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Beta Decay Studies of Neutron-Rich Nuclei

BY

Mark Steven Curtin

A Dissertation
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Physics

1985

ABSTRACT

Beta Decay Studies of Neutron-Rich Nuclei
By

Mark Steven Curtin

The half-lives of eight neutron-rich light nuclei have
been measured using the Reaction Product Mass Separator at
NSCL. Utilizing a 30 MeV/A l.0 beam from the K500 cyclotron
at the National Superconducting Cyclotron Laboratory it was
possible to generate sufficient yields of exotic nuclei to
determine half-lives. The previously unknown half-lives of

15 l

7
Be and C are reported within this thesis along with the
9 ll 12 12 lb 15
half-lives of Li, Li, Be, B, B and B providing a
check on the accuracy of the experimental technique. The
half-lives were obtained through repeated measurements of
the time interval between the detection of a heavy-ion

reaction product and its associated beta. Yield information

from the experiment suggests the existance of a reaction

mechanism intermediate between direct and fragmentation
mechanisms namely,<nue in which the neutron-excess of the
target plays an increasingly important role in the yields of
very neutron-rich nuclei. Shell model predictions for the
beta decay of these nuclei are presented and compared to the
measured values. This experiment also provided the first
significant test of the mass separating properties of the
RPMS. The performance of the RPMS is discussed in appendix

A.

ACKNOWLEDGMENTS

First and foremost I would like to thank my advisor,
Dr. J.A. Nolen, Jr. for suggesting this thesis project and
for his dedicated help and guidance throughout both my
undergraduate and graduate careers. Without his help and
friendship this thesis would not have become reality. I
would also like to thank Hobson Wildenthal and Alex Brown
for sharing with me their insight into the nuclear shell
model. Many thanks go to Leigh Harwood and Al Zeller for
their valuable advise concerning magnetic systems and to
Steve Bricker for his work on the RPMS. I would like to
thank the entire staff at the Cyclotron Laboratory for
making the Lab a pleasant place to work (and sometimes
live). To my fellow graduate students I would lumeto say
that your friendship and good times will always be
remembered. In particular, I wish to thank Jim Duffy and
Andrea Micallef for their constant friendship and to the
racquetball duo Jack and Don for the "good times".

Finally, I wish to thank my family and the Capen
family for their constant love and support throughout this
endeavor. To my brother Mike, with whom I have been
fortunate to share many of my ideas and dreams, thank you
from the bottom of my heart. To my mother whose constant
love provided the necessary motivation to complete this
work, thank you. Lastly, I would like to thank my fiance

Mary for her love, patience and understanding throughout

this last and difficult year.

11

LIST OF FIGURES

FIGURE PAGE

1-1

Chart of the Nuclides illustrating neutron-rich

nuclei whose particle stability has been established
(grouped according to the laboratory where the
measurement was made)............................. 5

Schematic illustration of heavy-ion collision
mechanisms as a function of reaction cross-section
(equivalent to impact parameter) and bombarding

enerSYOOOOOOOOOIOOOOOOIOOOOOOOOOOOOOOOOOOOOOOOOOOO 7

Diagram displaying neutron-rich isotopes created
using the deeply-inelastic and fragmentation
mecnanismSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0000.0000 8

Conceptual illustration of the participant-

spectator picture using a reaction geometry

taken from the fireball model. The overlap region
corresponds to the "hot" participant region whereas

the projectile and target remnants represent cooler
objects........................................... 11

Schematic drawing illustrating the different regions
associated with a heavy-ion collision as a function
of the normalized impact parameter B.............. 13

Isotopic cross-sections (before the ablation stage)
calculated with the hypergeometric dispersion

relation. The fireball model was used where

the size of the projectile and target nuclei are

given by nr’ (r - 1.2 x A°"’ fm)................ 16

Isotopic cross-Sections (before the ablation

stage) calculated using the Ciant-Dipole-Resonance
dispersion relation. The fireball model was used

where the size of the projectile and target

nuclei are given by ur’ (r - 1.2 x A°"’ fm)..... 17

Calculated values of the excitation energy and

number of nucleons remaining in the projectile
spectator as a function of the normalized impact
parameter 8 using the fireball model.............. 18

The extreme single particle orbits obtained by
solving the non-relativistic Schrodinger equation
with a Hoods-Saxon plus spin-orbit potential...... 25

Chart of the Nuclides depicting the different
effective interactions used for various
mass regionSOOOIO0..OOOOOOOOOIOOOOOOOOO0.0.0..0.. “7

2’3

2-6

2-7

2-8

2-9

111

Comparison of half-lives calculated for the
Gamow-Teller beta decay of the sd-shell nuclei

with five or more excess neutrons with experimental

measurements. The solid line represents the shell
model predictions using the USD interaction of
Hildenthal. Experimental values are taken from
[Hi83] and references sited within................

Comparison of the beta Q values calculated for

the decays of the sd-shell nuclei with five or more
excess neutrons with experimental values. The solid

line represents the predicted beta Q values using
the USD interaction of Wildenthal. Experimental
values were taken from [W183] and references sited

withinOOOOO0.0.00000000000000000000000000.0.00...

Camow-Teller beta decay branching ratios predicted
for the decay of 17C using the Reehal-wildenthal
interaction. The predictedflhalf-life is ~100 ms
when a 5/2 ground state J is assumed (quenching
has been included)..............................

Camow-Teller beta decay branching ratios predicted
for the decay of ‘70 using the Millener-Kurath
interaction. This full Zhw calculation predicts

an inversion of the 3/2 and the 5/2 states

in "C in addition to predicting a much longer
half-life (quenching factor has been included)....

Camow-Teller beta decay branching ratios calculated
using the Reehal-Wildenthal interaction. The ground

state of "N was predicted to be ‘/, with N31 of
the branching strength populating neutron unbound
States in"00..0.I...OOOOOOOOOOOOOOOOOOOOOOOO...

Gamow-Teller branching ratios predicted for

the decay of ‘58 using the Millener-Kurath [MK]
interaction. The calculation predicts a 9.7 ms
half-life with all decays populating neutron
unbound states in "C............................

Gamow-Teller branching ratios predicted for HLi
using the [MK] interaction. Calculation predicts
an extremely short half-life with a 20% branch to
the ground-state of HBe.........................

Gamow-Teller branching ratios predicted for HBe
using the [MK] interaction. The calculation
predicts a strong (98%) branch to the lowest
lying 1 state in 1"B............................

“9

50

52

53

SN

55

S6

57

3-8

A'3

iv

Schematic illustration of a 35 MeV/A 22Ne beam
traversing a thick carbon foil. The energy loss
calculations were performed using the code DONNA.. 59

Schematic diagram illustrating the electronics
used for half-life experiment on the RPMS........ 63

Schematic drawing of the focal plane detector
arrangement used in the half-life measurements
on the RPMSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO..0. 6“

Spectrum of the E detector signal vs. the particle
identification function illustrating the energy
characteristics of the reaction products hitting

the focal plane detector system.................. 67

Linear fit to mass centroids demonstrating
the quality of the particle identification
functionOOOOOOOI.00....OO...OOOOOOOOOOOOOOOIOOIOO 68

Illustration of the mass islands corresponding
to different isotopic species.................... 69

Spectrum of the fast background component

believed to originate from thermal neutrons.

The heavy-ion gate was placed around the

long-lived lithium isotopes...................... 72

Decay curves with their corresponding best
fits for the 8 neutron-rich isotopes measured
in this experimentOOOO...00......00.00....0...... 77

Coordinate system used for magnetic optical systems
following the notation of TRANSPORT.............. 9A

Pictorial drawing of the RPMS. The beam

inflector magnet is the first component

at the left, followed by the target chamber,

aperture holder, quadrupole doublet, Wien

filter (5 m long) with high voltage supplies on

the top right end, magnetic dipole and pivoting

”tail" with quadrupole doublet and focal plane
detectors at the right end....................... 106

Photograph of the Spellman high voltage supply
(surrounded by wax to prevent sparking) mounted
directly to the wien filterooooo.OOOOOOOOOOOOOOOO 107

Illustration of the angle-changing technique 0
used for the RPMS with scattering angles of O ,
15 and 30 explicitly shown..................... 109

A-5

A-6

A-7

A-8

A-9

A-10

A‘11

Maximum achievable dispersion for the Mark VI
Wien filter assuming a magnetic field limit

of N70 Gauss. The magnification of the system

is unity for all calculations and the solid
angle is roughly constant over the entire

energy range.....................................

Schematic drawing of the X and Y beam envelopes
for two different optical modes of the RPMS......

One dimensional histograms calculated with
RAYTRACE for the three mass groups A-N9.50,51
assuming 0-25 at 20 MeV/A. a) With quadrupole
axis same as the Wien filter axis. b) With the
quadrupole axis displaced by u cm to reduce the
affect of chromatic aberrations..................

Calculation of a ray's displacement at the exit,

of the Wien filter as a function of the momentum
illustrates the large discrepancies between second-
order calculations and ray tracing for large
momentum ranges..................................

Calculation of the momentum bandpass of the
RPMS With the 3x18 OffsetOOOOOOOOOOOOO00.00....O

Two-dimensional histogram calculated with
the program RAYTRACE, illustrating the mass
separation at 20 MeV/A.........................

Vertical position vs. particle ID signal for

a) low mass dispersion b) intermediate mass
dispersion 0) high mass+dispersion. In a) Z-116
groups are seen with ’H‘ , ‘He2 , ’Li’ , ’2Be“
and "Bs forming the horizontal M/Q-3.0 line.
Diregtly abqve this line one can see 'Li’ , 1‘Be“
HBs , “C‘ having M/Q values 2.67, 2.75, 2.80
and 2.67 respectively. In b) the dispersion was
increased to eliminate ‘Li and NC with
electronic gates eliminating the Z-1 and 2-2
species. In 0) the dispersion was maximized in
order to eliminate as many M/Q-3.0 species as
possible........................................

4.

113

116

117

118

123

vi

LIST OF TABLES

TABLE PAGE

Table 2-1. Single nucleon matrix elements for p-sd
' shell model orbits........................... N2

Table 2-2. Coefficients used to determine coulomb
energy differences between nuclei............ N6

Table 3-1. Comparison between half-lives from the
present investigation, previous studies
and shell model predictions................. 76

Table N-1. Half-lives extracted from the different
‘ runs in the experiment which were used to
determine the "best" half-life values....... 85

Table A-1. Definition of the coordinates used in the
ion optical program TRANSPORT............... 95

Table A-2. Optical design parameters for the RPMS...... 119

Table A-3. Velocity, dispersion and M/Q scaling
features of the RPMS........................ 122

TABLE OF CONTENTS

LIST OF FIGURES00000000000000000000 ...... 0.0.0.000.

0... 11

LIST OF TABLES00000000000000000000000000....00000.00000 Vi

Chapter 1 - Introduction to the Study of Exotic Nuclei

Chapter 2

Chapter 3

3.1

3.2

3.3

Introduction and Motivation..............

Heavy Ion Production Mechanisms..........
Decay StUdieSO. ....... 00000000000000.0000

Effective Interactions...................

.. . 3
.... 19
.... 22

- Theory of Beta Decay and the Shell-Model

Introduction to Fermi and Gamow Teller Beta

Decay00000000000000000000000.00.00.000000

Introduction to Shell-Model Formalism....

Decay and Half-life Predictions..........

- Half-life Measurements of Neutron-rich
Introduction.............................
Experimental Set-up and Procedure........
Data Analysis............................

Result8000000000000000000000.00.000.00000

... 29
. 35
. . N5
Nuclei

... 58
... 61
... 65
... 73

Chapter A - Summary and Recommedations for Future Study
u.1 Summary and Conclusion......................

A.2 Recommendations for Future Study............

Appendix A - The Reaction Product Mass Separator

A.1 Design Concepts for Recoil Ion Analyzers
A0101 IntrOductionOO0.000000000000000000.00

A0102 Beam Optics Notationoooo000000000000.
A.2 Motivation for a Mass Seperator at NSCL.....
A.3 The M.S.U. Reaction Product Mass Seperator...

A.“ Testing and Performance of the RPMS..........

LIST OF REFERENCESOO 000000 000000.0000000900000000.0000.

79

81

86

93
101

10“

125

Chapter 1 — Introduction to the Study of Exotic Nuclei

1.1 Introduction and Motivation

The field of nuclear physics is dedicated to the study
of dynamical and structure aspects associated with a system
of nucleons interacting via the strong force. Until
recently, the testing ground for experimental investigations
of such nuclear systems has been limited to nuclei residing
on or near the valley of stability. Similarly for light
nuclei (ASAO) investigations of nuclear dynamics has been
restricted to relatively cold normal-density nuclear systems
where single-particle descriptions of the observed phenomena
prevail. The contemporary understanding of such combinations
of protons and neutrons belonging to the described regime is
based on a shell model theory. Although present day shell
model theories have proven extremely successful over limited
regimes, many questions concerning their global validity
have remained unanswered. Questions concerning the
appropriateness of spherical shell model descriptions for
nuclei far from the valley of stability may certainly be
raised since it is well known that the model breaks down at
the onset of regions of deformation. Can existing mass
theories be extended out to the very limits of particle
stability? If not, what are the implications associated with
the breakdown of existing systematics? In addithnuto the

many interesting questions concerning structure aspects of

2
exotic nuclei there are equally as many questions related to
the dynamical characteristics of hot high-density nuclear
systems. A vast preponderance of our current knowledge is

restricted to normal nuclear density (p,) and near zero

temperature (T~0). What then is the equation of state of
nuclear matter under extreme conditions of temperature and
pressure? Many of the suggested questions could not be
answered if not for the emergence of heavy-ion collisions as
a viable testing ground for such studies.‘

Heavy-ion collisions have added a new dimension to the
study of nuclear physics by providing accessability to vast

new territories lying outside the near-stable, p-po and T-0

domain. A range of differing experimental efforts have
emerged that study nuclear phenomena as a function of one

or more of the parameters (Tz,p,T). For instance one

experimental effort is directed toward the study of beta
decay of exotic nuclei which isolates in relative purity the
isospin dependence of nuclear systems. Structure and decay
investigations of exotic nuclei have already benefiAed
greatly from this new branch of physics. Experimental
investigations of the dynamical characteristics of such
collisions are also under way, yet the lack of detailed
theoretical predictions makes the experimental results
difficult to interpret.

The primary motivation of this thesis is to ascertain

information concerning the production and decay modes of

3

light neutron-rich nuclei. In addition another objective was
to help develop the necessary tools to facilitate beta decay
half-life measurements using high-energy heavy-ion beams at
NSCL. To accomplish the indicated objective, chapter one
deals with the current experimental status of heavy-ion
production mechanisms and decay studies followed by the
contemporary limits of our understanding of effective
interactions. Chapter two will review the shell-model
approach to beta decay and an appendix will be provided to
discuss the Reaction Product Mass Separator which was
developed and used for the decay studies given in chapter 3.

Finally, in chapter four, I will present my
suggestions and recommendations for future study using the
RPMS in light of the results presented here and availability

of different beams at NSCL.

1.2 Heavy Ion Production Mechanisms

There can be no denying that the study of exotic
nuclei has experienced a renaissance within the last two
decades due chiefly to the advantages associated with high-
energy nuclear reactions. Evidence for the prolific nature
of high-energy nuclear collisions for the production of

exotic nuclei began to take shape in the mid 1960's with the

0 ll 12 lb

15
discoveries of He, Li, Be, B, and B [0e66, P065,

P066]. Experiments using high-energy proton spallation of

u
Uranium extended our knowledge of the sodium isotopes [Th75]
past the limits of the s-d shell and in so doing radically
modified existing mass theories. Meanwhile, in Dubna heavy-
ion transfer reactions produced nearly 30 previously
unobserved nuclei in the low A region of the Chart of

Nuclides [Ar69, Ar70, Ar71a, Ar71b]. This work was extended

'00 23

at Orsay using Ar on .U at 6.6 MeV/A and resulted in the
observation of A new isotopes [Au79]. As accelerator
technology improved, high-energy heavy-ion beams became
available to the physics community for the production of
exotic nuclei. The first experiments utilizing high-energy
heavy-ion beams for the production of exotic nuclei began in

the late 1970's at the Lawrence Berkeley Laboratory (LBL)

000

[Sy79] using an Ar beam at 205 MeV/A. Within a year's

no
time, another experiment utilizing a rare Ca beam again at

LBL demonstrated the existence of 1“ new isotopes [We79].
Figure 1-1 illustrates the present day boundaries
associated with the light neutron-rich nuclei and indicates
some of the major contributors to establishing their
particle stability.

Concurrent with these experimental investigations,
schematic models describing the collision of two heavy ions
began appearing in an effort to resolve the observed

differences between high and low-energy heavy-ion phenomena.

A large class of these models took as their foundation

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classical physics thereby describing heavy ions as 'macro'-
entities composed of member nucleons. This classical
treatment relied on the impact parameter to describe the
collision dynamics and the resultant aftermath of nuclei.

It was found that a large percentage of the observed
heavy-ion phenomena could be explained by a relatively few
number of reaction mechanisms whose boundaries were
dependent on the projectile energy and impact parameter of
the collision [8079] (see figure 1-2). 0f the reaction
mechanisms illustrated in this figure, fragmentation and
deeply-inelastic transfer have proven exceptionally prolific
in the production of neutron-rich nuclei as discussed
earlier. The relative ability of fragmentation compared to
deeply-inelastic mechanisms for the production of exotic
nuclei can be seen in figure 1-3. The basic difference
between fragmentation and deeply-inelastic mechanisms for
the production of exotic nuclei resides in the dependence of
the target nucleus. At lower energies where the collishmu
time is longer than the transit time of a nucleon at the
Fermi level, the nuclei respond coherently during the
collision characteristic of a mean field interaction [Ne78].
Therefore, during a deeply-inelastic collision, neutrons
will migrate from the more neutron-rich target nucleus into
the projectile nucleus until the N/Z ratio of each member
equals the N/Z ratio of the composite system. This proves
advantageous since it is possible to produce nuclei having a

greater number of neutrons than the original projectile

 

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Figure 1-2. Schematic illustration of heavy-ion collision
mechanisms as a function of reaction cross-section
(equivalent to impact parameter) and bombarding energy.

        

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which is not the case for projectile fragmentation. However,
if high-energy 'exotic' beams are available, fragmentation
has definite advantages over the deeply inelastic mechanism

for the production of exotic nuclei. These advantages are:

i) The use of thicker targets can enhance the

yield of exotic nuclei by ~10 [3079].

ii) Greater kinematic focussing at these energies
directs a larger fraction of the total yield
into a tight, forwardly-directed cone [Cr75]
proving more compatible with the solid-angle

characteristics of existing spectrometers.

iii) The energy distribution of projectile fragments
is observed to be narrow [V179] reducing the
required momentum transmission of the spectrometer

system.

Combining the advantages given in i) and ii) result in a

factor of 106 improvement for fragmentation mechanisms when
compared to deeply-inelastic mechanisms. Quantitative
estimates of the isotopic cross-sections for projectile
fragmentation can be obtained using the fireball model

[We76, 6077].

10
The fireball model describes a heavy-ion collision in
terms of a two (three) stage abrasion-ablation (-FSI)
process as shown in figure 1-N. The peripheral collision
between a high velocity projectile and stationary target

results in the formation of three entities
1) Target spectator
ii) Projectile Spectator
iii) Participant

The model relies on the impact parameter to determine the
number of nucleons in each of the three final state entities
by calculating the volume overlap between the projectile and
target nuclei. The projectile spectator (representing the
exotic isotope) has nearly the same velocity as the original
beam except for the energy required to break the nuclear
bonds associated with the abraded nucleons as will be
discussed in chapter 3. The number of nucleons remaining in

the projectile fragment is given by

Aps- ApC1-F(v.B;S)J (1’1)

where F(v,B;s) represents the volume sheared away from the

incident projectile during impact. The dimensionless

11

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parameters v and 8 specify the relative size and impact

parameter characterizing the collisioninnde's signifies a

shape dependence. If both ions are assumed spherical with

sharp radii, four differing functional forms for F(v.B)

result depending on the region in v-B space describing the

collision (see figure 1-5)

2 3 2 2 l 2
F: - [1-(1-u > / Iii-(ext) J /
1/2 2
FII - 3/u(1—v) [1;g) -
V
l 2 2 3 2 2 l 2
1/8(3(l:3) ’ -[1-(1-u ) / JE1-(1-u) J ’ )(1;§)
H V
1/2 2 1/2 3
F111 - 3/u(1-v) (1:§) “[3(1-v) —IJ(1;§)
V V
FIV - 1
where
v - __5:__
Rp+ RT
8 - ..3---
R + R

(1-2)

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v/>/’
’ v = 1/2
V 0.5176:- ----- --———-—-—-1-
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Figure 1-5. Schematic drawing illustrating the different
regions associated with a heavy-ion collision as a function
of the normalized impact parameter 8.

1A

The different regions in v-B space are interpreted

physically as

I) A cylindrical hole is gouged in the nucleus Ap

(which is larger than AT)

II) A cylindrical channel is gouged in Ap, with a

radius smaller than that of Ap.

III) A cylindrical channel is gouged in Ap, with a

radius larger than that of AT.

IV) All of Ap is obliterated by A (whose radius is

T

larger than that of Ap).

Since regions I and IV result in the destruction of the
projectile fragment, only regions II and III will be

considered. Isotopic cross-sections may then be calculated

using
o(Z,A) - C(Z.A)o(A) (1-u)

where

15

2 2
0(A) - n{[b(A+0.5)] — [b(A-0.5)] } (1—5)

and the function C(Z,A) describes the ground-state proton-
neutron correlations in the projectile just before impact.
Two differing dispersion relations were used in the isotopic
cross-section calculations with figure 1-6 employing a
hypergeometric dispersion relation [Ra77]1nule figure 1-7
represents the isotopic cross-sections resulting from the
Ciant-Dipole-Resonance dispersion relation [M078]. The
results indicate relatively large isotopic cross-sections
for the abrasion stage however, the ablation stage will act
to reduce the primary distributions. The exact amount of
this reduction requires detailed information on the
fragments excitation energy and its angular momentum. One
popular prescription used to predict the fragment's
excitation energy involves calculating the difference in
surface area between the abraded fragment and that

corresponding to a sphere having the same volume.

Multiplying by the surface energy coefficient 0.9 MeV/fm2
predicts the excitation energy as shown in figure 1-8. The
resulting values for low-mass fragments are not very
realistic and generally do not predict enough energy for
nucleon emission. Furthermore, the theory assumes that this
energy has equilibrated throughout the entire fragment which
also represents a questionable assumption. At relativisth:

incident energies, the model assumes that angular momentum

16

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19
has not been acquired by the projectile fragment. The
remaining step would be to use something like an evaporation
code to predict the particle emission.

In concluding, we mention that two heavy-ion
mechanisms exist which provide favorable yields of exotic
nuclei. Fragmentation seems preferable to deeply-inelastic
transfer due to reasons discussed previously. A fireball
model was used to describe what occurs during fragmentation
and then used to predict isotopic cross-sections. Although
models exist which can predict the ablation stage of a
collision they are generally quite poor and contain
nonverifiable assumptions associated with the magnitude and
distribution of excitation energy. Thus in practice it has
become standard to reduce the primary yields by a factor of

ten to estimate the secondary yields [M080].

1.3 Decay studies

Until the late 1960's, beta decay data was limited to
nuclei lying relatively close to the valley of stability.
This limitation was imposed by the lack of adequate
production mechanisms capable of providing sufficient yields
of exotic nuclei so that their decay modes could be studied.
A significant contribution to the study of decay properties
of exotic nuclei occurred in the late 1960's when high-
energy proton spallation reactions were used to produce

large quantities of neutron-rich nuclei. Using an intense

20
beam of 2N CeV protons from the CERN proton synchrotron on

targets of Iridium and Uranium resulted in half-life

ll 27_3

determinations of Li and lNa [K169]. Coupling the
large production cross-sections associated with spallation
reactions with thick targets and intense beams resulted in
high yields of neutron-rich nuclei out to the very limits of
the sd shell. Experimental half-life determinations were
limited to alkali elements (Li,Na,K) since the technique
employed required the isotopes to diffuse through a heated
graphite foil where they would undergo surface ionization,
reacceleration and finally identification using a mass
spectrometer. Continued improvements and modifications of

the accelerator and mass spectrometer resulted in the half-

!2 108-50

life of Na (f-shell nuclei) and the observation of K

[K172]. More detailed experiments measuring delayed neutron
emission probabilities (1%”, beta Q values, and various JTr

assignments were undertaken for the same sodium isotopes

[R07N]. Pushing this work to the limit half-life

29 31

measurements for the daughter nuclei Mg were obtained
at the same facility [De79]. Concurrent with the work
performed at CERN, a group at Brookhaven National Laboratory

(BNL) undertook the study of Tz- +5/2 sd shell nuclei

13 10 19

[A176]. Using heavy-ion beams of C, 0, and F, they were

able to produce and measure masses, half-lives and

21 23 29 31 33 35

spectroscopic properties of 0, F, Mg, Al, Si, and P

21

representing the entire set of Tz- +5/2 nuclei contained

within the sd shell. In the lower mass region of the chart

I O
of nuclides, the Be(t,p) reaction was used to generate

12

Be and its half-life was then deduced as ~2N.0 ms [A178].

6 l 0

Similarly, using 31 MeV Li ions on a Be enriched BeO

in
target resulted in the half-life measurement of B [A174].

Quite recently, another significant advance occurred
which demonstrated a tremendous potential for extending
decay studies out to the neutron-drip line for light nuclei.
This new reaction mechanism essentially turned the
spallation mechanism around and used high-energy heavy-ions
as the projectile. The first half-life measurements

employing fragmentation of high-energy heavy-ion beams were

'00

obtained at Lawrence Berkeley Laboratory (LBL) using Ar at

9

285 MeV/A on Be. The experiment resulted in half-lives for

22 32
8 neutron-rich nuclei two of which ( O and Al) were first

time measurements [Mu82]. The new technique demonstrated the
potential benefit of heavy-ion beams for the study of exotic

nuclei, in particular, their decay modes. Recently, within

1 3
the last year the half-life of B was measured to be

I. 12

11.0 t 1.0 msec. using an 8N MeV/A 0 beam on a 0 target
[Du8u].
Limitations on the heavy-ion approach were mainly due

to low beam intensities and inadequate isotope separation.

22
The first results obtained at Michigan State University,
(presented in chapter 3), verify the tremendous capability
of heavy-ion reactions for the study of light neutron-rich
nuclei and paint a promising picture for future studies. In
addition to the MSU group, a Bordeaux-Ganil collaboration is
actively involved in decay studies and should provide
adequate competition in extending measurements well out

toward the neutron drip line [La8u].

1.“ Effective Interactions

One of the primary goals of nuclear science is the
determination of the effective nucleon interaction in the
context of the nuclear many-body problem. The achievement of
this goal is contingent upon acquisition of detailed
experimental information related to how the free nucleon
interaction must be modified in the presence of other
nucleons. Two schools of thought have emerged as to the most
advantageous method to be employed in the pursuit of this
goal. The first such school advocates a phenomenological
approach involving the determination of one- and- two- body
matrix elements, (comprising the model Hamiltonian)- through
a numerical least squares fitting procedure [Ch76]. The
effective Hamiltonian is generated in a truncated spherical
shell model basis through the use of a selected set of
empirical energy level data taken from nuclei believed to be

well described by this restricted Hilbert space. The

23

ultimate utility of such an approach can be determined when
experimental data emerges which may be compared to the
corresponding predicted features calculated with this
interaction. Although this effective interaction has been
specifically tailored to describe energy level data of
nuclei contained deep within this restricted model space,
other observables such as spectroscopic factors, ft values,
magnetic and electric transitions, and various magnetic and
electric moments will provide an independent check on the
quality of the resultant interaction [Br80a,Br80b]. When
this comparison is made, one generally observes remarkable
agreement for nuclei not far removed from those used to
generate the Hamiltonian. This outstanding agreement is of
course at the expense of introducing a sizable number of
free parameters.

In contrast, the second school of thought utilizes an
empirically determined nucleon-nucleon interaction which is
then modified through the use of many-body mathematical
techniques to account for the influence of the nuclear media
[Br71]. Although somewhat more fundamental than the
aforementioned phenomenological method, (since this method
results directly in an eloquent decomposition of the
interaction into free nucleon and many-body aspects), this
'realistic' approach is plagued by many difficulties
associated with the importance of various Feynman diagrams
as well as the procedure for summing them. When comparing

overall agreement of the 'realistic' and 'phenomenological'

2N

predictions to existing data, one must concede the greater
predictive capability to the 'phenomenological' approach.
Thus, it is in the context of the 'phenomenological'
approach that the salient features displayed by nuclei far
from stability will be discussed. The remainder of this
section will be devoted to the description of such a
phenomenological shell model technique.

Two basic features of this empirical shell model
approach must be elucidated namely, the choosing of an
appropriate model Hamiltonian and the selection of a
suitable truncated shell model space in which the model
Hamiltonian can be diagonalized. The model Hamiltonian
employed consists of one- and- two- body matrix elements

having the following form

1 1
a1 + 2 vklmnakalaman (1'6)

~ T
H - 2 eia1
where

e - single particle energies

1
Vklmn - two-body matrix elements
a: - single nucleon creation operator (1.7)

31 - single nucleon annihilation operator

Since the matrix elements of the model Hamiltonian must be
adjusted to fit energy level data, one is required to choose

a suitable basis set in which the energy diagonalization can

25

 

 

 

"30-05-037
‘ ‘ ~_°rl%§_uo) [so] ('OOSn)
- p (21 [40] -
3fiw30l_- Iplwl ,’ 0,5,2151t30]
\ -l." 1 p 3/2 ‘4) [32]
‘ 41-5314

‘ M10112] (“Nu

M-- 1:29] ’Mmm] (4°00

 

1 ‘fl
fi‘ ‘ ‘ 0 [.1 ‘ ‘ f 01 1/2 (2) [0] (16°)
‘ ‘ £133.“, [5]

m---_fll.m.--- “(2)91 (41-1.)

Figure 1-9. The extreme single particle orbits obtained by
solving the non-relativistic Schrodinger equation with a
Woods-Saxon plus spin-orbit potential.

26
be done. Futhermore, due to computational limitations
[Se68], one is forced to choose a finite subset of the
complete basis set and it is within this subset that the
wavefunctions will be expanded. Thus, it becomes imperative
to make a judicial choice of this subset if one is to have
confidence in the resulting set of wavefunctions. The

extreme single particle orbits (031/2,0p,/2,0p,/2,0d..,/2

,...), obtained through solving the non-relativistic
Schrodinger equation with a Woods-Saxon plus spin-orbit
potential, supply a suitable complete basis set (see figure
1-9). This basis set exhibits natural energy partitions
associated with shell closures which may be exploited in
making the proper choice of truncated model space. The
empirical shell model approach requires a three way

subdivision of the complete basis set

1) closed core
ii) active orbits (1.8)

iii) forbidden higher lying orbits

Thus, a nucleus characterized by A nucleons will have A-Ac

valence nucleons distributed among N active orbits in such a

way as not to violate the Pauli principle, where AC nucleons

are contained within an inert core. An individual valence
nucleon which occupies a specific shell model orbit will

interact with the core nucleons through the one- body matrix

27
elements which depend simply on the orbit quantum numbers.
Likewise, the valence nucleons interact amongst themselves
through a residual interaction characterized by the
remaining two- body matrix elements. These two- body matrix
elements depend on the individual j's of each particle as
well as the total J and T (and in one case also depends on

A). For example, in a full s-d shell calculation, one

assumes sum inert 016 core with valence nucleons distributed

among the active orbits (0d ,1s,/ ,0d ) such that the
2

5/2 3/2

higher lying orbits (0f,/ ,Og,/ ,1p,/ ,...) are
2 2 2

inaccessible. The corresponding Hamiltonian consists of 3
single particle energies plus 63 two body matrix elements
which are fit to 200-300 well-known energy levels found in
nuclei near the interior of the model space. The resulting
effective interaction is then used to generate a family of

wavefunctions wnTJv where

n - number of nucleons occupying the active orbits
(A-Ac)

J - total angular momentum (1.9)

T - total isobaric spin

v - counting index which identifies a particular

eigenstate of the nJT set

28
These wavefunctions then comprise the entire predictive
content of this empirical shell model approach and are used
to compute other observables against which experimental data
may be compared. Detailed calculations for beta decay will
be presented in chapter 2 of this thesis using wavefunctions
obtained from various 'phenomenological' interactions as

discussed above.

Chapter 2 - Theory of Beta Decay and the Shell-Model

2.1 Introduction to Fermi and Gamow Teller Beta Decay

Our current understanding of both the strong and weak
interactions has benefited greatly from the study of nuclear
beta decay. Since its first observation, nuclear beta decay
has represented a formidable curio which, like many curios,
resulted huaisubstantial advance in our understanding of
nature. From the unexpected observation of the continuous
energy spectrum characterizing the emitted beta particles,
which resulted in the prediction and eventual observation of
the elusive neutrino, to the role played in the downfall of
parity conservation [Le56,Le57,Wu57]- nuclear beta decay has
made a profound mark on contemporary nuclear science.
Furthermore, nuclear beta decay holds the promise of
providing a testing ground from which the neutrino rest mass
may be extracted [Ma69], which if accomplished would have
repercussions on the cosmological scale [St79]. In addition,
beta lifetime measurements prove extremely important in the
determination of stellar evolution since they represent the
slowest process in the primary nuclear burn cycle. As
indicated, the importance of beta decay to the discipline of
physics is multifaceted.umking it impossible to accurately
describe all aspects of this interdependence in a limited

amount of space. Therefore, the intention of this

30
introduction is to discuss the salient features of beta
decay and how measurements of its associated properties will
contribute to our knowledge of nuclei, particularly nuclei
far from stability.

Nuclear beta decay may be coined a semi-leptonic
process which involves the interaction of leptons with
hadrons and, as such, provides a unique setting in which to
study the coupling of leptonic and hadronic degrees of
freedom. The elementary processes thought to occur in

nuclear beta decay proceed in one of the following manners

n + p + e + C (electron emission) (2.1)

p + n + e + Ve (positron emission) (2.2)

where the electron neutrino Ve acts as a silent partner irx

the beta decay process except that it carries away 1/2 h of
spin and an energy which is determined utilizing Fermi-Dirac
statistics to describe the three body final state. The
formalism developed for handling a three body final state
using Fermi-Dirac statistics was able to describe the shape
of the observed beta spectrum. Likewise, it is the deviation

from the mv- 0 spectrum shape which proves to be a sensitive

test for the determination of the neutrino rest mass. The

first of these two processes represents the decay of the

31
free neutron which has an observed half-life of 623.6 1 6.2
seconds and provides information on the axial vector

coupling constant ga. The second process, representing the

decay of the free proton, is energy prohibited by
approximately 1800 Kev due to the greater rest mass energy
«on the right side of equation (2.2). Although nature does
not permit the free proton beta decay, this decay can occur
in the presence of a nucleus since the proton may draw the
necessary energy from the surrounding nuclear medium.
However, this energy exchange mechanism quite naturally
introduces nuclear degrees of freedom into the problem which
could wash out the resemblance between nuclear beta decay

and the elementary processes given in equations (2.1) and

(2.2). Observation of super-allowed J"? 0++ 0+ (T-1) beta
transitions indicate that this is not the case for Fermi
beta decay. On the other hand, observation of Camow-Teller
transitions does reveal a strong influence of the nuclear
medium on the corresponding lifetimes. This discussion of
beta decay will be limited to only super-allowed and allowed
decay mechanisms which are characterized by the following

selection rules and comparative half-lives

Fermi Transitions 2.9 5 log ft,/ 5 3.7
2

AJ - O
An-no

AT - o (2.3)

32

electron emission }
positron emission

Gamow-Teller Transitions N.N S log ft,/ 5 6.0
2
AJ - 11,0 ( 0 + 0 forbidden )
An - no
AT ‘ 1190 (20“)

AT _ i1 { + electron emission }
z - positron emission

The formalism developed for the study of allowed beta decay
classifies transitions according to pure Fermi, pure C—T, or
a mixture of both types of decay. Comparative half-lives of
allowed beta transitions may be written in terms of Fermi

and C-T matrix elements

K

ftix, ' g; a<r> + g; a<cr) (2'5)

 

where
l
B(F) - Fermi Decay Matrix Element

- Camow-Teller Decay Matrix Element

g - Vector coupling constant (2.6)

g - Axial vector coupling constant

33

223i!92119-§ _..
(m cz)’c - (1.775N1 t 0.00004)x10 ergz- cms-sec
e

This representation requires the determination of two

constants gv and ga which is best accomplished by measuring

the lifetimes of J"- 0’» o’ (T-1) Fermi transitions which

yield a value for gv along with measurements of the free

neutron lifetime resulting in a value for g; + 3g; . It

should also be mentioned that it has become customary to

decompose gv into yet more fundamental constants

e; - G’cosz(00) (2.7)

where

C - Weak Interaction Coupling Constant (2.8)

Oc- Cabbibo angle

The constant C is generally determined from the'decay of the
pi and 003(00) reflects the nuclear media contribution with

a value approaching one, implying less contribution of the
nuclear degrees of freedom. The most recent values of these

two terms are [Du83]

5 _2

o - (1.16632 1 o.ooooz)x10- CeV (2.9)

3N

cos(ec) - 0.97N8 t 0.0003 (2.10)

It has become apparent that the study of Fermi beta decay
reveals important information concerning the vector nature
of the weak interaction while also providing detailed
information on the isospin mixing properties of the Coulomb-
nuclear interaction.

Next, we focus our attention on G-T decays which
exhibit more complicated phenomena involving participation
of many nuclear degrees of freedom and resulting in a
substantial altering of the elementary processes. Camow-
Teller transitions involve both a spin and isospin changing
operator, whereas Fermi transitions simply involve an
isospin rotating operator. Thus G-T decays will provide
information on the spin mixing components of the nuclear
interaction which are believed to be comparatively large in
view of the fact that the nuclear interaction seems to have
little or no isospin mixing capability. Futhermore, G-T
transitions are valuable in evaluating the resemblance

between initial and final state wave functions which may

have differing J1' and T. Camow-Teller transition matrix
elements are observed to vary substantailly for differing
mother-daughter systems which is not the case for Fermi
transition matrix elements which almost always exhibit only

small deviations from perfect overlap. Before meaningful

35

structure information can be extracted from a comparison
between predicted and measured strengths, one must first
address the question of or renormalization arising because
of model assumptions as will be discussed in detail later.
For shell model calculations involving the full s-d shell,
this renormalization factor is seen to be fairly constant
having a value of approximately 50% as confirmed by (p,n)
reactions [0080].

One may well expect that G-T beta decay will provide
information on the coupling of low lying single particle
states to this high lying collective state. Likewise, G-T
decay provides an easily accessible test of empirical shell
model calculations which employ the isospin formalism. The
remaining portion of this chapter will deal quantitatively
with the shell model approach to allowed beta decay and
finish by presenting the predicted features of G-T decay for
light neutron rich nuclei for a variety of model

assumptions.

2.2 Introduction to Shell-Model Formalism

Comparative half-lives of allowed beta transitions, as
seen in equation (2.5), may be written in terms of Fermi and
Gamow-Teller matrix elements. For computational purposes
associated with the empirical shell model approach, it
proves conveinent to rearrange the aforementioned equation

into the following form

36

C

t; -
/. Irv+ fZC]B(F) . [fa+ fSZJB-(GT) (2.11)

 

where

fv - phase space factor for Fermi decay

fa - phase space factor for Camow-Teller decay

fF - phase space factor associated with electron

ec
capture for Fermi decay

(2.12)

f::- phase space factor associated with electron

capture for Camow-Teller decay

The constant C appearing in equation (2.11) measures the

+ +
pure Fermi decay strength which, when extracted from 0 + 0
Fermi transitions in the s-d shell, has the value 6170:“

[W178] comparing favorably with previously reported values

2
[Br78,La73-Wi80,Ti78]. The remaining constant [ga/gv) has
been incorporated into the modified Gamow-Teller matrix
element B'(CT). The utility of this formulation resides in
the complete separation of the structure dependence

contained in the matrix elements and the energy dependence

37
contained in the phase space factors. Futhermore, this
decomposition of partial half-lives into Fermi and G-T decay
components allows information to be extracted about both the
vector and axial vector interactions responsible for allowed
beta decay.

Fermi beta decay involves a transition between isobaric
analog states (I.A.S.) which, assuming charge independent
interactions, are identical. The inclusion of charge
dependent interactions breaks this exact analog symmetry
through the introduction of isospin mixing and a
corresponding coulomb energy shift which may be calculated
from the Isobaric Mass Multiplet Equation (I.M.M.E.). This
resultant energy shift changes the beta Q-value for the
transition requiring modification of the phase space factor
while isospin mixing necessitates a correction factor in the
Fermi matrix element. Evaluation of the Fermi matrix element
is straight forward resulting in

3(5) - [T(T-1) - T T (I-e) (2.13)

)5
21 2f if

where (1-e)-0.995 t 0.003 [W178] and represents the
deviation from perfect overlap due to isospin mixing. The
fact that this value lies close to 1.00 indicates that the
symmetry breaking is very weak. As mentioned earlier the
resulting energy shift will influence the final state

interaction between the leptons and hadrons which is usually

38
accounted for by introducing small multiplicative factors to

the phase space factor [K083].

6R - energy-dependent terms

AR - energy-independent terms (2.1M)

where these terms correct for the final state
electromagnetic interactions which modify the corresponding
phase space factors. Furthermore,1electron capture is seen
to compete with positron decay which introduces atomic
degrees of freedom into the problem. This however, does not
introduce a large uncertainty into the calculation since the
atomic wavefunctions are known with high precision.

This concludes the discussion of super-allowed beta
decay and directs the discussion toward Gamow-Teller
transitions which characterize the decay of light neutron
rich nuclei. The beta decay of neutron rich nuclei does not
proceed through the Fermi decay component since the isobaric
analog states increase in energy-as one decays back toward
the valley of stability. Thus the Gamow-Teller decay
component represents the only type of allowed decay which

simplifies equation (2.11)

t1 I (2.15)
f B'(GT)

 

39
The determination of the C-T matrix element proceeds from
the evaluation of linear combinations of one body matrix

elements 0 and single nucleon matrix elements S

JIJZ J1j2

according to

- (_ ) 2 p. s
x§t23§?‘77 Tzr “T2 Tzi J‘J’ 333’

(2.16)

The entire predictive capability of the empirical shell

model approach is reflected in the 0 elements, which

J1J2

reveal tuna degree of configuration mixing generated by the

model Hamiltonian and are calculated from

T AJ-1,AT-1
<w,111£a3‘u ajzl lllvi>

/2

 

DJ (2.17)

J - T
‘ 2 {(2AJ+1)(2AT+1)}

wheretnmetriple bar indicates reduction in both spin and
isospin and the wavefunctions are obtained from the
empirical shell model approach as explained in section
(1.N). The single nucleon matrix elements may be calculated

using

SJIJz- 183/ Svl < 9(niliJi)1 0T 1 9(n21232)> (2°18)

NO
and reflect the relative efficiency of the G-T operator at
converting model nucleons from one single-nucleon state to
another. The ratio of the axial vector to vector coupling

constants is taken to be

Isa/3v] - 1.2605 3 0.0075 (2.19)

which may be determined from the free neutron lifetime and

0+ + 0+ Fermi decays [W182]. The evaluation of SJ j follows
1 2

from knowledge of the aforementioned constant and

<‘/,|| 1 111/,> - /6 (2.20)

3.). 6

(9(n111j1)11 O llp<nzlzJ2)) ' V/FEIITT Cl‘lz 1112 Ijsz

I - IR R r dr (2.21)

 

CJ1J2_[(_)11+l/2_Jz Z/erj-IITT 5
1-12 --‘-§f::f ------- 1132
(2.22)
.. .. 11+1/2’J; 2(23 +1) 1/2
( ) 1 21‘+1 1 6J2v121‘/26'jiv-liil/2]

in

The resulting free nucleon values of SJ j for the various
1 2

active orbits employed in the calculations are given in

table (2.1). When the free nucleon values are used along

with the D to calculate partial lifetimes, one observes

JlJZ

systematically shorter lifetimes relative to experiment.
This 'quenching' of the or strength is believed to originate
from a variety of sources such as model space truncation
effects which include both core polarization and high lying
collective states involving the forbidden orbits
[Ma67,Sh7A]. Other effects include non-nucleonic degrees of
freedom such as delta resonances, mesonic exchange currents
and relativistic corrections to the nucleon wavefunctions
[Ch71,Ba75,Kh78,Mu73,To79]. The empirical alternative to the
exact calculation of this renormalization is to treat the

as parameters in a least squares fit to experimental

8.11.12

values of the G-T matrix elements [Br78]. When this was done
for the universal s-d shell interaction (USD) of Wildenthal
[W182] an orbit independent scale factor of 0.77 emerged,
representing a 69% increase in the predicted lifetimes as

compared to those obtained using the free nucleon 83 j
1 2

values.
The final issue to be discussed concerns the

evaluation of the phase space factor fa which when

determined allows the partial half-lives to be calculated

’/a
I]:
e/a
0,1
1,2
i/a
3/2
'/z

1,:

Table 2-1. Single nucleon
model orbits.

J.

112

TABLE 2.1

SJ J, (Free Nucleon)

 

-fl.797
7.506
8.881

'9.N9N
9.49“

-2.502
7.912

'7.077

7.077

matrix elements for p-sd shell

43
and compared to existing experimental values. Following the
prescription of Wilkinson and Macefield [W174], one may
obtain phase space factors accurate to within -0.5% for
nuclei used in this study. Evaluation of the phase space
factor starts from the analytic expression for f due to a

chargeless point nucleus

r, - (‘/,,)[2W3-9W§-8]P, + (l/,,)wo ih(w,+p,) (2.23)

where Wo equals the total electron end point energy

1/2

(electron rest mass units), Po-(Wo-1) and higher order

corrections are introduced through the multiplicative

factors given below

6 . 6 . 6 (2.211)

The resulting total phase space factor may then be written

as

fa - abaaaer, (2.25)

with the most important phase space correction factor being

GWM which is calculated in the form

44

n
6WM - exp[ 2 an(1nEo) 1 (2.26)

the an coefficients are gdven in [Wi74]. These values were

calculated assuming a uniform spherical charge distribution
whose radius was adjusted to fit electron scattering and
muonic x-ray data. Energy-dependent 'outer' radiative
corrections to order alpha, finite nuclear mass and
screening effects associated with atomic electrons were also

included in the 6WM correction factor. The factor 6R

accounts for the outer radiative correction to orders 202

and 220’ and is given by

'0 5

6R - 1 + 3.67x1o" |2| + 3.60x10- 22 (2.27)

where Z is the atomic number of the daughter nucleus. The

final correction factor 6 incorporates the effects of the

D

diffuseness of the charge distribution

3 l 36

.. . -6.
6 - 1 + 1.8.10 |z| - 1.2x1o |z|wo (2.28)

The evaluation of the total phase space factor depends most

critically on the beta Q value of the transition, an

approximate Es dependence, which requires an accurate

determination of coulomb energy differences between initial

45
and final states. These coulomb energies were assumed to

follow

.1/3

AEC(Z,A)- £c(Z)[2(Z+1)/AJ (2.29)

where the values of 50(2) were obtained from empirical

analog state binding energy differences and the neutron-

proton mass difference. The values for 50(2) are listed in

table (2.2) and supply the last component necessary for
determination of Camow-Teller transions using the empirical
shell-model approach. The following section utilizes this
formalism to predict G-T decay modes and half-lives of

neutron-rich nuclei.
2.3 Decay and Half-life Predictions

Beta decay features of neutron-rich nuclei have been
calculated using the shell-model formalism discussed in the
previous section. A variety of different model-space
assumptions and effective interactions have been used (see
figure 2-1) in order to obtain a comprehensive set of
predictions for many light neutron-rich nuclei. The most
complete set of beta decay predictions which include all

Tzs 5/2 nuclei falling within the sd shell were carried out

using the USD interaction [W183]. The USD interaction was

46

 

TABLE 2.2
Z 50(2)
8 3.509
9 3.999
10 4.300
11 4.787
12 4 5.020
13 5.495
1“ 5.695
15 6.086

Table 2-2. Coefficients used to determine coulomb energy
differences between nuclei.

u7

...... :2. .. ”32.2.2... 2... ._.. .22

.mcouuog mmml mso0gm> :00 000: m:0~000:00:0 0>00000~0
..-u mesmaa

0:03:00 2.0 05002.60 333:: 2.0 00 0.22.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0: 0:
_ . .1_
T0 ... ... .0 —:
s . a a . 0
8 ,8 8 8 ...
v. N. 3 o. o
m m m m m m . a
m. 2 m. I n. ~. . e
0 0 0 0 0 0 0 e 6
ON 2 o. ... w. m. e. e e
z z z z z z z z z z
nw - .~ ow m. o. t w. e x
o o o o o o 0 o o co 00Le+c:x-3
v~ n~ - 5 ON m. e e e
u T u u a h. u ... .
a ow m~ v~ n~ - .~ o~ e
2.022626262620211...
. 5 .5 mm a. n e ..

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

flex 6: 02 .0: .026 0: 0: unfit—... ...
en n N a
_< _< _< _< _< _< _< .< _< <_..
en 0n mm en mm Nn .n on ow .e~ ..
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#8
constructed using the isospin formalism and limited to a
fixed one-booy spectrum and a set of two-body matrix

elements which have been scaled by the A dependent factor

(18/A)°. . Predicted half-lives have been scaled by 1.69 to
account for the observed or quenching within the sd-shell
[Br83]. The calculated half-lives are compared to existing
experimentally determined half-lives in figure 2-2. Due to
the strong influence of beta Q values on the half-lives of
neutron-rich nuclei, a comparison between measured and
calculated Q values is presented in figure 2-3 which
provides insight into discrepancies originating from the
energy dependent contributions.

Beta decay predictions were extended down into the
p-shell orbits to include light neutron-rich nuclei that had

low-lying negative parity states. Level structures for 355/2

17 17 is 19
and decay modes were calculated for C, N, O. and N

using the Reehal-Wildenthal Hamiltonian [Re73] which spans

the space (Op,/ ,Od,/' .131/ ) [Cu81.Cu82]. The ground
2 2 2

state of "N was calculated to be ‘/,-, well separated from

17
its first excited state. However, 11) C the three lowest

1'

lying states (5/2+, 3/2 ,‘/2+) were predicted within 570 Kev

of each other making the ground-state J1r assig ment

difficult. Coupling this with the observed ground-state

13

inversion (‘/2+) of C forced us to consider all three Jn

H9

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50

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51

17
values as reasonable candidates for the ground-state of C.

17 is
Decay modes and half-lives for C and N are shown in

figures (2-“,2-5,2-6) where the half-lives have included the
0.6 quenching factor discussed earlier. It is observed that

exclusion of spin-orbit partners, such as Od,/ in this
2

calculation, results in a shorter predicted half-life than
observed experimentally [M070]. This can be attributed to
the mixing of differing phases associated.with spin-orbit
partners as seen in equation (2.22). In order to eliminate
this effect, additional calculations were done using the
Millener-Kurath interaction [M175] which represents a full

2hw calculation. Of particular interest are the predicted

17 15 ll 1»
decay modes of C, B, Li, and Be which are shown in

figures (2-7,2-8,2-9). These predictions prove interesting
since it is possible to extract spectroscopic information
about the parent and daughter nuclei through a half-life
measurement as will be discussed in section 3.“ of this

thesis.

52

 

 

 

 

 

 

 

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17N

Figure z-u. Gsmcw-Teller bete decey trenching ratios
predicted for the decay of "c using the Reehel-Hildenthel
interection. The predicted half-life is -100 as when a 'l,’
ground stete J' is essueed (quenching hes been included).

53

WP mundane

VQ‘ 3|

 

ucxmmu em K"
1" I

 

 

 

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a- 1" ’2 . 0.7‘ 80¢ vzi L“
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17N

Figure 2-5. Ganow-Teller beta decay branching ratios

predicted for the decay of "C using the Hillener-Kurath
interaction. This full 2h» calculation predicts an inversion

of the 'l.’ and 'l,’ states in "C in addition to predicting
a such longer half-life (quenching has been included).

5M

Isobel-61’

 

EXCIIAIIOI m DEVI
I

 

 

 

 

. an ‘\ '
9m

wi- _. 320:0 .. -

1/ 332
. vz' w
2-
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130

Figure 2-6. Gamow-Teller beta decay branching ratios
calculated using the Reehal-Hildenthal interaction. The

ground state of "N was predicted to be ‘l.. with “31 of the
branching strength popoulating neutron unbound states in "o.

55

    

 

 

 

 

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23.00?
zone? no no 312'
usoo<r
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CAflS/Z‘)
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5.00» —— es: (512')
3." ma“)
'11:"! m - (235:1) - n as
0.74 (512‘)
0.00 45 0.00“]?!
ISC

Figure 2-7. Ganow-Teller branching ratios predicted for the

decay of ”B using the Hillener-Kurath [MK] interaction. The
calculation predicts a 9.7 as half-life with all decays

populating neutron unbound states in "C.

56

 

 

 

 

 

 

news-cu
2&00T-
zen sxa‘
mqgo.t "Li
3
.5.
,. taco-r
2
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U
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us.

Figure 2-8. Gamow-Teller branching ratios predicted for the

decay of “Li using the [HK] interaction. Calculation
predicts a very short half-life with a 20$ branch to the

ground state of HBe.

57

 

 

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Figure 2-9. Ganow-Teller branching ratios predicted for the

decay of HBe using the [MK] interaction. The calculation
predicts a strong (98!) branch to a 1’ state in ‘“B.

chapter 3 - Half-life Measurements of Neutron-rich Nuclei

3.1 Introduction

The primary objective of this experiment was to utilize
the high-intensity heavy-ion beams provided by the K500
cyclotron for the production of neutron-rich light nuclei
and to measure their corresponding half-lives. In addition,
this experiment would serve as the first significant test of
the mass separating capabilities of the Reaction Product
Mass Separator (RPMS). The performance of the RPMS is
discussed in appendix A, as are its design and construction
aspects. This experiment utilized an isotopically enriched
1.0 beam on targets of 3’Be and 1“Ta for the production of
light neutron-rich nuclei. The target thickness was chosen
to stop the primary beam so that projectile fragments could
be observed at a 00 scattering angle. A schematic diagram
which depicts a 35 MeV/A 22Ne beam stopping in a 1.u mm2
carbon foil is shown in figure 3-1, illustrating what is
believed to occur within the target. At any location within
the target, an incident projectile may undergo a nuclear
fragmentation producing reaction products that must then
traverse through the remaining target material. The reaction
products have lower 2 values than the beam and, therefore,

more range allowing them to escape from the target. The code

DONNA has been used to calculate the energy loss of both the

58

59

 

 

 

 

 

 

 

 

 

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4°?

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pr

% (10 L0 L2

v

22

Figure 3-1. Schematic illustration of a 35 MeV/A Ne beam
traversing a thick carbon foil. The energy loss calculations
were performed using the code DONNA.

60
beam and fragments as they pass through the target. The
reaction products emerge with a broad.range of velocities
due to the distributed source within the target. The sudden
reduction in velocity associated with the nuclear collision

was calculated using

E n
A( _) - _1 (3-1)
A .
ps
where
A(E/A) - reduction of the projectile
fragment's energy per nucleon
Aps - number of nucleons in the
projectile-spectator
n - number of nucleons removed from (3-2)
the incident projectile
X - binding energy per nucleon of the

incident projectile

‘The large overlap of velocities between differing isotopic
species suggested by the calculation. indicates that for

thick targets the velocity slits at the end of the Wien

61
filter may have limited value. During the actual experiment
the target thickness was reduced (via a target rotation)
until the first indications of increasing background in the
focal plane detector system were observed. This technique
allowed isotopes with Z closer to that of the beam to be
observed and studied. The experiment also produced valuable

information concerning the isotopic yield dependence on
target material. For instance, using the 1"Ta target
resulted in a moderate rate of HBe whereas the ’Be target
did not produce any significant HBe rate, this target

material dependence was even more dramatic when l7C rates
were compared. This same target dependence was also see in
the Ganil work which provided the primary motivation for

using the heavier targets [Gu83].

3.2 Experimental Setup and Procedure

9
'The experiment consisted of bombarding targets of Be

10 I. 5

and ‘Ta with a 30 MeV/A 0 + beam extracted from the K500
cyclotron at the National Superconducting Cyclotron
Laboratory (NSCL). The experiment involved repeated
measurements of the time interval between the detection of a
heavy-ion reaction product and its associated beta, a
technique similiar to that employed by the Lawrence Berkeley

collaboration [Mu82]. The electronics setup used during the

62
experiment is shown in figure 3-2. During the actual
experiment the electronics could be run in one of two
possible modes corresponding to continuous-beam mode or
gated-beam mode. With continuous beam it was possible to
accumulate (within a reasonable time) enough statistics on
heavy-ion reaction products to optimize the isotope of
interest on the focal plane detector system. The gated-beam
mode was used when actual half-life measurements were
underway. Central to the electronics setup is the BEAM-OFF
gate generator (located near the center of figure 3-2) which
was used to eliminate the beam for a designated time period.
Elimination of the beam was iniciated with a TTL signal from
the BEAM-OFF gate generator and accomplished by shifting the
phase of the cyclotron RF (observed to eliminate the beam
within 40 usec). A quartz oscillator pulser feeding a scaler
provided the time information necessary to determine half-
lives (i.e. a clock) and was monitored frequently throughout
the run to insure stability. The focal plane detector system
consisted of a 2-dimensional position-sensitive proportional

counter [0r81] followed by a solid-state detector telescope
made up of a 300 mm2 x 100 um (Si) AE detector backed by a

500 mm2 x 5 mm (SiLi) E detector, as shown in figure 3-3.
The detector system was omly 1.0 m down line from the last
quadrupole doublet, just outside a 10 mil stainless steel
vacuum window. A pair of horizontal and verthxu.defining

slits were positioned directly in front of the 2-dimensional

63

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Figure 3-3. Schematic drawing of the focal plane detector
arrangement used in the half-life measurements on the RPMS.

65
proportional counter allowing the removal of interfering M/Q
species. Beta decay half-life measurements were carried out
one ion at a time since many different isotopic species had
similiar or identical M/Q values. This technique proved
useful since it would allow simultaneous measurements of all
isotopic species hitting the detector system. The beam off
time interval was adjusted to the longest lived species so
that ions stopping in the E detector had a good chance of
decaying before the arrival of the next ion. In addition to
on-line analysis all data were written to tape for more

complete analysis at a later date.

3.3 Data Analysis

Data analysis was carried.out in a tape-playback mode
using the histogramming program SARA [Sh85] on a VAX 750.
Data written to tape during the experiment consisted of two
differing types corresponding to beam-on and beam-off
events. Beam-on information consisted of five signals
providing particle identification along with horizontal and
vertical position information. Beam-off information
consisted of energy signals from the solid-state telescope
and time information from a pulser feeding a scaler. Heavy-
ion reaction products were identified using a particle
identification function (P.I.D.) coupled with vertical
position information related to the M/Q of the isotopic

species. The P.I.D. function was constructed using the AE

66
and E signals from the solid-state telescope according to

the following relation [Mu82]

(3+ AB) ' -E =-A z (3.3)

It should be mentioned that the expression stated above is
less valid when the ion loses a small amount of energy in
the second detector. Deviations from the functional form
given in (3.3) were seen for a small percentage of events in
this experiment as shown in figure 3-A, however the overall
quality of this functional form was very good as seen in
figure 3-5. Plotting vertical position vs. the particle I.D.
function results in islands corresponding to differring
isotopic species as illustrated in figure 3-6.iUecing 2-
dimensional contours around various isotopic groups allows
their beta decay spectra to be accumulated. Beta decay for
nuclei contained within this study either represent mother-
daughter decays or simple decays where the daughter nucleus
is stable or long-lived. The histogramming code was written
to allow up to a maximum of six half-life curves to be
generated simultaneously during a single run if simple beta
decay is appropriate. However, if a mother-daughter decay is
appropriate then only the mother and corresponding daughter
decay curves can be accumulated during a single run.
Histogramming the time interval distribution between a

specific beam-on event and all subsequent beam-off events

67

 

 

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Particle Identification Function

Figure 13-“. Spectrum of the E: detector signal vs. the
particle identification function illustrating the energy
characteristics of the reaction products hitting the focal
plane detector system.

 

MSU-85-455

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(AE+E)I'78 _ (E)'.78 = 22 AOJB

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N
hd
m 2.. _ II
N Be .
O< bliss
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8 Be ) l '48
3.
LI 9
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100 L 6Li‘ l
9U
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CHANNEL NUMBER
Figure 3‘5. Linear fit to mass centroids demonstrating

the quality of the particle identification function.

69

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Conummuams.

70
occurring within the beam-off time interval results in a
beta decay'cnn~ve corresponding to that particular isotope.
The channel to time conversion factor was obtained using the
pulser frequency recorded during the run (for many of the
runs this calibration was 0.610“ ms/channel). A lower level

energy gate of 2-3 MeV was placed on the electron energies

6
to insure that the He decays did not enter into the decay

curves for runs taken at M/Q-3. The efficiency for observing
a beta following a heavy-ion event should be approximately
50% due to the detector geometry and agrees well with the
efficiencies observed. To check the beta efficiencies, the
number of betas observed within each beam-off time interval
were monitored and the results will be presented in section
a of this chapter. Once the decay curves were generated a
least squares fit assuming a simple exponential plus
constant background was performed with the program
LEASTSQUARES to determine the half-life;

For the more complicated mother-daughter decays the
method used required a second beta to follow the first beta
within a fixed time period [T ms]. Setting this time value
equal to approximately 2 half-lives of the daughter
significantly cleaned up the mothers decay curve without
severely reducing the total number of events. It is expected
that this condition would result in approximately a factor
of 2 reduction in the total number of events in the parent

decay curve. The daughter's decay half—life could also be

71
extracted by taking the time difference between the first
and second betas and histogramming the resulting time
distribution. This method of dealing with mother-daughter
decays proved very effective and even allowed some
spectroscopic information to be extracted from the
resulting half-lives. For a number of runs a fast component
was observed in the beta decay spectra which is believed to
come from thermal neutrons generated during the beam-on
time. Thermal neutrons within the room having a
characteristic energy of i/MO eV (corresponding to
velocities around 2 m/msec) will eventually come in contact
with the room walls (or whatever) and undergo a (n,Y)
capture. The resulting Y can then be picked up in the solid-
state E detector and produce a "decay time" characteristic
of the room. In order to estimate the effect of this fast

component (Hi the resulting half-lives a contour was placed

1 1
around a long-lived isotopic species such as Be and its

decay curve was accumulated (see figure 3-7). By scaling the
number of events contained within the fast background
component with the number of heavy-ion events contained
within the contour results in a comparatively weak
contribution to the "true" beta decay half-life. Scaling
with respect to the number of heavy-ion events is justified
since the number of neutrons generated during the beam-on
time interval is proportional to the beam intensity. Details

associated with how these effects were taken into account

72

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component believed to originate
from thermal neutrons. The heavy-ion gate "'8 91'000 around th.

Spectrum of the fast
long-lived lithium isotopes.

Figure 3'1.

73
will be discussed in the next section along with the
resulting half-lives of the 8 neutron-rich nuclei observed

in this experiment.

3.“ Results

Half-life determinations for 8 neutron-rich light
nuclei are carried out assuming either a simple decay mode
or a mother-daughter decay mode. The experiment resulted in
basically three different runs which are labeled as A, B and
C. The parameters that are controlled in the analysis are

the following

i) Heavy-ion contour
ii) electron energy contour
iii) binning size

iv) [T] in mother-daughter decays
A discussion of how each of these parameters can affect the
extracted half-life will be given in section ”.1 along with
a summary of the "best" choices for each. Run A was taken
using a beam-off time interval of 0.7 sec. and a clock
frequency of 26.21u2 kHz. The RPMS was set to allow M/Q
species between 3.00 and 2.75 to reach the focal plane
detector system (see figure A-12 (b)). The isotopes observed

in sufficient quantity to allow half-life determinations

7H

11 lb 17 9 12 15

were Be, B, C, Li, Be, B and the daughter decay

l2 l2 3 17

of Be (i.e. B). Half-life determinations for Li and C
were hampered due to the short value of the beam-off time

interval as compared to their extracted half-lives. Previous

9

half-life determinations for Li gave 17511.0 ms which
allows approximately u half-lifes to be observed. Usingea
least squares fitting routine and assuming the curve to be
comprised of an exponential plus constant backgound resulted
in a half-life of approximately 150128 ms. However, the
constant background value was poorly determined and the fast

component associated with thermal neutrons was not taken
17

into account. The situation for C was similiar to that for

’Li indicating that another run should be undertaken with a

1'9

longer beam-off time interval (run C). The half-lives of B

i s
and B were determined using the simple beta decay

is
assumption. The resultant half-life of B is given in table

3-1 and represents our only measurement of this isotope. The

I 0e

half-life of B was averaged with the half-life

determination from run C and that result is given in table

11
3-1 as well. The half-life of Be (~13.8 sec.) could not be

determined yet it provided a method for obtaining the decay

time associated with the fast background component. To

12 12
determine the half-life of Be and its daughter B a

75
mother-daughter decay was assumed and resulted in the half-
lives given in table 3-1. Bun B was characterized by a beam-

off time interval of 0.52 sec. and the same clock frequency

1 l
as previously used. The RPMS was set for M/Q=3.5 with LA

also coming in with sufficient intensity to allow a half-

1 1
life determination. Since the daughter of Li is long-lived

a simple beta decay was used for its half-life determination

in
whereas for Be a mother-daughter decay was used. The
in.
statistics for Be were fairly low yet a good half-life
ii
measurement resulted which was also the case for Li (both

results are given in table 3-1). The half-life associated

1'0

with the daughter decay of Be was 10-11 ms indicating that

i 'e

the lowest lying 1+ state in B is below the neutron
threshold as shown in figure 2-9. The final run (run C)
contained essentially the same M/Q values that were seen in
run A, except the the M70 dispersion was increased and the

defining slits were narrowed eliminating many of the M/Q-3.0

1'0 9 1‘)

nuclei. Sufficient yields of B, Li and C allowed half-
life measurements of these nuclei. The beam-off time
interval was set at 2.04 sec allowing an accurate background
to be fit for the Li and C isotopes. The resultant half-life
determinations are given in table 3-1. The resulting decay
curves for runs A, B and C with their corresponding best
fits are shown in figure 3-8. Each curve has been truncated

in time for display in this figure. In each case the curves

76

 

 

 

Table 3-1
This Previous

Isotope Measurement Measurement Prediction
vLi 17311“ ms 175:1 msa 127 ms
HLi 7.710.6 ms 8.5:O.2 msa 3.5 ms
uBe 21.3:2.2 ms 2“.“23.0 msb 1“.7 ms
HBe “.210.7 ms --- “.7 ms
‘28 20.011.5 ms 20.n11.06 msc 22.7 ms
Ha 12.8:O.8 ms 16.1:1.2 msd 18.6 ms
HB 8.810.6 ms 11.0:1.0 mse 10.3 ms
‘7C 202117 ms --- (689,“87,396) ms

a) Reference [Ro7“] d) Reference [Aj76]

b) Reference [A178] e) Reference [Du8“]

c) Reference [Aj75] f) Reference [Br85]

Table 3-1. Comparison between half-lives from the present
investigation, previous studies and shell model

predictions

77

 

 

usuoas-oee
10'
1%:
1e'
1 9L1
‘.. l l A l 1 l I 12 L
200.0 “00.0 000.0 000.0 1000.0

 

 

 
 

 

 

 

L 1 142111

4

1211111

1

 

 

148e
‘.. 1 L L 1 4 1
.e 20.0 new ee.e «.0
"SEC
Figure 3-8. Decay curves with their corresponding best fits

for the 8 neutron-rich isotopes measured in this experiment.

78
were extended in the analysis to obtain a good determination

of the background.

Chapter “ - Summary and Recommendations for Future Study

“.1 Summary and Conclusion

The results presented in table 3-1 represent the "best"
half-lives as determined using a method of analysis
employing different combinations of the parameters listed in
section 3.“. The heavy-ion particle identification was made
using a combination of M/Q information (vertical position)
and particle 1.0. (via the solid-state telescope)
resulting in an unambigous particle identification as shown
in figures 3-5 and A-ii. The number of heavy-ion events
contained within each of the heavy-ion contours for runs A,
B and C are given in table “-1 along with the efficiency for
observing a corresponding event in the beta decay spectrum.
.All "simple" beta decay half-lives given in table “-1 were
obtained using every beta seen within the beam-off time
interval as opposed to using just the first beta within each
beam-off time interval. The relatively weak fast background
component was determined by placing a heavy-ion contour
around UBe for runs A & C and around the long-lived Li
isotopes for run B. The magnitude of the fast background
component was observed to be fairly small with half-lives
ranging from 3 to 5 ms. Only run B required careful
consideration of the fast background contribution to

extracted half-lives. Further investigations studing

80
possible correlations between the magnitude of the fast
background component and the electron energy did not reveal
evidence for the existance of such a correlation. The choice
of the electron energy gate did however change the extracted

half-lives with the largest deviation being around 9% for

V
Li (with the deviation representing mostly fluctuations

with a slight tendency toward predicting longer half-lives

17
for larger electron energy gates). The half-lives of C and

9
Li were taken directly from run C since run A had a

relatitnaly short beam-off time period. The shorter beam-off
time period resulted in a poorly fit background contribution
(which predicted too high a background contribution) and
thus a shorter half-life. The small time steps recorded
cunning the beam-off time period allowed the adjustment of
the time coordinate bin size. Too small a bin size resulted
in too few counts per channel to justify the use of a least
squares fitting procedure whereas larger bin sizes weighted
the decay constant strongly on the background. It was found
that the half-life dependence on bin size was around the 8%

level with larger bin sizes resulting in longer extracted

1 7

half-lives (although ,Li and C did show deviations from
this tendency). The mother-daughter decay modes were
characterized by a parameter [T] which was explained earlier
in section 3.3. This parameter was not found to affect the
extracted half-life significantly if its variation was

confined to around twice the daughter's decay half-life.

81
Shorter values of [T] substantially reduced the decay curve
statistics resulting in a poor overall fit.

In conclusion this experiment resulted in the half-
lives of eight neutron-rich light nuclei two of which
represent first time measurements. Error bars were typically
10% of the extracted half-life which proves competitive when
compared to previous measurements using similar techniques.
It is noted that the half-lives as determined from the
present investigation appear systematically shorter than
those obtained from previous measurements. The cause of this
discrepancy will be investigated in future experiments. The
background rate represented the major contribution to the
half-life uncertainty. Background events may have a number
of different origins such as the stainless steel vacuum
window. Since a substantial number of reaction products were
observed to stop within the AE detector it is reasonable to
assume that some of the heavier isotopes stopped in the
stainless steel vacuum window from which their emitted betas
would have a clean path to the detector system (this may be
eliminated with some appropriately placed magnets). In
addition this experiment produced valuable data concerning
the performance of the RPMS which will aid in the design of

the phase II device.

“.2 Recommendations for Future Study

82

The initial results of the first half-life measurements
using the RPMS provide a promising outlook for continuation
of these studies using different beam and target
combinations. More detailed spectroscopic studies resulting
in branching ratio determinations via beta-gamma coincidence
experiments should also be possible due totnuerelatively
background-free environment provided by the RPMS. Beta-gamma
coincidence experiments are important because branching
ratio»data provide more direct comparisons to shell model
predictions than do half-life determinations. In addition to
branching ratio data, beta-gamma coincidence experiments can
be used to obtain excited state energy informatnniforthe
daughter nucleus, mass determinations via beta 0 value

measurements, and may provide the information necessary to

11
make J assignments. One particular experiment of

considerable interest is associated with the beta-gamma

in

coincidence for the decay of Be to the predicted 0.9“ MeV

i w '
state in B. The gamma signature should be relatively clean

since the branching ratio to this state is predicted to be
~98 % and could provide confirmation of the result obtained
in the present experiment. Another recommendation for future
decay studies is the development of a “n neutron detector.
Calculations as verified by existing experimental data
indicate that as one moves away from the valley of stability

the neutron threshold energies become small giving rise to

83
beta-delayed neutron emitters thus the need for beta-neutron
coincidence experiments.

Further suggestions center on experiments to establish
optimized yields for neutron-rich nuclei using different
beam-target combinations. Results from the present
experiment suggest significant advantages associated with
heavier targets for the production of neutron-rich nuclei.
If this tend continues, as is suggested from the Ganil work
[Cu83], then the use of thorium and uranium targets should
provide even greater yields of neutron-rich nuclei than the

tantalum target used in the present study. Exploiting

22 '00
heavier beams such as Ne and Ar will allow the study of

neutron-rich nuclei in different mass regions. A proposal to

22
use Ne at 25 MeV/A on a thorium target has been accepted

and will be carried out this spring. It is anticipated that

17 10-20
this reaction will provide sufficient yields of B,

19-21
C and N to allow half-life determinations. The observed

deviation from projectile fragmentation systematics suggests
that a quasi-elastic or deeply-inelastic production
mechanism may be the dominant mechanism responsible for the
isotopic yields. Since both of the aforementioned mechanisms
are characterized by yields which peak near the grazing
angle it will be important to measure isotopic yields as a

function of scattering angle. Experiments performed away

0
from 0 will allow the use of thinner targets (since the

8“
beam can then be stopped in a faraday cup) which will result
in reaction products of higher velocity and less energy
spread. This concludes the section on recommendations for
future study and demonstrates the vast potential for
extending current investigations on exotic nuclei out to the

very limits of particle stability.

85

owns CA C®>Hm @Lm mm>HHIMHMS HH<

ouHH1mHm: amen 829 no con:HELouou on» a. now: so: one: mosam> *

 

5—HNON eNmHmmp maaswm mzzp coop on.

o.owm.w. o.o«m.m. oaosfim opm. omm mo.

w.owm.m_ m.o«:.m. oaosfim om_~ m_m— mi.

m..wm.om a a 2 ma.

>.oam.= a a 2 :mm ems.

m.mwo..m ..mwm.om o a : mam. . mznm om“.

.o..no.m 8229.8 ma.. . . mam. 8m..

. 8.0.2.2 . maaa.m .zao. . .2..

z.«me. .mmnom. m.ae.m com ..mz .4.
«\.p «\.p «\.~ 8008 muco>m muco>o muco>o encuomH

o cam m cam < cam mmooo 0 com m cam < mom

.1: manna

Appendix A

1.1 Design Concepts for Recoil Ion Analyzers

A.1.1 Introduction

A recoil mass analyzer is a device or instrument which
employs electric and magnetic fields to achieve a desired
separation between ions of interest and those considered as
background. The separation is most commonly a spatial one
lfldu81] although temporal separations are also used as in a
time-of-flight spectrometer [Pi8“]. The primary function of
a separator is to dump the beam so that only a very small
portion if any reaches the detector or collector. The second
function of the apparatus.is to separate the recoil nwclei
according to mass or-M/Q since mass and charge can not be
uncoupled in the electromagnetic force equation. The
difficulty associated with the design of a ion separator can
be appreciated when one observes that the ratio of
background events to 'good' events may reach values as high
as 10M or 10H for some heavy ion reactions. The majority
of this background is due to the beam with the remaining
fraction attributable to undesirable events produced
simultaneously with the 'good' events during the reaction. A

specific separator design must be taylored to the phase

86

87
space characteristics of the emerging reaction products.
These phase space characteristics vary dramatically from one
reaction mechanism to another, thus providing a natural
classification scheme for separators according to the type
of reaction products to be separated. Within this

classification scheme mass separators fall into one of four

catagories given by

i) Fusion-Product Separators
ii) Fission-Product Separators
iii) Spallation-Product Separators

iv) Fragmentation-Product Separators

For both fusion-product separators such as the Selector for
Heavy-Ion reaction Products (SHIP) at Gesellschaft fur
Schwerionenforschung in Darmstadt [Mu81] and the MIT-BNL
Recoil Mass Separator (RMS) [0180] and fragmentation-product
separators such as the Reaction Product Mass Separator

(RPMS) at NSCL, beam elimination is critical since reaction

products are peaked at ch Ah excellent review of existing
mass separators and their design features is given in
[En81]. The goal of this section will be to present
techniques applicable to the design of general separators
with subsequent sections making the transition from general
to specific design considerations taking selected examples

from the design of the Michigan State Reaction Product Mass

88
Separator (RPMS). The formalism developed in tJua following
sections apply equally well to the design of spectrometers
which differ from separators in that they allow direct mass
measurements. With this difference noted the remaining
discussion will use the words separator and spectrometer
interchangably.

Within the last 25 years significant advances in our
understanding of charged particle optics have been
witnessed. Beginning with the emergence of a first-order
matrix formulation of charged particle optics in the late
1950's [C058,Pe61] to the completion of an extended second-
order treatment in the mid 1960's [Br67], the field has
experienced a steady and rapid growth. With the second-order
tnatrix formulation acting as a foundation, 3 computer code
called TRANSPORT became available in the early 1970's
[Br70,Br73] ushering in a new era of computer assisted
spectrometer design. Extension of the matrix algebra to
higher-order has met with resistance because of the
cumbersome nature of evaluating a prohibitively large number
of matrix elements associated with standard beam line
components. In addition it is a commonly held belief that
alternative methods such as raytracing prove more efficient
for the determination of higher-order aberrations than would
ea generalized third-order matrix theory. Although more CPU
intensive, raytracing has the advantage that it includes all
higher-order aberrations which is accomplished by

numerically integrating the exact equations of motion as the

89
particle traverses through the system and thus in principle
is only limited by the accuracy of the user inputted
electric and magnetic fields. The program RAYTRACE has been
used extensively to design a number of magnetic
spectrometers [K081]. Recently, raytracing codes such as
MOTER [Th79] have been developed which employ a
sophisticated optimization algorithm capable of adjusting up
to “0 system parameters in order to achieve a maximized
system resolving power. Using a Monte Carlo simulation
process, MOTER is capable of reducing or eliminating higher-
order aberrations through the appropriate choice of system
parameters thus improving tremendously on its predecessor
RAITRACE. Although raytracing techniques prove extremely
powerful for the reduction of higher-order aberrations, it
is the first and second-order formulations that paint a
clear and concise picture of how one should view the
transport of charged particle beams. Thus it is through the
understanding of the matrix formulation that one gains the
insight or 'intuition' necessary for a systematic approach
to spectrometer design. In many respects the development of
a first-order solution represents the most difficult and
critical aspect associated with achieving the best possible

spectrometer system. This is true for two major reasons:

i) The first-order imaging and dispersion represent
the largest contribution to the spectrometer's

resolving power thus permitting higher-order

90
aberrations to be treated as perturbations on the

first-order solutions.

ii) The choice of the first-order configuration
affects the magnitude of all resulting
higher~order aberrations and the ease with
which these aberrations can be reduced or

eliminated.

Before discussing the procedure for obtaining first-
order solutions it is important to review the important
parameters associated with charged particle trajectories
through magnetic and electric fields. The ion parameters
which determine the trajectory of the ion through an
electromagnetic system are its charge 0, mass M, and
velocity V. Since M and 0 always appear togetJun~ as M/Q in
the force equations it is possible to reduce the required
ion parameters to two, either (M/Q,V) or (M/Q,P). In
1addition to time ion parameters, the dispersive and imaging
properties of common magnetic and electric field devices
used in spectrometer systems must be discussed. There exist
three basic electromagnetic devices capable of providing

first-order dispersion, they are:

i) magnetic dipole (momentum dispersion)
ii) electric field (energy dispersion)

iii) Wien filter (velocity dispersion)

91
Various combinations of the above devices can be used to
obtain M/Q, P/Q, T/Q and V dispersion corresponding to mass,
momentum, energy and velocity spectrometers respectively.
Another important class of electromagnetic devices are the
quadrupoles which provide first-order imaging for the
system. Because quadrupoles act as perfectly astigmatic
lenses they are usually found as doublets in spectrometer
systems in order to achieve focussing in both transverse
coordinates. However in a number of spectrometers the
dispersive plane imaging can betachieved directly from the
dipole field eliminating the need for a quadrupole doublet
but still requiring a y-imaging quadrupole. The first-order
focusing strength associated with a magnetic dipole is
proportional to the bend angle through the device and can
only produce dispersive plane focusing. The remaining
ingredients required to determine first-order solutions are
the physical and practical constraints imposed on the

system. These constraints generally revolve around

i) envelope size which determines the aperture
requirements of the differing electromagnetic
elements used in the spectrometer.

ii) available area which determines the maximum
physical size of the spectrometer.

iii) available electric and magnetic field strengths
which determine the overall dispersion and

imaging properties of the spectrometer.

92

A majority of the constraining criteria can be directly tied
to economic limitations. Finally, one must always keep in
mind the primary objective of any particular spectrometer
design, namely the type and degree of spectrometer
.selectivity needed for the physics under investigation. In
general one is often required to compromise the 'best'
possible design to insure the flexibility of the device,
allowing a range of differing experiments to be carried out.
Differing first-order systems are then composed of a
combination of the aforementioned elements in order to
achieve a desired first-order solution subject to the
imposed constraints. In general more than one first-order
solution exists which can satisfy the first-order criteria.
These differing solutions correspond to differing optical
modes of the system, and reflect such differences as point-
to-point v.s. point-to-parallel imaging or the number of
cross-overs etc. To chose the best first-order solution
involves a number of considerations as discussed earlier but
one suggestion states that the source of second and higher-
order aberrations is related to the magnitude of the first-
order transfer coefficients and their derivatives. Once the
fist-order solution has been chosen then techniques for the
elimination of higher-order aberrations come into play
starting with those of second-order.

A general prescription has been put forth describing

how to eliminate arbitrary Nth-order aberrations [Br70]

93

without significantly affecting the (N-1)th-order solutions.

This method relies on the matrix formalism to describe a

specific Nth-order coupling coefficient in terms of products
of first-order Taylor coefficients and a Greens function
which contains additional combinations of first-order Taylor
coefficients. The next section will deal with this in a
quantitative way and indicate the procedure used to reduce

higher-order aberrations.

A.1.2 Beam Optics Notation

In order to put the treatment of charged particle
optics on a more quantitative foundation we need to
establish a coordinate system and notation which is
conducive to the understanding of beam transport theory. The
Serret-Ferenet coordinate system, shown in figure A-1
represents such a system where an arbitrary 'ray' or
trajectory is defined relative to the 'central ray' of the
system. This 'central ray' may correspond to a particuhm~
P/Q as for a momentum spectrometer, M/Q as for a mass
spectrometer, T/Q as for an energy spectrometer, or V as for
a velocity spectrometer depending on the type of
spectrometer under investigation. The matrix formulation
employs a set of 6 coordinates (see table A-I) which are
used to describe the spatial and dispersive characteristics

associated with an arbitrary ray. For the sake of

9“

MSU°84'6 47
communes:

my. 9. ¢.2. y

p
8--I+-
P0

   

 

 

 

 

 

Figure A-t. Coordinate system used for magnetic optical
systems following the notation of TRANSPORT.

95

Table 1—1

x- radial displacement of the arbitrary ray with

respect to the assumed central trajectory.

e- the angle this ray makes in the radial plane

with respect to the assumed central trajectory.

y- transverse displacement of the ray with respect

CO the assumed tPIJCCCOPY.

o- the transverse angle of the ray with respect to

the assumed central trajectory.

i- the path length difference between the arbitrary

ray and the assumed central trajectory.

6p- the fractional momentum deviation of the ray from

the assumed central trajectory.

Table A-1. Definition of the coordinates used in the ion
optical program TRANSPORT.

96
completeness it will be shown how the matrix formulation
evolves from the exact equations of motion governing a
charged particle in a static magnetic field.
The matrix approach starts by describing a charged

particle trajectory in terms of a Taylor's expansion

x(t)-i (x|x§y:6§¢:6;°) X:Y:9g¢:5go

(A-1)

K A u v

X0) XoYoeo¢05

- k A
x(t)-2 (ylxoy.95¢:6p

X

Po

where x(t) and y(t) represent the transverse position of the
particle as a function of its distance along the central
trajectory (t). The subscript 0 indicates the coordinate
values associated with the ray at the object location (t-O).
The general curvilinear equation of motion for a charged

particle in a static magnetic field is given by [Br70]

d’T Q i +
P ___ - _ (-_ x 8) (A-2)
dT’ P

9
where Q is the charge of the ion, P its momentum, T its
position vector and T the distance traversed. Equation (A-2)

has made use of the fact that P is a constant of the motion

..p
and B represents the magnetic induction. Substitution of the

expression (A-i) into a coordinate specific form of the

97
equation of motion allows the Taylor coefficients to be
solved in terms of the magnetic field. If the magnetic field
is such that it can be expressed in terms of an anti-

symmetric scalar potential in the y coordinate.
¢(x,y,t)- _¢(xo—Y9t) (A’Z)

a significant simplification results. Condition (A-2)
requires the magnetic field to be everywhere perpendicular

to the magnetic midplane (y-O) and allows the description of

the magnetic field B(x,y,t) throughout all space if the

normal derivatives (in the x coordinate) of By(0,0,t) are

known. TWuatmedian plane magnetic field posessing this type
of symmetry may be described in terms of a multipole

expansion

n

By(x,0,t)- Bp 2 Kn(t) x (A-3)

where Kn(t) is proportional to the nth partial derivative of

By with respect to x on the central trajectory.

Substituting the multipole expansion of the magnetic field
given in (A-3) into the field dependent Taylor coefficients
results in coupling coefficients having the following

multipole strength dependence

98

 

1 -.
(xi|x§y§92¢:8g )- 1 “° 1 I. (t)
° Kixiu1leij

+ (terms involving K

where n-(k+1+u+v+x) and

11

t k
Iin(t)- { Gi(t.t) Kn(t) R (xlak) (Y|31)

(akpnk) 61(X01K).(901D)1(6p°.x) }

(Skunk) E { (Yopx)p(¢09\l)}

G,(t,1)- (x(t)|6(1))

G2(tpT)' (6(t)le(1))

G,(t.t)- (Y(t)I¢(I))

G.(t,t)- (¢(t)I¢(I))

o'eee

(i)

1 d1 (A-5)

(A-6)

Median plane symmetry conditions restrict aberrations to

those which contain y and/or e an even number of times.

Specifically, the minus sign in (A-“) is used when y and/or

41 appear 0,“,8,12,... times and the plus sign is used when

99
they appear 2,6,10,... times. The general form of the
coupling coefficients given in (A-“) represents a powerful
result which may be used to determine the optimum location
of a correcting multipole field which is located at the

value of t giving rise to a maximum in Iin(t)' Although this

technique provides a method of eliminating higher-order
aberrations it generally becomes impractical for n23 and in
some cases introduces differing aberrations of the same
order that limit the obtainable resolving power of the
device. For most spectrometer designs it is sufficient to
carry this solution out to second-order in which case a
ray's position on the focal plane is given by

xf--1)(xi<:1i)011 11%} (XIGIQJM‘iGJ (Ii-7)

where

(x|d1) - first-order Taylor coefficients
(xld a ) . second-order Taylor coefficients

1 J

01 C {xpe!Ya¢a6me6p}

where the mass dispersion coordinate 6m, similiar to the
momentum dispersion coordinate 6p, has been introduced to

fascilitate discussion of mass spectrometers. Again the

100
assumption of midplane symmetry results in the following

simplification

(x|y°)-(x|¢o)-(y|xo)-(y|6.)- 0 (A-8)

As stated earlier the coupling coefficients are dependent on
the multipole field components of order equal to or less
than the order of the coupling coefficient. The goal of
spectrometer design is to achieve the maximum resolving
power fxn~1a specified phase space transmission through the

device as is economically feasible. Resolving power for an

isotope separator is defined by

Rm- M/8M (A-9)

where 6M represents the full width at half maximum of a peak
at mass M. For a given object size Ax and magnification m of

the spectrometer system, Rm is directly proportional to the

system dispersion Dm-(xldm):

Rm-Dm/mdx (A—10)

where the dispersion is a direct measure of the spatial
separaticnici between focussed species of M and M+AM at the

focal plane implying the relation:

101

Dm- d(M/AM) (A-11)

Thus high resolving power is achieved through a combination
of large dispersion and low magnification at the focal plane
location. The methods outlined in this section will be used
to describe the design of the RPMS in the following

sections.

A.2 Motivation for a Mass Separator at NSCL

Recently, heavy ion reaction mechanisms such as
fusion, deep inelastic, and fragmentation have proven
prolific in the production of exotic nuclei. Utilization of
the high yields associated with these complex many-body
collisions is contingent upon the development of analyzing
systems capable of separating relevant events from a
plethora of unwanted events as well as transporting these
events of interest‘to-a background-free environment where
they may be studied using conventional detector systems. A
major branch of nuclear physics is devoted toward the study
of exotic nuclei, their stability, their decay modes, and
their half-lives. The nature of heavy ion collisions make
them promising candidates for extending this field of study
out to the very limits of particle stability. The
fragmentation mechanism which is seen to dominate at high

projectile energies is particularly promising since the

102
observed phase space volume associated with the reaction
products is remarkably compatible with the acceptance
capabilities of spectrometer systems used to study such
nuclei. Combining the contributions from thicker targets and

kinematic focussing features associated with high-energy

fragmentation should improve yields by approximately 10‘
over deeply-inelastic transfer reactions. From the
standpoint of spectrometer design, narrow angular
distributions are a welcome sight since they reduce the
effect of geometric aberrations on the mass resolving power.
Likewise, narrow momentum distributions reduce chromatic
aberrations that could degrade the mass resolving power.
However, even more importantly are the economic
considerations surrounding the use of large acceptance
spectrometer systems which require large-gap magnetic and
electric fields. Another important feature associated with
ttm high-energy nature of fragmentation is related to the
charge state distribution of the emerging reaction
products which is peaked at the fully-stripped value for low
mass fragments and provides yield gains of 2 or 3 over
conventional reaction mechanisms which spread a given mass
over many differing charge states.

Disadvantages associated with fragmentation reaction
products are their high electric rigidities which require
large values of the electric field integral to achieve high

resolving power. Although this does not represent a serious

103
problem for low mass nuclei where the percentage-wise
separation of differing M/Q species is relatively large, it
can represent a significant problem when heavier mass
reaction products are under investigation. Likewise heavier
mass fragments, unlike the lighter mass fragments, do not
concentrate a given mass species into a single charge state

thus reducing the overall collection efficiency.

0
Furthermore, the emerging reaction products are peaked at 0

requiring elimination of the beam which can be many orders
of magnitude more intense than the isotopes under
investigation. These problems although troublesome in no way
outweigh the benefits associated with the fragmentation
mechanism which in many cases provide the only known way to
reach the very exotic isotopes. The major advantages
associated with recoil separators when compared to ISOL type
separators are the shorter detection and collecbunitimes
allowing extremely short-lived species to be investigated
and elimination of ion source efficiency factors which bias
specific isotopic species. Although some overlap in
capabilities exist between the two techniques, they may
clearly supplement each other for the study of exotic
nuclei.

Taking advantage of the high intensity heavy ion beams
available from the K500, a mass separator would prove
tremendously useful for the study of exotic nuclei

particularly their half-lives and decay modes.CM'primary

10“
interestanwathe measurements of half-lives which require
relatively high beam intensities which is exactly where NSCL
will be the most competitive. The coupling of high intensity

beams with larger spectrograph transmission should produce

estimated increases of 10‘ in exotic nuclei yields enabling
new particle stability determinations as well as half-life

measurements.

A.3 The M.S.U Reaction Product Mass Separator

The primary goal in the development of a mass
separator at NSCL was tc1design and build a device capable
of utilizing the competitive features associated with heavy
ion beams available from the K500 cyclotron for the
production of exotic nuclei. The separator should employ
magnetic and electric fields to achieve the fast 'on-line'
isotope separation necessary for the study of short-lived
species and should focus reaction products of a particular
M/Q in x, y, and velocity on a mass-dispersive focal plane
thereby eliminating the need for a large focal plane
detector system and its accompanying background problems.

The phase I RPMS meets such design criteria by triple-
focussing reaction products, of 30 MeV/A or less, directly
from the target to a mass-dispersive focal plane
approximately 1“ m down line [No8“]. The RPMS achieves M/Q

dispersion through the use of an E X B device (Wien filter)

105
followed by a magnetic dipole and may be classified as a
standard Aston mass spectrometer arrangement. A pair of
quadrupole doublets are used to achieve the required imaging
where the first of these doublets is located directly in
front of the Wien filter and provides collimation of the
initially diverging reaction products. The remaining doublet
rides on the movable tail section just following the
Inagnetic dipole and focusses separated isotopes to a point
on the focal plane (see figure A-2). At the core of the RPMS
sitting on a movable undercarriage is a 5 m MARK VI Wien
filter on loan from the Berkeley Bevatron. The Wien filter
employs a +250 kv Glassman supply and a -“00 kV Spellman

supply to generate a uniform electric field (Ew) throughout

its “" gap. Since the entire Wien filter moves, it proved
most conveneint to mount the high-voltage supplies directly
to their corresponding feed-throughs so they could travel
with the velocity filter (see figure A-3). The Wien filter

magnetic field (8”) is achieved with a pair of current

sheets providing a maximum field of 600 Gauss @ 600 amp.
limited by available water-cooling. Just following the Wien
filter located at the pivot point of the RPMS is a large-gap
(6") dipole magnet acquired from Cornell which provides a

maximum field strength (Bw)max-“.3 kG (power supply

limited). The leading pair of large 8" aperture quadrupoles
were obtained from the Space Radiation Effects Laboratory

(SREL) and the remaining less massive “" quadrupole doublet,

106

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ucm anon—go ouaomumm .aco ugh: 20.. oz... :0 2.2.3.3 smegma» mu... :3...
Ammo~ I m. no.3: so; .aozsou 0322.323 [032. 9:5..an .Lonlmgo
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Louoouue. moon ssh .mzmx oga uo usuaogv ~a_moaoum .~1< anon—m

 

 

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107

 

Table A-3. Velocity, dispersion and M/Q scaling features of
the RPMS.

108
obtained from Maryland. sits atop the movable tail section.
The movable tail section is supported.and controlled by a

screw wench bolted to the top of the dipole and provides

variable tail angles between 00- 20°. Anaperture is
positioned behind the target to shield the Wien filter
cathode and prevent plate scattering. In addition, a pair of
horizontal velocity slits are positioned at the velocity
dispersive plane between the Wien filter and Cornell magnet
to privide additional velocity selection.

Two features of the M.S.U. RPMS make it unique among
mass separators first, it is the only triple-focussing
device designed for heavy ion reaction products with

energies greater than 5 MeV/A and secondly, it is not

0 O
confined to a 0 scattering angle but can be varied from 0.-

o
30 . The variable scattering angle was accomplished in such

a way as to limit the area swept out by the device thereby
allowing it to fit within the confines of the available
experimental area. As shown in figure A-ll this was done by
placing the pivot point of the device directly under the

dipole and using an 'inflector' magnet, located just before

0
the target, to swing the beam through :15 . The variable

scattering angle is beneficial because it eliminates

‘ 0
problems associated with the beam at O and it allows the

study of isotopic yields from predominantly non-

fragmentation mechanisms.

109

INX . IO .02!

 

CENTERLIPG OP RPMS AT=
o. —
'50 -.-

w ........

IS‘
.412

.; fifnnce'r Posmou son:

  

DWOL‘ .50

 

  
   
    
 
 

HVOT
NNNT

 

Figure A-Hn Itllustration of the angle-chaggingotechnique

used for the RPMS with scattering angles of O , 15 . and 30

explicitly shown.

 

110

The first-order optical design was obtained with a
modified version of TRANSPORT which had all 'path-length'
terms, contained in the fifth column of the first-order
matrices, replaced with mass dispersive terms similar to the
way momenth1<dispersive terms are used in the sixth column
of the same matrices. The first and second-order Wein filter
matrix elements of Ianoviciu [Ia7u] were calculated
separately with the code TRANSE [Ha80] and then input into
TRANSPORT as non-adjustable parameters. All calculations
involving the Wien filter assumed a 5 m length with a
magnetic field strength of H70 Gauss and maximum electric
field strength of no KV/cm. For high velocity reaction
products, mass resolving power limitations are dominated by

the electric field integral wadl which for the MARK VI Wien

filter is approximately 2 x 107 V. Although the electric
field integral dominates mass resolving power for high
rigidity fragments, it is always possible to increase mass
resolution at the expense of phase space acceptance
indicating that a more appropriate figure of merit may be

the total electric field strength parameter given by

V - E x l x d x w ~ ”.0 x 10 V-m (A-12)

where

 

111
E - electric field strength (40 kV/cm)

1 - effective length of BH (5m) (A-13)

d - field gap (0.1 m)

w - width of electric field plates (0.2 m)

Figure A-S, taken from [Ha81], illustrates how mass
dispersion depends on the energy of the reaction products
for a typical RPMS optical layout. Two different first-order
solutions, as shown in figure A-6, resulted from the
requirement of point-to-point imaging in both the dispersive
and non-dispersive planes and zero velocity dispersion at
the mass dispersive focal plane. The basic difference
between the two solutions is that solution (1) requires
slightly greater quadrupole focussing in order to achieve
the intermediate y cross-over not found in solution (ii),
otherwise they may be considered equivalent. The
contribution of higher-order effects on the mass resolving
power were examined with the code RAYTRACE, the results of
which are shown in figure A-7 (a). The results illustrate
the limitations on mass resolution, which are directly
attributed to chromatic aberration induced by the
quadrupoles, manifested through the large (xIGG) term. This
effect was reduced by offsetting the first quadrupole
doublet with respect to the Wien filter which had the effect
of reducing the momentum band-pass of the RPMS in such a way

as to significantly improve the resolving power of the

 

 

 

 

Zfir 75
0(08A/2)
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(cm/V.) KV/cm)
|.5- ‘45
LO 0 (238U) 4 30
0.5?- “ l5
0‘ 2 5; I6 20 510 :00 200

E/A (MeV)

Figure A-5. Maximum achievable dispersion for the Mark VI
Wien filter assuming a magnetic field limitcfl'u70 Gauss.
The magnification of the system is unity for all
calculations and the solid angle is roughly constant over
the entire energy range.

113

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115
device as shown in figure A-7 (b). A significant discrepancy
between the first-order resolving power and that calculated
with RAYTRACE stressed the importance of higher-order
chromatic tmnwns when large momentum bandpass is allowed as
illustrated in figure A-8. A two-dimensional histogram
calculated with the program RAYTRACE illustrates the type of

mass resolution predicted for the RPMS when one assumes a

O 0
1 X u angular acceptance and a 112% energy bandpass for

nuclei having 20 MeV/A (see figure A-10 and accompanying
table A-2). The RPMS transmission was calculated as shown in
figure A-9 and shows a transmission for the central mass of
approximately 115% with the +12% energy rays showing higher
transmission than the -12% energy rays. This concludes the
discussion of the design and construction features of the
RPMS. The next section will discuss the initial testing and

performance of the RPMS.

A.“ Testing and Performance of the RPMS

Initial testing of the RPMS required threading a 35

MeV/A “‘N5+ beam through the system to check its over-all
alignment and imaging characteristics. Scintilators where
placed at the target, intermediate velocity dispersive
plane, and the focal plane providing various beam viewing
locations. Verification of the RPMS aliegnment was hindered

by the H" offset between the leading quadrupole doublet and

116

MSU-85-O4O

DISPLACEMENT VS. AP (WIEN FILTER ONLY)

 

 

 

 

 

I TURTLE
A RANTRACE
3L) ‘5
A
E '. a
:2 L"' .
In A
g T .- ,
cn-LO- I ' . . " -
ES A
A
A
-10r ’ ‘ ‘ -
A
A
‘3
.5.0 l 1
(100 ZOIK)
AP

Figure A-8. Calculation of a ray's displacement at the exit
of the Wien filter as a function of the momentum
illustrating the large discrepancies between second-order
calculations and ray tracing for large momentum ranges.

117

 

 

 

 

MSU-85-041
.A.\
75.0%“ o ..
g .
g 5001' ‘
LL
U.
U
0 C
25.0 . ' 4
0.0 L1 1 L g 1 _,
-10.00 0.00 10.00 20.00
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Figure A-9. Calculation of the momentum bandpass of the
RPMS with the offset axis.

118

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120
Wien filter which required the beam to skim within 1 cm of
the botdmnn plate of the Wien filter. Although some
difficulty was encountered an intermediate image was
achieved at the velocity dispersive planeeuuiallowed the
Wien filter electric field to be tested and roughly
calibrated. Varying the electric and magnetic field
strengths produced the anticipated vertical displacements at
the velocity dispersive pdane thus verifying that the Wien

filter was performing as a velocity filter. With both Bw and

the tail angle at zero an image was obtained at the focal
plane. The imaging properties of the quadrupoles could not
be checked easily because of the quadrupole steering induced
by the off-axis displacement of the beam. The alignment
difficulties did not pose a significant problem however,
since the reaction products easily make it through the
system. Converting to a thick Be target and a focal plane
detector system consisting of a 2-dimensional proportional

counter (see section 3.1) backed by two large area (17.7

cm’) Si(Li) detectors immediately produced heavy-ion
reaction products at the focal plane detector system. To
establish a mass reference point, a search for 'beam
velocity' alpha particles was undertaken. These alpha
particles had a characteristic signature associated with
their punch through energy. Once the alpha particles were
centered on the detector it was possible to scale to lower

velocity M/Q-2 reaction products by turning down the

121
electric field strength and decreasing the quadrupole

strengths. This procedure resulted in the appearance of
+ +
‘Li’ and ‘°B‘ with a hole between associated with the

particle unstable 'Be“+isotope. The next step was to scale
to differing M/Q reaction products leaving the velocity bite
constant. This was done by moving the tail angle and
readjusting the quadrupole strengths. The final diagnostic
was to see if the dispersion scaled as expected which

, B , and

required similiar percentage increases in E2w , B c

w
tail angle. An example of increasing the mass dispersion is
shown in figure A-11. A summary table indicating the
different scaling laws is presented in table A-3.

Although the qualitative performance of the RPMS has
proven impressive, some questions still remain concerning
the first-order imaging properties of the device. Further
investigation of the performance of the RPMS will be
continued in upcoming runs. It would prove enlightening to
place the detector system at the velocity dispersive plane
and quantitatively study the properties of the Wien filter.
Other interesting questions associated with the transmission
of the RPMS must be investigated in order to attatch cross-
sections to observed nuclei. Although a sizable amount of
work remains, the ability of the RPMS to separate heavy-ion
reaction products and allow half-life determinations has
been demonstrated. In my opinion, studies of low mass nuclei

using the RPMS can continue with studies of the RPMS itself

 

Scaling

Parameter

Constant

Parameter

122

Table

Quadrupoles

A'3

 

 

 

P a

V.- 8w, Bw - Central Velocity

+P

+P

Percentage Change

Dm- Mass Dispersion

B 8
w w

4»? I»?

- -P

through Wien

+P

Filter

tail

Table A-3. Velocity, dispersion and M/Q scaling features
of the RPMS.

 

 

 

' v v v v v v v '

PHYSICAL

 

 

 

 

 

PARTICLE I. D. T

Figure A-12. Vertical position vs particle ID signal for

a) low sass dispersion b) Higher sass dispersion c)
maxi-us sass dispersion. 1." a) lot-.6 groups are seen with
'H' . 'He' . ’ti' . "Be’ and 1'3' forming the horizontal
Mid-3‘9 line..Directly spore this line one can see 'Li' .
“le’ . “l' and ”c' having H/Q values 2.67. 2.75. 2.80
and 2.61 respectively. In.c) the dispersion was increased to
eliainate 'Li' and "c' with electronic gates eliminating
2-1 and 2 species. In c) the dispersion was sasiaized in
order to elisinate as say MIG-3.0 species as possible.

12“

being carried out in parallel.

 

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