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IMPLEMENTATION OF A ,B-NQR SYSTEM AT THE NSCL
FOR GROUND STATE QUADRUPOLE MOMENT
MEASUREMENTS

presented by

RANKOTHGE R. WEERASIRI

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.—-————- i

IMPLEMENTATION OF A ﬂ-NQR SYSTEM AT THE NSCL FOR
GROUND STATE QUADRUPOLE MOMENT
MEASUREMENTS

By

Rankothge R. Weerasiri

A THESIS

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

MASTER OF SCIENCE
Department of Chemistry

2007

ABSTRACT

IMPLEMENTATION OF A ﬁ-NQR SYSTEM AT THE N SCL FOR GROUND
STATE QUADRUPOLE MOMENT MEASUREMENTS

By

Rankothge R. VVeerasiri

The nuclear electric quadrupole moment, Q, is a direct measure of the nuclear
charge distribution, and provides an important test of nuclear structure models. The
B detected nuclear quadrupole resonance (ﬂ-NQR) method is a technique to measure
ground state Q of unstable nuclei.

A B—N QR system has been constructed at the N SCL. Several challenges had to be
overcome to build the ﬂ-NQR system, including the implementation of multi—radio
frequencies, high rf magnetic ﬁeld strength, short rf application time due to the short
half-life of exotic nuclei of interest. The new system has four function generators to
produce the required rf signals for I S 2 nuclei. The rf signals are ampliﬁed to a
maximum of 250 W. After the ampliﬁer, a switched LCR system is used to maximize
power delivered to the rf coil. Six variable capacitors, a 50 Q resistor or impedance
matching transformer, and an rf coil represent the complete LCR circuit.

An rf leak test performed on the constructed system showed no signiﬁcant rf leak-
age from the high voltage rf box, which holds the resistor, transformer, and variable
capacitors. Rf magnetic ﬁeld strengths were measured to be 18.2 G and 17.6 G for
frequencies of 700i10 kHz and 1200i10 kHz, respectively, at maximum power.

First application of the new ﬂ-NQR system will be a precision measurement of the
Q of 37K. A value 114.7:t38.2 mb has been reported in the literature, and a new value
with reduced error is important to test the predictions of 3d shell model calculations.
The Q of 35K will be measured to ﬁnd evidence for inﬂuence of weak proton binding

energy in the Q of this very neutron-deﬁcient nucleus.

T 0
my mother, my family,
all my teachers

and friends

iii

ACKNOWLEDGMENTS

I am very grateful to my advisor, Professor Paul F. Mantica, for giving me the
opportunity to come to USA and to study at the MSU/NSCL, for his kind and patient
supervision, valuable guidance and encouragement during the total time period.

I wish to express my sincere gratitude to Dr. Kei Minamisono, who gave many
helpful advice and useful suggestions to fulﬁll the project successfully.

I thank my guidance committee including Professor Dave Morrissey, Professor
Hendrik Schatz and Professor B. Alex Brown for their valuable guidance.

I like to thanks all of my teachers in the Department of Chemistry / MSU and at
the N SCL

I would like to acknowledge my thanks to all the present and past members of
the beta group at the NSCL including Dr. J. Pereira, Dr. T. J. Mertzimekis, S. N.
Liddick, A. D. Davis, B. E. Tomlin, J. Stoker and J. Pinter who gave lot of help and
a friendly environment to work.

I also like to thank all the members of Professor Dave Morrissey’s group including
Chandana Sumiththrarachchi who let me to stay in his home when I ﬁrst came here.

My sincere thanks to all the staff of the NSCL, especially the design group and
the electronic group.

Finally, I like to thank Professor Rohini Hewamanna and Professor Pali Ma-

hawatte, University of Colombo, Sri Lanka, who encouraged me to study further.

iv

Contents

Introduction 1
1.1 The nuclear electric quadrupole moment ................ 1
1.2 Importance of the quadrupole moment measurements ......... 2

1.3 The quadrupole moment measuring techniques ............. 4

2 ﬁ-NQR Methodology 7
2.1 Spin polarization ............................. 7
2.2 Implantation of nuclei and preservation of polarization 1n a host crystal 13
2.3 Hyperﬁne interactions .......................... 13
2.4 NMR search through ﬁ-ray asymmetric angular distribution ..... 16
2.4.1 ﬂ-ray asymmetric angular distribution ............. 16

2.4.2 Manipulation of spin polarization ................ 18

2.4.3 Depolarization technique ..................... 19

2.4.4 Adiabatic fast passage (AFP) technique ............ 19

2.4.5 Extraction of quadrupole moment ................ 21

3 ﬂ-NQR Equipment Implementation 25
3.1 Radio frequency generation ....................... 27
3.2 RF ampliﬁcation ............................. 30
3.3 LCR circuitry ............................... 31
3.4 Rf coil ................................... 33
3.5 Stepper motor controlling system .................... 37
3.6 Vacuum relay switching ......................... 38
3.7 RPVO71 module .............................. 44

4 ﬁ-N QR system tests 48
4.1 Calibrating of stepper motor controllers for variable capacitor operation 48
4.2 Testing the whole system ......................... 49
4.2.1 RF leakage test .......................... 49

4.2.2 Cold switching conﬁrmation ................... 49

4.2.3 Low power test .......................... 51

4.2.4 Maximum rf ﬁeld test ...................... 52

4.2.5 Capacitance limits on LCR circuit ................ 53

5 ﬂ-NQR Application to 35"37K

5.1 Quadrupole moments of the nuclei in 3d shell .............
5.2 Quadrupole moments of potassium isoto es ..............

5.3 Quadrupole moment measurement of
5.4 Quadrupole moment measurement of 3

3K ...............
5K ...............

5.5 Experimental details ...........................

6 Summary

Bibliography

vi

54
54
55
57
58
59

62

65

List of Figures

1.1
2.1
2.2

2.3
2.4

2.5

2.6

2.7
2.8

2.9
2.10

3.1
3.2
3.3
3.4

3.5

Prolate and oblate shapes of nuclear charge distribution .......
The momentum transfer in a fragmentation reaction. .........

Schematic representation of yield and polarization curves of fragmen-
tation reaction. ..............................

The momentum transfer in a pick-up reaction. .............

a). Polarization of 37K in KBr and b). 37K ion yield as functions of
relative momentum in the proton pick-up reaction. ..........

Energy levels of I =3 / 2 nuclei under magnetic ﬁeld and magnetic ﬁeld
+ electric ﬁeld gradient. .........................

Deﬁnition of the Euler angles for description of the principal axis of
the electric ﬁeld gradient. ........................

Angular distribution of 6 particles from polarized nuclei. .......

The motion of nuclear spin under strong static magnetic ﬁeld and ro-
tating magnetic ﬁeld ...........................

Spin inversion in AFP technique .....................

a) Three frequency sets corresponding to different values of quadrupole
coupling constant for a I = 3/ 2 nuclei b) Double ratio vs coupling
constant ..................................

Schematic representation of the overall ﬁ-NQR system ........
3D drawing of the rf box .........................
Schematic representation of the radio frequency generating system.

Schematic representation of dips in the LCR resonance curve because
of gain reduction feature of the rf ampliﬁer. ..............

Schematic representation of a the LCR circuit .............

vii

10
11

12

14

17
18

20
22

24
26
28
29

32

3.6

3.7
3.8

3.9

3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18

3.19

4.1
4.2
4.3
5.1
5.2
5.3
5.4
5.5
5.6
5.7

3D drawing of the of the rf coil bobbin and the schematic representation
of the orientation of the coil bobbin ................... 34

Inductance of rf coil vs turn number. .................. 36

Schematic representation of the circuit used to measure the DC char-
acter of the rf coil. ............................ 36

Magnetic ﬁeld strength of the 17/17 coil as a function of direct current. 37

Schematic representation of stepper motor controlling system ..... 39
Schematic representation of power supply for motor controllers. . . . 40
Schematic representation of switch time measuring circuit. ...... 40
Relay switch response time. ....................... 41
Circuit diagram of relay switch controllers ............... 43
Relay switch control and rf gate signals ................. 43
Schematic representation of triggering and timing system ....... 44

Schematic representation of writing a program to the memory of RPVO71. 45

Schematic representation of a timing program of pulsed-beam depolar-

ization method for I =3 / 2 nuclei ..................... 46
Schematic representation of timing programs of continuous beam de-

polarization technique and AFP technique for I 23/ 2 nuclei ...... 47
Switch control signal and rf signal. ................... 50
LCR resonance frequencies at low power test. ............. 51
The circuit for the power tests. ..................... 52
Quadrupole moments of T=1/2 nuclei in the 3d shell .......... 55
Quadrupole moments of potassium isotOpes. .............. 56
Partial decay scheme of 37K ........................ 57
Transition frequencies for the quadrupole moment of 37K ...... 58
Decay scheme of 35K. .......................... 59
Transition frequencies of 35K ...................... 60
,B-NMR setup at NSCL .......................... 61

viii

List of Tables

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
4.1
4.2
4.3

Available function generators. ...................... 30
Technical details of the RF ampliﬁer. .................. 31
Technical details of the vacuum variable capacitors. .......... 32
Variation of inductance with turn number of rf coils. ......... 35
Variation of magnetic ﬁeld strength of the rf coil (17/ 17) with current. 35

Node address hardware conﬁguration ................... 37
Speciﬁcations of relay switches. ..................... 38
Switch response time of relay switches. ................. 41
Upper and lower limits for stepper motors. ............... 49
Results of the rf leakage test. ...................... 50
High power tests of the whole system ................... 53

ix

Chapter 1

Introduction

1.1 The nuclear electric quadrupole moment

The nuclear electric quadrupole moment is a quantity that describes the shape of
the nuclear charge distribution. A quadrupole moment of zero indicates a spherically
symmetric charge distribution. By convention, the value of the quadrupole moment
is taken to be positive for a prolate—shaped charge distribution and negative for an
oblate-shaped charge distribution, as shown in Figure 1.1. The electric quadrupole

moment operator is given as,

eQ = /p(f')r2(3cos26 — 1)d'v, (1.1)

where 862 is the quadrupole moment, p(F) is the charge density, F - (130, gb) in polar

coordinates and dv is the small volume at point r.

A
r

 

 

 

   

X

Oblote shape Prolote shope

Figure 1.1: Prolate and oblate shapes for non-zero electric quadrupole moment.

1.2 Importance of the quadrupole moment mea-
surements

The quadrupole moment is a valuable tool in the investigation of nuclear structure as
it provides detailed information on the spatial distribution of nucleons. For instance,
when the proton number Z is near a magic number (eg. Z =2,8,20,28,- - - etc), the
quadrupole moment changes from plus (one proton below magic number Z) to mi-
nus (one proton above magic number Z), suggesting good single—particle states for
these nuclei. As an example, the quadrupole moment of 39K (Z=20-1) is +58.5:i:6
mb [1] and the quadrupole moment of 418C (Z =20+1) is -156:l:3 mb [2]. The qua-
drupole moment can indicate the existence of conﬁguration mixing among states like
in the deuteron (3D1 state mixing with 381 state is compatible with the measured
quadrupole moment of 2.8 :l: 0.2 mb [3]).

The quadrupole moment is also an indicator of the nuclear core deformation.
When the nucleus has a stable core plus one-valence neutron, the single-particle shell
model cannot explain a non-zero quadrupole moment, as the neutron is neutral. As

an example, the quadrupole moment of 170 with the 160 core and valence neutron in

the 1d5/2 shell, is —25.78 mb [4]. The presence of a quadrupole moment of 170 can be
explained by the core deformation induced by the valence neutron. In the higher-mass
region, large quadrupole moments are observed that are several times larger than the
single-particle shell model predictions. As an example, the quadrupole moment of
§g4Bi is -700 :i: 200 mb [2], which contains an even number of neutrons and one odd

proton outside the shell closure at Z =82. The calculated quadrupole moment using

single-particle shell model equations [5],

 

J_
Q =Q- [ “2”” ] (13)
Sp mt (J+1)(2J+3) ’ '

is 246.4 mb. In equation 1.2 and 1.3, Qint is the intrinsic quadrupole moment, Qsp
is the spectroscopic quadrupole moment, I is the nuclear radius and J is the nuclear
spin. The intrinsic quadrupole moment is the quadrupole moment of a deformed nu-
cleus whose orientation is ﬁxed in space. However, quantum-mechanically, a deformed
nucleus and its orientation are described by a wave function. In a ﬂ-NQR experiment,
we can measure only the projection of the intrinsic quadrupole moment to the ref-
erence axis that is called the spectroscopic quadrupole moment. The enhancement
of the experimental quadrupole moment implies large core deformation due to the
collective effect of nucleons. The nucleons in the unﬁlled shells move in a net nuclear
potential produced by the core. This potential is not the spherically symmetric one of
the shell model, but undergoes deformation. Therefore, even in the ground state, the
core is affected by the nucleons in the unﬁlled shell because of their non-spherically
symmetry.

The shape of the nucleus is one of the most important properties in understanding
nuclear structure far from the stability line. From the experiments of the interaction
cross—section measurements, nuclear matter radii can be determined. However, the

nuclear charge radius of 8B determined by the ﬁ-NQR measurement is 20% larger

than the matter radius of 2.45 fm determined from the interaction cross-section mea-
surement [6]. Moreover, the measured quadrupole moment of 8B by ﬁ-NQR method
is twice as large as the theoretical value predicted by conventional shell model calcu-
lations. This may be a result of the presence of proton halo due to the small proton
separation energy (140 keV) as claimed by T. Minamisono et al. [6]. However, the
Coulomb force among the protons, in opposition to the nuclear force, may prevent
the growth of the halo structure and push the protons inside the Coulomb barrier. In
addition, the last valence proton of 8B lies in a 1193/2 state and the centrifugal barrier
is also against the formation of proton halo. M. Fukuda et al. measured the matter
radius of 8B using cross section measurements at projectile energies of 40 MeV/ A
and 60 MeV/ A and proved that it is comparable with the charge radius extracted
from the ,B-NQR measurement [7]. This proves that ﬂ-NQR technique could be used

as a tool to measure the radial extent of the nuclei.

1.3 The quadrupole moment measuring techniques

The ground state quadrupole moment of exotic nuclei can be obtained using several
different techniques. As an example, the quadrupole moment can be deduced from the
reduced transition probabilities, B(E2). For even-even nuclei, rotational energy levels
are much simpler than in odd-even or odd-odd nuclei. Therefore, even-even nuclei
are preferentially used to extract B(E2) values and to deduce the intrinsic quadru-
pole moment. However, the B(E2) connects two states and extraction of quadrupole
moment of a respective state is theory dependent.

Laser spectroscopy is another technique used to measure the quadrupole moment
that involves hyperﬁne interactions of atoms. A laser beam induces transitions among
hyperﬁne levels, which are a result of coupling of electron spin with nuclear spin. The
hyperﬁne magnetic coupling constant ( A ) and hyperﬁne quadrupole coupling constant

( B ), deduced from the resonance laser frequencies, can be used to deduce the magnetic

 

moment and the quadrupole moment. Restrictions in the laser spectroscopy technique
include the desired simple electronic structure of the system and limited available laser
frequencies.

Microwave spectroscopy can be applied to measure the quadrupole moment of
gas phase molecules. This technique is closely related to laser spectroscopy hyperﬁne
structure measurements. The intensity of the molecular beam should be at least 1017
pps to have a good accuracy [8]. Far from the stability line, the production rates of
isotopes are well below this limiting value.

Low temperature nuclear orientation is another method to determine the ground
state quadrupole moment. Lowering the temperature to the milliKlevin range induces
nuclear polarization, from which the quadrupole moment could be extracted from the
anisotropic distribution of 'y and ﬂ rays. In general, the lifetime of the nuclei under
investigation should be may minutes or longer, due to the time required to orient the
nuclear spin ensemble. For the study of exotic nuclei, lifetimes are typically in the
millisecond range.

The method that will be discussed in this thesis is the Beta Nuclear Quadrupole
Resonance ﬁ-NQR method. It has several advantages over the above-mentioned tech-
niques. In contrast to B(E2) measurements, the ﬂ-NQR technique is capable to mea-
sure the ground state quadrupole moments of odd-even or odd-odd nuclei with theory
independent way. The ﬂ-NQR method uses a strong magnetic ﬁeld that de—couples the
electron and nuclear spin that excludes the requirement of simple electronic structure
in laser spectrosc0py. The ﬂ-N QR technique is sensitive to the beam intensities even
around 101 pps that is about 16 orders of magnitude lower than in microwave spec-
troscopy. This technique is capable to cope with nuclei having lifetimes as low as 10
ms that is much shorter than the requirement in low temperature nuclear orientation
technique.

In addition to the advantages stated above, implementation of ﬂ-NQR method at

the NSCL is desirable, because the NSCL facility is capable of producing spin po-

larized [3 emitting nuclei far from the stability line. Low production rates and short
lifetimes are the major limitations in the quadrupole moment measurements. The B-
NQR technique is one of the best methods to measure quadrupole moment detecting
spin polarization by ﬂ-ray asymmetry even with those limitations. Another advan-
tage is that it is implemented as an improvement of the present ,B-NMR system that
has successfully measured spin polarization by ﬁ-ray asymmetry in several previous
experiments. The ,B-N QR is a technique to measure nuclear electric quadrupole mo-
ment of unstable nuclei taking advantage of ﬂ-ray asymmetric distribution from spin

polarized-nuclei and a detailed explanation is given in chapter 2.

Chapter 2

ﬂ-NQR Methodology

The ﬁ-ray detected Nuclear Quadrupole Resonance (ﬁ-NQR) is a technique to mea-
sure nuclear electric quadrupole moments of unstable nuclei taking advantage of the
ﬂ-ray asymmetric-angular distribution from spin-polarized nuclei. The ,B-N QR tech-
nique has four principle requirements.

1. Nuclear ensemble must be polarized.

2. Polarization must be maintained for the nuclear lifetime.

3. There must be electric quadrupole interactions to observe the quadrupole mo-
ment.

4. Destruction of polarization by applied radio frequency (rf) magnetic ﬁeld.

Each requirement will be explained in detail in the following sections.

2. 1 Spin polarization

The nuclear spin polarization is one of the major requirements of the ﬁ-N QR tech-
nique. The nuclear spin is a result of the coupling of intrinsic spin of the nucleons
to the orbital angular momentum of nucleons. The nuclear spins are, in general, ran-
domly oriented. Therefore a sample of nuclei has zero net spin orientation. However,

if the nuclear spins are preferentially oriented relative to some external reference, the

nuclei are said to be spin polarized. In quantum mechanics, the spin polarization can
be considered as a linear distribution of population in magnetic sub-states given by
equation,

P: Emam/I, (2.1)

where P is the nuclear polarization, m is the magnetic quantum number, am is the
population of magnetic sub-state m and I is the nuclear spin.

Low temperature nuclear orientation, laser optical pumping, nuclear reactions,
etc., can generate polarization. In this thesis, production of polarization by intermediate-
energy nuclear reactions is considered. In projectile fragmentation, nucleons in the
overlap region of the target and the projectile are removed and the remaining part of
the projectile moves as the projectile-like fragment with almost the same velocity of
the incident projectile. In this process, which is essentially peripheral, momentum is
carried away by the removed part and as a result the projectile-like fragment gains
an angular momentum L, which leads to the spin polarization of the projectile-like
fragment as shown in ﬁgure 2.1. According to the experiment done by Asahi et al,
the magnitude and the sign of the polarization change from low momentum to high
momentum [9] relative to the central momentum of the projectile-like fragment shown
in ﬁgure 2.2. By convention, the polarization is positive when the spin is parallel to
the vector {1‘0 x f)’, where 50 is the momentum of projectile and p" is the momentum
of projectile-like fragment. One of the important features of polarization induced by
fragmentation is that zero polarization at the peak of the yield curve, and higher
polarization where the yield is low. Therefore, low counting rates are expected in the
polarization measurements.

In the intermediate-energy regime (E/A = 20 - 200 MeV), the nucleon pick-up
reaction has a signiﬁcant contribution [10], speciﬁcally when the mass of the projec-
tile is close to the mass of the pro jectile-like fragment. In a pick-up reaction, a target

nucleon is preferentially picked up when that nucleon has the Fermi momentum and is

 

K [P
K\\
L \
X K
L R
p < p0 p > p0
Nea-side Far-side K

L=-RxK

P P

Figure 2.1: The momentum transfer in a fragmentation reaction in the case of a
Coulomb dominant near—side collision [9]. Here, p0 is the momentum of the incident
projectile, p is the momentum of the projectile-like fragment, R is the vector pointing
from the projectile-like fragment to the removed portion, L is the angular momentum
gained by the pro jectile—like fragment and K is the momentum of the removed portion
in the projectile rest frame.

Polarization

Yield

 

 

- P

y

8

Figure 2.2: Schematic representation of yield and polarization curves of fragmentation
reaction in the case of near-side collision with a heavy target [9]. Zero polarization is
observed at the peak of the momentum yield curve and the sign of the polarization
changes from low momentum to high momentum relative to central momentum of
projectile-like fragments.

10

 

Projectile

 

P0

Figure 2.3: The momentum transfer in a pick-up reaction in the case of attractive
far side collision in a light target [11]. Here, p0 is the momentum of the incident
projectile, p is the momentum of the projectile-like fragment, R is the vector pointing
the position of the picked-up nucleon, L is the angular momentum gained by the
projectile-like fragment and K is the linear momentum of the picked-up nucleon in
the projectile rest frame.

aligned along with the direction of momentum of the incident projectile [10]. The pick-
up reaction is also a result of a peripheral collision. The picked up nucleon introduces
an angular momentum to the projectile as shown in ﬁgure 2.3 because of velocity
difference between the picked up nucleon and the projectile. When the primary beam
momentum is comparatively higher than the Fermi momentum, signiﬁcant spin po-
larization can be expected from the pick-up reaction [11]. In the pick-up reaction, the

highest polarization occurs around the peak of the momentum yield curve as given

in ﬁgure 2.4.

11

 

P(%)
O 10 -§ 03 do
I

 

 

 

(b)

37K ion yield
on
O
o

 

 

 

I

-2.0 -1.5 4.0 -0.5 0.0 0.5 1.0 1.5 2.0
(P-p,)/po(%)

 

Figure 2.4: a) Polarization of 37K and b) 37K ion yield as functions of momentum of
37K to the central momentum of 37K [11]. 37K is produced by the proton pick-up

reaction of 36Ar + p —-> 37K with a beam energy of 150 MeV/ A and implanted in a
KBr single crystal. Maximum polarization occurs near the peak of the yield curve.

12

2.2 Implantation of nuclei and preservation of po-
larization in a host crystal

Polarized nuclei are implanted in a host crystal, which has an electric ﬁeld gradient.
In the ﬁ-NQR technique, the polarization is measured by the angular distribution
of 6 particles. Therefore, polarization has to be preserved until the B decay occurs.
Depolarization occurs due to two main processes: spin-lattice relaxation and spin-spin
relaxation. Spin-lattice relaxation or longitudinal relaxation is a result of interaction
between nuclear spin with the surrounding crystal lattice that is characterized by the
spin-lattice relaxation time T1. In the process of spin-spin relaxation, or transverse
relaxation, polarization is destroyed due to the interaction between opposite spins.
This process is characterized by spin-spin relaxation time T2. The spin polarization
is preserved with the help of a strong external magnetic ﬁeld H0 and symmetric
environment in the crystal. In addition, the strong magnetic ﬁeld is helpful to avoid the
possible reduction of the polarization through coupling between the nucleus and the
orbital electrons during its ﬂight from the ﬁnal degrader to the host crystal. The strong
magnetic ﬁeld prevents the coupling of the nuclear moments with the ﬂuctuating
electromagnetic ﬁelds produced by the radiation damages during the implantation

process into the crystal.

2.3 Hyperﬁne interactions

In the presence of a strong magnetic ﬁeld H0, a nuclear spin energy level breaks
degeneracy into several magnetic sub-states (Zeeman splitting) represented by the
magnetic quantum number as shown in ﬁgure 2.5. The energy of the magnetic state,
Em, is given as,

Em = —mguNH0 = hu, (2.2)

13

Ex :-I= 3/2

 

-3/2

 

 

 

-1/2

 

 

+1/2

 

 

 

+3/2

Magnetic Magnetic +electric
interaction interactions

Figure 2.5: Energy levels of I =3/ 2 nuclei under magnetic ﬁeld and magnetic ﬁeld +
electric ﬁeld gradient. In the presence of magnetic ﬁeld energy level splitting have
equal spacing however under the inﬂuence of electric ﬁeld energy spacing become
uneven.

where g is the nuclear g-factor , V is the frequency corresponds to the energy Em,
h is the Plank constant and p N is the nuclear magneton. The transition frequency,
which corresponds to the energy difference between any adjacent magnetic sub-state
is called the Larmor frequency, V L' In ﬂ-NQR experiments, a host crystal is used with
an electric ﬁeld gradient given as,

(121/

h

here, Vii is the electric ﬁeld gradient along it -axis in the crystal and V is the
electrostatic potential in the crystal. The electric interaction shifts the energy levels
from the Zeeman splitting as shown in ﬁgure 2.5, because of the interaction between
the quadrupole moment and the electric ﬁeld gradient. The largest component of the
electric ﬁeld gradient eq and the asymmetry parameter 1) of the crystal are deﬁned

as,

[Van] < [Vny < le2|: 89 = sz- (2-4)

14

The Hamiltonian for magnetic and electric interactions is given by, 2.5,

HzHAI+HQ

2(1Q
h 41(21 — 1)

 

I

where, Q is the electric quadrupole moment, e is the electronic charge, I is the
nuclear spin, I z is the third component of nuclear spin operator, 1+,I_ are the
raising and lowering Operators and i9 and d) are the rotating angles around z and Y
axis respectively. If the quantization axis is selected parallel to the external magnetic
ﬁeld H0, the electric part of the Hamiltonian (second term in equation 2.5) can be

re-written, using the Euler angle deﬁned in ﬁgure 2.6, as,

 

HQ = €22Q4I(2I1—1)l%(300826 — 1) + (gSiHQHCOSQWQIg — 1(1 +1»
+ (3 sin 20 - gsin 26cos 2gb + 1222 sindsin2¢)(1+1z + I21+)
+ (3 sin 29 — gsin 29cos 2¢ — 1% Sin951n2¢)(I—IZ + 121—)
+ (5:— sin2 6 + Z—(cos26 + 1) cos 205 — 2'3 sin6’sin2¢)13_)
+ (2 sin2 0 + :1-7(cos2 0 + 1) cos 205 + 2% sin63in2d>)13)] (2-6)

When the electric interaction is weaker than the magnetic interaction, the electric
part of the Hamiltonian HQ can be considered as a perturbation to the magnetic
part of the Hamiltonian HM. In the ﬁrst-order perturbation calculation, the energy
levels Em are given as,

e2qQ [3c052 0 — 1+ rysin2 9cos 26
41(21 — 1) 2 2

 

 

Em = —mg/iNH0+ ] [3n12—I(I+1)] (2.7)

Because of m2 dependence, the m states are not equally split as shown in ﬁgure 2.5.

The transition frequency u( between two adjacent magnetic states is given

mHm—l)

15

V _ gltNHo + quQ 3 [3c0320 — 1 + nsi1120cos 2o
(mHm-l) — h h 41(21 — 1) 2 2

 

 

 

][1 — 2m].
(2.8)

As an example, in the case of I =3/ 2, three resonance frequencies are 1/ L — l/Q, V L

and 1/ L + l/Q with 6:0 and 77:0 and the split between highest and lowest transition

frequencies equals twice quadrupole coupling constant 21/Q.

3e2qQ

I/Q = m (2.9)

2.4 NMR search through ﬂ-ray asymmetric angu-

lar distribution

2.4.1 ﬂ-ray asymmetric angular distribution

B decay is caused by the weak interaction which violates parity conservation [12].
Therefore, the angular distribution of ﬂ-particle emission is not symmetric relative to
the polarization direction as shown in ﬁgure 2.7, where ,B-rays are detected by placing
two sets of ﬂ-ray detectors at 00 (up) and 1800 (down). The angular distribution of

3 emission is given by equation,
N(6) ~ 1+ AP cos 6, (2.10)

where, N (6) is the number of 6 particles detected at an angle 9 between the direction
of ﬁ-ray and polarization P and A is the asymmetry parameter. The magnetic sub-
state energy levels can be examined by inducing a polarization change that is detected

by a change of N (6) The magnetic sub-state energy levels are related to the nuclear

16

 

 

b)

 

 

H
‘9-
A
>< o
V
"<1

 

 

 

 

0 Y
X
x
Z
[t
A Z
L}
. Z
Y i
c) 0 ¢ .y 2
¢ 9
x d) 45 .
O
¢9
X
x

Figure 2.6: a). Deﬁnition of the Euler angles for description of the axis of the electric
ﬁeld gradient where X,Y and Z are the coordinate of the crystal and x,y and z are
the coordinate in a lab frame. b—d). And its detailed circumstances of rotation from
the 9 = q5 = 0 state where 0 is the angle between Z and z axis and 45 is the angle
between Y and y axis.

17

E: Up detector 1:3

P¢0 =
H. P 0

 

c:::1 Down detector :1

Figure 2.7: Angular distribution of ,8 particles from polarized nuclei. [3 emission is
isotropic in the absence of polarization and it becomes asymmetric in the presence of
polarization in an external magnetic ﬁeld.

magnetic and electric moments and this point is discussed in the next section.

2.4.2 Manipulation of spin polarization

The spin polarization can be considered as a linear distribution of population among
magnetic sub-states as given in equation 2.1. Radio frequency (rf) is used to manip—
ulate the spin polarization by inducing transitions between two adjacent magnetic
sub-states. This leads to an equilibrium of the magnetic state populations. In the
presence of strong magnetic ﬁeld and without electric ﬁeld gradient, only one transi-
tion frequency, The Larmor frequency, is required for spin depolarization. However,
in the quadrupole moment measurement, several transition frequencies are required
to manipulate the population among energy levels, as the energy gaps are not equal
as discussed in section 2.3. The difference of the polarization before and after the
depolarization is a measurable property that is discussed later. There are two main
methods to manipulate the spin polarization with rf: depolarization and AFP tech»

niques.

18

2.4.3 Depolarization technique

In the presence of a strong magnetic ﬁeld H0, spin precesses around the ﬁeld axis at

an an ular fre uenc w . The e uation of motion for s in recession is iven as
O a

f a _.
90? = th x H0, (2.11)

where 7 is the gyro-magnetic ratio. For N MR, an rf magnetic ﬁeld H1, which rotates
at angular frequency 021, is applied perpendicular to the H0 as shown in ﬁgure 2.8.
In the rotating frame of H1, nuclear spin feels effective magnetic ﬁeld He f f and
precesses around H e f f as shown in ﬁgure 2.8 b),
af— hfxuf +wi+1f1 H" —[H'+J1+ff] (212)
at _ fl] 0 7 1 eff — 0 ,7 1 ' '
At the resonance, “’1 /7 is equal to H0 and H1 is equal to H e f f' As a result, the spin
precesses around the He f f = H1 that is perpendicular to H0 as given in ﬁgure 2.8
c) and as given in equation,

af

Due to time averaging, the spin expectation value along the z-axis I z becomes zero.
Therefore, spin polarization vanishes as it is deﬁned as the expectation value of the

z—component I z of the spin normalized by the total spin I as given in equation,

P=<?>. (mg

 

2.4.4 Adiabatic fast passage (AFP) technique

In this technique, the rf is swept once over the resonance frequency that results in an
inversion of the population between two adjacent magnetic sub-states. Two adiabatic

conditions have to be fulﬁlled to achieve efﬁcient AFP process. Firstly, the rf magnetic

19

E:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.8: The motion of nuclear spin under strong static magnetic ﬁeld and rotating

magnetic ﬁeld, here x,y,z are coordinates in lab frame and 112', yl, zlare coordinates in
rotating frame. a). Spin precession around the strong external magnetic ﬁeld b). Spin
precession around the effective magnetic ﬁeld in the rotating frame of H1 c). Spin
precession around the H1 = H e f f at resonance. d). Spin inversion in AFP process

20

ﬁeld strength H1 and frequency sweeping speed should satisfy the ﬁrst condition given

887
(1w
dt ’

(whim? >> (215)

 

where dw is the frequency modulation and dt is the frequency modulation time.

Secondly, H1 must be stronger than the local ﬁeld H L at the nucleus given as,
7H1 >> VHL- (2.16)

According to the relationship in 2.15, the sweeping speed should be less than the
angular velocity of spin precession around He ff so that the spin follows the change
of the effective magnetic ﬁeld. In addition, according to the relationship in 2.16, the
If magnetic ﬁeld should be strong enough to prevent any coupling of the nuclear spins
with local ﬁelds. When there is a static magnetic ﬁeld and perpendicular rf magnetic
ﬁeld, the spin precesses around the effective ﬁeld as explained in previous section.
Under the adiabatic conditions when the frequency is swept once, the direction of the
effective magnetic ﬁeld is inverted. As a result, the bulk spin is also inverted as shown
in ﬁgure 2.8 (1). Spin inversion makes the NMR signal two times larger than that in
depolarization technique as explain in the next section. However, higher rf magnetic
ﬁeld strengths are required to satisfy the AFP condition compared with depolarization
technique. In the ﬁ-NQR technique, spin inversion needs several applied frequencies
in sequence. As an example for a I =3/ 2 nuclei, three transition frequencies rfl, rf2
and rf3 are required. Three frequencies have to be applied in a sequence of 1,2,3,1,2,1

as shown in ﬁgure 2.9 in details.

2.4.5 Extraction of quadrupole moment

The quadrupole moment is extracted from the change of the spin polarization during

the rf spin manipulation. In the depolarization technique, the ratio between up and

21

 

= Population

 

-3/2 — — "—— '-—- '— *-
-1/2 —I—' T — —I T J _
trrr;;::

 

 

 

 

 

 

 

rf1 rf2 rf3 rf1 rf2 rf1

 

Transition frequency

Figure 2.9: In the case of I =3 / 2, spin inversion in AFP technique. Rfl inverts the pop-
ulation between magnetic state -3 / 2 and -1/2 and rf2 inverts the population between
-1/2 and 1 / 2 states and so on. Total inversion of population occurs after applying the
sequence of rf1, rf2, rf3, rf1, rf2 and rf1.

down counters is calculated for both If ﬁeld on (Ron) and off (R0 f f)’

_ l + APO _ 1 + AP]
Raff - grin}; Ron — ng—Tu-T (“7)

The difference AP = P0 — P1 reﬂects the change in the magnetic sub-state population
distributed to the rf excitation, the geometrical factor, 9 f’ is attributed to the imper—
fect symmetry of the experimental setup, for example, slight changes of efﬁciencies of
up and down counters. The geometrical factor is cancelled when the double ratio is

calculated as given in equation,

R
RD = 7%? a 1+ 2A(P0 — P1) = 1+ 2AAP. (2.18)

The obtained signal R D is maximum when AP is maximum (APzPO with P1 =0). In
the AFP technique, the double ratio gives twice as large an asymmetry change than

in depolarization technique as shown in equations,

_ 1+APO _ l—APO
Raff—Wm Ron—gfma (2-19)

22

R
RD = —1% z 1+ 4APO. (2.20)

One of the most important features in the quadrupole moment measurement is
that several transition frequencies are needed to manipulate the population among
energy levels, as energy gaps between adjacent m states are not equal to each other as
discussed in section 2.3. In depolarization technique, one resonance frequency equal-
izes population between two adjacent magnetic sub-states and reduces the spin po-
larization partially resulting in a small polarization change AP and hence small R D'
For I =3/ 2, the partial depolarization with one resonance frequency leads to only a
10% change of total asymmetry (AAP) and it needs hundred times more counting
time to reach the same statistics as in full depolarization, since the required time to
reach certain statistics is proportional to the ﬁgure of merit, 1/P2Y, where Y is the
yield . These facts strongly indicate the importance of the total depolarization for a
reliable and an eﬂicient measurement.

For I =3/ 2, the transition frequencies are calculated from equation 2.8 given in
sub-section 2.3, as a function of qu/h, and a set of three frequencies are applied
simultaneously. As discussed before, the split of highest and lowest transition fre-
quencies is proportional to l/Q. If the R D is measured as a function of the electric
quadrupole-coupling constant VQ, at the true coupling constant there is resonance
as shown in ﬁgure 2.10. With the known electric ﬁeld gradient of the host crystal,
the electric quadrupole moment can be extracted. For the extraction of quadrupole
moments are needed coupling constants of different isotopes measured in the same

crystal where one of the quadrupole moments is known,

kRO’IUTI 21971011177.
I 2.21

unknown Qunknown

Here, X represents the experimentally measured coupling constants.

23

a) Rf frequency b) R o =1+2AP

 

 

 

 

 

 

 

 

w
True coupling ------- --H+-- ..................... ----
constant <
|—~l
VL
H 2 V0 H
V scan Scan ][
V0 V0

Figure 2.10: a). Three frequency sets corresponding to different values of quadrupole
coupling constant for a I = 3 / 2 nuclei. b). Double ratio vs coupling constant. When
correct set of frequencies are applied which corresponds to the true coupling constant,
signiﬁcant change of RD can be observed.

24

Chapter 3

ﬂ-NQR Equipment Implementation

A ﬂ-NQR system is being implemented as an upgrade of the )B-NMR system at
the NSCL with its ﬁ-NMR technique capabilities left intact. The ﬁ-NQR system
can be more efficient to perform ﬁ-NMR measurements as well. During the upgrade,
several important points were taken into consideration as summarized in the following
section. In a magnetic moment measurement with the B—NMR technique, only one
transition frequency is needed because the spacings are equal among the nuclear
magnetic sub-state energy levels under a strong external magnetic ﬁeld. On the other
hand, in a quadrupole moment measurement with ﬁ-NQR technique, those spacings
become uneven as a result of the electric interactions introduced in the magnetically
interacting systems as explained in chapter 2. Therefore, the B—NQR system must
handle several different transition frequencies in sequences or almost simultaneously
in order to efﬁciently equalize or inverse the population of the magnetic sub-states.
Application of multiple-frequency NMR requires fast switching among these different
transition frequencies because the exotic nuclei of interest have very short life-times
(in millisecond range). Also, a high radio frequency (rf) magnetic ﬁeld strength is
one of the important requirements for efﬁcient measurements in both ﬂ-NMR and
ﬁ-NQR techniques, especially when the AFP technique is performed. A signiﬁcant

current should ﬂow through the rf coil to exert a high magnetic ﬁeld (> 10G), which

25

........ Rf signals

 

''''' Logic signals
FG Function generators 250W
LAN Local area network ampliﬁer
" """"""""""""""""""""" Rf box
Mixer $50 .0
. Relay switches

 

 

_________ //f///

Pitta?

. .. . .2. . _ .5- . _® i Six Variable

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
i ' -
-i!l--:---i----i---®Gates relay 5 capacitors
I - |. i i 1 i switch 5
i ! il FGl FG2 FG3 FG4 Driver ' """ :
a | . . I. ...... : I ....... E f
l i I : —+ I
I _ ' _ . _ . i 2 1 2 '
il_'1:_-.'_1RPV071P ----- _._._._.| ,
Six motor iNMR
VME bus drivers chamber
LAN I
l Spdaq ! > Device server

 

 

 

 

 

Data U Vault

 

Figure 3.1: Schematic representation of the overall ﬁ-NQR system, which contains
six LCR circuits and is capable of handling four different radio frequencies at this
moment depending on the number of function generators.

leads to a large voltage drop across the If coil in the kV range. Therefore, all the
components in the LCR system should operate at the high voltage (>1 erms)
and high current (>7-5rms) including high voltage capacitors, a high power resistor,
vacuum relay switches etc. In the present system, a 250 W rf ampliﬁer is used to
produce high rf magnetic ﬁeld strength. The schematic representation of the overall
,B-NQR system is shown in ﬁgure 3.1.

There are four function generators, which produce different transition frequencies

26

relevant to speciﬁc electric coupling constant. A pulse pattern generator, RPVO71,
triggers the function generators in sequence. Each rf signal is gated using the same
signal that triggers the function generator. After gating, the rf signal goes to a 250 W
rf ampliﬁer and then to a LCR resonance circuit. A 50 Q resistor or a transformer fulﬁll
the impedance matching between the ampliﬁer and the rf coil. A 50 Q resistor, six
variable capacitors and an rf coil make up virtually six independent LCR circuits. The
variable capacitors are controlled to tune the circuit to a speciﬁc frequency by stepper
motors, which are remotely controlled by stepper motor drivers. Relay switches are
used to select one of the LCR circuit out of six, depending on the transition frequency.
These relay switches are remotely controlled by a switch driver system to which TTL
control signals are sent by the RPVO71 pulse pattern generators. An rf box contains
the impedance matching transformer, a 50 (I resistor, six variable capacitors, six relay
switches, six relay switch drivers and a DC power supply for the switch drivers as
shown in ﬁgure 3.2. The rf coil, which produces rf magnetic ﬁeld for NMR, is placed
in the vacuum chamber in the middle of the NMR magnet. The rf coil and the rf box
are connected by a coaxial 50 0 cable. Each component will be explained in detail in

the following sections.

3.1 Radio frequency generation

Four different radio frequencies can be handled in the present system using four
function generators manufactured by Agilent Technologies. Some technical details of
the function generators are given in the table 3.1. The function generators can be
triggered internally or externally using TTL logic signal to start a linear frequency
sweep. The rf signals are gated by a module (X2M-01-411B / Pulser Corporation)
using trigger signals from RPVO71. The rf signals from different function generators
are gathered to one path by a logic OR gate (433A / ORTEC) and sent to a 250 W

ampliﬁer. The overall representation of the radio frequency generation and related

27

Stepper motors Rf output
. > . x, .

it

1.5“

I III: -.

I

- ‘V!‘ V .-
ipgl

.1: ..

l‘.

 

Figure 3.2: 3D drawing of the rf box.

instruments are shown in ﬁgure 3.3. The 33220A function generators have LAN ports
and are assigned their own IP address. The 33250A function generator has a serial
port, which is connected to a device server (USB 10 / LANTRONIX) with a LAN
port and IP address. A program, 33220A.tcl, written in Tel script is used to control
the device. In the control program, the carrier frequency, the amplitude of output
voltage, Sweep or FM mode, frequency modulation range and modulation time are
speciﬁed. In sweep mode, the function generator steps the speciﬁed frequency region
by changing the frequency every 40 ns. Thus, the sweep time determines the sweep
frequency resolution. In FM mode, the step is much ﬁner than that in sweep mode.
Selecting a trigger mode from IMM or EXT, an internal triggering or an external
triggering can be activated, respectively. In FM mode, only IMM trigger can be
selected. For the depolarization, sweep mode or FM mode and IMM trigger should

be used and for AFP, sweep mode and EXT trigger has to be used.

28

 

From other
Function generators - ------- ~>

 

 

Mixer ---> to ampliﬁer

 

 

 

 

Gate
signal ! Rf

 

 

 

 

NIM to TTL
converter

 

 

 

 

 

 

NIM

 

 

ECL to N IM
converter

 

 

 

ECL

 

 

RPVO71

 

 

 

LAN / serial

Control
program

 

 

I------>

VME bus

 

PC

 

 

Figure 3.3: Schematic representation of radio frequency generating system. Four func-
tion generators are triggered by RPVO71 and one rf signal out of four is selected by
the same gate signal as the one used for function generator triggering.

29

Table 3.1: Available function generators. Four function generators are used in the
system, which manufactured by Agilent Technologies. Three of them can generate rf
up to 20 MHz and one can generate rf up to 80 MHz.

Type 33250A 33220A
Quantity 1 3

 

 

 

Frequency range

1 qu - 80 MHz

1 IIHZ - 20 MHz

 

Amplitude

10 mVpp - 10 Vpp

10 mVpp - 10 Vpp

 

FM frequency range

2 InHz - 20 kHz

2 mHz - 20 kHz

 

 

 

Sweep time 1 ms - 500 s 1 ms - 500 3
Control singal via Serial (RS232) LAN
Output impedence 50 f2 50 f2

 

 

 

 

 

3.2 RF ampliﬁcation

In order to obtain a rough idea of the NMR resonance frequency at an early stage of
an experiment, a wide frequency modulation is useful to cover wider search area. This
requires a high rf power since the resonance-line width is ﬁnite, <10 kHz in general.
Also, for the AFP technique, a larger rf power is required that in the depolarization
technique as discussed in the sub-section 2.4.4. In the present system, a 250 W rf
ampliﬁer is used, which was manufactured by EMPowr RF Systems and capable of
amplifying signals with frequencies from 0.15 to 230 MHz. The maximum rf magnetic
ﬁeld strength is expected to be ~15 G at 1 MHz with this ampliﬁer. The ampliﬁer
can be remotely controlled and monitored through a serial port with a device server
and LAN connection. A program, rfamp.tcl, written in Tel script is used to control
the device. The gain of the ampliﬁer is variable between 33 and 58 dB. A cooling
fan system protects the ampliﬁer from overheating. When there is a signiﬁcant signal
reﬂection from the load, the gain is reduced to protect the ampliﬁer from any damage.
Such a response appears as dips in the LCR response curve as shown in ﬁgure 3.4
indicating the limit of the ampliﬁcation. Some technical details of the ampliﬁer are

given in table 3.2.

30

Table 3.2: Technical details of the RF ampliﬁer.

 

 

 

 

 

 

 

 

 

 

Power output (nominal) (W) 250
Power output (max) (W) 300
Max. power gain (dB) 58
Frequency range (MHz) 0.15 - 230
Impedance (Q) 50
Max. input (mVpp) 600
A
a, Dips
g
{a
E

 

V

Frequency modulation width .

 

Figure 3.4: Schematic representation of dips in the LCR resonance curve because of
gain reduction feature of the rf ampliﬁer.

3.3 LCR circuitry

A11 efficient ﬂ—N QR technique needs relatively high If magnetic ﬁeld. To achieve high
ﬁeld, an LCR circuit is employed. The present LCR circuit contains an inductance (rf
coil) L , a capacitance (variable capacitors) C and a resistance (50Q)R as shown in
ﬁgure 3.5. In a series LCR system, at the LCR resonance frequency, the impedance
Z is equal to the resistance R of the circuit that is the minimum impedance for
the circuit that could be achieved. This is caused by the equality of the inductive

reactance X L and the capacitive reactance X C at the resonance,

22 = R2 + (XL — x0)2

 

XL = 27rfL
1
X0— 27TfC' (3.1)

31

Table 3.3: Technical details of the vacuum variable capacitors.

 

 

 

 

 

 

 

Model number CVDD—1000-158 C/UCSXF 1500 CMV1-4000—0005
Type ceramic glass ceramic
Number of capacitors 2 2 2
Capacity range (pF) 25 - 1000 20 - 1500 25 - 4000
Max. voltage peak (kV) 9.0 4.5 5.0
Turn number 24 30 12

 

 

 

 

 

From

ampliﬁer .

\

  

 

A —— c
r—Ww

/|l’

Ferrite core

R

 

L

 

 

—— _

——

Figure 3.5: Schematic representation of the LCR circuit, where A represents 50 Q
impedance matching resistor and B is the impedance matching transformer. Path A
or B will be selected depending on the experimental conditions.

When X L is equal to X C” the impedance of the system becomes R and the frequency

that gives this condition is called the resonance frequency given by,

1

= 2am. (3.2)

 

fR

By changing L and / or C the resonance frequency varies. The C is varied using variable
capacitors to tune the system for a speciﬁc frequency. There are six vacuum variable
capacitors, manufactured by Jennings Technology, and their technical details are pre—
sented in table 3.3. The capacitors are remotely tuned by stepper motors, which are
explained in section 3.5. Impedance of the LCR circuit should be matched to the out-
put impedance of the ampliﬁer, which is 50 Q. The impedance matching minimizes a
reﬂection of the rf signal back to the ampliﬁer from the LCR circuit that distorts the

rf signal. There are two options in the system to match the impedance. One is to use

32

a 50 Q, 250 “7 resistor and the other is to use an impedance matching transformer.
The transformer has two coils around a ferrite core: the primary coil is connected to
the rf ampliﬁer and the secondary coil is connected to rf coil. 1111pedance matching of

the transformer is achieved using the relation,

51;. = fig, (33)
NP NS

where the R p and R S are the resistances and NP and NS are the turn numbers of
primary and secondary coils, respectively. Nominal resistance of the secondary coil is
~1 Q, the turn number is ~ Np/Ns = 1/7.

A Quality factor Q, which is given by,

=27rfL=_j:_ (3.4)

Q R Af’

 

deﬁnes the resonance response of the LCR circuit. The Q is lower for the resistor
system because the R is equal to 50 9 compared with R ~ 1 Q of transformer system.
As a result, the 50 Q resistor gives a low magnetic ﬁeld strength but a broad power
output distribution over a wider frequency range; most useful in the depolarization
technique. On the other hand, the Q is higher for the transformer system in a narrower

frequency range that is useful in the AFP technique.

3.4 Rf coil

A new coil bobbin was designed to hold thicker magnet wires and to ensure the
accuracy of the angle of the implantation crystal with respect to the external magnetic
ﬁeld axis. The crystal holder is an integral part of the coil bobbin, and holds the crystal
at an angle of 450 relative to the magnetic ﬁeld. This angle minimizes scattering and
self-absorption of 6 rays detected by up (00) and down (1800) H detectors relative to

the magnetic ﬁeld. The angle between the external magnetic ﬁeld and the crystal is

33

Groove for the coil

  
  

Catcher holder

 

 

 

 

a).
b).
A [:1 Bobbin
A I
Beam
Rf ann/ 1:
HO Crystal holder

[3 detector
Figure 3.6: a). 3D drawing of the If coil bobbin. b). Schematic presentation of the
orientation of the coil bobbin. Catcher holder is an integral part of the bobbin and
holds the crystal with an angle of 450 with respect to the Ho.
00. There is minimum angular dependence of rf transition frequency as a function of
this angle. A schematic representation of the coil bobbin is given in ﬁgure 3.6. Several
rf coils were made with the same bobbin shape and different turn numbers. Each
rf coil has two equal windings in a Helmholtz-like geometry to achieve a uniform rf
magnetic ﬁeld in the location of the host crystal. All If coils were wound using gauge
24, Belden magnet wire (8078). A thicker wire was required to decrease the heat

generation as the high voltage drop across the coil. The inductances of the coils were

34

Table 3.4: Variation of inductance with turn number of rf coils.

 

 

 

Turn number Inductance (pH)
15/15 14.6
17/17 20.7
20/20 27.2
25/25 44.0

 

 

 

Table 3.5: Variation of magnetic ﬁeld strength of the rf coil (17/17) with current.

 

 

DC (A) magnetic ﬁeld strength (G)
0.0 0.0
0.1 0.3
0.2 0.7
0.3 1.0
0.4 1.4
0.5 1.7
0.6 2.0
0.7 2.4
0.8 2.7
0.9 3.1
1.0 3.5

 

 

 

 

measured with an LCR meter (ELECTRO SCIENCE INDUSTRIES - model 253) as
summarized in table 3.4. The inductances were plotted as a function of turn number
to establish a relationship between these two parameters as shown in ﬁgure 3.7. A
variable DC power supply and a Gauss meter (FW BELL - model 5080) were used
to measure the DC character of the coil using a setup as shown in ﬁgure 3.8. Results
are summarized in table 3.5 and shown in ﬁgure 3.9. According to the results of this
test, a relationship between magnetic ﬁeld strength H1 and current I was established
as given in equation,

H1 = 3.431. (3.5)

This relation was used to calculate the rf magnetic ﬁeld strength that assuming linear

relationship is valid at higher magnetic ﬁelds also, as explained in the section 4.4.

35

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- 2 _

90 L 0.0747N 0.1092N
f 80
3 70
‘1 60 //r
3 5O
‘ 40 /
g /
g 30
E 20 /

10

0 I I I
,Q 10/10 20/ZQ_ 30/30 _. 40/40
Turn number N / N
Figure 3.7: Inductance of rf coil vs turn number.
Gauss meter
[ l I‘—
Gauss meter
probe
Variable DC RF coil
power supply

Figure 3.8: Schematic representation of the circuit used to measure the DC character

of the rf coil.

36

 

 

 

 

 

 

 

 

 

 

 

4
H1 = 3.4312!

,- 3.5 -/
S9- /

3 /
.. 2.5
I /
2 2 '
a /
.9 1.5
a /
a) 1 /
(U
2 0.5

0 I T I I I

0 0.2 0.4 0.5 0.8 1 1.2

Current I (A)

Figure 3.9: Magnetic ﬁeld strength of the 17/ 17 coil as a function of direct current.

Table 3.6: Node address hardware conﬁguration.

 

 

 

 

 

 

Node addresses
J3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 X X X X X X X X
2 X X X X X X X X
3 X X X X X X X X
4 X X X X X X X X

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.5 Stepper motor controlling system

In experiments to search a nuclear quadrupole resonance by scanning the rf, different
of rf signals have to be applied. For each signal, the capacitors require adjustment to
have correct impedance matching. The variable capacitors are remotely adjusted by
stepper motors, which are driven by motor controllers with serial port connected to a
device server and LAN. The program testR4.tcl is a Tcl script written to control the

stepper motors. The motor controllers are manufactured by Eggert Electronics, model

37

Table 3.7: Specifications of relay switches. Switch 011 and off times were experimentally
measured.

 

 

 

Type GRGCBA 335 GRGHBA 318 CH 1
Voltage (kVpeak) 2 7 2.5
Max. DC current (A) 6 10 25

On time 200 )13 1.6 ms 3 ms

Off time 160 us 0.8 ms 1.2 1118
Coil resistance (Q) 1000 1000 80
Coil voltage (V) 24 -30 24 - 31 12

 

 

 

 

 

SSCIB, and six controllers are connected in a ”daisy chain” as shown in ﬁgure 3.10
to control the six stepper motors manufactured by Superior Electrics, model MO61.
In the daisy chain, control signals ﬂow through controllers in series. A node address
is assigned to each motor controller by setting J3 jumpers on the controller board as
shown in the table 3.6. The motor controller board can be damaged if the power is
supplied without connecting a motor. To avoid any accidental damage to the motor
controllers, the power is supplied to a motor controller through a relay switch, which
is activated only with jumper pins in an 8-pin high-density Amp connector (TYCO
ELECTRONICS- Model 206434-1) as shown in the ﬁgure 3.11. Without connecting
stepper motors to the Amp connectors, the power supply for the motor controllers
remains disconnected. A motor controller box designed at the N SCL contains all the
motor controller-boards, the motor controller-relay switches, DC power supply and

device server for LAN connection.

3.6 Vacuum relay switching

In the ﬂ-NQR technique, several rf signals are applied within a very short time interval
in millisecond range. The switching time between rf signals should be very short, few
milliseconds, because of the short lifetimes of the exotic nuclei of interest. The rf
switches also should be able to handle high power. Therefore high power vacuum

relay switches were selected. The switching times were measured for three types of

38

SSC1 B
Motor controller

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Motor 1
A1
Node1 -
Device A2
server . Bl -
SerIal 32 -
P. 3 TX T82
In
no 2 RX
5 G Power supply
30V DC
TS3 : AC
TX RX G
LAN
PC TX Rx G ‘
Node2
T82
Motor2
TX .
RX T83 A1
G A2
B1
82
To nodes
3 - 6

 

 

 

Figure 3.10: Schematic representation of stepper motor controlling system. Each con-
troller controls one motor and 6 controllers are connected in series (daisy chain)

39

Motor controller

 

 

 

 

 

T7

 

 

 

 
 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Controller
DC power
30V
Male Amp plug pin
- conﬁ uration
Relay sw'tCh L from 9motor side
SWitCh — (T yco electronics /
DC power 5v _‘ Model 206434-1)
Motor controller box G ' QTOUNd
ME .12 212
,v:
/ I l
Jumper inside L__._,,_ 3; Motor
the Amp plug G

 

 

 

 

 

 

 

Figure 3.11: Schematic representation of power supply for motor controllers. The
jumper and the relay switch make sure that the power to the controller remain turned

off, when motors are not connected.

 

P-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
Channel1
Relay WWI ,,
o—c . __
Switch «mm»... —
controller _____________2
E..; ................................... 4’
g + ............................... -,,ChanneI2
TTL — Oscilloscope

Figure 3.12: Schematic representation of switch time meas

uring circuit. A DC signal

was switched by a TTL signal and an oscilloscope measured both signals.

40

Table 3.8: Switch response time of six relays (GRGHBA 318) measured after con-
structing the system.

 

 

Switch number On time (ms) Off time (ms)
1 1.5 0.6
2 1.5 0.7
3 1.4 0.7
4 1.6 0.7
5 1.7 0.8
6 1.8 0.7

 

 

 

 

 

 

 

 

 

 

 

 

. . . .i
‘ 1 ' ' ' ‘ ' ' z ' : x z :1 'I t -‘ z 1 1 ' ' z ' : 3 ‘ 1 L t 1 1 1 z 5 ' ' 1 t 3 1 1 1 1 I 1 - 1 1 I 1 : L 1 I 1 L - 1

.::::]:::r§T:..§:.:‘rrf,::rt 7:.:;..: 71171;.17r.-:.::31.11:§:.:r§.r.11.
. . . . I I I I i . Swrtch control signal .
Emma-12.51a- ' ' i I '1 't” ' ~:112'Murmwwmmmrarwwmxmm
-..' )- - . . i z I [ If. . , . . _ _
.................... a . . I. .. .... . . . . . . . . . . . “-1.... . . . . . . . . . . . . . . . . . . . . . . ....
W H H i W
n n . . f. I e . . . ' u
; ' - ° - r ' SWItch response SIgnah
' ' ' 4:» o . . I.
. . .+. [
‘ . l

 

 

 

 

Figure 3.13: Response time of switch number 1, extracted from oscilloscope.

vacuum relay switches manufactured by GIGAVAC with different maximum voltage
and current limits. Some technical details of those relay switches are given in table
3.7. To measure the switching time, a TTL signal was used as the control signal of
the relay through a switch driver circuit and a DC signal was switched on and off by
the relay. Both switch on time and off time were measured with an oscilloscope as
shown in ﬁgure 3.12. The results are summarized in table 3.7. The switching times

of all the relays are short enough for the ﬂ-NQR system. The GR6HBA318 relay

41

switch was selected for the system because of the high maximum voltage and current
and suﬂ'icient switching time, considering the decay lifetime of the 37K in the ﬁrst
experiments that would be done to test the system as explained in the chapter 5.
However, depending on the experimental requirements, other types of relay switches
could be used. Six GR6HBA318 switches were purchased and installed in the rf box
and the switching times were checked for each relay. The results are summarized in
table 3.8 and a typical response is shown in ﬁgure 3.13. During the switch on time
period, a jitter was observed as the mechanical nature of the relays. A switch on time
of 2 ms would ensure that mechanical operation of relay close is complete.

The relay switches are controlled by switch controllers, whose circuit diagram is
given in ﬁgure 3.14. The RPVO71 module triggers these switch controllers, which is
explained in section 3.7. The relay switch controller has two main parts as shown in
the ﬁgure 3.14. The left part of the equipment will be located in the Data U, including
a NIM standard chassis that accepts the TTL control signals from RPVO71. The right
part of the equipment is located inside the rf box, which will be placed inside the vault
during the experiment. The vault equipment accepts TTL signals from the Data U
equipment through a patch panel and works as a signal ampliﬁer. The two parts of
the controller are separated by an optical coupler (4N 35) to prevent any noise coming
from high power rf signals to the data U. Coil resistance of the present relays is
1000 {I and range of operating voltage is 24 to 30 V. The voltage across the relay
coil is determined by a resistor labeled as R1 in the ﬁgure 3.14, which is 27 SI for
GR6HBA318 switches.

The vacuum relay switching is operated in cold switching mode. Therefore, rf
signal is on and off before the relay switch is on and off, respectively as shown in
ﬁgure 3.15. This will prevent high power sparking at the contacts of the switches and
possible distortion of the rf signal. This cold switching mode will also increase the

lifetime of the switches.

42

 

 

 

    

 

 

 

 

 

 

     
 

 

 

1 N2222

I
' k
l 0.1 F 1N914A
I b_ ’u
| 1K Relay T—_
12V I 1K
0 ‘ I L R1
1 Kg : b—O. lpF 220pF 27.0
I 2N2222
E | 8K
l
: ——II—
TTL 1K I 50;: F
I
1N2222 l —
l
l
I
I
l
I

Figure 3.14: Circuit diagram of relay switch controllers. The two parts of the circuit
are separated'by an optical coupler (4N35) to minimize the possible noise coming to
the data U from the rf box.

Relay on time Relay off time

 

Switch control

 

 

 

 

 

 

 

 

signal

Rf gate

signal
H 0
2ms 1 ms

Figure 3.15: Relay switch control and rf gate signals. The rf gate signal is open within
the limits of switch control signal to avoid any hot switching.

43

 

 

 

 

Clock N'M ‘0 RPVO71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TIL
NIM to
TTL V ECL t0 NIM

l

v I

, Data

FG Cyclotron rf Relay sw'tCh acquisition
controllers system

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.16: Schematic representation of triggering and timing system controlled by

the RPVO71.

3.7 RPVO71 module

RPVO71 is a 32—channel pulse pattern generator manufactured by REPIC CORPO-
RATION according to the VME standards. The RPVO71 controls all the triggering
and gating signals of experimental components and timing programs as shown in ﬁg-
ure 3.16. A timing sequence is written to the memory of the RPVO71 through the
VME bus. The memory of the RPVO71 has 65K bins and each bin is divided into
32 channels. Writing 0 or 1 to each channel in the memory bins will result in low or
high output levels respectively, according to the clock signal given to the RPVO71 as
shown in ﬁgure 3.17. Time resolution of the RPVO71 depends on the clock signal that
can either be external or internal (50 MHz) source. As an example, if the frequency
of the clock signal is 2000 Hz, timing resolution is 0.5 ms (the bin position is incre-
mented every 0.5 ms). Since the total memory length is 65K long word, the maximum
time span would be about 30 s. For the proposed ﬂ-N QR experiments at the NSCL,
several timing programs will be used. Figure 3.18 shows a possible timing program
for the pulsed-beam depolarization method. Timing programs for continuous-beam

depolarization method and AFP method are shown schematically in ﬁgure 3.19 a) and

44

Channel number

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Memory bin
1 2 3 4 5 5
1 1 0 1
2 1 0 0
4 0 1 0
[ L Clock frequency 2000 Hz
-- 0.0
1» 0.5
«1.0
54.5 .
— #20
L H L H L H
Output ,,Elapsed time ms

Figure 3.17: Schematic representation of writing a program to the memory of RPVO71.
The output signals are shown in the lower part with the external clock frequency of
2000 Hz.

45

TTL logic

Beam

llllllll ....... Rf,
llllllll ....... RIZ

IIIIIIII ? .......

| l ........ Count

 

 

 

 

 

 

 

 

 

Time

Figure 3.18: Schematic representation of one cycle of the timing program of pulsed-
beam depolarization method for the I =3/ 2 nuclei. Beam is pulsed and when beam
is off rf signals are applied. At the end of rf signal application, the counting gate is
opened.

1)), respectively. A control program for the RPVO71 can manage experiments using
continuous beam depolarization (NQR ONOFF), pulse beam depolarization (NQR
DEP) and AF P (NQR AFP). All programs are currently capable of handling up to
the I =2. In all three programs, rf on time, relay switch on and off times and switch
conﬁguration must be speciﬁed. For the NQR ON OFF program, the counting on and
off times must be speciﬁed. The NQR DEP program requires the beam on and off
times and the number of repetitions of the rf in a cycle. For the NQR AF P program,

the beam time and the rf count on time are needed. New timing sequences can be

programmed depending on the different experiments.

46

al- TTL logic

_l.llll
ill

Rf2

 

 

 

[
___—l

 

 

 

Rf on counts

 

 

 

r j— -- Rf off counts

‘
7

Time

 

 

b).

 

TTL logic

 

 

Beam

 

 

 

 

 

Mil llllll... RI.
[le [LIL III
j] [I RI.

 

 

 

 

Counts

 

 

A
7

Time

Figure 3.19: Schematic representation of one cycle of the timing programs for I =3 / 2
nuclei a). Continuous beam depolarization technique; Selecting IMM trigger (inter-
nal), several frequency sweeps occur during one rf gate signal b). AF P technique. In
between two beam pulses, rf signals are applied before and after counting.

47

Chapter 4

ﬂ-N QR system tests

Several tests were performed to evaluate individual components and the whole B-NQR

system.

4.1 Calibrating of stepper motor controllers for
variable capacitor operation

For the safety of the motor controlling system, upper and lower limits for the capac-
itors were set in the motor controlling program. A LCR meter was used to identify
the lowest and highest capacitance of each capacitor. Thereafter, the number of steps
taken by a stepper motor required to cover this range of capacitance was determined.
The turn number of a capacitor was calculated using the number of steps taken by a
stepper motor per revolution (200 steps/revolution). The results are summarized in

table 4.1.

48

Table 4.1: Upper and lower limits for variable capacitors. The number of motor steps
needs to cover the capacitance range of each capacitor was measured and lower and
upper limits were set in the motor controlling program.

 

 

Capacitor Lower Capacitance Upper Capacitance Turn no.

/ Motor position [1F position pF

number (steps) (steps)
01 0 25.2 2400 4000 12
02 0 24.7 2400 4000 12
03 0 28.9 6500 1500 32.5
04 0 34.7 5900 1500 29.5
05 0 41.7 4900 1000 24.5
06 0 39.5 4950 1000 24.75

 

 

 

 

 

 

 

 

4.2 Testing the whole system

4.2.1 RF leakage test

An rf leakage test was performed to make sure that system works without radiating
signiﬁcant rf levels to the surroundings. An electro-magnetic radiation monitor (N AR-
DAR / 8616) was used and no signiﬁcant leakage of rf ﬁeld was observed (less than
0.1 mW/cm2) around the well-shielded rf box. The rf coil was placed inside the vac-
uum chamber, which has several openings. Signiﬁcant rf ﬁeld was observed, about 100
mW/cm2, near these openings. During an experiment all these openings are closed,
except the plastic windows which facilitate the 0 ray emission to the detectors. The rf
leakage near the window was measured as a function of the distance and summarized
in table 4.2. However, when the distance is around 6 inches, the measured rf ﬁeld is
negligible. This window will be inside the N MR magnet during normal operations.
During the bench—top tests, all the vacuum chamber openings have to be covered with

aluminum foil that minimize the rf leakage.

4.2.2 Cold switching conﬁrmation

Before applying high power to the system, each variable capacitor was tested by

supplying 2000 :l: 100 kHz rf with 100 ms sweep time without ampliﬁcation. Switch

49

Table 4.2: Results of the If leakage test. The rf leakage was measured near the window

of the vacuum chamber, where rf coil is placed during an experiment.

 

 

 

 

Distance from window Rf strength
of the vacuum chamber (mW / cm?)

0 104

1 12.5

2 7.0

3 1.2

4 0.7

6 0.05

 

 

 

 

>-

L...

 

-- zoom! - -ch2' LOOVQj'ML00mS'A Ch2' .r 6

 

Vzoomv- - ‘chz- 1.00 v 9‘

 

   

  

 

{1
.ﬁ
+l

..t

 

 

Figure 4.1: Switch control signal and If signal from switch one and capacitor one

extracted from oscilloscope.

on time and off time were set to 2 ms and 1 ms, respectively for all switches. The

output voltages of the function generators were set to 500 mVpp and the switch on

and off times were measured. One of the main objectives of this test is to make sure

that system is working in the cold switching mode. According to the results, the time

differences between switch on and rf on, and switch off and rf off were in safe time

limits speciﬁed by the switch control program as shown in ﬁgure 4.1.

50

700 kHz 1000 kHz 1300 kHz

..r..;....;.............;....;... ....;.

  

  

lsoomv- - -cn2- 1.00v Q; 40i0m5'a c
‘ ‘ ' g 640.20%:

Figure 4.2: LCR resonance frequencies at low power.

4.2.3 Low power test

The whole system was tested with three different frequencies at low power, for which
three LCR circuits with capacitor numbers 1,2 and 3 were used. Rf signals with fre-
quencies 700:1:100 kHz, 1000i100 kHz, 1300:l:100 kHz were applied to the capacitors
1, 2, and 3, respectively. The N QR ONOFF timing program was used with a 500 ms
on time and a 500 ms off time. Sweep time was set to 100 ms. The output voltages
of the function generators were 500 mVpp. Three capacitors were tuned, using motor

controller program to have the resonance frequencies as shown in the ﬁgure 4.2.

51

Direct point

  
    
 

Ampliﬁer Variable
capacﬂor

  

 
 

Rf coil

0
'0

  
 

     
 

.-.
0'. ‘~.
§
‘
..-¢"

   

 

 

 

Matching ., .— "'
transformer “““ 5 Voltage
. dIVIder
*
Function : "——
generator
Test point

Figure 4.3: The circuit for the power tests. A voltage divider is used to reduce the
high voltages to a measurable voltage by oscilloscope at test point.

4.2.4 Maximum rf ﬁeld test

In order to demonstrate a capability of the system to perform, for example, quadrupole
moment measurement of 37K that is explained in chapter 5, the whole system was
tested with three transition frequencies. The 250 W rf ampliﬁer was used with gain
of 58 dB. The N QR ONOFF timing program was used with a 5000 ms on time and
a 5000 ms off time. Sweep time was set to 100 ms. At ﬁrst, at low input region (10
and 20 mVpp) output voltages were measured directly (direct point) and through a
voltage divider (test point) to ﬁnd the ratio between these values. A capacitor bridge
was used as a voltage divider. A simpliﬁed version of this circuit is shown in ﬁgure
4.3.

The input voltage was increased gradually and the output voltage was measured
at the test point. The direct output was calculated using the ratio established between
direct and test point voltages. The results are shown in table 4.3. Beyond the input of

220 mVpp, interference of rf signal was observed due to the rf reﬂection. Measurements

52

Table 4.3: High power test of the whole system.Values given in brackets are not

directly measured.

 

 

 

 

Capacitor Frequency Input Output Output Ratio [11
kHz (mVpp) direct (Vpp) test point(Vpp) (G)

l 700:}:10 10 92 3.9 23.4 1.8
20 150 7.8 23 1.9

120 (1049) 45.6 10.9

200 (1619) 70.4 16.9

220 (1748) 76.0 18.2

2 1200i10 10 157 6.6 23.6 0.9
20 313 13.6 23 1.9

120 (2760) 78.4 10.9

200 (2714) 118 16.5

220 (2898) 126 17.6

 

 

 

 

 

 

 

 

were stopped at 220 mVpp due to the distorted response curve. The rf magnetic field

was calculated using the equation,
m = 3.431, (4.1)

where m is established between magnetic ﬁeld strength and the current in the DC
character measurement of the rf coil and Vpp is the voltage across the rf coil. Maximum
magnetic ﬁeld strengths were calculated for 37K experiment, are at 700 kHz and
1200 kHz to be 18.2 G and 17.6 G, respectively. These ﬁeld strengths are sufﬁcient
to conduct AFP experiments on 37K and 35K.

4.2.5 Capacitance limits on LCR circuit

When all the motor positions are set to zero, the system shows resonance at about
2100 kHz indicating minimum capacitance of the system of ~270 pF. At maximum
capacitance of the 4000 pF capacitor, the lowest resonance frequency is ~400 kHz.

Combining the two 4000 pF capacitors reduces the maximum resonance frequency to

~370 kHz.

Chapter 5

ﬁ-NQR Application to 35"37K

The new ﬁ-NQR system is capable of measuring quadrupole moments of nuclei up
to I =2, according to the results of system tests explained in the last chapter. In
this chapter, the proposed experiments to measure quadrupole moments of the 3d
shell nuclei 37K (I7r=3/2+, t1/2=1.22 s) and 35K (I7r=3/2+, t1/2=178 ms) are

discussed.

5.1 Quadrupole moments of the nuclei in sd shell

A good agreement between experimental [2] and theoretical [13] (OXBASH) quadru-
pole moments for isospin T=1 / 2, sd shell nuclei, in general, is observed as shown in
ﬁgure 5.1. The trend of the quadrupole moments can be explained as follows. When
one single nucleon is in the 1d5/2 shell, the quadrupole moment takes a negative
value. The quadrupole moment changes sign as the 1d5/2 shell is ﬁlled, in agreement
with the single particle shell model. When the valence nucleons occupy the 231/2
orbit, the quadrupole moment is zero, as the total angular momentum is equal to
1/ 2. When the 1d3/2 shell has one nucleon, the quadrupole moment again is negative
and changes sign as the 1d3/2 shell is ﬁlled. The same type of systematic behavior

of the quadrupole moment is expected for T=3 / 2 nuclei in the 3d shell. However, as

54

o P - odd experimental — P - odd theoritical

 

 

 

 

 

 

250 o N - odd experimental ------- N - odd theoritical?
200— l
150-
3 100“ .. l
2% 50-
o g
-5) " o .
-1(Di i
-150 . . . .

15 Z) 25 3) 35 40

Mass number

Figure 5.1: Experimentally measured quadrupole moments of T =1 / 2 nuclei in the 3d
shell, which have good agreement with theoretical prediction (OXBASH).

few (about 7 nuclei) measured quadrupole moments are available for T = 3 / 2 nuclei,
especially in the neutron-deﬁcient region. Measuring the quadrupole moments of the

T = 3/ 2 nuclei is essential to test the predictions of standard shell model and other

mean-ﬁeld theories far from the stability line.

5.2 Quadrupole moments of potassium isotopes

Only four nuclear quadrupole moments have been measured for potassium isotopes
as shown in ﬁgure 5.2. 39K and 41K are stable isotopes and 40K is a long-lived
isotope at the line of stability. 37K is the only unstable potassium isotope that has
a known quadrupole moment lying in the neutron-deﬁcient region. The odd-A K
isotopes are believed to have one proton hole in the 1d3/2 shell. The quadrupole
moment should be positive according to the single-particle shell model. When the
K isotopes become more neutron-deﬁcient, a signiﬁcant deviation from shell model-

expectations may occur, because of the low proton binding and core deformation.

55

 

 

 

 

200 _.._________.-,,._r,,-k# _-.
150 37
K 41 K
100 . 35 ] 39 o
A 0 K o K I
e 50+ ‘
O o
0 Theoretical value
-50 ~ _ 40 K
0 Experimental value I
.100 ~ 0
'150 I r 1 ﬂ

 

34 35 30 37 30 39 4o 41 42
Mass number

Figure 5.2: Measured quadrupole moments of potassium isotopes of 37K [15], 39K [16],
40K [17] and 41K [18] and theoretical prediction (OXBASH)(model space sd and

interaction w).

Already, 37K exhibits a large quadrupole moment than, 39K and 41K, although the
experimental value has a large error. Therefore, high precision measurements of the
quadrupole moments of the neutron deﬁcient K isotopes are of great interest. T.
Minamisono et al. measured quadrupole moment of 8B as 68.3i2.1 mb [6] and it is
twice as large as shell model prediction. The proton separation energy of 35K is 78
keV and much lower than that of 8B (137.5 keV), therefore it is expected that the
proton distribution spreads out radially and give rise to a higher quadrupole moment
than predicted. If quadrupole moment of 35K is higher than predictions indicates
the presence of unusual core deformation. T. Minamisono et al. claimed that 8B is
a proton halo nuclei. The low separation energy of 35K makes it a candidate for a

proton halo as well.

56

3/2+ 37

ty2=1.228

 

Q = 6148.8 keV

 

 

 

+
1_8 0 5/2
/° > 2796.1 keV
98.2 % 3/2 +
s gs
ix, = 35 d
37
Ar

Figure 5.3: Partial decay scheme of 37K . The energy levels are not in scale.
5.3 Quadrupole moment measurement of 37K

37K is a 0+ emitter with a half-life of 1.22 s. 37K decays predominantly to the
ground state of 37Ar with a branching ratio of 98.2% as shown in the ﬁgure 5.3. This
main 6 decay branch is of a Gamow-Teller and Fermi mixed type with the asymme-
try parameter of -0.598 [19], [20]. The quadrupole moment of 37K was measured as
100:1:30mb [15] by the laser-spectroscopic technique on an atomic beam. The qua-
drupole moment of 37K will be re—measured for commissioning of the new ﬁ-NQR
system, since its value is roughly known and large polarization of 37K has been es-
tablished [11]. A potassium di-hydrogen phosphate (KH2PO4) or KDP single crystal
will be used as the host crystal because its electric ﬁeld gradient, q, at the potassium
site is experimentally known [21]. The asymmetry parameter of the electric ﬁeld gra—
dient n, is equal to zero because of its symmetric crystal structure (tetrahedral) [22],
which gives a simple resonance structure. The nuclear energy levels can be calculated
using the ﬁrst order perturbation theory to obtain the transition frequencies. From
the quadrupole moment of 37K and q in KDP, the quadrupole coupling constant,
qu / h , for 37K is 3.4 :l:1 MHz. The corresponding set of three transition frequencies
for the I =3 / 2 ground state are 413 kHz, 1286 kHz and 2113 kHz at the magnetic ﬁeld

57

 

 

 

 

 

1: 3,, m
g 9° -3/20'1/2
V2.5“ ..o°.
>0 .o°.
U 24 O...
0:) ...oo° “‘A 3/2” 1/2
3 -« ,0” ‘2“
31.5 ..9.. “J‘.A
‘0': 1‘ .0.... “2““
C ..0°.. “AA“
:3 0051|.E::..-.....:::I.g..-I...I.......'......--..- -1/201/2
g 0 “A2A1“ I I f
g 0 1 2 3 34 4 5
quh (MHz)

Figure 5.4: Transition frequencies for the quadrupole moment (37K) calculated from
ﬁrst order perturbation theory at 0.4 T. The dots are the calculated transition fre-
quencies and the solid line represents three transition frequencies corresponding to
the known coupling constant for 37K implanted into KDP.

strength of 0.4 T as shown in ﬁgure 5.4. The set of three frequencies will be scanned
in accordance with the calculation shown in ﬁgure 5.4 to cover the error associated
with qu / h. The quadrupole moment of 39K will be used as the reference to deduce
the quadrupole moment of 37K. According to the literature, the quadrupole moment
of 39K is 61.5 $1.5 [23]. There for the systematic error, that can be expected for the
quadrupole moment of 37K will be less than 5%. The statistical error will be very

small because of the high counting ratio of 37K and approximately 30 hrs counting

time may be enough to achieve this statistics.

5.4 Quadrupole moment measurement of 35K

35K is a 6+ emitter with a half-life of 178 ms. The 35K decay has four dominant tran-
sitions including transitions to three different excited states and to the ground state of
35Ar as shown in ﬁgure 5.5. The asymmetry parameter is uncertain (estimated range:

+0.60 — —0.32) but spin polarization was observed in a previous NSCL experiment

58

 

t% =178 ms

QEC= 11881 keV

+
3/2
—-1§-%—> 5572.7 keV

+ +
26% (3/2, 5/2 )

 

2982.8 keV

 

+
AL» ——5-’l— 17505 keV
+
19 % 3/2 93
1% = 1.77 s
35Ar

Figure 5.5: Partial decay scheme of 35K. The energy levels are not in scale.

(01039-II) [24]. The quadrupole-coupling constant for 35K is 2.3:l:0.7 MHz, based on
the known q in KDP and the theoretically-calculated (OXBASH) quadrupole moment
of 72 mb. Therefore, the set of three transition frequencies are 553.43 kHz, 594.56 kHz
and 1744.56 kHz at 0.3 T as shown in ﬁgure 5.6. Assuming 30% error in the coupling
constant, the set of 3 frequencies will be scanned in accordance with the calculation

in ﬁgure 5.6.

5.5 Experimental details

The production yield and the polarization of 37K and 35K were measured via intermediate-
energy pick up reactions in the previous NSCL experiments (01039 —I and II) [11], [24].
For the production of 37K, the collision between the primary beam of 36Ar with an
energy of 150 MeV/ nucleon and a 564 mg/cm2 9Be target will produce 37K through
the charge pickup reaction. The beam will be set at an angle of +20 relative to the
normal beam axis to produce a spin-polarized beam. The full angular acceptance of
the A1900 will be used and the momentum acceptance limited to 1% using a slit

at the second intermediate image. A momentum +05% higher than the peak yield

59

m

 

 

 

 

 

 

 

 

 

 

A 3 _.. . - a __ ._-..___.- _ [Uh—Mi]
E -3/2<+ -1/2
2 2.5 .oo'.
3 ,. 3/2» 1/2
8' 1.5 .= ﬁ
t .0... ..°.. [
s 1 =
E 0!::...O...’...........:.:: :0...’............. -1/20. 1/2
(D P ,‘ _
g 0.5 ...°o o...
h .0. .0.
I'- O O'. I 23 l

0 2 4 6

qu/h (MHz)

Figure 5.6: Transition frequencies of 35K calculated by ﬁrst order perturbation theory
at 0.3 T. Dots are calculated transition frequencies and solid line represents three
transition frequencies that correspond to the coupling constant.
momentum of 37K will be chosen. An achromatic wedge (450 mg/cm2, AI) will be
used at the intermediate image to separate secondary particles based on the relative
energy loss. Under an external magnetic ﬁeld, 37K will be implanted into the host
KDP crystal, as shown in ﬁgure 5.7, tilted by 450 relative to the secondary beam
axis to increase the effective implantation thickness and to minimize the absorption
and scattering of ,6 rays from stopped nuclei by the crystal itself. According to the
previous 37K experiment (01039-I) at the NSCL, the 37K beam will have high purity
( 98%, [11]). Particle identiﬁcation will be performed using a PIN detector in the
beam line just upstream of the NMR magnet by AE—TOF (between PIN and rf of
the cyclotron) method. The ﬁnal counting rate of ,8 particles in two sets of detectors
is predicted to be 350 pps/pnA (based on 50 pnA of primary beam intensity).

35K nuclei will be produced in the same charge pickup reaction as 37K but followed

by two-neutron evaporation. The 35K beam will be treated in the same way as the

60

,B—NMR magnet

B—detectors\

l l

 

 

Collimator

 

 

Si-PIN detector

beam

H .
R

 

/
\ D Secondary
U

Rf coil Degrader

Host crystal

T J

Figure 5.7: B-NMR setup at NSCL.

 

 

 

 

 

 

37K beam . The ﬁnal counting rate of )8 particles in two sets of detectors is predicted
to be 5 pps/pnA based on the previous 35K experiment (01039—II) at the NSCL. 34Ar
constitutes a signiﬁcant contaminant in the 35K beam.A shield to cut off 6 rays with
energy lower than about 5000 keV, will be used to reduce the 34Ar contribution to

the spectrum.

61

Chapter 6

Summary

The Quadrupole moment is a direct measure of the deviation of charge distribution
of a nucleus from its spherical shape. Therefore, it is zero for spherical-shaped nuclei
and takes positive value and negative value for prolate-shaped and oblate-shaped
deformed nuclei, respectively.

The quadrupole moment is used as an important observable to investigate the
nuclear structure, as it changes sign over a shell indicating the presence of a proton
hole or an odd valence proton, respectively. The quadrupole moment can be used as
evidence for the presence of conﬁguration mixing in the nucleus. Core deformation
is also a concept that can be investigated by quadruple moment measurements, es-
pecially in the heavy-mass nuclei. The measured large quadrupole moments of heavy
nuclei helped to establish the collective effects of valence nucleons on the core de
formation. The quadrupole moment can be used to extract the charge radius of the
nucleus, which is important to understand the radial extent of a nucleus.

There are several techniques to measure the quadrupole moments including laser
spectrosc0py, low temperature nuclear orientation, nuclear quadrupole resonance tech-
nique, and microwave spectroscopy. Each technique has its own advantages and dis-
advantages.

The ﬂ-NQR technique moreover, is probably the most effective method to mea-

62

sure nuclear electric quadrupole moments of exotic nuclei. The technique requires an
ensemble of spin-polarized ,6 emitting nuclei. At the NSCL, nuclear spin polarization
is produced directly in intermediate-energy heavy-ion reactions. Both nucleon pickup
and removal reactions can be used to generate polarizations of order 1% or greater
for nuclei a few nucleons away from the projectile.

The ﬂ-N QR method requires a host material with a non-cubic lattice structure.
Polarized nuclei are implanted in a crystal with an electric ﬁeld gradient placed in a
strong magnetic ﬁeld. The strong magnetic ﬁeld helps to preserve the spin polariza-
tion that can be depolarized due to the spin-lattice relaxation and spin-spin relaxation
processes. In addition, Zeeman splitting is induced by the magnetic ﬁeld. The electric
interactions shift the evenly spaced energy levels because of the electric ﬁeld gradient
of the host crystal. The spin manipulation is performed by applying rf magnetic ﬁeld
perpendicular to the external magnetic ﬁeld. Several different transition frequencies
are required for the depolarization because of the uneven energy gaps among mag-
netic sub-states. There are two spin manipulation techniques as depolarizatiOn and
AF P technique. In the depolarization technique, spin precesses around the effective
magnetic ﬁeld that is a result of the external magnetic ﬁeld and at the resonance, the
spin precess around the rf magnetic ﬁeld and the spin polarization vanishes. In the
AF P technique, an rf is swept once over the resonance frequency that leads to the
spin inversion. The spin inversion makes the NMR effect two times larger, however,
it needs higher rf magnetic ﬁeld than that in the depolarization method.

The ﬂ—NQR system described in this thesis was designed to meet the criteria listed
above. The system is an upgrade of the previous ﬁ-NMR system at the NSCL. It has
a multi rf capability, utilizing four function generators to produce four different tran-
sition frequencies. A 250 W rf ampliﬁer is used to achieve the high magnetic ﬁeld
for spin manipulation .A LCR circuit is used to match the output impedance of the
ampliﬁer. A high voltage drop will exist in the LCR circuit and the individual com-

ponents of this circuit were chosen to be capable of handling high voltages. All the

63

variable vacuum capacitors can handle high voltage up to ~5 kV and are remotely
tunable by a stepper motor controlling system. Vacuum relay switches are used to
select the capacitors depending applied frequency to realize highest quadrupole mo-
ment for LCR circuit. The vacuum relay switches are able to handle high voltages.
The response time of the relay switches are fast,(few milliseconds) and in an accept-
able limits comparing with the life—tine of the exotic nuclei of interest. The resistor,
capacitors, switches are all contained in an rf box. All variable functions of the rf box
and function generators are remotely controllable.

The complete ﬁ-NQR system was tested at high power (58 dB ampliﬁcation). No
rf leaks were observed. The maximum ﬁeld at the rf coil was ~18 G for 700 and 1200
kHz testing frequencies.

The minimum capacitance of the system was measured as 270 pF indicating that
the maximum resonance frequency is limited to 2100 kHz at the present conditions.
Minimum resonance frequency of 370 kHz was achieved by combining two 4000 pF
capacitors.

.The ﬁrst application of the new ﬁ-NQR system will be to measure the quadru-
pole moments of the neutron deﬁcient odd-A K isotopes. The physics goal is to ﬁnd
evidence for low binding of the valence proton in 35’37K. The quadrupole moment
measurement can provide direct information as the radial charge distribution of these
nuclei.

In these proposed experiments, 36Ar primary beam with an energy of 150 MeV/ A
and 9B production target with the thickness of 564 mg/cm2 will be used. The charge
pickup reaction produces both 37[K and 35K nuclei are produced by charge pickup
reaction followed by two neutron evaporations. A KDP single crystals will be used as
the host crystal and ﬁ-count rates of 37K and 35K are expected as 350 pps/pnA and

5 pps/pnA, respectively.

64

 

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66

        

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