, a neutron-neutron scattering experiment is tech-
nically impossible. As a result, the only viable means was to use the final-state inter-
action to probe the n-n interaction. It was suggested over forty years ago that breakup

reactions would be very important for the study of the neutron-neutron interaction

[21, 22]. The early attempts to study the neutron-neutron scattering length am, used
the 2H(n,p)2n reaction [23, 24, 25]. In these experiments, the proton spectra exhibit
two peaks at angles near zero degrees. These experiments are complicated to analyze
because proton-neutron and neutron-neutron interactions (as measured by scattering
length) are on the same order of magnitude, and the three-body nature of the exit
channel provides additional complications. Consequently, there have been fairly large
discrepancies among results from 3-nucleon reactions [20]. To address these problems,
there are experiments which use the reaction 2H(7r‘, 7)2n [15, 20, 26]. This reaction
is superior because only two of the three particles in the exit channel are strongly in-
teracting. Regardless of which reaction one uses to study an", a theory that accounts
for the final-state interaction between the neutrons is used to interpret the data.
The use of final-state interactions (FSI) in the studies of am, has provided many
useful results since the first experiment. Currently, the world average value for am. is
—18.59 :1: 0.27(experimental):l:0.30(theoretical) fm [20]. It is the purpose of this work

to show that FSI is also a viable way to study the neutron-rich unbound nuclei.

1.4 Studies of Unbound Nuclei with FSI

There have been two previous experiments that used the PSI to study unbound nuclei
in the literature [27, 28], and both of them were performed at the NSCL. The aim
of both of these experiments was to search for the low-lying states of ”Li, which is
critical for the understanding of the 11Li two-neutron halo.

The isotope ”Li is an N=7 isotone, which is a member of a family of nuclei with
seven neutrons. The systematics of the level crossing of the N=7 isotones is shown
in Figure 1.4. It is a very well documented fact that 11Be, the lightest bound N=7
isotone, is the crossing point where parity inversion occurs, and that the ground-state

of 11Be is actually an intruder s-state, and not the p—state that would be predicted

 

by a simple shell model. It has been suggested by Sagawa et al. that this inversion
phenomenon would continue for the lighter and unbound N =7 isotones [29], suggesting
that the low-lying states of ”Li may be a s-state. An experimental observation of
the ”He would also help to establish this trend.

The first experiment, by Kryger et al. [27] (Figure 1.5), probed the ”Li through
the use of sequential decay neutron spectroscopy. In that experiment, an incident 80
MeV/ u 18O beam irradiated a carbon target, and coincident events between neutron
and ”Li were detected in a collinear arrangement. It is assumed that by fragmenting
an initial nucleus, it is possible to populate many unbound states, including ”Li.
This first experiment observed a ”Li state that corresponded to either a ground
state or, if this feeds an excited state of ”Li, then to an excited state with E, a: 2.7
MeV. The second experiment, by Thoennessen et al. [28], was a repeat of the Kryger
experiment, but with improved resolution (Figure 1.6). The scattering length of the

observed low-lying s—state was established to be a, < —20 fm for ”Li.

1.5 The Objectives of This Work

The present work has three objectives. The first is to investigate the influence of the
initial state and to demonstrate the selectivity of the method. This was done with
1”’11'”Be as projectiles. The results show that, as expected, the observed momentum
distributions depend on how the product was formed. (This shows that it is necessary
to go beyond a picture where ”Li is formed as a separate identity, which much later
decays in flight. This picture would obviously be correct for a very narrow resonance.)

The second objective is to repeat the experiments by Kryger et al. and Thoen-
nessen et al. [27, 28] with a set of different initial nuclei. This will help to establish
that the previously observed interaction in the l = 0 channel is not an artifact of

the initial nucleus; since the 18O and the 12“Be have very different structures. The

l , , ,1

1 I ' l l
150 14N 13c 128 “Be 10Li 9He

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 7 6 5 4 3 2
Atomic Number 2

Figure 1.4: Shown here is the systematics of the level crossing in the N=7 isotones.
In the y-axis is the eigenvalue energy of the 5‘ and %+ states, which is the difference
between the energy of the state( E ‘) and the neutron separation energy (5,). Shown in
the insets are the wave functions x(r) = rR(r) of corresponding single particle states
calculated with a Woods-Saxon potential. The 15O is very tightly bound, while the
11Be is very loosely bound (as evident by the long tail in the wave function), and
the unbound ”Li is characterized by a scattering wave. The nuclei ”Li and ”He
are studied in the present work, which suggests 3 states at S 50 and S 200 keV,
respectively. The p state shown for ”Li is that discussed in the works of Caggiano
et al. [12]. The state near 1.1 MeV in ”He has been observed in the double charge
exchange reaction and in multinucleon transfer.

 

 

 

 

400 LT I T r T T T T 17 T T I T j I I T Tj 7 I P I
- ' .,
_ I .
300 —' -‘
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0 .
l L J l I l L l 1 q f L l 1 l f l l l l I l L
-4 -2 O 2 4

Vn -— VF (cm/ns)

Figure 1.5: Data from Kryger et al. [27]. The relative velocity of the ”Li+n system is
fitted with an estimated background and a simulated velocity difference distribution
from a computer simulation which included the experimental resolution, acceptance,
and efficiencies. The fit shown is for a resonance with E, = 50 keV and I‘ = 100 keV.
The authors concluded that the state was either a ”Li ground state or an excited
state with E, z 2.7 MeV.

11

 

Counts

 

 

 

Vn'Vf (cm/us)

Figure 1.6: Data from Thoennessen et al. [28]. Shown here are the computer sim-
ulation results (solid), which include contributions from an s-wave with a, = —30
fm (dot-dashed), p-wave with E, = 538 keV (dashed), and estimated background
(dotted). The essential feature of this data is the pronounced peak at zero relative
velocity, which is interpreted as a low-lying s—state with an a, < —20 fm.

12

results confirm the finding by Kryger et al. and Thoennessen et al. [27, 28] that in
”Li the lowest neutron state must have the spin and parity 1/2+, an intruder from
the s, d shell. It has been pointed out by Thompson and Zhukov [30] that the pres-
ence of a 131/2 state just above the threshold of the ”Li+n system is essential for
the understanding of the binding of the 11Li two-neutron halo. They suggest that
an interaction characterized by an s-wave scattering length of the order of -20 fm or
numerically larger is required. This is in agreement with the previous experiment [28]
and the present work.

The third objective is to look for a low-lying s-state in the ”He. For ”He, there
have been resonances observed near 1.2 MeV (and also at higher energies) by Seth et
al. [13] and by von Oertzen et al. [32]. The mass assignment given for ”He by Audi
and Wapstra [31] is based on the weighted average of these two observations. The
data presented in this work suggests that the lowest state, missed in the previous

work, has l=0 and lies approximately 1 MeV lower.

1.6 Outline

The remainder of this work is based on the results from experiment 97017, which is the
third experiment to study the unbound nuclei 7He and ”Li using FSI. The details of
the experimental setup will be covered in Chapter 2. A detailed discussion regarding
the theoretical model, and the calculation of the final-state interaction is presented
in Chapter 4. Chapter 3 discusses the data reduction procedures, including aspects
of detector calibration and proper event selection. Chapters 5, 6, and 7 contain the

results for 7He, ”Li, and ”He respectively.

13

Chapter 2

Experiment 97017

The experiment was performed in the NSCL N4 vault between 8/14/97 and 8/ 22 / 97.
Subsequent sections provide details regarding various technical aspects of the exper-
iment.

The primary beam of came from the cyclotron, and the radioactive beam was
produced in the A1200 fragment separator. The radioactive beam was then directed
to the N4 vault through a sequence of magnets in the transfer hall. Figure 2.1 shows
the layout of the apparatus.

This experiment requires kinematic measurement of both the charged fragments
as well as the neutrons produced from the fragmentation. The neutrons were detected
using the two N SCL Neutron Walls [33]; two large arrays of position-sensitive neu-
tron detectors. The first neutron wall was placed 5 meters from the target position
in the forward direction, and the second wall was 0.5 meters immediately behind the
first. The fragments produced in reactions in a ”Be target were deflected away from
the Neutron Walls with a 1.5 Tesla sweeping magnet. Particle identification of the
fragments was achieved with a two dimensional gate on the energy-loss, which was
measured by an array of 58.2 mg/cm2 silicon-strip detectors, and the total energy,

which was measured by an array of sixteen plastic scintillator detectors downstream

14

ECR N4 Vault

 

 

 
  
 

 

     
 

   
 

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/////A .. . .1 v . / fi' : . . .
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K1200 A1200 Transfer
Cyclotron Fragment Hall
Separator

Figure 2.1: Schematic of the NSCL. The primary beam from the K1200 cyclotron
reacts with a production target in the A1200 fragment separator, which then produces
the radioactive beam used in this experiment. The secondary beam is directed to the
N4 vault by the magnets in the N4 vault.

from the target. The neutron energy was determined by a time-of-flight measurement.
A thin, fast plastic detector was placed in the flight path after the production tar-
get and before the beam enters our experimental vault to provide an event-by-event
identification of our secondary beam.

The details of the apparatus will be discussed in subsequent sections in this chap-

ter. Figure 2.2 shows the layout of the experimental vault.

2.1 Radioactive Beam

This experiment was performed at the N SCL using a secondary beam of 30 MeV/ u
12.11.1036 on a 200 mg/cm2 ”Be target. The mid-target energy of the secondary
beams is estimated to be 27.9, 27.7, and 27.5 MeV/ u for ”'11'”Be respectively. These
radioactive beams were produced with the projectile fragmentation technique. Gen-
erally, the production of a radioactive beam with this technique uses a primary beam

which is broken up at a production target, and the reaction fragments are subse-

15

Reagan
.35 8582

 

Loews o Gama
war—LBBm
38,—. mg

mg
HBBEEom
0:33

How—3. ems
NEoEE cam

    

$8023—
95. Scam

 
 

Bumbag

Seaman 8m 2 <
Bob 88m

2822 N

 

H E

Figure 2.2: Experimental setup at the N4 vault of the NSCL.

16

SEC:

3w.__..._.

3:me
wEESm

EE<
.zzszczim
27:5

353:7.
.5296

:33
:EEuZ

4.va

 

Figure 2.3: Photograph of N4 Vault

9Be Production Target

Achromatic Degrader (Wedge)

 

 

 

Momentum Selection Slits Slits for secondary
beam selection

Figure 2.4: The A1200 Fragment Separator. (Figure courtesy of NSCL design group)

quently purified by a series of dipole magnets and an energy-loss degrader. In this
experiment, the primary beam was produced by the K1200 cyclotron. The ”Be sec-
ondary beam was produced using a primary beam of 80 MeV/ u 1”O at 150 pnA on a
1455 mg/cm2 ”Be production target, and is purified with the A1200 fragment separa-
tor with a 725 mg/cm2 27Al degrader. The production of the 11Be and ”Be secondary
beams was accomplished with an 80 MeV/u l3C primary beam with a beam current
of 75 pnA on a 1900 mg/cm2 ”Be production target, degraded with a 233 mg/cm2
(llBe) and a 525 mg/cm2 (”Be) Al degrader. Momentum slits were set to 3% for

”Be, and to 1% for 11’”Be. Figure 2.4 shows a schematic of the A1200.

2.2 NSCL Neutron Walls

The neutrons were measured by the N SCL Neutron Walls, which are two large-area
position-sensitive neutron detectors designed and built at the NSCL. Details of the
construction and various technical aspects can be found in [33]. Each of the Neutron
Walls consists of twenty-five Pyrex glass cells which are filled with NE—213 liquid

scintillator, which has the dimensions of 200 cm wide, 7.62 cm high, and 6.35 cm thick.

18

Side View Front View

Photomultiplier tubes

 

say”
r ' Hr
[ ' 16 Pyrex cells with

4 ‘ : 4,, NE-213 liquid scintillator
ii (200 x 6.35 x 7.62 cm)

  
  
 
  

Aluminum Cover

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

,-,.-.c'p..',.,-,o.o.:.o_p_-...o‘o.o u,-,.‘-..,.,. -,-‘, .0,D,I.I,O,I_O‘I‘o.|,I,I.I.o,'.I,-,l'l,o.-’n_n.-.o.¢[..I.~,I,C_o,l'a'n.l,a,0,c,0_|.i0_ .u.. ;;;;

Figure 2.5: NSCL Neutron Wall Detectors. (Figure courtesy of NSCL design group)

The center-to—center distance between the detectors is 8.55 cm. These rectangular
cells are tapered to a circle of 7.5 cm diameter, and a photomultiplier tube (PMT) of
the same diameter is attached to the cell with optical epoxy. A large aluminum frame
secures these cells to each other, and an aluminum covering shields these detectors
against ambient light.

During the experiment, the two neutron walls were arranged at zero degrees with
respect to the incident beam. In positioning the Neutron Wall detectors in a back-to-
back manner, we approximately double the detection efficiency without sacrificing the

position resolution from having a singular neutron detector with twice the thickness.

19

2.3 Plastic Scintillator Array

The total energy measurement is made by the plastic scintillator array. The array
consists of sixteen BC408 plastic scintillators, each with the dimensions of 40.64 x 4
x 2 cm. It is positioned with its normal at approximately 23 degrees to the beam
direction, with the scintillators approximately 170 cm from the target position. Each
of these scintillator bars has one PMT attached to each end of the plastic scintillator.
Although the PMTs are larger than the plastic scintillators, it is possible to arrange
the plastic scintillator so that there is no dead space in the array by using a staggered
arrangement. The scintillators are arranged in two parallel planes 4.75 cm apart. The
plastic scintillator bars are not optically shielded from each other, so it is possible for
the light output from one detector to scatter to a neighboring detector. Even though
the array is placed outside the magnet, it is necessary to shield the PMTs from the
external magnetic field with p-metal shields.

Previous experiments have shown that beam interaction with the fragment scintil-
lators can produce a considerable amount of neutrons. Only neutrons produced from
the reactions with targets are of interest, so copper bricks were placed immediately

behind the plastic scintillators to shield the neutron wall from these neutrons.

2.4 Silicon Strip Detector

In addition to the total energy, an energy-loss signal (AB) is needed for particle
identification. This signal is provided by the silicon strip detectors. There are two
silicon strip arrays, each is a 250 pm thick square with 5 cm sides. There are thirty-
two 3.125 mm strips in each detector, with sixteen strips in each of the horizontal and
vertical directions. The silicon strip detector is placed 15.24 cm behind the the target

position, so each silicon strip corresponds to a solid angle coverage of approximately

20

1.2 degrees. The two silicon strip arrays are placed side by side to increase coverage

after the target, with a 2 mm gap between the detectors.

2.5 Sweeping Magnet

The secondary beam and the reaction fragments are deflected away from the neutron
wall by the 1.5 Tesla sweeping magnet. The magnet has a 7.5 inch gap with pole faces
that are 13 inches wide and 26 inches long. Originally, this was a 1.7 Tesla magnet
at the Bevalac with a 6.5 inch magnet gap. The gap was extended to increase the
acceptance of the Neutron Walls [34].

Both the plastic scintillator detector and the silicon strip detectors are housed in
a vacuum chamber that fits inside the gap of the sweeping magnet. The silicon strip
detector sits inside the magnet gap and has to be water-cooled because the magnet
generates a considerable amount of heat. The target pod is attached to the front of

the chamber.

2.6 Electronics Setup

The mastergate is generated when there is a coincidence between the event in the
Neutron Walls and the fragment detectors. If a coincidence event is detected, a veto
signal is sent to the electronics to give the computer time to read out the TDCs and
the ADCs. However, if there is no coincidence, then only 1 out of N times (where
N is the downscale factor set) will the event be recorded. In other times, a FAST
CLEAR signal is sent to reset the electronics to allow new data to be recorded. The

downscaled data is used to determine the absolute normalization of the data.

21

Top View

 

 

2:
.
F . 3 "
“I .
= '
.
I
.r
l
'1
It
'I
'u
'1
H
'I
'l
'I
II
II
II
\\\\\\\\\\\\\\\\\\\\\\\

 

Magnet _

 

 

 

   

 

 

 

   
 

 

 

#47143".
lsfiivilftll

 

    

 

 

 

 

 

 

 

 

Target Plastic Scintilators

/E
[MI

Silicon Strip Detectors

 

Figure 2.6: Bending Magnet and Fragment Detector Array.

22

Chapter 3

Data Analysis

3.1 Velocity Difference Analysis

The main objective of this experiment is to measure the energy of unbound states
in a two-body system. In the center of mass system, the total kinetic energy of a

two—body system is given by the relation

E, = lqu

2 rel (3.1)

where the ,u is the reduced mass, and V”, is the relative velocity between the fragment
and neutron. Thus, a measurement of the relative velocity is also a measurement of
the energy of the system. The relative velocity in the center-of-mass system can be
related to quantities measured in the laboratory frame. Looking at Figure 3.1, it is
apparent that le = Vf — V". For a small 0, [Wet] = V, — V", where the differ-
ence between V, and V, is simply a scalar difference of the fragment and neutron
velocities. Both the neutron and fragment velocities are measured quantities in this
experiment. Previous FSI experiments [27 , 28] have used a collinear geometry to de-
tect a neutron in coincidence with a fragment. The neutron detectors were 12.7 cm in

diameter, which represents a solid angle coverage of 1.15 msr [36]. The neutron walls

23

 

 

6,8He, 9Li

Figure 3.1: Kinematic diagram of the core+n two—body system. V, V“, Vf denotes
respectively (in the lab frame), the velocity of the fragment+n system, neutron, and
fragment velocities. VnCM and VmM denotes (in the center-of-mass frame) the
neutron and fragment velocities. For small 0, Vrd 2 VI — Vn
offer greater detection efficiency because of greater angular coverage. The increased
angular coverage also affects the way data is analyzed, and the details of the analysis
will be presented in this section.

In this experiment, only neutrons which are detected within five degrees of a
detected fragment are analyzed. Assuming that the coordinates of the fragment and

the neutron are given as Xf(a:f,yf, 2f) and Xn = (:rn, ymzn) respectively, then the

relative angle between the two is simply:

Xf - X
6 = '1 —" .2

The choice of angular cut 0 is a compromise between energy resolution and number
of events. A smaller angular separation between the fragment and the neutron would
improve the resolution of the velocity difference distribution, but a larger angular

cut would increase counting statistics at the cost of sacrificing resolution. Figure

24

3.2 shows the detection probability as a function of velocity difference of the two-
body system with masses corresponding to a 6He+n system decaying at 440 keV,
which is the current tabulated value for the decay. The simulation accounts for the
detector size, acceptances (including the shadowing from the magnet), and resolutions
of the experimental setup, so the use of a mono—energetic energy distribution gives
an idea of the resolution of the experimental apparatus. The asymmetry of the two
peaks is caused by acceptance effects, because neutrons moving faster than beam
velocity are more likely to be found within angle 6 of a fragment than those neutrons
moving more slowly. Ideally, the velocity difference distributions would have two sharp
peaks at the velocity corresponding to the decay energy and minimal intensity at zero
relative velocity. This figure shows that a five degree cut offers a good combination
of resolution and counting statistics for the 6He+n system.

The analysis using the relative velocity distribution of an unbound two-body sys-
tem has some inherent advantage over using an invariant mass spectra. The energies
of interest are on the order of a few hundred keV or less, and an analysis using relative
velocity accentuates the sensitivity in this low energy region. As shown in the energy
scale on Figure 3.2, the window between -1 and 1 cm/ns represents 0 to 500 keV
for a system with mass parameter corresponding to a 7He. For very small energies,
even though the peaks may not be fully resolved (as shown in Figure 3.3), there is
a very significant change in the line shape of the distribution. This is important for
the low-lying s-states in both the 10Li and 9He.

The relative velocity distributions corresponding to the s-state for the 9Li+n and
8He+n systems are shown in Figures 3.4, 3.5, 3.6, and 3.7. These calculations used
energy distributions computed from the technique that will be described in Chapter
4. Without going into much detail at this point, it is sufficient to mention that a nu-

merically larger scattering length as corresponds to a stronger final-state interaction,

25

Em...___.j

Decay Energy [MeV]

 

1.5 1.0 0.5 O 0.5 1.0 1.5
0-5 [lllllllllllll I l l IFTIIIIIIHHI‘
r—H h 5“} :
(é .. "{.‘\\ (‘1. .4
0.4 — v 1. ‘ ~ —
E . (l, '\ 19° . 1‘ -
Q / \ \. “~--- I/
S h ll \ ‘\ 9° /-\\
_ I \ / .
0.3 ~ \ - , \\ _
E . (P \ '~\8°-’ , 4
"-l .. r \ h, \\ -l
2% _ H \ ‘ I / \ .
f/ o \ I I
n >- I 5 . 4
O 0.2 _ j/ ‘. .‘ \\ \. I / _.
5.: - I/' - \ I
c: " o I ‘
o - I. fl . \ \. 73., l/
.8 O 1 h 11.1] \‘ .' \ \ I, \\
g o _ /'lr’ g0 \\ ' \ // ,l \
" a" / \ X o /
Q i. 2 \ \ \\6/ ’I /

 

 

 

V -V [cm/ns]
f n

Figure 3.2: Detection probability of decay of a two-body system with the mass param-
eters of 7He with a sharp energy distribution E, = 440 keV. Shown is the detection
probability as a function of angular cut for the fragment-neutron coincidence event.
For comparison, an :r-axis containing the energy scale is also shown this relative ve-
locity distribution. The calculations here include acceptance effects (including the
shadowing of the magnet) as well as resolution effects. As the angular acceptance
increases, the resolution deteriorates as the two peaks eventually merge together.
Ideally, there should be no intensity in the region of V, — Vn = 0, but as the angular
cut expands to much beyond 5°, the contribution in that region becomes significant
due to poorer resolution.

26

. __ .."

 

 

 

 

 

_ 0 MeV
a .. -4
E 1.5 — —
Q _
:1. .
a» .
=1 _ ,- 0.1
L5 1 _ 5 .
cu ~ ‘
ID " 5’ 3
a? * "‘
8 * i
g 05 — ',/;-.\ 0.2/ _
a) ’ \ .-" ~\.
H /; . .
a " / 'I .. 1 ‘t‘ \\

z" : . 1 -
P 1.0 ’ . 'l \ ‘ .1 \ '.
" / d. >/ /{I’ .'\ 0.4 /."/‘\ \\ .-
0 ,. a... ;..,—Jr'n,..;; 4 Lu _../. 1-:5111. \‘L
-2 -1 O 1 2
V f-V [cm/ns]
n

Figure 3.3: Detection probability of decay of a two-body system with the mass pa-
rameters of 7He with sharp energy distributions. Shown is the detection probability
as function of decay energy, and in all cases, the angular cut is fixed at 5°. This cal-
culation includes all acceptance and resolution effects of the experimental apparatus.
The method of using velocity difference is very efficient for low energy events and the
efficiency decreases for higher energy. At around E, = 0.2 MeV, it becomes possible
to resolve two separate peaks from the velocity difference spectra.

27

 

0.7 T I ffil T T Y I' r I r T 1 I

 

TTj'

-40 fm ,
0.6 ~ \ -
: / :
. , \ \\
0.5 /, :26 _

f \
i /;
0.4 f

Detection Probability [1/cm/ns]

 

 

 

 

V f—Vn [cm/n3]

Figure 3.4: Detection probability of a 9Li+n system breaking up isotropically after
being formed from llBe. Shown here are calculated velocity distributions for a, =
0,—5, —-10,—20,-40 fm for a 5° angular cut.

which corresponds to a more narrow relative velocity distribution. Figures 3.4 and
3.5, show the detection probability as a function of velocity difference of some select
a, for the 9Li+n system. Figures 3.6, and 3.7 show the total detection probability
for events to falls into different angular cuts for various scattering lengths. Larger
angular cuts will reduce the sensitivity for larger numerical scattering lengths since
the contribution from zero decay energy increases with numerically larger scattering
length.

Figures 3.8 and 3.9 show the same calculations for the 8He+n system breaking up
from an initial 12Be. It demonstrates that even at a 10—degree angular cut, there was
sufficient sensitivity to detect the difference among different scattering lengths. This
is important because in the case of 8He+n system there is limited counting statistics,

and it will be necessary to increase the size of the angular cut.

28

 

0.28_.+..,....,.,.,,.,
_‘ : 40fm j
g 02 : (£30.) 1
a. ' *— (Va"\ 3
b : -"l- “\' 4
a 0.16 _ / (i -
ID b ,’ h ‘
B : :5 \\ .
O 0.12 — ," /::|6 \ ‘1. a
a E // \‘\ j
9: . '/ 1 .

1‘ \

1% 0.08 .— // / ’.’5\ \ \‘\ :1
O
Q

 

 

 

 

V f--Vn [cm/ns]

Figure 3.5: Detection probability of a 9Li+n system breaking up isotropically after
being formed from 12Be. Shown here are calculated velocity distributions for a, =
0, —5, —10, —20, —30, —40 fm for a 5° angular cut.

 

0.8 _ . . . . . . . I ,
0.7 l
0.6
0.5 C
0.4

0.3 :

Total Detection Probability

0.2 ;

0.1 f

 

 

 

 

l 2 3 4 5 6 7 8 9 10
Angular Cut [Degrees]
Figure 3.6: Total detection probability of a 9Li+n system breaking up isotropically

after being formed from llBe. Shown here are curves for a, = 0, —5, —10,—20, —40
fm as a function of angular cut for neutron-fragment coincidence events.

29

 

0.5 I I *I I I r I D

Total Detection Probability

 

 

 

10

l 2 3 4 5 6 7 8
Angular Cut [Degrees]

'1 'tc '

 

Figure 3.7: Total detection probability of a 9Li+n system breaking up isotropically
after being formed from l2Be. Shown here are curves for a, = 0,—5,—10,—20,—4O
fm as a function of angular cut for neutron-fragment coincidence events.

 

 

 

 

I r I I T
.— O.8 - 40m 2
2 ~ / «
E r "~\
:g I‘ /”’.20\‘\ q
“:1 “-6: [936“ j
E I/ A \.
:5 / ’ ‘5 \ \
g I // \1
o O 4 "‘ /’ \ -‘
a: . o \ .
c: .
.g I [l7 )\ .
8 0.2 _ ,/ ‘3 _
3 b l f, ‘ \ u
/’ \\
Q . / \
I/, ’ ‘\\
0 .11 a5? /1 4 l . X‘mh
-2 -1 O 1 2
V f-Vn [cm/ns]

Figure 3.8: Detection probability of a 8He+n system breaking up isotropically after
being formed from 11Be. Shown here are calculated velocity distributions for a, =
0, —5, —10, —20, —4O fm for a 10° angular cut.

30

 

Total Detection Probability

 

 

 

 

1 2 3 4 5 6 7 8 9 10
Angular Cut [Degrees]

Figure 3.9: Total detection probability of a 8He+n system breaking up isotropically
after being formed from 11Be. Shown here are curves for a, = O, -5, —10,-—20, —4O
fm as a function of angular cut for neutron-fragment coincidence events.

3.2 Silicon Strip Detectors

The role of the silicon strip detectors in this experiment is to provide an energy-loss
(AE) signal for particle identification. As a charged fragment passes through the
detector, it loses energy proportional to the square of its charge, making it possible
to perform particle separation based on the charge of the fragments. The energy cal-
ibration was done using a 228Th source. 228Th and its daughter nuclei decay, yielding
mono-energetic a-particles with energies listed in Table 3.1. A typical calibration

spectrum from the energy calibration is shown in Figure 3.10.

31

"—7

. ' ‘1! AJ'I

r" .Vnw. 'i'
J

Silicon Strip Calibration Using 228Th Source

 

 

 

 

 

 

10000 [ . 5.423 MeV

~—~——_V _-AP——_ 5.686 MeV

; __ _ _ ,_ 6.288 MeV

1000 5 f _ 6.779 MeV

g n- __ 8.784 MeV
8 100
10

1 l l l
0 500 1000 1500
Energy (Arb Units)

Figure 3.10: Silicon strip Energy calibration spectra with 228Th source.

Table 3.1: Kinetic energy of the 0 particles for the decay of 228Th.

 

 

JS—OjOpe Energy of 0 (MeV)
"mm 5.423

224Ra 5.656

22°Rn 6.288

216Po 6.779

212Po 8.784

 

 

 

 

32

 

3.3 Plastic Scintillators

3.3.1 Energy Calibration

The fragmentation of the primary beam on the production target produces secondary
beams of various nuclear isotopes. The so—called ‘cocktail beam’ is obtained from
the widening of the A1200 selection slits, and allows various nuclei with the same
momentum to enter the N4 vault and be used to calibrate the plastic scintillators.
This is a standard energy calibration procedure. The cocktail beams were set with
the following rigidity (Bp) settings: 2.692 Tm, 2.358 Tm, 2.0275 Tm, and 1.4016
Tm. In addition, four targets (200 mg/cm2 9Be, 300 mg/cm2 9Be, 123 mg/cm2 27Al,
and 540 mg/cm2 Al) were used to degrade the cocktail beams to provide more data
points for the calibration.

Particle identification of the cocktail beam is performed with beamline time vs.
energy loss (AE) spectra, and a typical spectrum is shown in Figure 3.11. A two-
dimensional gate on the beamline time versus the energy loss is used to select the
desired secondary beam. Given the identity of the fragment and the Bp of the particle,

the energy is given by Equation 3.3.

 

2
E = «931.52 + (2907925330 — 931.5, (3.3)

where E is the energy per nucleon in MeV, and B p is magnetic rigidity in Tesla-meter.
We have assumed that energy loss through the two PPAC detectors is negligible. The
energy-loss through the silicon strip detectors, as well as through the target, needs
to be determined for accurate energy calibration for the scintillators. The target
energy-loss was calculated with the INTENSITY code, and the energy-loss through
the silicon strips is known because it is directly measured. Figure 3.12 shows typical

energy calibration spectra.

33

a. Mr.“

 

 

20 . 1

he
VI
5.”

 

 

 

 

9 . i
g g 51132
E $310131:
10 ’1.” 31—93.,
a .-.,..-.n--- ":3 .-._
5'5 1: :58”: i‘
5 6H8??? :3. '2} ,
0 . 1 l . l
0 500 1000 1500
Beamline Time (Arb. Units)

Figure 3.11: Typical AE vs. beamline time spectrum from a typical ‘cocktail’ beam
calibration run. The start signal comes from the plastic scintillators and the stop
signal comes from the beamline timer, so that a short time-of-fiight (TOF) represents
slower particles. For a fixed Bp, beams with the same A/Z ratio have the same TOF.
The energy resolution of the plastic scintillator has an energy-dependent response.
In addition, the light output from the scintillators is dependent on the charge of
the fragment. The energy resolution for helium isotopes for the energy range in
this experiment is 3.7 i 0.8% as determined by the FWHM of the peak divided by
the energy at the peak. For the lithium isotopes, the resolution is 4.7 :l: 0.7%, and
for beryllium, the resolution is 4.0 :l: 1.0%. For the fragments of interest in this
experiment, it is reasonable to assume an energy resolution on the order of 4 :l: 1%.
As we change the Bp settings, we also get different kinds of particles into our
cocktail beams. The end result is that not all of the fragment detectors would have

the same species of isotopes used for calibration. Table 3.2 summarizes the various

beryllium, lithium and helium isotopes used in this energy calibration.

34

 

700 T I I TI—T r I I I I I T T I I I

 

 

 

 

600 ; —6— He — y = 0.295x + 32.486
_.— Li - — y = 0.444x + 28.646 .
_ -o- Be — — y=0.609x +4730 0 ;
500 j i
I—‘ b .1
> . .
Q) _ .
2 400 r 1
hand > -t
>5 ~ 4
8° 300 3 €
a r d
”I :
200 j j
E j
100 — j
I 1
O 1 1 I l 1 1 1 L L 1 1 l 1 1 1 1 1 1 1
0 200 400 600 800 1000

Light Output [Arb. Units]

Figure 3.12: A typical energy calibration spectrum for the plastic scintillator. The
energy from cocktail beam runs is plotted against the light output from the plastic
scintillator. Shown here is the energy calibration for detector 13.

Table 3.2: ‘Cocktail’ beam calibration summary. Summarized here are the contents
in the ‘cocktail’ beams with different Bp settings and the detectors which were able to
be calibrated. Detector 1 represents the detector with most deflection, and detector
16 is nearest to the beam axis.

 

 

 

 

Bp (Tm) | Runs Contents of ’Cocktail’ Beam Detectors Calibrated I
2.692 75-81 10,11,12138 7"8’9Li, 4""8118 12—16
2.358 42-52 9’wBe 7’8’9Li 4’E’He 9-16
2.028 55-61 9,1038 7’8’9Li 4’6He 5-16
1.402 63-74 7’9Be 6‘7Li 3’4He 1-10

 

 

 

 

 

 

35

3.3.2 Fragment Identification

The fragment identification is achieved with a two-dimensional gate on the AE vs.
total energy. As mentioned earlier, the AE from the silicon strip is proportional to
the 22 of the particles, thus providing the charge separation of the particles. The
total energy measured by the plastic scintillators provides isotopic separation. Figure
3.13 shows the particle identification of the 6’E‘He and 9Li.

The plastic scintillator array is placed downstream from the sweeping magnet,
and as a result, fragments of the same velocity will strike different scintillators. So, in
addition to having the AE vs. E gate, the combination of the plastic scintillator array
and the sweeping magnet allows for some spatial separation between the different
isotopes. Table 3.3 summarizes the predicted scintillator bar that will be illuminated

by a particular nucleus with the specific kinetic energy per nucleon (MeV/ u).

3.3.3 Multiple Fragment Hits

There are events in which more than one fragment scintillator detector was illumi-
nated. The cause of such an event is either two fragments striking the plastic scintilla-
tors (such as a 6He and 4He) or cross-talk from an adjacent detector (the scintillators
are placed adjacent to each other without light shielding). The events which cor-
respond to a single plastic scintillator hit comprise of 90.5% of the events. Table
3.4 summarizes the distribution of plastic scintillators illuminated by the fragments.

Only single-hit events from the plastic scintillators are used for the analysis.

3.3.4 Fragment Velocity Measurement

The fragment velocity was calculated by using the measured kinetic energy of the
fragment at the time of the reaction. Since the plastic scintillators measure the post-

target, post-silicon trip energy, it is necessary to account for the energy-loss in the

36

 

12

10

Energy Loss (MeV)
00

 

 

 

 

 

A 100 A A 200 A A 300
Total Energy (MeV)

 

Figure 3.13: Particle identification for two different fragment detectors. The array of
sixteen plastic scintillators measures the total energy, and the different positions of
the plastic scintillators help with isotope separation. The energy loss was measured
by an array of silicon strip detectors positioned downstream from the target. The
figure on the left shows an energy-loss vs total energy spectrum of the 12‘” scintillator
bar, which was farther away from the beam axis than the 16‘” bar. The energy scale
used in the two figures is correct for the helium isotopes. Since the light output of
the plastic scintillators decreases when the charge of the particle increases, a scale
factor of approximately 1.4 is needed to obtain the correct energy for 9Li. While
bar 12 detects mostly 6He and 9Li, bar 16 detects only 6f‘He, and very little 9Li.
Even though 9Li and 6He have the same A/Z ratio, the 6He fragment will have a
wider momentum spread than 9Li from the fragmentation reaction, where the spread
is characterized by a = 00%, where A is the mass for the incident nucleus
and AF is the mass of the reaction fragment. Consequently, there was an appreciable

amount of 6He measured, but not 9Li.

37

Table 3.3: The trajectories of various charged fragments as they pass through the
sweeping magnet. The fragments are assumed to be at zero degrees relative to the
beam direction, passing through the center of the magnet gap. The calculations are
done based on the work by [34], which uses a measured field map of the magnet to
integrate the trajectories of the fragment. Detector 1 is the detector farthest from the
beam axis, and the detector 16 is the nearest. Values between X and X +1 correspond
to a fragment predicted to hit bar X + 1 (such that 13.9 means the portion of bar 14
closer to the beam axis). At energies close to 30 MeV/ u, the 8He fragments take a
trajectory that strikes the plastic scintillators nearest the beam direction. A higher
beam energy would have improved the resolution of the experiment, but the reaction
fragments would have been insufficiently deflected by the sweeping magnet.

 

 

 

 

Predicted Plastic Scintillator Position

Energy (MeV/u) 11Be 1°Be 8He I2Be 4He 6Be
6He 3He

30.0 11.2 10.1 15.1 12.2 7.2 3.0
29.5 11.1 10.0 15.0 12.1 7.0 2.8
29.0 11.0 9.9 14.9 12.0 6.9 2.7
28.5 10.9 9.8 14.8 11.9 6.8 2.6
28.0 10.8 9.7 14.7 11.8 6.7 2.5
27.5 10.7 9.6 14.7 11.7 6.6 2.3
27.0 10.8 9.4 14.6 11.6 6.5 2.2
26.5 10.5 9.3 14.5 11.5 6.4 2.1
26.0 10.4 9.2 14.4 11.4 6.3 1.9
25.5 10.3 9.1 14.3 11.3 6.1 1.8
25.0 10.2 9.0 14.2 11.2 6.0 1.6
24.5 10.0 8.9 14.1 11.1 5.9 1.5
24.0 9.9 8.7 14.0 11.0 5.7 1.3
23.5 9.8 8.6 13.9 10.8 5.6 1.1
23.0 9.7 8.5 13.8 10.7 5.4 1.0

 

 

 

 

 

 

 

 

 

 

Table 3.4: Fraction of neutron-fragment coincidence events as a function of number of
bars which detected a fragment. For the neutron-fragment coincidence events, 90.5%
are detected by one plastic scintillator. Events with multiple scintillator hits are not
used for analysis.

 

[Total Bars Fired [I Fraction of Events |

 

 

1 0.905
2 0.093
3+ 0.002

 

 

 

 

 

38

target and the silicon-strip detectors. The energy-loss through the silicon is known
from the silicon-strip energy calibration. It is assumed that the nuclear reaction

occurred at the mid-target position, so the total kinetic energy of each fragment is:
Ef = Eplastic 'l' Esz'licon + Etargeteloss, (3.4)

where E f is the mid-target energy, and Etargeteloss is the energy loss of the fragment
as it passes through the target. The velocity is related to the kinetic energy by the

relation:

 

 

2
1

me?

where m is the mass of the fragment.

3.3.5 Fragment Velocity Resolution

There are three major factors that contribute to the velocity resolution of the frag-
ment. The discussion of velocity resolution is most conveniently expressed with re-
spect to momentum resolution, and the relationship between momentum resolution

0,, and velocity resolution 0,, can be approximated as:

a?

(3.6)

a. = ——3,
m7

where 7 = 1 / P, and p and m are momentum and the mass of the fragment.
This relationship can be obtained by taking the derivative of the equation p = ymv,
and replacing the differentials dp and dv with up and 0,. For the energy range of
interest here (mid-target energy of around 27.7 MeV/ u), y = 1.030, so that essentially,
0,, = 0,, / m.

The spread in momentum contributed from the target energy-loss can be obtained
from the spread in energy. The relationship between the energy spread and the

momentum spread can be approximated as:

1
UPEIoss : EOE/70837 (3'7)

39

Table 3.5: Stopping power parameters for beryllium, lithium, and helium nuclei pass—
ing through 9Be target. Tabulated here are the parameters Co and CI for a fit to a
form of S (T) = COT C‘, where T is the kinetic energy per nucleon of the nucleus. The
unit of the stopping power is MeV/(mg/cmz). Total energy loss can be estimated by
multiplying the target thickness (in units of mg/cmz), with the mid-target energy.

 

 

Isotope Co 01
Beryllium 3.9039 -0.8128

Lithium 2.1997 -0.8131

Helium 0.9804 -0.8139

 

 

 

 

 

 

 

 

where 0pm... is the contribution in momentum (measured in standard deviation 0)
from the target energy-loss (03103,). This relation can be derived by simply taking
the expression energy E: E2 = p262 + mzc“, which means EdE = czpdp. Since
p/ E = v/c2 = B/c, one readily obtains the result in Equation 3.7. For a small spread
0pm” and 03103,, one can replace those differentials with these widths.

The stopping power is an energy-dependent quantity, and we obtained our es-
timates in units of energy per unit target thickness (MeV/(mg/cm2)) by using a
power-law fit in the form of S (T) = C'OTC1 to the tabulated values from the works
of [40]. S (T) is the total energy loss and T is the kinetic energy per nucleon. For
the energy range of 20 to 40 MeV/ u, the appropriate constants (where the stopping
power is expressed in units of MeV/(mg/cm2)) are summarized in Table 3.5. The
energy-loss of the entire fragment can be estimated by multiplying the target thick-
ness (in units of mg/cmz), with the mid-target energy. As mentioned previously, the
mid-target energy is on the order of 27 .7 MeV/ u for the cases here. There is a 5%
error assigned for these predicted energy-loss estimates, as suggested by the authors
in [40].

To first order, the energy distribution of the reaction fragments after they pass
through the target can be modeled by a rectangular distribution since the reactions

can occur near the front or the back of the target with equal probability. A rectan-

40

gular distribution of width 20 has a standard deviation of w/\/1_2. Thus, as a rough

approximation, the width of this energy distribution 0510,, can be taken as:

Ef—Eb

0'Eloss : [if—W: (38)

where E f is the energy per nucleon of the reaction fragment after it traveled through
the entire target with its initial energy taken to be the beam energy, E, is the energy
per nucleon of the beam after it has traveled through the target, and A f is the mass
of the reaction fragment.

As mentioned in Section 3.3.1, the energy resolution of the plastic scintillators
is taken as 4% from the result of the cocktail beam calibration. Given the energy
resolution of the plastic scintillators expressed as 05,“, the contributed momentum

width OPE,” can be approximated as:

EaEres

apErca = C [E2—_ m2c47 (3.9)

where E is the total energy, and m is the mass of the fragment.

 

The momentum slits of the A1200 are set at 3% for 12Be and 1% for 11Be. As-
suming a rectangular distribution, the momentum spread from the beam abeam can

be approximated as
AP

0 = —, 3.10
pbcam m ( )

where AP is the momentum acceptance of the beam.
These resolution effects can be added in quadrature so that a; = 032:... + 035m +

031mm. Tables 3.6 and 3.7 summarize the resolution effects from each of these three
contributions. The velocity resolutions expressed in both units of momentum as well
as velocity. In the case of an incident l2Be projectile, the effects of each of these
contributions on the overall velocity resolution are very comparable. Although the

11Be beam has a smaller momentum spread than 1("Be (1% momentum acceptance

versus 3%), there is an increased spread in the target energy-loss, since 11Be loses

41

r!

Table 3.6: Resolution of momentum and velocity measurement of the plastic scin-
tillators with incident ”Be beam. Listed here are the contributions from target
energy-loss, momentum spread in the ”Be beam, and energy resolution from the
plastic scintillators.

 

 

 

 

Total Target Beam (”Be) Energy Res.
Fragment MeV/c cm/ns MeV/c cm / ns MeV/c cm/ns MeV/c cm / ns
8He 34.5 0.13 26.2 0.10 15.9 0.06 15.9 0.06
6H8 23.0 0.11 15.7 0.08 11.9 0.06 11.9 0.06
9Li 27.9 0.09 11.8 0.04 17.9 0.06 17.9 0.06

 

 

 

 

 

 

 

 

 

 

 

Table 3.7: Resolution of momentum and velocity measurement of the plastic scin-
tillators with incident 11Be beam. Listed here are the contributions from target
energy-loss, momentum spread in the 11Be beam, and energy resolution from the
plastic scintillators.

 

 

 

 

Total Target Beam (”Be) Energy Res.
Fragment MeV/c cm / ns MeV/c cm / ns MeV/c cm/ns MeV/c cm/ns
gHe 34.6 0.13 30.3 0.11 5.3 0.02 15.8 0.06
6He 22.5 0.11 18.8 0.09 4.0 0.02 11.9 0.06
9Li 24.8 0.08 16.2 0.05 5.9 0.02 17.8 0.06

 

 

 

 

 

 

 

 

 

 

 

more energy going through the target. Thus, the overall resolution of the 12“Be
beams is about the same.

All of these resolution effects are included in the computer simulation used for
data analysis. The contribution from the resolution from the silicon strip detectors
(nominally 1-2 % is typical for such detectors) is very minimal and will essentially
have no effect on the resolution, since the typical energy loss through the silicon strip

detectors is on the order of 10 MeV or less for 9Li and 6'8He.

3.4 NSCL Neutron Walls

The NSCL neutron wall array is a large-area position-sensitive detector. Each of

the two walls has dimensions of 2 meters by 2 meters, and has a neutron detection

42

efficiency on the order of 12 % for 30 MeV neutrons [35]. More detailed discussions

on this detector can be found elsewhere [35].

3.4.1 Neutron Identification

Crucial in this experiment is the ability of this detector to distinguish the difference
between a neutron signal versus a 7- ray signal. This is achieved with the method of
pulse-shape discrimination. The light-output as a function of time is not the same
for for a neutron and a 7—ray. More specifically, a greater portion of a 'y- ray pulse
comes from the beginning part (fast) of a pulse as compared with a neutron signal. If
both the fast portion of the signal and the total size of the signal are measured, then
it is possible to separate the neutron and y-ray events. A pulse-shape discrimination
circuit discussed by [35] is used in this experiment. This circuit takes the anode
signal from the neutron wall PMT as an input, and outputs four signals for the
QDCs: (1) signal proportional to the size of the head of the signal (QFAST), (2)
signal proportional to the total charge of the anode pulse (QTOTAL), (3) attenuated
QFAST signal, (4) attenuated QTOTAL signal. Attenuated signals are necessary
because the neutron wall signals have a large dynamic range. The threshold on
the neutron wall detector was set to 1 MeVee (MeV electron-equivalent); the same
amount of light output that comes from a one MeV electron. A typical spectrum of

the neutron wall identification is shown in Figure 3.14

3.4.2 Multiple Neutron Hits

As in the case of the plastic scintillators, multiple—hit events can also occur for the neu-
tron detectors. A sophisticated approached used in reference [50] to process multiple-
hit events is not needed for the present work since the events studied here are the

single neutron-coincidence events. While a single neutron can produce neutron pulses

43

Table 3.8: Fraction of neutron coincidence events as a function of number of bars
which detected a fragment. For the neutron-fragment coincidence events, over 90%
are detected by only one neutron wall cell.

 

] Total Neutron Cells Fired ]] Fraction of Events ]

 

 

1 0.923
2 0.067
3+ 0.003

 

 

 

 

 

in multiple neutron wall cells, approximately 92.3% of the fragment-neutron coincide
events includes only 1 neutron wall cell. Table 3.8 summarizes the distribution of the

multiple neutron events.

3.4.3 Position Calibration and Resolution

Positions on the neutron walls are determined by taking the time difference between

the left and the right detector, and bear the following relationship:
X=CI(TL—TR)+02, (3.11)

where X is the x-position on a neutron wall detector, and the T L and TR are the
values of the fragment-detector started, neutron-wall stopped times. 01 and 02 are
calibration constants that need to be determined on a detector-by-detector basis.
Since background 7—rays evenly bombard the entire width of a neutron detector, the
position calibration is simply a matter of analyzing the y-ray-gated time difference
spectra. Each of the neutron wall cells is 2 meters wide, so the proportionality
constant 01 = 2.0 meters/ AT, where AT is the width of the 7-gated time difference
spectra. 02 is an offset constant chosen such that the center of the neutron wall has
the position of zero meters. The y-position is obtained by the knowledge of which
neutron wall cell observed the neutron event.

One important question regarding the neutron wall is the position resolution of

44

 

  
 

 

 

 

 

(Proton Reaction) ‘ *" .-
A 300 P ' >3 ' _
é " ' _'
“é _ ‘ Ga a rays . ,[
33, 200 - -
E“
m _. 4
<
m . - l l 3..
0‘ 100 h '1" "8 ' _

. . 8434“" Neutrons (Carbon Reaction)
0 1 '.-‘ l A I A l ‘
QTOTAL (Arb. units)

Figure 3.14: Neutron identification in this experiment was achieved through pulse-
shape discrimination. Shown here is the fast (QFAST) portion of the neutron wall
signal plotted versus the total pulse size (QTOTAL). There are three distinct bands in
the spectra. The top band represents 'y-rays, while there are two bands corresponding
to neutron events. One of these bands comes from the reaction with the proton in
the liquid scintillator, and the other comes from interactions with the carbon.

45

the detector. This is determined by using the so—called ‘shadowbars’ during the
experiment.

During the run, brass bars (the aforementioned shadowbars) with the dimension
of 3”x 2%” x 12” (7 .6cm x 7 .0 cm x 30.5 cm) are placed 173 cm away from the target
position. The front neutron wall is 500 cm away from the target, while the back
neutron wall is 550 cm away. From simple geometric considerations, we see that the
’shadow’ casted by these shadowbars will have the size about 22 cm x 20 cm. With
each neutron wall being 7.62 cm tall, each shadowbar should have effects that can
be observed across at least two adjacent neutron detectors, with one cell completely
shadowed. These effects were observed.

In order to extract the background neutrons as well as the position resolution, the
following approach was taken. The neutron distribution across a neutron wall cell in
the absence of a shadowbar is known. Typically, the distribution resembles Figure
3.15. If the resolution of the neutron wall is perfect, we know that in the presence of
a shadowbar, the distribution of the neutrons would resemble Figure 3.16.

In this ideal case, a sharp dip would be present in the distribution, where the
height of this sharp dip would represent the background neutrons detected. In this
case, there would be a sharp drop-off in the neutron distribution in the region where
the shadowbar shields the neutron wall. Ideally, there would be no neutrons in the
region of the cell shielded by the shadowbar. However, there can be some counts in
this region that came from some other sources, such as neutron scattering from an
adjacent cell. To account for this, an additional fitting parameter H is introduced.
H corresponds to the neutrons not coming directly from the beam reaction with the
target, and thus is a measure of the background.

If the resolution of the detector is characterized as:

 

f(:1:) = x/2l7fa exp[(:6 — 1:0)/202], (3.12)

46

3% T T T T I T I T T I T T I T I T T Y T

 

 

 

 

250 ~ —
: ° 000
o o
200 ’— (>0000 000 o -1
>\ F o 0
ca : o “’99 «>0 0 .
1: ’ <9 000° ‘
_ o -
‘2 150 . (9000 0 0°00 ]
I— ~ 0 ° 00 o .
:- 0°
_ <9 °®&
100 ” <9 0 ° '7
E °°°
L 00 390690
_ o oo 00 4
50 _ o o o a
_ 0 ° -
0° 0
:o° Q’d
0 L j l l 1 1 1 L l l L l l L l 1 l l l o
-l -0.5 0 0.5 1

Neutron Wall Position [meter]

Figure 3.15: Neutron distribution on cell 9 without shadowbar

and the ideal response of a given neutron wall cell can be taken as the neutron
distribution in the absence of the shadowbar, and the shadowed region has a response
of H (as in Figure 3.16) , one can perform a two-parameter fit with the shadowbar
data by varying both H and a. This analysis is performed for cells 9 and 13.

Figures 3.17 and 3.18 show the shadowbar data of cell 9 (middle of the front
neutron wall) and cell 13 (near the top of the front neutron wall).

According to both of these fits, a FWHM of 12 cm for the Gaussian response
function for the neutron wall seems to fit the shapes of the shadow bar curves quite
well. Cell 9 is the neutron wall cell that is closest to the beam direction. A detector
resolution of 12 cm and a background parameter H=6 seem to fit quite well. We
expect around 113 events in the region covered by the shadowbar, so the fit suggests
that around 5% of the events in cell 9 are background events. A similar analysis
performed on Cell 13 (H=10, expected count=109) suggests that we have about a 9%

background for that particular cell.

47

 

 

 

 

3m T T T T T T T Tr IT I T T T T ‘ T T T
C .
)- -<
250 _ 1
* 0 000
200 '- 0 0000 00000 —1
o
2.“ ° ° 0°
'3 F 0%0 000 4
c: f o co
3 150 ~ 0" 0 °. 0 .
g " 6‘100 <90 .
H o ‘
. 00 <
. & q
' 0%» 1
_ oo o
_ 0 0° 06900 1
50 _ <9000 0 1
° 0 4
000 Q);
0 l A 1 A l L L A l L L J l W A A o
-1 -0.5 0 0.5 l

Neutron Wall Position [meter]

Figure 3.16: Hypothetical neutron distribution on cell 9 in presence of shadowbar,
where perfect resolution is assumed.

 

 

 

300W 4
J
. OData .
. ell .
250- C 9 -—FWHM=O.2m :
m t 000 o —FWHM=0.12m .
g 2002 <>.. 000. .° ------ FWHM=0.03m I
q .— "f?
o i
3 .
3.150—
3 .
g I
0100—
U :
50:
029°.n..1..1n1.

 

 

-l -0.5 0 0.5 1
Neutron Wall Position [meter]

Figure 3.17: Neutron Wall cell 9 shadowbar spectra. Shown are the fits using
FWHM=0.2, 0.12, and 0.03 meters, with background parameter H = 6. The best-fit
uses FWHM=0.12 m (a = 5.1 m) for neutron response function, and the H = 6
corresponds to a 5 % contribution to background.

48

 

300 ’- ' ' ' V I V V T 7 I r r 1 r I r v 7 T ‘
: 0 Data :
- Cell 13 .
250 f -— FWHM=0.2m -
H t ——FWHM=0.12m .
L 1
E — ------ FWHM=0.03m .
8 200 ’— 0 _
<5 c
H b
g, 150 .
Z!
5
o 100
U I-
50 l

 

 

 

 

-1 -0.5 O 0.5 l
Neutron Wall Position [meter]

Figure 3.18: Neutron Wall cell 13 shadowbar spectra. Shown are the fits using
F WHM=O.2, 0.12, and 0.03 meters, with background parameter H = 6. The best-fit
of uses FWHM=0.12 m (a = 5.1 m) for neutron response function, and H = 10
corresponds to a 9 % contribution to background.

In the works by [35] it was concluded that the position sensitivity of the neutron
wall approaches 7.65 cm (FWHM) for high-energy neutron events. This value was
extracted through the use of a collimated source at different positions of the neutron
wall. The analysis performed on these shadowbars suggests a substantially worse
resolution (FWHM of 12 cm versus 7.65 cm).

Because the size of the neutron wall cell is only 7.62 cm, it suggests a better
position resolution is obtained vertically as compared to horizontally. A rectangular
distribution with a width of 7.62 cm is equivalent to a Gaussian distribution with
a = 2.2 cm (Gaussian equivalent to FWHM=5.2 cm). This is less than 50% of the

FWHM=12 cm in the horizontal direction. In terms of standard deviation 0, the

position resolution is on the order of 0,, = 5.1 d: 1.0 cm.

49

1400 Y'YTTI'T"I""['FTTITrr

 

 

 

 

 

 

 

 

 

 

r J
1200 E 1
1000 } 1
~ I
'2 800 l lOns J
8 E <——-> 1
(J 600 i {
400 3 {
200 E -
O»..J..-J..17...1..J...J.
0 100 200 300 400 500
TDCRead-Out

Figure 3.19: TDC calibration spectrum

3.4.4 Time Calibration and Resolution

The time-to—digital converters (TDC) in the experiment are all calibrated with a
pulser that generates random pulses at adjustable intervals. A typical interval is 10
ns. By pulsing the TDCs with this pulser, we easily calibrate our TDCs. A typical
spectrum from this calibration is shown in Figure 3.19.

The time-of-flight of the neutron is measured with a start trigger that comes
from any one of the plastic scintillators and the stop trigger that comes from the
neutron wall. Thus, it is possible to have sixteen possible start triggers and thirty-
two possible stop triggers. With issues such as different cable lengths and delays, it is
necessary to have a common reference for the time-of-flight (TOF) measurements. A
t"°Co source was placed between the neutron walls and the plastic scintillators, thus
providing an absolute timing reference for TOF measurement. Figure 3.20 shows
a typical spectrum from this calibration. The time resolution as measured with

standard deviation 0 is 2.1 ns.

50

4% I I T T T I T I T 7 I I T I T I T I T I

 

 

350 :- 60Co y-ray TOF Spectra 7;

300 L 1

E .

a E ‘
In. 250 :- 7
N ’ A
a zoo :~ 9
r: » l
8 : 1
U 150 r d

 

 

 

 

1 AL A L 1 1 A 1 A l A L L

 

 

100 200 300
Time of Flight [n8]

Figure 3.20: 6°Co y-ray T OF spectrum. The peak shown has a FWHM of 5 ns.

3.4.5 Neutron Velocity Measurement

The neutron time-of-flight is measured with respect to the fragment detectors. Thus,
in order to obtain the total neutron time-of-flight from the target, it is necessary to
obtain the velocity of the fragment measured in coincidence. This can be done by the
procedure outlined in Section 3.3.4.

The velocity of the neutron is then given as

D.
12,, = DT——_’ (3.13)
6+9”

where Du is the distance traveled by the neutron, D, is the distance traveled by
the fragment from the target to the scintillator, which is approximately 170 cm for
all detectors, 0, is the velocity of the fragment (Section 3.3.4), Tfn is the neutron
time-of-fiight measured with respect to the fragment detector. The Tfn is measured

by taking the average time between the left and the right neutron wall TDC signals.

51

Table 3.9: Resolution of momentum and velocity measurement of neutron wall detec-
tors with an incident 12Be beam. Shown are the contributions from resolution from
the fragment velocity resolution, time resolution, and position resolution effects.

 

 

 

 

Total Frag. Velocity Time Res. Position Res.

Fragment MeV/c cm/ns MeV/c cm/ns MeV/c cm/ns MeV/c cm/ns
8H6 8.2 0.24 1.5 0.04 7.4 0.22 3.0 0.09
6H8 8.1 0.24 1.3 0.04 7.4 0.22 3.0 0.09
9Li 8.1 0.24 1.1 0.03 7.4 0.22 3.0 0.09

 

 

 

 

 

 

 

 

 

 

 

3.4.6 Neutron Velocity Resolution

Because the fragment velocity is used to extract the neutron velocity, all of the res-
olution issues discussed in Section 3.3.5 apply to the neutron velocity resolution.
Since the fragment velocity resolution is fragment dependent, the neutron velocity
resolution is also fragment dependent. In addition, there is the contribution from
the resolution of the neutron time-of-flight measurement. Shown in Tables 3.9 and
3.10 are the neutron velocity resolutions expressed in both units of momentum and
velocity for initial 12Be and 11Be projectiles. The tables show the contribution to
the resolution from the fragment velocity resolution, time resolution, and position
resolution effects. The dominant effect in the neutron velocity resolution is the time
resolution of the time-of-fiight measurement, and the fragment velocity resolution is
the smallest contribution. The neutron velocity resolution is quite a bit worse than
the fragment velocity resolution; the resolution as measured in standard deviation 0
is approximately a factor of two larger than the fragment velocity resolution. Thus,
the neutron velocity resolution dominates the resolution of the relative velocity dis-

tribution.

52

Table 3.10: Resolution of momentum and velocity measurement of neutron wall de-
tectors with an incident 11Be beam. Shown are the contributions from resolution from
the fragment velocity resolution, time resolution, and position resolution effects.

 

 

 

 

Total Frag. Velocity Time Res. Position Res.

Fragment MeV/c cm/ns MeV/c cm/ns MeV/c cm/ns MeV/c cm/ns
8H8 8.1 0.24 1.5 0.04 7.4 0.22 3.0 0.09
6He 8.1 0.24 1.3 0.04 7.4 0.22 3.0 0.09
9Li 8.0 0.24 0.9 0.03 7.4 0.22 3.0 0.09

 

 

 

 

 

 

 

 

 

 

 

3.5 Particle Tracking Issues

The ability to track the reaction products as well as the neutrons is essential for
the selection of collinear events. The experiment was set up with two parallel plate
avalanche counter (PPAC) detectors in front of the target and as aforementioned,
silicon strip detectors after the target. For inexplicable reasons, the position infor-
mation from the PPAC detectors did not agree with tracking from the silicon strip
detectors. The same problem was found in the two other experiments that ran with
the identical setup. The silicon strip detector signals are considered most reliable
because they provided correct particle identification signals (as we will see later in
our data analysis). As such, PPAC signals were discarded from the analysis.

Without the use of pre—target tracking, it was necessary to make certain assump-
tions about the characteristics about the incident secondary beam. In this work, the
beam is assumed to have taken a straight path to the target.

Originally, as in other experiments done with this setup such as those in Jon
Kruse and Jing Wang’s thesis [34, 50], the silicon strip detectors were to provide the
post-target tracking. Because the silicon detectors contain some dead strips, there
are events where either the :r or the y coordinate of the event are missing. Although
silicon strip detectors could not be used for tracking, it was possible to obtain the

information from the plastic scintillator bars.

53

The plastic scintillators are placed approximately 170 centimeters away from the
target and downstream from the bending magnet. At a width of 4 cm, the scintillator
bar has an angular coverage of 1.35 degrees, which makes it just slightly larger than
the angle subtended by the silicon strips. The x-position information is contained
within which detector was struck by the charged fragment. For each of the 6”3He and
9Li, we assume the scintillator bar that has the largest number of counts of the given
isotope represents the :r = 0 position. For 6He and 9Li, bar 13 represents :1: = O, and
for 8He, it is bar 15.

Because the time signals of the PMTs on the plastic scintillators relative to the
silicon-strip detector were also recorded, the time difference between the top and
the bottom PMT on each scintillator can provide y—position information. This is
completely analogous to the procedure for determining the :r-position on each of
neutron wall cells.

In addition to the benefit of an increased number of available events for analysis,
the use of the plastic scintillator for tracking is very important from another stand-
point. The width of the beam spot for the experiment (as measured by FWHM), is
on order of 2.5 cm, which covers eight silicon-strip detectors. Since the beam-spot
is large compared to the distance of the silicon strip detector behind the target, it
means that there will not be much correlation between which strip is hit versus the
angle it is deflected from the beam axis. By tracking with the plastic scintillators,
the additional flight path improved the ability to track.

In conclusion, the final manner by which the particles were tracked turned out to
be superior than the method originally planned, since this allows the analysis of events

that would have been difficult to analyze without complete kinematic information.

54

3.6 The Fitting of the Velocity Difference Data

Each set of velocity difference data is fitted to a combination of a computer simulated
velocity difference distribution and a background. It was found that a background
component is necessary to describe the data. In the previous experiments by Kryger
et al. and Thoennessen et al. [27 , 28], a background of a thermal neutron source of
the form x/Eexp(—E/T) was used. After accounting for the detector efficiencies
and acceptances, the relative velocity distribution of the background takes a near-
Gaussian shape. In the present work, an event-mixed background is used instead of
the thermal neutron background assumed by [27, 28].

The essential idea behind event-mixing is to combine data from two different phys-
ical events and treat them as a single event. The combination of two different events
simulates a data set of which one does not expect to have any physical correlation, and
it can be used to model the background in the experiment. For the neutron-fragment
coincidence data collected in this experiment, the event-mixed analysis would use the
fragment data from one event and the neutron data from another event. The analysis
uses the same event selection procedures, and the distribution is one where there were
no correlations between the fragment and the neutron. As will be shown here, the
event-mixed velocity difference distribution can be obtained by folding the velocity
difference distributions of the neutron and the fragment.

Let’s assume that there are two distributions, wn(vn) and w f('Uf), which are ve-
locity distribution functions of the neutrons and the fragments normalized to unity.

The velocity difference is then defined as:
Av = v, — 1),, (3.14)

If the two distributions are independent, then the probability of obtaining some 11,
and 22,, is simply:

d2w(vf, '0") = wn(Un)'IUf(Uf)d'Und'Uf (3.15)

55

This means that the probability distribution of a velocity difference can simply be

written as:
’0" ’Uf

vnA’u

 

dw2(Av, U") = wn(vn)wf(Av + vn).]( )dvndAv (3.16)

Since the Jacobian J ($15) = 1, the differential probability can simply be expressed

as:
dw(Av) _
dAv —

/ wn(vn)wf(vn + away, (3.17)
Once both the neutron and the fragment velocity distributions are known, a simple
folding of the two distributions will give a distribution that corresponds to uncorre-
lated fragments and neutrons. Typically, the FWHM of the neutron and the fragment
velocity distributions are on the order of 1 cm/ns. The velocity distributions for the
neutrons and the fragments are tabulated in Appendix A.

In our velocity difference analysis, there will be a significant fraction of the events
where the measured neutrons and the fragments are not correlated. This may be
caused by neutron interaction with the target or other final-state interaction with the
reaction fragments. For example, the case of a 9Be(12Be,6He+n)X reaction, where, in
addition to a 6He fragment being produced, there are four other neutrons available
in the system. Consequently, the detected neutron might have never interacted with
the 6He. In addition, it is also possible that 12Be can break up into 6He + 4He +
2n. Furthermore, it is possible that an observed neutron may have interacted with
the target instead of the fragment of interest. With the estimate of a background
distribution, we then can proceed to simulate the events associated with various
p—wave and s-wave scattering which allows for comparison with experimental data.
The velocity difference distribution from the final-state interaction is simulated with a
computer simulation which accounts for the detector resolution and acceptance effects

in addition to energy-loss straggling through the target and silicon-strip detectors. In

the computer simulation, it is assumed that the unbound system is populated by

56

the fragmentation in the target and then experiences an isotrOpic decay. The energy
distribution of this decay is calculated with the potential scattering model, which will
be discussed in detail in Chapter 4. Because the energy calibrations are not perfect,
it is possible to have a systematic shift in the spectra, and the absolute position of
the theoretical curve is allowed to be shifted arbitrarily to fit the data. In general,
such a shift is small, on the order of 0.1 cm/ns or less. The best fit was obtained
by changing the relative contributions amongst the background and the predicted

distributions from final state interactions using the minimum x2 method.

57

Chapter 4

Model of the Reaction of the

Final-State Interaction

This section discusses the simple model for the formation of the unbound nuclei in

the final states as well as the manner which the final-state interaction is calculated.

4.1 Fragmentation Mechanism for Breakup

For a system where the reaction fragments are produced as a result of a fragmentation
reaction of a stable projectile, the momentum distribution can be described as a

Gaussian with width 0
K (A — K)

A _1 , (4.1)

0:00

where A = mass of the original (unreacted) nucleus, K = mass of the emerging
fragment, and a typical value for 00 is 90 MeV/c [37] for high-energy reactions.
Equation 4.1 can be derived with a model using two assumptions: (1) The pro-
jectile breakup is a fast process (thus the sudden approximation is valid), and (2)
The emerging fragments from the breakup have the nucleon momenta from the initial

projectile. These assumptions were first put forth by Feshbach and Huang [38] but it

58

was shown by Goldhaber [37] that these results can be derived by using a statistical
model where the nucleons in the initial projectile have minimal correlation with each
other. In addition, it was also shown that the 00 parameter can be related to the
Fermi momentum via the relation 00 = pf/\/5.

The measurement of the 00 parameter from this experiment will show that the
present data is consistent with this Goldhaber picture. The 00 parameter, which
characterizes the momentum transfer from a fragmentation reaction, is extracted here
by measuring the width 0 of the fragment momentum distribution and then using
Equation 4.1. However, the distribution would be broadened by the target energy-
loss, momentum spread from the incident beam, as well as energy-resolution of the
detectors. Since the momentum resolution of the fragment momentum measurement
has already been discussed (Section 3.3.5), it is a straight-forward task to extract the
value for 00.

The extracted value of 00 for various fragments for 11”Be as well the momen-
tum resolution are listed in Tables 4.1 and 4.2. The momentum distributions of the
fragments are shown in Figures 4.1, 4.2, and 4.3. The a of the fragment momentum
distribution and its error were assigned by taking the average and the standard devi-
ation of four different methods of measurement. The four methods are: (1) Gaussian
fit of distribution and extract a, (2) Assuming the distribution to be a triangular
distribution and extract a, (3) Actual computation of the standard deviation of the
data over the entire distribution, and (4) measuring the FWHM of the distribution
and assume a Gaussian distribution when extracting a a (dividing by 2.35).

The values of extracted 00 are smaller than the canonical value of 90 MeV/c.
However, it has been experimentally observed that 00 diminishes with decreasing
beam energy [39]. Figure 4.4 shows the data with various reactions at different beam

energies. Murphy and Stokstad [39] observed momentum widths 00 of 65 and 60

59

MeV/c for 6’7Li respectively from a 9Be + Au reaction at 27.4 MeV/ u. The results
from [39] are obtained from using a beam energy very comparable to those used in this
experiment. The measured 00 in this experiment are consistent with these results,
with the exception that the 8He momentum distribution with incident l2Be seems
somewhat narrower.

In the case of the momentum distribution of the 9Li fragments from the breakup
of 11Be, there exist theoretical techniques to predict the distribution. In particu-
lar, one can use the model of a knock-out reaction, where one proton in the 11Be is
knocked out and the momentum distribution of the 10Li is deduced. In the rest frame
of the projectile and if sudden approximation is valid, the momentum of the remain-
ing fragment equals that of the knocked-out nucleon. Consequently, the momentum
of the fragment can be determined by simply integrating the neutron momentum
probability over the impact parameter. The integration was done using a black disk
approximation. A detailed discussion on this technique can be found in [41]. The
calculation performed in this analysis is similar to those used in [8, 9]. Although
the deduced momentum distribution in this case is the for the 10Li, the momentum
distribution of the 9Li can be taken as 9/ 10 of the 10Li distribution. Figure 4.3 shows
the calculated distribution for a single neutron-knockout reaction transformed to the
laboratory system. The resolution correction has not been included; it would broaden
the peak by approximately 4 MeV/c.

The excellent agreement between the experiment and theory on the 9Li momentum
distribution data suggests that the sudden approximation is valid, and that reaction
products are projectile-like fragments. In addition, the extracted 00 value indicates
that the momentum transfer from the reaction will be small and it would allow us to
assume that the reaction fragments have the same momentum distribution as they

had within the beam projectile. The fact that the recoil effects can be neglected here

60

 

Table 4.1: Goldhaber 00 parameters extracted from incident 11Be projectile. All val-
ues tabulated are in units of MeV/c and are expressed in terms of standard deviation
0. Shown tabulated here are the extracted 00, the estimated contribution from the
momentum resolution, and the measured momentum spread of the fragment. Since
the halo neutron in 11Be is so loosely bound, it means that it would not contribute
much Fermi momentum to the system. Consequently it might be more correct to use
A = 10 for the incident 11Be. The extracted 00 parameter from the use of both of
these assumptions are shown.

 

 

[ Fragment 00(A = 11) 00(A = 10) Resolution 0“,,
8He 43.1:t1.4 50.0i1.6 34.6 75.1:t1.7
6He 64.5:l:2.8 68.4:l:3.0 22.5 ll4.0:i:4.8
9Li 57.021253 76.5:t7.1 24.8 80.4:l:6.7

 

 

 

 

 

 

 

 

Table 4.2: Goldhaber 00 parameters extracted from incident 12Be projectile. All val—
ues tabulated are in units of MeV/c and are expressed in terms of standard deviation
0. Shown tabulated here are the extracted 00, the momentum resolution, and the
measured momentum spread of the fragment.

 

 

Fragment [ 00 Resolution 0”,,
8H8 52.0:t13.4 34.5 94.8:l:21.3
6H8 63.1:l:7.5 33.0 116.3:f:13.2
9Li 66.5:t9.2 27.9 107.4:t13.9

 

 

 

 

 

 

 

61

 

 

 

 

 

 

 

250° ? - magmas]
'2'; : ° 9Be('2Be,(’I-le+n) j
S 2000 T 0 Resolution 1
0 > ‘ 6’0 4
2 i H .° 1. 1‘2" ‘
o 1500 - : - . °° —
F‘ , . 0. ° 4
if ’ z“ . : <5 4
3 1000 ; :' " .°° ‘3 I-
G ' o' $ °°° ‘3:
a [ '0. 0 3° 0 .
U 500 I - '. ., . i
+ K 0’ ‘3? Z i
r . .6 fl
0 T 1 JP 1 w 4L— 1_1 Re: i +

500 1000 1500 2000 2500

Total Momentum [MeV/c]

Figure 4.1: 6He Momentum distribution measured in neutron coincidence. The dis-
tribution from incident ”Be is shifted by +500 MeV/c and is normalized to the
same area as (“Be,6He+n) spectrum for the purpose of comparison. Also shown is
a distribution of the total momentum resolution calculated at mid-target energy of
approximately 28 MeV/u, corresponding to a total momentum of 1370 MeV/c. The
curve has been shifted down for display purposes.

 

 

 

 

 

 

120 BMW
[ ’ 9Be(”Be,8l-Ie+n) ;
E 100 f ° °Be(”Be,8He+n) i
g : Resolution ‘
80 — a
2 , H , .
o P o .
m . .
s 60 i , i
3. . . - . . ‘
{g 40: 0'. o '-
a + . ° 4
U 20 L j . ° 1
: k . . OO O I]

O L . 9 i . r .0 1 . . . 9 1 r 1 r .
1000 1500 2000 2500 3000

Total Momentum [MeV/c]

Figure 4.2: 8He Momentum distribution measured in neutron coincidence. The dis-
tribution from incident 12Be is shifted by +500 MeV/c and is normalized to the same
area as (”Be,8He+n) spectrum for the purpose of comparison. Also shown is a dis-
tribution of the total momentum resolution calculated at mid-target energy of 27.7
MeV/u, corresponding to a total momentum of 1840 MeV/c. This curve has been
shifted down for display purposes.

62

 

a r -f- , ......... f ........
1000 L . gBe(”Be,9Li+n) —Resolution 2,

E f o gBe(nBe,9Li+n) """ Theory :

> _ .

g 800 r n '3: .

. b: 0% 4

o ’ a P

~ 600 — : : J

LI >- .0: ; 00 0“?

8. ' i

t... t

m

H

C:

:3

O

U

 

 

 

 

 

1500 2000 2500 3000
Total Momentum [MeV/c]

Figure 4.3: 9Li Momentum distribution measured in neutron coincidence. The distri-
bution from incident ”Be is shifted by +500 MeV/c and is normalized to the same
area as (“Be,9Li+n) spectrum for the purpose of comparison. A calculated momen-
tum distribution of 9Li using single neutron knock-out from a 11Be and then rescaled
by 9/ 10 is shown (dashed line). Also shown is a distribution of the total momentum
resolution calculated at mid-target energy of 27 .7 MeV/u, corresponding to a total
momentum of 2060 MeV/c. This curve has been shifted down for display purposes.
will simplify the calculation of the final-state interactions.

In addition to the fragment momentum distribution measurement, an attempt was
made to measure the fragmentation cross sections. The results are summarized in
Table 4.3. This measurement should be only taken as an order—of-magnitude estimate.
While we do not attempt to make a theoretical prediction for the production cross
section for ”He, it is possible to make an estimate for the 10Li cross section from
11Be breakup using the technique proposed by [42]. Using this theory, which uses an
eikonal model to calculate the cross section of the breakup, a total single-particle cross
section of 15.6 mb was obtained (stripping: 12.0 mb, diffraction dissociation: 3.6 mb).

Using spectroscopic factors obtained from [43] (Table, 4.4) 0(“Be,9Li+n(1sl/2))=25

mb was obtained. The estimated observed cross section is on the order of 6 mb.

63

 

 

 

 

 

‘T [T ‘ T T TTTTTTI T TTTj—TTTI Tfi TT'T]
0
IZO"
+ .
noo- [ . ]
A wa3— [ J
{J 80? ,I’ V g 1 1
> I
I
160’ I, A
b [I o "
I
40- P:
g d,
O
20' O
1 11111111 1 11111111 1 lllllJiL L 111111:
I '0 IOO IOOO

Figure 4.4: The systematics of 00 as a function of projectile bombarding energy [45].
It is clear that there is a trend of increasing 00 with increasing beam energy in the
region between 10 to 100 MeV per nucleon. The reactions corresponding to these

data points can be found in [45].

Table 4.3: Production cross sections of 7'9He, and ”Li

 

[Fragment [[ 12Be (mb) I 11Be (mb) [ 1"Be (mb) [

 

 

 

 

 

7He 28.2 32.2 10.5
9He 1.1 0.35 - -
loLi 5.0 6.2 - -

 

 

 

 

Table 4.4: Spectroscopic Factor for (”Be,”Be) and (”Be,9Li) obtained from [43]

 

 

 

 

 

 

Reaction State Spectrosc0pic Factor [
(”Be,”Be) 31/2 0.74

p3/2 1.27

(is/2 0.18
(”Be,9Li) p3/2 2.29

191/2 0.35

 

 

 

 

64

«QRQI-nu-m‘fi

4.2 Model for Calculation of Final-State Interac-
tion

The potential scattering model calculates the interactions between the neutron and
the core fragment in the unbound systems. This model is similar to those used in [28,
44]. In essence, the calculation assumes that a reaction mechanism described in the
Goldhaber model applies in the case at hand, thus allowing the sudden approximation
to be made. As such, the neutron wave function after the breakup reaction is taken to
be the same as that of the initial nucleus. The neutron wave functions are calculated

using a single-particle Woods-Saxon potential:

_ V0
_ 1+ exp[r—;—’9-]’

 

V(7") (4.2)

with ro=1.25 fm and a = 0.7 fm. For each final-state interaction calculation, the
potential well depth is adjusted to reproduce the known binding energy of the initial
state, and the momentum and energy distributions of the final state are calculated
based on some presumed scattering length a, (l = 0) or decay energy (I > 0). The
spin-orbit interaction is included in the effective potential V0. It is reasonable to use a
purely real potential in this model because the states probed here are predominantly
single-particle states. In probing the the core + n unbound systems, the first excited
states of the core are much higher compared to the unbound states. As such, there will
not be much coupling between the low-lying states of the unbound systems studied
here with the excited states of the core, which allows it to be treated as elastic
scattering between the two bodies. The lowest excited states of the core in the
systems analyzed in this work are shown in Table 4.5.

The neutron wave function of the initial state is then expanded with the final-state
continuum eigenstates, which for an unbound system asymptotically must become the

free-particle solution for angular momentum. The bound initial state is characterized

65

Table 4.5: The lowest known excited energy for 6”He and 9Li taken from [51].

 

[ IsotOpe I] First Excited State (MeV) ]

 

 

 

 

 

 

 

 

6H8 1.797 i 0.025
8H8 2.8 :f: 0.4
9Li 2.691 2]: 0.005
as:
,.
were = ”:5 ) no.m.<6,¢>, (4.3)

and the continuum eigenstates in the core + n unbound nucleus have the eigenfunc-

tions:
at (r)

 

mm = Y11.m1 (6’, <15), (44)

where k denotes the wave vector in the lab frame, lo,mo and ll,m1 denote the initial
and final angular momentum states. The amount of overlap between these two wave

functions becomes:

awe) = al.,z.6m.,m. [0 mm uf.<r>dr. (4.5)

In the present model, the recoil effects from the breakup have been neglected.
However, the presence of recoil terms could induce transitions to states with angular
momenta other than [1,m1. This effect may be important for the 11Be breakup.

The continuum wave function as obtained from solving the Schrodinger equation

is asymptotically the spherical free-particle solution for angular momentum:

A00?) = $606 — k) Home, (4.6)

and the momentum distribution is given simply as:

W?) = — awe) Home) . (4.7)

66

 

After integrating over the delta function and summing over final states and averaging,

the expression simplifies to:

(4.8)

 

4.3 Parameterization of the Continuum States

An important quantity in the parameterization of the continuum states is the phase
shift 6,. In terms of phase shift 61, the solution of the Schrodinger equation far away

from the potential with an azimuthally symmetric V(r) which vanishes as r -+ 00 is
R10") 2 azk [cos(6,)j1(kr) — sin(61)nl(kr)] , (4.9)

where R,(r) is the radial wave function, k 2 [27:15 , ,u is the reduced mass of the two
body system, and j,(kr) and nl(kr) are the regular and irregular spherical Bessel
functions.

In practice, R,(r) is a numerical solution to the Schréidinger equation. By com-
paring R,(r) far away from the potential with the asymptotic form of the continuum
wave function, one can directly obtain the phase shift (Equation 4.9). For I > 0
resonances, the energy of resonance is specified, and V0 of the Woods-Saxon potential
is adjusted while keeping a and r0 fixed so that the phase shift changes from 7r/2 to
—7r / 2. This is a reasonable to vary simply one parameter because the detailed shape
of the potential is not important for low-energy neutron scattering.

At zero energy and for l = 0 (s-wave), it is convenient to introduce a quantity

scattering length as. Using effective range theory, a, can be expressed as
kcotéo = —i + lroki’ (+0 (1:4)) (4 10)
a, 2 ’ °
and for k —> 0, the scattering length a, can be expressed as

(4.11)

Since the scattering length can be related to the ratio between the phase shift and the
wave vector, the potential can simply be adjusted to reproduce the desired s-wave
scattering length. In the presence of attractive potentials, the scattering length is
positive, and a numerically negative scattering length a, represents unbound states.
The equivalent energy of the virtual state can be expressed as E = h2/2ma3. This is
a very useful result because it implies that the energy of bound and unbound states
can be determined by performing low-energy scattering experiments to determine the
scattering length. The ability to deduce the energies of the bound and unbound states
without needing to know the details of the potential is an important feature of this

technique.

4.4 Computing Energy Distributions

The computer code which generated the energy distributions used in this analysis was
based on programs F811 and BDELTA written by P.G. Hansen. In order to compute
an energy distribution as a result of the final-state interactions, a few input parameters
are needed. First, one needs to specify the size of fragment that the neutron is being
scattered from, and one also must choose the resonance energy (I > O) or scattering
length a, (l = 0). In addition, the effective binding energy of the neutrons in the
initial states is needed. The values used in this analysis are summarized in Table 4.6,
and the wave functions of the corresponding effective binding energies are shown in
Figures 4.5 and 4.6. These initial states are then expanded into the eigenstates of the
final unbound states to obtain the energy distributions.

Some examples of the expansion of the bound initial states with the continuum
eigenstates are shown in Figures 4.7, 4.8, 4.9, and 4.10. The model used to com-
pute the final-state interaction is dependent on both the initial and the final states,

and thus, different initial states can influence the calculated final-state interactions.

68

Table 4.6: Effective binding energies of neutrons in ”'ll'loBe nucleus.

 

 

 

 

 

 

 

 

 

 

 

Nucleus State Effective Binding Wood Saxon Depth
‘ Energy (MeV) (MeV)
TrBe 131/2 3.169 64.369
(Sn=3.169 MeV) 0121/2 3.489 38.514
Dds/2 4.95 74.737
I[Be 1.91/2 0.503 55.962
(Sn=0.503 MeV) 0193/2 6.6 47.646
”Be 131/2 8.49 87.605
(Sn=6.812 MeV) Ops/2 6.81 50.916

()5....,....,.,..,....,....,....

 

Amplitude [fm‘l/z]

 

 

 

ML 1 L l L l l l l L J L I l l J 1 441 1 1 l l l l 1 l .l

0 5 10 15 20 25 30
fm

 

Figure 4.5: Radial wave function X00“) of the s-state in 11”Be. The long tail in the
neutron wave function of 11Be is a result of the low binding energy.

69

 

O
0‘1
l
S
or:
(D
8
1

-1/2
I

Amplitude [fm

 

 

 

0 5 10 15
fm

Figure 4.6: Radial wave function X00) of the p-state in 11”Be.

In the case of the 7He energy distribution, the p—neutrons from the 12Be are less
tightly bound than those from llBe (binding energy of 3.489 MeV versus 6.6 MeV).
A smaller binding energy results in a slightly more diffuse neutron wave function,
which enhances the contributiion to lower energy with a initial ”Be nucleus (Figure
4.7). In the case of the ”Li energy distribution, such an effect is much more pro-
nounced (Figures 4.8 and 4.9), because the diffuse wave function of the 11Be neutron
(Figure 4.5), has a significant contribution to the region of low decay energy. The

energy distribution for a 9He calculated from an incident 11Be is shown in Figure 4.10.

70

 

 

 

 

 

[IIVY'TTTMITV‘YTITTTT'MTTTITTTTTITYTTj
———12
'-‘ 2 — Be
T2 " 11
g : ........ - Be
fl 1-
hi
>. i
H
"-q __
(I)
g: ..
o .
Q 1 — a -
>5 - 1 «
OD . '1 ]
H ‘.
Q) . ‘- 4
G » 1
Ln . 1
O 7 lllllllLlLALLIIAIIJLILIIAIllllLHJIxfi
0 0.5 l 1.5 2 2.5 3 3.5 4

Decay Energy [MeV]

Figure 4.7: Energy Distribution of 6He+n system at E1: 450 keV calculated using
the potential scattering model using initial 11’”Be nucleus.

 

 

 

 

 

 

5'
E

:4 'l

.3: ‘
m
G
d.)
O
>5

9.? a
D
‘3
LL]

1

O 1 44 l 1 1 1 l 1 1 l 1 1 1 1 LL 1
0 0.2 0.4 0.6 0.8 1

Decay Energy

Figure 4.8: Energy Distribution of 9Li+n expanded using a ”Be s—state and the

unbound states of 9Li. Shown are the energy distributions corresponding to various
Scattering lengths.

71

 

 

 

 

 

5 _ 1 m l r r l v T r r r 1

P 40 fm 3

9 4 ‘
a) 3 -30

z ~

2. 3 5 1

.‘r 1

s? 1 ‘ -2° :

m ’ \ _‘

g I .

a) 5 :

E. 2 rm 1

3° [.110 \ 2

a) 5 ‘-.j\\ 7

G E K. j

m l [f 1‘ —1

L ‘.. \_\‘ :

[:— 0 ~\ \ -:‘-\\‘ _

0 1 1 1 1 1 1 1 1 L 1 417 17 1‘7- 1‘77‘1‘ ‘ 7" ‘

0 0.2 0.4 0.6 0.8 l

Decay Energy [MeV]

Figure 4.9: Energy Distribution of 9Li+n expanded using a llBe s-state and the
unbound states of 9Li. Shown are the energy distributions corresponding to various
scattering lengths.

 

 

 

 

5 PM 1 r I I I r T I r ..

i 40 fm E

g 4 L :1
g -30 3
:2. 3 i ' 3
{7 i

.1? z, \ -2o :
m 3. J
a 4
d.) i .
DD E"-10 -1
H t: ,\.\ _
o 1 N j
1: 3 ‘\~ :
m 1 :- Q‘ _1
O 1 1 1 1 . 1 1 1 1 . L‘ 1‘ T‘ETTT-“777 "3

O 0.2 0.4 0.6 0.8 1

Decay Energy [MeV]

Figure 4.10: Energy Distribution of 8He+n expanded using a llBe s-state and the
unbound states of 8He. Shown are the energy distributions corresponding to various
scattering lengths.

72

 

Chapter 5

6He+n

5.1 Introduction

The p—resonance in the unbound 7He was first observed by Stokes and Young in 1967
by a means of a 7Li(t,‘°’He)7He direct reaction using a 22-MeV triton beam [46] on a
0.4 mg/cm2 7Li target, and the resonance energy (peak position) was measured to
be E, = 420 :1: 60 keV with I‘ = 170 :1: 40 keV. The current literature value for the
p—resonance for 7He of E, = 440 :1: 30 keV and P = 160 :1: 30 keV was reported in 1969
[10] by the same authors through a repeat of their original experiment with the same
beam energy, but with a thinner target (100 11g/cm2 of 7Li). The present work will

perform three separate measurements on the 7He using final-state interactions.

5.2 Results

Figure 5.1 shows the velocity difference spectra scaled to number of incoming 10*11'12Be

beams particles. The asymmetry of the two peaks is caused by acceptance effects:
neutrons moving faster than the 6He fragments are more likely to be found within

5 degrees of the fragment than the slower neutrons. The two important features of

73

the spectra are (1) the 11Be spectrum has a greater intensity near the zero velocity
difference region than the ”Be spectrum and (2) the low intensity of the 6He + n
spectrum with an incident ”Be nucleus. The first feature can be attributed to the
low binding energy of the s-state of the 11Be neutron, and these slow (halo) neutrons
correspond to zero velocity difference. The second feature illustrates that the 6He is
formed mainly by a-particle knockout, which is not accompanied by fast neutrons.

The experimental data is fitted with simulated velocity distributions generated
using energy distributions computed from the potential scattering model (Chapter
4). The data is fitted using techniques already described in Section 3.6. Figures
5.2, 5.3, and 5.4 are 6He+n velocity difference spectra with no correction for neutron
detection efficiency. Each of the fits shown represents the lowest x2 fit. The energy
for the p—state was found to be 448 :1: 23, 452 :1: 19, and 422 :1: 20 MeV for ”’ll'loBe
initial nucleus, respectively. The uncertainty is taken as the range in the resonance
where Ax2 < 4, corresponding to 95% confidence level. Using the average of these
three values and the standard deviation as an error, a resonance of 440 :1: 16 keV
is obtained. The results presented in this analysis are consistent with the current
literature value of E, = 440 :1: 30 keV measured by [10].

The potential scattering model does not have a separate parameter specifying the
width of a resonance. The selection of a resonance energy specifies the set of contin-
uum eigenfunctions used to expand the bound initial states. The energy distribution
from the expansion of the ”*“Be can be found in Figure 4.7. The width I‘ as mea-
sured by the FWHM of the energy distributions from the initial 11Be (”Be) nucleus
is 273 MeV (252 MeV). They are not in agreement with the previous literature value
of I‘ = 160 :t 30 MeV [10]. However, the data shown here shows a good fit using a
broader energy distribution.

As a demonstration for the sensitivity of the method, Figures 5.5, and 5.6 show the

74

 

p—A
N
l
.]
_
_.
-
_.
_.
..
d
..
d
_
..
..
_
..
..
..
_,
fi
.1]
..

p—s
O
I

l

1- ’ i \ .1
: off * 5*; f f @166
$9,.‘6 {- i O-. -

i— \
i
O 413191-1-li1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1

-3 -2 -1 0 1 2 3
Vf-Vn [cm/n3]

 

 

Detection Probability [10'7 per 0.2 cm/ns]
O\
,1
31..

Figure 5.1: Velocity difference spectra of 6He+n scaled to the number of incoming
beam particles. The scale has not been corrected for geometrical acceptance and
detector efficiency. The uncertainties are purely statistical. Depending on the initial
nucleus, the velocity difference spectrum can have a very different appearance even
though it is the same resonance being probed. In the case of the incident 11Be, the
enhancement near zero relative velocity comes from the loosely-bound neutrons in
the s-state, which do not interact in a 6He+n system.

75

 

 

350 r T T T T T T Y r I T Y T T T T

 

 

. . . , . . . r44. .
. Data 9131«.(”Be,‘5116+n)x ;
300 ’ — Event-Mix j
" - p-statc ]
""" d-state 1
2 250 Best Fit 1 1 j
E If \ I
o! 200 I \\ ‘ j
g I \ [I 1 j
a 150 I \ I l '2‘
:1 I \ 1 .
Lo) 1 I ‘ I
100 I \ I \ j
I 1.— f’ 1 «
I ,/ \ \ \ \ .
50 / / / \1 i
J/ ’ I 9 «L

- 7 \
O . .
-3 -2 -l 0 l 2 3

Vf--Vn [cm/n5]

 

Figure 5.2: Velocity difference spectrum of the 9Be(”Be,6He+n)X system. Shown are
the experimental data with statistical error bars, the computer simulation of a p-wave
resonance at 450 keV, a d-wave resonance with 5 MeV of effective binding energy,
and an event-mixed background. The best fit consists of: event-mixed background:
36%, p-wave: 62%, and d-wave: 2%.

 

1800vvvvurvvvrr+nr....,....,,...

’ 9 ll 6 f

> Data Be( Be, He+n)X 1

15m _ ..... S'state _

_ --p-statc *

_ ' —Event-Mix J
1200 BestFit

Counts/0.2 cm/ns

 

 

 

 

V f-Vn [cm/ns]

Figure 5.3: Velocity difference spectrum of the 9Be(“Be,6He+n)X system. Shown
are the experimental data with statistical error bars, the computer simulation of a
p-wave resonance at 450 keV, a s-wave (a,=0 frn) scattering, and an event-mixed
background. The best fit consists of: the background: 39%, p-wave: 44%, and 3-
wave: 17%. The contribution of the non-interacting scattering of the loosely-bound
neutron in the 11Be describes the essential difference between the 11Be and 1"’Be data.

76

 

V T T T Y I 1 I T T Y T T T I Y V V T
I I I l

 

 

 

 

 

. , . . . .
I 9 10 6 .
[ ' Data Be( Be, He+n)X .
250 _ '— Event-Mix -
: - — p-state 1
~ Best Fit
m ' I
E 200 .7 I I
o _ ‘ I‘ 1
0! , I \ 1
O 150 ' I 1 l ‘
E r , 1 1 1
c: L , 1 , 1
:1 . \ \
O I I _.
U 100 L I \ I l
I I ‘ / ‘
50 '— / —_\_ ‘ \ .1
. / - \ 1
> / ' \\\
, (/ 7 7‘; Q .
0 .‘1'1’111111m1111111111171‘fi‘_
-3 -2 -l 0 l 2 3
Vf—Vn [cm/us]

Figure 5.4: Velocity difference spectrum of the 9Be(”Be,6He+n)X system. Shown
are the experimental data with statistical error bars, the computer simulation of a
p-wave resonance at 420 keV and an event-mixed background. The best fit consists
of: the background: 26%, and p-wave: 74%

best fit using a p-state resonance energy in the range between 400 and 500 keV. The
region covered by the 100-keV band encompasses the range of the statistical errors
limited by the counting in the experiment. However the use of a x2 minimization
suggests (Figure 5.7) a much better precision in determination of the energy, on the
order of 20 keV.

The background generated using an event-mixing technique accounts for approx-
imately 40% of the total intensity of the velocity-difference distributions for 11'”Be
projectiles, and 26% for the ”Be. Even though the 12Be can be fitted with only a
p-resonance on top of the event-mixed background, the fit is slightly improved by in-
troducing a d-wave resonance with effective binding energy of 5 MeV (See Table 4.6).
For the incident 11Be nucleus, the fit also includes an s-wave component in addition

to the event-mixed background. The inclusion of an s-wave scattering at a, = 0 fm

for the 11Be initial state was required to describe the data, and can be interpreted as

77

350 » T T V T T V V V Y 1 v T r v I v v 7 v ‘ 1 r v r I v 1 1 r 1
_ 9Be(lZBe,6He+n)X 3
300 j .1

 

250 :
200 :

150 :

Counts/0.2 cm/ns

100:

so:

 

 

 

O . i A A l . . A 1 l 1 i i A 1 4 4 LL 1 i 1 r L l L A A i
-3 -2 -1 O l 2 3
V f—Vn [cm/ns]

Figure 5.5: Error estimate of p-resonance in the 9Be(”Be,6He+n)X. The shaded
region represents the theoretical fits for the region 400 < E, < 500 keV, and the solid
line represents the E, = 450 keV fit, which is the minimum x2 fit.

 

18% Y T T T I T Y T T I V Y Y Y T ti T T I T I I' T I V T Y T
p

I—i h‘
N LII
8 8

Counts/0.2 cm/ns
\O
8

 

 

 

 

V f-Vn [cm/n5]

Figure 5.6: Error estimate of p-resonance in the 9Be(11Be,6He+n)X. The shaded
region represents the theoretical fits for the regions between 400 < E, < 500 keV,
and the solid line represents the E, = 450 keV fit, which is the minimum x2 fit.

78

 

\]

T I I I I I I I I I I I I

 

2
Reduced—x
h
"'I‘"'I""I“"I““IT“'I"'

Llllll_llllllllllllllIllJJlllllllll

 

 

 

O l l l L l I l J l l l l l l l l

350 370 390 410 430 450 470 490 510
Decay Energy [MeV]

Figure 5.7: Reduced-x2 of fits to 9Be(”‘l1’10Be,6He+n)X data as a function of the
decay energy of the p-state. For the 12“Be reaction, the minimum X2 uses three
separate components in the fit. The minimization procedure uses the 22 data points
between -2.1 cm/ns and 2.1 cm/ns. The four free parameters used in the fitting
are the 1) total intensity (taken to be the same as the total number of events), 2)
systematic shift in the computer-simulated relative velocity spectra (Section 3.6),
and 3) the relative intensities amongst three different components requires two free
parameters for fitting. This yields 18 degrees of freedom. In the case of 10Be, there
is a total of 19 degrees of freedom because there is only a two-component fit in the
spectrum. The curves shown correspond to a second-order fit for the reduced-x2, and
the dashed lines represent the reduced-x2 value that corresponds to a 95% confidence
level. Using this as a guide, the typical uncertainty is on the order of 20 keV.

79

Table 5.1: Approximate occupation of the available neutron orbitals in the reaction
9Be(‘d‘Z,7He)X.

 

I Projectile 0d5/2 181/2 0p1/2 0193/2
12Be 1.0 0.4 0.4 2.0
11Be 0.2 0.8 0 2.0

 

 

 

 

 

 

 

 

 

 

the non-interacting s-state neutrons from the 11Be detected together with the 6He.

The need for a non-interacting s-wave component to describe the 7He data with
the 11Be projectile seems very apparent; since the 7He exists as a p3/2-resonance, an
interaction in the l = 0 channel is not expected. Using the observed spectrosc0pic
factors of 11Be [9, 54] as a guide, we can estimate the occupation of the available
neutron orbitals for 9Be("‘Z,7He)X (Table 5.1). Approximately 28% of the available
neutron orbitals are in the non-interacting s-state. This appears to explain why
there is so much intensity in the region of zero relative velocity. However, there is
one problem with this reasoning: 12Be also contains a significant s-component in the
initial state.

A simple shell-model predicts that 12Be is a closed shell, and therefore there would
be no occupancy in the s-state. However, recent data by Navin et al. [55] observed
direct evidence for the breakdown in the shell closure in 12Be. For a single neutron-
removal from 12Be, a spectroscopic factor of 0.53 :l: 0.08 was obtained for the 131/2
state and 0.45:t0.07 for the 0p1 /2 [55]. An estimate of the occupation of the available
neutron orbitals based on these spectroscopic factors is also shown in Table 5.1.
Approximately 10% of the neutrons are in the s-state, which is about one-third as
many as the reaction in 11Be. One might ask why there was no need for a separate
s-state fit in the fitting of the 12Be data. The reason is that the velocity difference
corresponding to a scattering at a, = 0 fm from a 12Be projectile has the same shape

as the event-mixed background. This is not true in the case for 11Be, where the

80

l9

Ill

in

relative velocity distribution for the s—wave is narrower than the event-mixed spectra
(Figure 5.3), which caused by the fact that the s—state neutron of the 11Be is much
more loosely bound than the 12Be. Part of this contribution is presumably included
in the event-mixed background. Thus, the enhancement at zero relative velocity for
initial 11Be is a result of low binding of the neutron in the s-state, not merely because

of the existence of the s-state.

81

Chapter 6
9Li+n

6.1 Introduction

In 1985, Tanihata et al. [4] first reported that 11Li possesses an unexpectedly large
interaction cross section. This large cross section is due to the fact that 11Li is a
three-body system consisting of a 9Li core and two loosely-bound neutrons. Even
more intriguing is the fact that 10Li is an unbound system, so the stability of the 11Li
is partly due to the neutron-neutron pairing force between the two halo neutrons.
Thus, understanding the 10Li nucleus is critical towards the understanding of the
11Li three-body problem, as it is essential to understand the interaction between any
binary subsystems. The neutron-neutron interaction is well known, so considerable
effort has been put forth in studying the 10Li.

An issue of considerable debate is whether the ground state of 10Li is a p—state, as
predicted by the simple shell model, or a low-lying s-state. As mentioned earlier, in
Section 1.4, there is evidence suggesting that an intruder s-state is the 10Li ground
state. Since the first time 10Li was observed, by Wilcox et al. [49] in 1975, there has
been a number of interesting experimental results with regard to this nucleus. A good

summary of the experimental results on 10Li can be found in [12, 28]. There are a

82

 

 

 

number of observations of peaks which were interpreted as p—state resonances, most
recently by Caggiano et al. [12].

The difficulty with a virtual state having 1 =0 and essentially single-particle strength
is that it does not exhibit a resonance-like structure. In the energy spectra of the final
state, it will manifest itself by a rapid rise in cross section just above the threshold
followed by a slow decay towards higher energies. The resulting line shape is asym-
metric with ”energy” and ”width” roughly comparable (See Figures 4.8, 4.9). There
two previous experimental results [27, 28] (Section 1.4) both observed evidence for an
interaction in the [=0 channel with scattering length a, < —20 fm via a central peak
in the region of zero relative velocity. In addition, Zinser et al. [44] from GSI reported
an experimental observation of the l = 0 interaction using a breakup of 11Be at 280
MeV/ u. The observed neutron angular distribution suggested an s-ground state with
scattering length a, < -20 fm from an analysis that averaged over an estimated recoil
contribution. The same effect was seen in 11Li; the group argued that since the 11Li
is very loosely bound, the stripping of one of these neutrons would not likely excite
the 9Li core, and hence, the discovered s-state therefore must be a ground state [44]
(Figure 6.1). A subsequent experiment confirms this assertion, demonstrating that
only 7.5:t2.5% of 9Li formed from proton-stripping of 11Be are in the 2.7 MeV excited
state [53]. The objective of the present work is to confirm the low-lying s-state in
10Li by using 12“Be as the initial projectiles and to pin down the angular momentum

assignment making use of our knowledge of the structure of 12“Be.

6.2 Results

The velocity difference distribution between the detected neutrons and the 9Li frag-
ment are analyzed in the same manner as the 7He. Figure 6.2, shows the velocity

difference spectra scaled to the incident 10'11’128e projectiles. The 10Be projectile can-

83

 

 

llBe+'ZC—-)n-1-”‘Z+X

 

 

 

0.01 l l I l _L
o 10 20 30 4o 50 60
pr (MeV/c)

Figure 6.1: Data from Zinser et al. [44]. Shown are the radial momentum distributions
of the select fragments detected with neutron coincidence from an incident 11Be. The
most important feature of this data is the narrow momentum distribution of the
observed 9Li, compare to that of 7Li. The solid curves through the lithium data are
momentum distributions calculated using a potential scattering model similar to the
one used in this work. The curve through the 7Li data is a distribution corresponding
to an s-wave scattering with a, = 0 fm, while the curve through the 9Li data is
calculated using a, = —20 fm. In both cases, there is a component of a p—wave
resonance at 0.42 MeV.

84

not break up into 9Li and a fast neutron, so the absence of counts in this channel
shows that discrimination against neutrons from the target is satisfactory. The data
from the 11Be beam are clearly narrower than those from the 12Be, which can be ex-
plained from the fact that 11Be neutron is very loosely bound. As discussed in Section
4.4, the diffuse tail in the neutron wave function enhances the low energy region of
the energy distribution, making the energy distribution for an s-state narrower for an
initial 11Be versus that of a l2Be projectile. That difference in the energy distributions
also can be observed in the narrowing of the velocity difference distributions (Figures
3.4 and 3.5). Thus, like the 6He+n data present in Chapter 5, we see that the initial
states can effect the observed final-state interaction in 9Li+n data.

The results from the 9Be(”Be,9Li+n)X reaction are shown in Figure 6.3. The
data is fitted using four different components: 3, p, and d—waves, and event-mixed
background. Both the introduction of the p and (1 components improves the fit of the
data. A p—wave resonance at approximately 0.5 MeV has been observed by [12, 48],
and is included in this analysis. Because of the low relative intensity with the p-state
(approximately 7%), the fit is rather insensitive to the energy of this resonance. The
most pronounced feature in the data is a central peak near zero relative velocity.
This is also the essential argument why this peak represents an interaction in the
s-state. Energy distributions corresponding to interactions in the s-state with a l2Be
projectile can be found in Figure 4.8. A strong s-state interaction corresponds to
a narrower energy distribution and thus would result in a narrow, central peak in
the relative velocity distribution. Figure 6.4 shows the data compared to fits using
different scattering lengths as, and Figure 6.5 shows the reduced-x2 as a function of
scattering length. Using an analysis where Ax2 < 4, corresponding to 95% confidence
level, an s-wave interaction of at least a, < —10 fm is deduced.

The data from the 9Be(“Be,9Li+n)X reaction shown in Figure 6.6. The analysis

85

 

p—a
O

I I I I I I I T I I I I I I I I I I If] I I I I I I I I I

9Be(10’11’12Be,9Li+n)X 0 12Be
- 11
Be

_ — 10 .
Be

00

I I
3

I

“ ‘ é
’ “I
P m“ '1' 1;. i- .w‘?” l
O W*l-11*1 1*1*1-1-1-l-1-1_1-.S&._£.3&
-3 -2 -1 O 1 2 3
Vf-Vn [cm/n8]

Detection Probability [10'7 per 0.2 cm/ns]

 

 

Figure 6.2: Velocity difference spectra of 9Li+n with three different initial nuclei
scaled to the number incident beam particles. Because of the loosely-bound s-state
of the 11Be, the peak near zero velocity is narrower than that from l2Be. Note that
the 10Be projectile cannot break up into 9Li and a fast neutron, so the absence of
counts in this channel shows that the discrimination against neutrons from the target
is satisfactory.

86

 

 

 

 

 

 

1 .rj....,....,....,....Tr...
9 12 9 -
200 [ Be( Be, L1+n)X 0 Data _
L """ s-wave ‘
w """"" p-wave
:
E d-wave
o 150 7 ' —Event-Mix ‘
0! Best Fit
3
g 100 '- l” \s -‘
o » , " .
U " \‘ J
I. ._\|. ‘
50 J”/ “\ I d f
// i, “ \ I i.
' I, ‘ \\ .1 i
. .. ,
O I."r“:/ "I'd-A, J . t ,‘..‘"=-.._ -
~3 -2 -l O l 2 3 ‘1
a
V-V [cm/n8]
f n ].

 

Figure 6.3: Velocity difference spectrum of the 9Be(”Be,9Li+n)X system. Shown
are the experimental data with statistical error bars, the computer simulation of a
p-wave resonance at 538 keV, a a,=-25 fm s-wave scattering, a d-wave scattering with
an effective binding energy of 5 MeV, and an event-mixed background. The best fit
consists of: the background: 48%, p-wave: 7%, d-wave: 6%, and s-wave (a,=-25 fm):
39%.

 

LT—T‘

I T T T V 1 T T T T I I T T I I V I T T I V V T T

200[—9Be(12Be,9Li+n)X . Data _‘
150 h

100'

Counts/0.2 cm/ns

50’

 

 

 

 

Vf-Vn [cm/n3]

Figure 6.4: Velocity difference spectrum for the reaction 9Be(”Be,9Li+n)X data with
best-fits using scattering lengths a820, -5, and -20 fm.

87

 

_ _

I I If I

11Be O----.___.-__-._--./

Reduced-x2
N

I

T j

 

 

 

 

-50 -40 -30 -20 -10 0
Scattering Length [fm]

Figure 6.5: Reduced-x2 of fits to 9Be(”*“Be,9Li+n)X data as a function of the scat-
tering length a, of the s-state. For an incident ”Be nucleus, the minimum X2 analysis
uses four separate components in the fit. The minimization procedure uses the 22
data points between -2.1 cm/ns and 2.1 cm / ns. The five free parameters used in the
fitting are the 1) total intensity (taken to be the same as the total number of events),
2) systematic shift in the computer-simulated relative velocity spectra (Section 3.6),
and 3) relative intensities amongst four different components requires three free pa-
rameters for fitting. This yields 17 degrees of freedom. In the case of 11Be, there is
a. total of 18 degrees of freedom because there is only a three-component fit in the
Spectrum. The dashed lines represent the reduced-X2 value that corresponds to a 95%
confidence level.

88

fl

Table 6.1: Approximate occupation of the available neutron orbitals in the reaction
9Be(AZ,”Li)X. The available neutron orbitals are the same for 9Be("“Z,9He)X since
the two unbound systems have the same number of neutrons.

 

 

 

Projectile Dds/2 181/2 0p1 )2 ]
18O 1.4 0.4 2.0
”Be 1.0 0.4 0.4
11Be 0.2 0.8 0

 

 

 

 

 

 

 

uses only three separate components: 3 and p—waves, and event-mixed background,
and the procedure is completely analogous to the analysis of ”Be projectile. Just
as before, a p—wave improves the fit, and the low contribution from the p—state (ap-
proximately 5%) makes it rather insensitive to the energy of the p resonance. Using
X2 as a guide, we see an s—state interaction corresponding to a scattering length of
a, < —20 fm. Figure 6.7 shows a comparison of using different scattering lengths.

Table 6.1 shows the approximate occupation of the available neutron orbitals in
the reaction 9Be("‘Z,”Li)X. We do not expect as much p—state in fitting the 11Be data
since the valence neutron is predominantly in the sd—shell. A greater contribution in
the p—state is expected from the ”Be projectile. Both of these effects are observed
in this experiment. The 18O projectile contains the highest occupancy in the p-state.
As expected, data from [28] (Figure 1.6) show the largest p—state contribution.

The data from both the ”“Be projectiles show evidence of a low-lying s-state for
the unbound ”Li. This result is consistent with findings by [27, 28, 44]. A comparison
of the results from ”Li and 7He data allows some important conclusions about the
final-state interaction technique. If one suspects that the unbound state of core+n
system is mostly a p-state, such as the 7He case, one might wish to start from an
initial state that also contains mostly p neutrons, such as the case of 10’”Be. The
7He data would suggest that using an initial state which has a loosely bound s—state

such as llBe may not be the best approach, since the s-state obscures the observed

89

 

1 6m ‘ T r T l V T l T I T T fl f7 T T I’ I I V T y I f T r y

 

 

 

1400 9Be(”Be,9Li+n)X ° Data -
""" s-wave j
a 1200 """" 'p-wave ;
E ' —Event-Mix j
o B tF't j
g, 1000 CS 1 .

o ,
E 800 ,1 ~
1: , 1 1
8 : 1
U 600 .' 1
400 "\ f‘. 1
/ \ 1
200 //’.' I

0 1 anr-fl-“J'x‘u-m 1 1 A...--1--£1~._4 . . 1 .
-3 -2 -l O l 2 3
V f-Vn [cm/ns]

Figure 6.6: Velocity difference spectrum of the 9Be(”Be,9Li+n)X system. Shown
are the experimental data with statistical error bars, the computer simulation of a
p-wave resonance at 538 keV, a a,=-25 fm s-wave scattering, and an event-mixed
background. The best fit consists of: the background: 47%, p-wave: 5%, and s-wave
(a,=-25 fm): 48%.

 

E

V I V fiT fir T V Y I Y Y r T I Y Y T I l T I T I ff T T T
p

-_9Be(”Be,9Li+n)x . Data ,1

é

§§

800:

Counts/0.2 cm/ns

 

 

 

 

-3 -2 -l O 1 2 3
V {V11 [cm/ns]

Figure 6.7: Velocity difference spectrum for the reaction 9Be(“Be,9Li+n)X data with
fits using scattering lengths a,=0, -5, and -20 fm.

90

interaction of the p—states.

Whereas the loosely-bound s-state of the 11Be makes the peaks in the relative
velocity distribution difficult to resolve in the 7He case, it makes the velocity distri-
bution narrower in the case of ”Li versus the use of a ”Be projectile. A narrower
relative velocity distribution does not necessarily translate into a stronger final-state
interaction, since the shape of the distribution is strongly dependent on the initial
states. Since there can be strong dependence on the initial states in the relative ve-
locity distribution of the final states, the fact that the results here corroborate the
findings of Thoennessen et al. [28] is important. The 11'”Be have a very different
structure from 18O, which is the projectile used in [27, 28], and the fact that inter-
actions in the I = 0 channel can be seen using all three projectiles makes a strong
case for the existence of a low-lying s-state in the ”Li. The observation of a strong
final-state interaction by using llBe (which has essentially no pf/z in the initial state)

proves the l = 0 assignment of this state.

91

 

 

 

Chapter 7

8He+n

7 .1 Introduction

The first experimental result on 9He was reported in 1987 by Seth et al. [13] using
a 9Be(7r‘,7r+)9He reaction with a 194 MeV 7r‘ beam. They found that states in
9He are at the energies of 1.13 :I: 0.10 MeV, 2.3 MeV (I‘ = 420 :l: 100 keV) and 4.9
MeV (I‘ = 500 :l: 100 keV) against neutron decay. [13]. Shortly thereafter, Bohlen et
al. [14] reported a set of 9He results from a double charge-exchange study using the
9Be(13C,13O)9He, at a beam energy of 380 MeV. They reported states at 1.8 MeV and
5.6 MeV against neutron decay. Figure 1.3 shows the data for both Seth et al. and
Bohlen et al..

The most recent measurement on 9He was reported in 1995 by von Oertzen et
al. [32]. Using a 9Be( 14C,14O)9He double charge-exchange reaction with incident beam
of 14C at 24 MeV/u , they reported states at 1.27 MeV (f‘ = 0.30 MeV), 2.42 MeV
(I‘ = 0.85 MeV), and 5.25 MeV against neutron decay. Figure 7.1 shows the data
from von Oertzen et al..

A common thread in all of these experimental results is that the lowest observed

state is relatively sharp (See Figures 1.3, 7.1). The authors in all three cases inter-

92

 

Y I rY—Vfiw' ijTrY 7‘ V I Y7 Y 'TTYYW’r

30

 

b ‘
[I “Be(I‘C.”0)9H° I
25: 337 MeV 0.——34.58(10)M0V I
a I ‘.60_6.4o M.E,-40.94(10)M0V ;
2' » i
, 1 7.9
3 20:- ] [ ( ) .3
U r- I 1 [ [I )I g 1
: 1l| [[ . m d
15- ‘ ' 1 ' l n 0' d
: I ‘41 " "I 1
t ' l ‘ °- 9 ‘
101— ' I "‘ .. 1
b
L . d
I- cl
L" '1

 

 

I
‘ . ‘ Sn--I.27(10)MQV
1 j I [I—
1 I
o LL11 14 LAAAL‘A -4: ‘l'h'[" I. . I.’

f "[
I°O’->"O+2n ‘
10.0 0 E‘ [HOV]

Figure 7 .1: Data from von Oertzen et al. [32]. Shown are the observed excited states
using a 9Be(14C,l4O)9He reaction. The energies are shown with reference to the lowest
observed state.

preted the lowest observed state as a p—state [13, 14, 32]. As mentioned previously,
9He is a member of the N=7 isotones, which parity inversion has been predicted for
the lighter members of this group. Parity inversion is well-documented for the bound
11Be, and observed in 1"Li by [27, 28] as well as this present work. 9He is the lightest

isotone in this family, and the most extreme test for this prediction.

7 .2 Results

Data for the 9He system was limited by statistics. Most of the beamtime for this
experiment was spent on the 11Be nucleus, so the data with incident ”Be has very
low statistics. Since the data with incident ”Be projectiles was too sparse to analyze,
it will not be discussed here. Because of the limited statistics for 8He+n data, the

size of the angular cut (Section 3.1) was expanded from 5 degrees to 10 degrees to

93

50 T T T r I T T T T I T T T T l T T Tr T I T T T T I T T T T

 

 

 

 

 

 

1

“ 4

" 9Be(“Be,8He+n)X ° Data .

"‘ [ a=0fm 1

g 40 ~ 1 _

E ; ' “Event-Mix :

Q
(\I 1
o 30 -
L. 1-
0 .
.3 1
Q 20 l
'13 1
0 I
U .
1o 1
0;,v,‘ 1. 1 1 1111 1111 ..
-3 -2 -l 0 1 2 3
V f-Vn [cm/ns]

Figure 7 .2: 9Be(“Be,8He+n)X data compared with event-mixed background at the
same total intensity (dashes) and best fit using a, = 0 fm (solid). The important
feature here is to observe that simple event-mixing cannot explain the data. In
the best fit using a combination of an a, = 0 fm distribution and an event-mixed
background, the fit failed to describe the narrow, central peak of the data. In that
case, the best fit here obtained uses 100% s-wave component and 0% event-mixed
background.

increase the available data for analysis. In spite of the decreased resolution that comes
from a larger acceptance angle, sufficient sensitivity remains to detect a final state
interaction (Figure 3.9).

The data here is analyzed in a very similar manner as the ”Li data. Figure 7 .2
shows two different fits: (1) Pure event-mixed background scaled to the same number
of events and (2) Best-fit using a combination s-wave (a, = 0 fm) and event-mixed
background. A distribution that consists entirely of event-mixed spectrum fails to
describe the peak near zero relative velocity. A best fit using a non-interacting 3-
wave does a better job than the event-mixed spectrum, but it is still unsatisfactory

at describing the narrowness of the relative velocity distribution.

Figure 7.3 shows 8He+n relative velocity data with fits using a8 = -10 fm. Figure

94

 

 

 

 

 

50. ......,....,...-,,...,.f..
' 9 ”B 8H ’ Data
.— : Be( e, e+n)X _____ s_wavc
g 40 ~ as: -10 fm --------- Event-Mix 1
E : Best Fit :
o 1 1 (a =-lO fm) .
N 1 s .
O 30 f 1 ‘ ' —Best Fit j
g 1 (a‘=0 fm) .
E 20 : " .
1:: ~ _
a t / -.
U / a .1
IO [— / 1 |\\ ‘
O ' -;.:’ :1'; 1”1 1 1 1 1 1 1 1 1 1 f.‘1:'1'1.1‘ par—1mm}-
-3 -2 -l 0 l 2 3
Vf-Vn [cm/n5]

Figure 7.3: 9Be(“Be,8He)X data with a fit using two components (solid): a,=—10 fm
(short dashes) and an event-mixed background (dots). The best fit here obtained
uses 71% s-wave component and 29% event-mixed background. Also shown for the
purpose of comparison is the best fit using only a combination of a, = 0 fm and an
event-mixed background (long dashes).

7 .4 shows the reduced-X2 as a function of scattering length between 0 and -40 fm. The
fit uses only an event-mixed background and a simulated relative velocity distribution
with a given scattering length. Simulated relative velocity distributions corresponding
to a final-state interaction of a, < -10 fm seem to offer the best fit to the data, which
is equivalent to a decay energy of less than 200 keV.

We propose that the present data represents the first observation of the low-lying
ground state of 9He. In addition, we further assert that this is the intruder s-state
that had been predicted to exist [29]. Figure 7.5 shows two shell-model calculations
from [47] using a Warburton—Brown model and compares them with results from Seth
et al. and von Oertzen et al. [13, 32]. The calculations both predict a low-lying s—state
as a ground state, as well as states of comparable energy to those observed by [13, 32].

The essential argument why the observed final-state interaction of the 9He cor-

responds to an s-state follows the same line of reasoning as the ”Li case. The 11Be

95

 

9Be(11Be,8He+n)X

FYITIIIITITIITIllllllllfflelljlllTlTrI—

 

 

llllll

lllLllllllllLlll11111111111]l

 

 

-50 -4O -30 -20
Scattering Length [fm]

C

Figure 7.4: Reduced-X2 of fits to 9Be(“Be,8He+n)X data as a function of the scatter-
ing length a, of the s-state. The minimum )8 analysis uses three separate components
in the fit. The minimization procedure uses the 12 data points between -1.1 cm/ns
and 1.1 cm/ns. The 3 free parameters used in the fitting are the 1) total inten-
sity (taken to be the same as the total number of events), 2) systematic shift in
the computer-simulated relative velocity spectrum (Section 3.6), and 3) the relative
intensities amongst two different components requires just one free parameters for
fitting. This yields 9 degrees of freedom. The dashed line represent the reduced-x2
value that corresponds to a 95% confidence level, showing that a scattering length

numerically larger than -10 fm best fits the data.

96

projectile contains essentially no 191/2 in the initial state and is predominantly in the 3-
state. The formation of a 8He+n system from 11Be comes from double proton removal,
with a neutron in the s-state. Since a final-state interaction is observed between the
neutron and 8He, this interaction cannot come from the p channel. This argument
precludes the possibility of having observed a low-lying p—state with an energy too
low to be resolved as two separate peaks (Figure 3.3).

This argument illustrates a very important point about the choice of the initial
projectile. The ability to select different initial states allows the experimenter to
discriminate which state gets probed, making it possible to make angular momentum

assignments.

97

 

 

 

$5 3/2__5/2+ 1:0 2'?
_ —3/2' W
—5/2+ W

2’ —2 '>"

H m
a, a
E _ A
m l¢0 E
u? 669% 0
. 1_. _ W cg:
UJ —1/2 1 r,

LIJ

_ —1/2'
Z: O

0— —1/2+—1/2+ m ‘0

WBP WBT LC KKS WVO

9H9

Figure 7.5: Proposed level scheme for 9He. Shown here are two shell-model calcu-
lations using the Warburton-Brown model (WBP and WBT) and the data from the
two experiments (Seth et al. (KKS) [13] and von Oertzen et al. (WVO)[32]) that are
used for the current tabulated value for the 9He mass in Audi and Wapstra [31]. Also
shown is the low lying s—state observed in this work (LC). Two separate energy scales
are shown. On the left is the energy scale measured with respect to the ground-
state energy, and the energy scale on the right uses neutron separation energy as a
reference.

98

Chapter 8

Summary

In this work, we have explored the PSI technique to study unbound nuclei, and made
measurements on 7""He and 10Li. Important experimental results can be summarized
as the follows:

1) The unbound nucleus 7He was studied with three different projectiles. 7He was
the easiest system to study, because the energy of the p resonance is much higher than
those we were trying to study in the other two cases. The energy of the resonance
was measured to be 440 :l: 16 keV, an improvement over the current literature value
of 440 :l: 30 keV.

2) It has been predicted that the unbound system 10Li has a low-lying s-state as
a ground state. The previous two experiments by [27, 28] used an 18O projectile and
found a strong interaction at low energy. This is the first relative velocity measure-
ment made with a projectile other than 180, and these observations also indicate a
strong interaction in the l = 0 channel, with scattering length a, <-10 fm. The fact
that a low-lying s—state has been observed using three different projectile places the
existence of this state on a stronger footing.

3) The first experimental observation for a low-lying s-state in the unbound 9He,

the lightest of the N=7 isotones, is reported. The s-state interaction is reported here

99

 

as a scattering length of a, 3-10 fm. The existence of this state has been predicted by
[29] but has never been observed until this work. However, the results are restricted
because of the low yields of a breakup reaction. A future study with a different inital
nucleus with improved statistics could be very insightful.

The study of nuclei near and beyond the neutron dripline continues to be the
ultimate test for nuclear models. The experimental limitations are the ability of
accelerator facilities to produce these exotic nuclei. With more powerful facilities
coming on line, it will be possible to use the final-state-interactions technique to
probe the unbound states of heavier nuclei. This work has demonstrated that a final-
state interaction is a promising technique to study these unbound systems. It also
shows that the choice of initial projectile can be very important to these types of

experiments, and good judgement must be exercised.

100

 

 

Appendix A

Data

The data from this experiment are contained in this appendix. The relative velocity
distributions are listed in Tables A.1, A2, and AB. In addition, the neutron and frag-
ment velocity distributions are listed in Tables AA to A9 The fragment and neutron

velocity distributins are used to calculate the event-mixed background (Section 3.6).

101

Table A.1: 6He+n relative velocity distribution. Shown are the total number of events
that satisfy the 5-degree angular cut binned in 0.2 cm/ns increments. The velocity
difference distribution V, — Vn for each of the 12’11’10Be projectiles is shown.

 

 

 

 

V, — Vn Incident Beam V, — V" Incident Beam
(cm/ns) 1"’Be 11Be 10Be (cm/ns) 12Be 11Be 10Be
-3.9 4 12 2 0.1 138 1011 85
-3.7 9 18 4 0.3 124 966 109
-3.5 6 21 l 0.5 162 993 144
-3.3 16 30 2 0.7 241 1147 194
-3.1 11 35 4 0.9 236 1170 218
-2.9 11 4O 7 1.1 203 901 166
-2.7 9 60 11 1.3 94 536 96
-2.5 12 67 8 1.5 57 329 48
-2.3 15 87 13 1.7 36 197 18
-2.1 16 120 6 1.9 28 161 17
-1.9 25 166 21 2.1 25 104 20
-1.7 38 183 27 2.3 29 105 14
-1.5 45 266 35 2.5 16 89 18
-1.3 82 419 64 2.7 12 67 14
-1.1 126 722 128 2.9 24 42 11
-0.9 259 1165 176 3.1 12 46 14
-0.7 256 1381 235 3.3 13 55 5
-0.5 234 1367 197 3.5 12 44 16
-0.3 185 1164 165 3.7 8 46 11
-0.1 135 1073 126 3.9 14 36 10

 

 

 

 

 

 

 

 

 

 

102

Table A2: 9Li+n velocity difference distribution. Shown are the total number of
events that satisfy the 5-degree angular cut binned in 0.2 cm/ns increments. The
velocity difference distribution V, — Vn for each of the 12'11'10Be projectiles is shown.

 

 

 

 

V, —- V" Incident Beam V, — Vn Incident Beam
(cm/ns) 12Be 11Be 10Be (cm/ns) 12Be 11Be 10Be
-3.9 2 3 0 0.1 183 1221 21
-3.7 1 2 1 0.3 126 845 16
-3.5 3 9 1 0.5 101 561 11
-3.3 7 7 2 0.7 76 378 10
-3.1 6 16 3 0.9 55 211 11
-2.9 5 18 0 1.1 52 126 12
-2.7 16 33 1 1.3 32 101 12
-2.5 11 30 3 1.5 16 64 3
-2.3 7 29 2 1.7 22 47 10
-2.1 20 47 3 1.9 16 26 6
-l.9 18 70 2 2.1 9 25 6
-I.7 29 73 5 2.3 11 30 3
—1.5 27 115 6 2.5 11 27 4
-l.3 46 147 10 2.7 9 22 2
-1.1 57 223 16 2.9 6 20 4
-0.9 86 369 10 3.1 7 22 5
-0.7 112 561 32 3.3 11 14 2
-0.5 127 758 22 3.5 13 16 3
-0.3 157 1151 19 3.7 7 19 2
-0.1 181 I276 27 3.9 I 19 2

 

 

 

 

 

 

 

 

 

 

103

 

 

Table A.3: 8He+n velocity difference distribution. Shown are the total number of
events that satisfy the 10-degree angular cut binned in 0.2 cm/ns increments. The
velocity difference distribution V, — Vn for each of the 12'11'108e projectiles is shown.

 

 

 

 

V, — Vn Incident Beam Vf - Vn Incident Beam
(cm/ns) 12Be 11Be 10Be (cm/ns) 12Be TIBe mBe
-3.9 0 0 0 0.1 9 33 O
-3.7 1 0 0 0.3 5 24 2
-3.5 0 0 0 0.5 6 12 0
-3.3 2 0 0 0.7 8 6 0
-3.1 1 0 O 0.9 3 5 0
-2.9 1 0 0 1.1 7 5 0
-2.7 0 0 0 1.3 4 6 0
-2.5 2 0 0 1.5 7 2 1
-2.3 0 0 0 1.7 4 6 0
-2.1 0 1 0 1.9 4 3 0
-1.9 0 2 0 2.1 5 3 0
-1.7 2 2 0 2.3 3 4 0
-1.5 3 1 1 2.5 1 1 0
-1.3 3 6 0 2.7 5 3 0
-I.l 4 5 0 2.9 2 1 0
-0.9 5 6 0 3.1 2 0 0
-0.7 11 12 0 3.3 2 0 0
-0.5 7 15 0 3.5 1 6 0
-0.3 7 29 0 3.7 4 0 0
-0.1 6 34 0 3.9 3 1 0

 

 

 

 

 

 

 

 

 

 

104

 

 

Table A.4: Neutron and fragment velocity distributions from the 9Be(mBe,6He-l-n)X
reaction. Shown here are the velocity distributions of the 6He fragments and the
neutrons from coincidence events. Only events with single neutron wall and single
fragment bar hits are shown here.

 

 

 

 

 

 

 

 

 

Velocity n 6He Velocity n ‘He Velocity 11 6He
(cm / ns) (cm / ns) (cm/ns)
0.0 0 0 4.0 46 1 8.0 425 434
0.2 0 0 4.2 65 0 8.2 353 207
0.4 0 0 4.4 73 4 8.4 244 76
0.6 0 0 4.6 74 7 8.6 189 30
0.8 0 0 4.8 91 10 8.8 113 6
1.0 0 0 5.0 104 32 9.0 77 0
1.2 0 0 5.2 119 46 9.2 48 0
1.4 0 0 5.4 136 53 9.4 45 0
1.6 1 0 5.6 198 103 9.6 28 0
1.8 5 0 5.8 256 155 9.8 26 0
2.0 5 0 6.0 329 217 10.0 25 0
2.2 9 0 6.2 403 327 10.2 26 0
2.4 20 0 6.4 470 415 10.4 21 0
2.6 22 0 6.6 597 596 10.6 14 0
2.8 39 0 6.8 685 858 10.8 15 0
3.0 49 0 7.0 602 1171 11.0 4 0
3.2 55 0 7.2 697 1191 11.2 4 0
3.4 49 0 7.4 660 1172 11.4 3 0
3.6 46 0 7.6 588 983 11.6 6 0
3.8 49 0 7.8 542 675 11.8 5 0

 

 

 

 

105

Table A5: Neutron and fragment velocity distributions from the 9Be(“Be,“He+n)X
reaction. Shown here are the velocity distributions of the “He fragments and the
neutrons from coincidence events. Only events with single neutron wall and single
fragment bar hits are shown here.

 

 

 

 

 

 

 

 

 

 

 

Velocity 11 “He Velocity 11 “He Velocity n “He
(cm/ns) (cm/ns) J] (cm/ns)
0.0 0 o 4.0 205 9T 8.0 2195 1764
0.2 0 0 4.2 211 6 8.2 1699 812
0.4 0 0 4.4 236 43 8.4 1146 254
0.6 0 0 4.6 286 64 8.6 728 77
0.8 0 0 4.8 341 130 8.8 449 11
1.0 0 0 5.0 397 188 9.0 300 2
1.2 O 0 5.2 489 276 9.2 255 1
1.4 0 0 5.4 654 431 9.4 149 0
1.6 32 0 5.6 861 587 9.6 106 0
1.8 35 0 5.8 1167 858 9.8 94 0
2.0 44 0 6.0 1553 1270 10.0 81 0
2.2 58 O 6.2 2072 1794 10.2 51 0
2.4 62 0 6.4 2746 2360 10.4 39 0
2.6 120 0 6.6 3429 3136 10.6 42 0
2.8 137 0 6.8 4013 4299 10.8 37 0
3.0 158 0 7.0 4179 5840 11.0 26 0
3.2 165 0 7.2 4226 6880 11.2 16 0
3.4 172 0 7.4 3844 6471 11.4 20 0
3.6 165 4 7.6 3323 5071 11.6 12 0
3.8 204 5 7.8 2847 3344 11.8 18 0

 

106

 

Table A6: Neutron and fragment velocity distributions from the 9Be(1(’Be,“He-+-n)X
reaction. Shown here are the velocity distributions of the “He fragments and the
neutrons from coincidence events. Only events with single neutron wall and single
fragment bar hits are shown here.

 

 

Velocity n “He Velocity n “He Velocity 11 “He
(cm / ns) (cm/ns) Lcm/ns)
0.0 0 0 4.0 43 2’ 8.0 335 337
0.2 0 0 4.2 59 5 8.2 303 129
0.4 0 0 4.4 65 9 8.4 190 42
0.6 0 0 4.6 75 15 8.6 111 8
0.8 0 0 4.8 72 26 8.8 63 1
1.0 0 0 5.0 94 47 9.0 49 0
1.2 0 0 5.2 109 68 9.2 33 0
1.4 0 0 5.4 126 82 9.4 22 0
1.6 0 0 5.6 165 146 9.6 17 0
1.8 3 0 5.8 219 187 9.8 10 0
2.0 0 0 6.0 260 268 10.0 14 0
2.2 5 0 6.2 365 371 10.2 8 0
2.4 16 0 6.4 418 459 10.4 10 0
2.6 23 0 6.6 519 547 10.6 4 0
2.8 41 0 6.8 547 594 10.8 6 0
3.0 38 0 7.0 624 687 11.0 7 O
3.2 45 0 7.2 572 882 11.2 4 0
3.4 58 0 7.4 568 1014 11.4 2 0
3.6 40 0 7.6 509 841 11.6 4 0
3.8 45 2 7 .8 437 600 11.8 4 0

 

 

 

 

 

 

 

 

 

 

 

107

Table A.7: Neutron and fragment velocity distributions from the 9Be(”Be,9Li+n)X
reaction. Shown here are the velocity distributions of the 9Li fragments and the
neutrons from coincidence events. Only events with single neutron wall and single
fragment bar hits are shown here.

 

 

Velocity n 9Li Velocity n Li Velocity n Li
. (cm/ns) fl (cm/ns) I] (cm/ns)
0.0 0 0 ' 4.0 27 0 V 8.0 185 8
0.2 0 0 4.2 43 0 8.2 133 0
0.4 0 0 4.4 34 0 8.4 70 0
0.6 0 0 4.6 46 0 8.6 68 0
0.8 0 0 4.8 42 1 8.8 60 0
1.0 0 0 5.0 57 0 9.0 45 0
1.2 0 0 5.2 56 l 9.2 40 0
1.4 0 0 5.4 77 3 9.4 24 0
1.6 2 O 5.6 83 13 9.6 22 0
1.8 2 O 5.8 127 51 9.8 15 0
2.0 3 0 6.0 139 136 10.0 16 0
2.2 7 0 6.2 184 218 10.2 9 0
2.4 9 0 6.4 238 333 10.4 8 0
2.6 12 0 6.6 318 590 10.6 7 0
2.8 20 0 6.8 366 806 10.8 5 0
3.0 16 0 7.0 370 963 11.0 3 O
3.2 31 0 7.2 374 747 11.2 3 0
3.4 28 0 7.4 330 345 11.4 2 0
3.6 31 0 7.6 231 194 11.6 1 0
3.8 24 0 7.8 214 65 11.8 3 0

 

 

 

 

 

 

 

 

 

 

 

108

Table A8: Neutron and fragment velocity distributions from the 9Be(12Be,9Li+n)X
reaction. Shown here are the velocity distributions of the 9Li fragments and the
neutrons from coincidence events. Only events with single neutron wall and single
fragment bar hits are shown here.

 

 

 

 

 

 

 

 

 

 

Velocity 11 13Li Velocity n TLi Velocity n 517
(cm/ns) (cm/ns) [hem/n8)
0.0 o 0 4.0 76 2 " 8.0 543 10
0.2 0 0 4.2 78 O 8.2 368 0
0.4 0 0 4.4 93 0 8.4 244 0
0.6 0 0 4.6 107 0 8.6 200 0
0.8 0 0 4.8 121 3 8.8 124 0
1.0 0 0 5.0 139 5 9.0 98 0
1.2 0 0 5.2 147 8 9.2 91 0
1.4 0 0 5.4 192 37 9.4 72 0
1.6 11 0 5.6 251 128 9.6 48 0
1.8 29 0 5.8 319 330 9.8 40 0
2.0 18 0 6.0 501 676 10.0 32 0
2.2 29 0 6.2 736 937 10.2 22 0
2.4 26 0 6.4 1044 1348 10.4 14 0
2.6 50 0 6.6 1490 2507 10.6 14 0
2.8 58 0 6.8 1880 3356 10.8 9 0
3.0 58 0 7.0 2206 4621 11.0 7 0
3.2 59 0 7.2 2149 3420 11.2 6 0
3.4 75 0 7.4 1763 1458 11.4 4 0
3.6 70 0 7.6 1275 424 11.6 4 0
3.8 56 0 7.8 894 58 11.8 0 0

 

 

 

109

Table A9: Neutron and fragment velocity distributions from the 9Be(“Be,“He+n)X
reaction. Shown here are the velocity distributions of the “He fragments and the
neutrons from coincidence events. Only events with single neutron wall and single
fragment bar hits are shown here.

 

 

Velocity n “He Velocity n 8He Velocity n “He
(cm / ns) (cm / ns) (cm / ns)
0.0 0 0 4.0 2 0 8.0 11 0
0.2 0 0 4.2 4 0 8.2 11 0
0.4 0 0 4.4 3 0 8.4 1 0
0.6 0 0 4.6 5 0 8.6 4 0
0.8 0 0 4.8 6 0 8.8 2 0
1.0 0 0 5.0 3 0 9.0 1 0
1.2 0 0 5.2 7 0 9.2 1 0
1.4 0 0 5.4 5 0 9.4 0 0
1.6 0 0 5.6 6 0 9.6 0 0
1.8 1 0 5.8 11 2 9.8 0 0
2.0 0 0 6.0 32 15 10.0 0 0
2.2 3 0 6.2 28 53 10.2 0 0
2.4 1 0 6.4 35 83 10.4 0 0
2.6 3 0 6.6 42 77 10.6 1 0
2.8 4 0 6.8 46 79 10.8 0 0
3.0 1 0 7.0 43 78 11.0 0 0
3.2 2 0 7.2 40 43 11.2 0 0
3.4 4 0 7.4 30 4 11.4 0 0
3.6 2 0 7.6 14 0 11.6 0 0
3.8 4 0 7.8 15 0 11.8 0 0

 

 

 

 

 

 

 

 

 

 

 

110

LIST OF REFERENCES

[1] T. Motobayshi, Y. Ikeda, Y. Ando, K. Ieki, M. Inoue, N. Iwasa, T. Kikuchi, M.
Kurokawa, S. Moriya, S. Ogawa, H. Murakami, S. Shimoura, Y. Yanagisawa,
T. Nakamura, Y. Watanabe, M. Ishihara, T. Teranishi, H. Okuno, R.F. Casten,
Phys. Lett. B 346, 9 (1995).

[2] R.W. Ibbotson, T. Glasmacher, B.A. Brown, L. Chen, M.J. Chromik, P.D. Cot-
tle, M. Fauerbach, K.W. Kemper, D.J. Morrissey, H. Scheit, and M. Thoen-
nessen, Phys. Rev. Lett. 80, 2081 (1998).

[3] B.V. Pritychenko, T. Glasmacher, P.D. Cottle, M. Fauerbach, R.W. Ibbotson,
K.W. Kemper, V. Maddalena, A. Navin, R. Ronnigen, A. Sakharuk, H. Scheit,
V.G. Zelevinsky, Phys. Lett. B461, 322 (1999).

[4] I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, Y. Yoshikawa, K. Sugimoto,
O. Yamakawa, and T. Kobayashi, Phys. Rev. Lett. 55, 2676 (1985).

[5] T. Kobayashi, O. Yamakawa, K. Omata, K. Segimoto, T. Shimoda, N. Taka-
hashi, and I. Tanihata, Phys. Rev. Lett. 60, 2599 (1988).

[6] NA. Orr, N. Anantaraman, S. M. Austin, C.A. Bertulani et al., Phys. Rev.
Lett. 69, 2050 (1992).

111

[7] J .H. Kelley, S.M. Austin, R.A. Kryger, D.J. Morrissey, N.A. Orr, B.M. Sherrill,
M. Thoennessen, J .S. Winfield, J .A. Winger, and BM. Young, Phys. Rev. Lett.
74, 30 (1995).

[8] A. Navin, D. Bazin, B.A. Brown, B. Davids, G. Gervais, T. Glasmacher, P.G.
Hansen, M. Hellstroéim, R.W. Ibbotson, V. Maddalena, B. Pritychenko, H.
Scheit, B.M. Sherrill, M. Steiner, J.A. Tostevin, J. Yurkon, Phys. Rev. Lett.
81, 5089 (1998).

[9] T. Aumann, A. Navin, D.P. Balamuth, D. Bazin, B. Blank, B.A. Brown, J.B.
Buth, J.A. Caggiano, B. Davids, T. Glasmacher, V. Guimarées, PG. Hansen,
R.W. Ibbotson, D. Karnes, J.J. Kolata, V. Maddalena, B. Pritychenko, H.
Scheit, B.M. Sherrill, and J .A. Tostevin Phys. Rev. Lett. 84, 35 (2000).

[10] RH. Stokes and P.G. Young, Phys. Rev. 178, 2024 (1969).

[11] H.G. Bohlen, B. Gebauer, M. von Lucke—Petsch, A.N. Ostrowski, M. Wilpert,
Th. Wilpert, H. Lenske, D.V. Alexandrov, A.S. Demyanova, E. Nikolskii,
A.A. Korsheninnikov, A.A. Ogloblin, R. Kalpakchieva, Y.E. Penionzhkevich,
S. Piskor, Z. Phys. A 344, 381 (1993).

[12] J.A Caggiano, D. Bazin, W. Benenson, B. Davids, B.M. Sherrill, M. Steiner, J.
Yurkon, A.F. Zeller, B. Blank, Phys. Rev. C 60, 064322 (1999).

[13] K.K. Seth, M. Artuso, D. Barlow, M. Kaleta, H. Nann, B. Parker, and R.
Soundranayagam, Phys. Rev. Lett. 58, 1930 (1987).

[14] HO. Bohlen, B. Gebauer, D. Kolbert, W. von Oertzen, E. Stiliaris, M. Wilpert,
and T. Wilpert, Z. Phys. 330, 227 (1988).

[15] R.F. Haddock, R.M. Salter, Jr., M. Zeller, J.B. Czirr, and DR. Nygren, Phys.
Rev. Lett. 14, 318 (1965).

112

[16] R. Honecker and H. Grassler, Nucl. Phys. A107, 81 (1968).

[17] B. Zeitnitz, R. Maschuw, and P. Suhr, Nucl. Phys. A149, 449 (1970).
[13] I. Slaus, Y. Akaishi, and H. Tanaka Phys. Reports 173, 257 (1990).

[19] GA. Miller, B.M.K. Nefkens, and I. Slaus, Phys. Reports 194, 1 (1990).

[20] OR. Howell, Q. Chen, T.S. Carman, A. Hussein, W.R. Gibbs, B.F. Gibson, G.
Mertens, C.F. Moore, C. Morris, A. Obst, E. Pasyuk, C.D. Roper, F. Salinas,
I. Slaus, S. Sterbenz, W. Tornow, R.L. Walter, C.R. Whiteley, M. Whitton,
Phys. Lett. B444, 252 (1998).

[21] H.S.W. Massey, Progr. Nucl. Phys. 3, 237 (1953).
[22] AB. Migdal Soviet Physics-JETP 1, 2 (1955).

[23] K. Ilakovac, L. G. Kuo, M. Petravic’, I. Slaus, and P. Thomas, Phys. Rev. Lett.
6, 356 (1961).

[24] K. Ilakovac, L.G. Kuo, M. Petravic’, I. Slaus, and P. Thomas, Nucl. Phys. B53,
254 (1963).

[25] M. Cerineo, K. Ilakovac, I. Slaus, P. Thomas, and V. Velkovic’, Phys. Rev. 133,
B948 (1963).

[26] RM. Salter, Jr., R.F. Haddock, M. Zeller, D.R. Nygren, and J.B. Czirr,chl.
Phys. A254, 241 (1975).

[27] RA. Kryger, A. Azhari, A. Galonsky, J .H. Kelley, R. Pfaff, E. Ramakrishnan,
D. Sackett, B.M. Sherrill, M. Thoennessen, J.A. Winger, and S. Yokoyama,
Phys. Rev. C 47, R2439 (1993).

113

[28] M. Thoennessen, S. Yokoyama, A. Azhari, T. Baumann, J .A. Brown, A. Galon-
sky, P.G. Hansen, J .H. Kelley, R.A. Kryger, E. Ramakrishnan, and P. Thrilof,
Phys. Rev. C 59, 111 (1999).

[29] H. Sagawa, B.A. Brown, and H. Esbensen, Phys. Lett. B309, 1 (1993).
[30] I.J. Thompson and M.V. Zhukov, Phys. Rev. C 49, 1904 (1994).
[31] G. Audi and AH. Wapstra, Nucl. Phys. A595, 409 (1995).

[32] W. von Oertzen, H.G. Bohlen, G. Gebauer, M. von Lucke-Petsch, A.N. Os-
trowski, Ch. Seyfert, Th. Stolla, M. Wilpert, Th. Wilpert, D.V. Alexandrov,
A.A. Korsheninnikov, I. Mukha, A.A. Ogloblin, S.M. Grimes, and TN. Massey,
Nucl. Phys. A588, 1290 (1995).

[33] RD. Zecher, Nucl. Instmm. Methods 401, 329 (1997).

[34] J .J . Kruse, Ph.D. Thesis. (1999)

[35] RD. Zecher, Ph.D. Thesis. (1996)

[36] SK. Yokoyama, Ph.D. Thesis. (1996)

[37] AS. Goldhaber, Phys. Lett. B53, 306 (1974).

[38] H. Feshbach and K. Huang, Phys. Lett. 47B, 300 (1973).

[39] M.J. Murphy and RC. Stokstad, Phys. Rev. C 28, 428 (1983).

[40] F. Hubert, R. Bimbot and H. Gauvin, At. Data Nucl. Data Tables 46, 9 (1990).
[41] P.G. Hansen, Phys. Rev. Lett. 77, 1016 (1996).

[42] J .A. Tostevin, J. Phys. C: Nucl. 25, 735 (1999).

[43] BA. Brown, Private Communications, 1999.

114

[44] M. Zinser, F. Humbert, T. Nilsson, W. Schwab, Th. Blaich, M.J.G. Borg, L.V.
Chulkov, H. Eickhoff, Th.W. Elze, H. Emling, B. Franzke, H. Freiesleben, H.
Geissel, K. Grim, D. Guillemaude—Muller, P.G. Hansen, R. Holzmann, H. Irnich,
B. Jonson, J.G. Keller, O. Klepper, H. Klinger, J.V. Kratz, R. Kulessa, D.
Lambrecht, Y. Leifels, A. Magel, M. Mohar, A.C. Mueller, G. Miinzenberg, F.
Nickel, G. Nyman, A. Richter, K. Riisager, C. Scheidenberger, G. Schrieder,
B.M. Sherrill, H. Simon, K. Stelzer, J. Stroth, O. Tengblad, W. "Itautmann, E.
Wajda, and E. Zude, Phys. Rev. Lett. 75, 1719 (1995).

[45] RC. Stokstad, Comments Nacl. Part. Phys. 13, 231 (1984).
[46] RH. Stokes and P.G. Young, Phys. Rev. Lett. 18, 611 (1967).
[47] BA. Brown, Private Communications, 1994.

[48] BM. Young, W. Benenson, J.H. Kelley, N .A. Orr, R. Pfaff, B.M. Sherrill, M.
Steiner, M. Thoennessen, J.S. Winfield, J.A. Winger, S.J. Yennello, and A.
Zeller, Phys. Rev. C 49, 279 (1994).

[49] K.H. Wilcox, R.B. Weisenmiller, G.J. Wozniak, N.A. Jelley, D. Ashery, and J.
Cerny, Phys. Lett. 59B, 142 (1975).

[50] J. Wang, Ph.D. Thesis. (1999)

[51] RB. Firestone, V.S. Shirley, C.M. Baglin, S.Y.F. Chu, and J. Zipkin, Table of
Isotopes, Eigth Edition, Volume I (John Wiley & Sons, Inc., 1996).

[52] R. Anne, R. Bimbot, S. Dogny, H. Emling, D. Guillemaud-Mueller et al., Nucl.
Phys. A575, 125 (1994).

[53] M. Chartier, J .R. Beene, B. Blank, L. Chen, A. Galonsky, N. Gan, P.G. Hansen,
J. Kruse, V. Maddalena, M. T hoennessen, R.L. Varner, To be polished.

115

[54] B. Zwieglinski, W. Benenson and R.G.H. Robertson, Nucl. Phys. A315, 124
(1979)

[55] A. Navin, D.W. Anthony, T. Aumann, T. Baumann, D. Bazin, Y. Blumenfeld,
B.A. Brown, T. Glasmacher, P.G. Hansen, R.W. Ibbotson, P.A. Lofy, V. Mad-
dalena, K. Miller, T. Nakamura, B. Pritychenko, B.M. Sherrill, E. Spears, M.

Steiner, J .A. Tostevin, J. Yurkon, A. Wagner, To be pvlished.

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