Magnetic Dipole Moment of the Short-Lived Radioisotope 55 Ni Measured by Beta-NMR ...

138 Pages·2009·4.82 MB·English

MAGNETIC DIPOLE MOMENT OF THE SHORT-LIVED
55
RADIOISOTOPE Ni MEASURED BY BETA-NMR
SPECTROSCOPY
By
Jill Susan Berryman
A DISSERTATION
Submitted to
Mi
higan State University
in partial ful(cid:28)llment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Chemistry
2009
ABSTRACT
MAGNETIC55DIPOLE MOMENT OF THE SHORT-LIVED RADIOISOTOPE
Ni MEASURED BY BETA-NMR SPECTROSCOPY
By
Jill Susan Berryman
N = Z = 28 56
The double shell
losure at in Ni has been investigated through
the measurement of the magneti
moment of a nu
leus one neutron removed from
this
ore. Nu
lear moments are fundamental, measurable properties that provide in-
formation on the stru
ture of nu
lei. The magneti
moments of doubly
losed nu
lei
± 1 nu
leon are of parti
ular importan
e, sin
e the properties of ea
h of these nu
lei
are determined by the orbit o

upied by that last nu
leon. Any deviation from theory
indi
ates the presen
e of higher order e(cid:27)e
ts su
h as
on(cid:28)guration mixing, meson
/
ex
hange
urrents, isobar ex
itation, and or even a breakdown of the shell
losure.
56
The Ni
ore has been shown to be soft, attributed to the strong proton-neutron
48
intera
tion, in
omparison to the Ca
ore. The small magneti
dipole moment of
57 T = 1/2 56
z
Cu, with − and residing one proton outside Ni, suggests the double
shell
losure at proton and neutron numbers 28 is broken. However, the experimental
T = +1/2 57 55
z
ground state magneti
moments of the nu
lides Ni and Co agree well
56
withshellmodelpredi
tions,albeitwitha(cid:16)soft(cid:17) Ni
ore.Thegroundstatemagneti
55 T = 1/2 56
z
moment of Ni, also with − but with one neutron removed from the Ni
56

ore
an provide
riti
al insight on the nature of the Ni
ore, and
an be a basis to
understand how the stru
ture of doubly-magi
nu
lei may
hange away from stability.
55 Iπ = 3/2 ,T = 204
− 1/2
The nu
lear magneti
moment of the ground state of Ni (
µ(55 = (0.976 0.026) µ
N
ms) has been dedu
ed in this work to be | Ni)| ± using the
β 55
-NMR te
hnique. A polarized beam of Ni was produ
ed by fragmentation of a
58 /
Ni primary beam at energy 160 MeV nu
leon in a Be target. The A1900 and RF
Fragment separators were used to eliminate all other beam
ontaminants. Results of
a shell model
al
ulation using the GXPF1 intera
tion in the full fp shell model spa
e
56
was found to reprodu
e the experimental value and support a softness of the Ni

ore.
55
Together with the known magneti
moment of the mirror partner Co, the
σ = 0.91 0.07
z
isos
alar spin expe
tation value h i ± shows a similar trend to that
Pg A = 28
established in the sd shell. E(cid:27)e
tive fa
tors for the system obtained from a
(cid:28)t to isos
alar magneti
moments, isove
tor moments, and M1 de
ay matrix elements
A = 55
were applied to matrix elements for
al
ulated with the GXPF1 intera
tion to
σ A = 55
z
obtainh ifor .Theresultsofthe
al
ulationshowthebestagreementwith
P µ σ
z
the experimental value for both and h i and imply that a universal operator
P

an be applied to both the sd and fp shells.
for eri
iv
ACKNOWLEDGMENTS
First and foremost, I would like to thank my advisor, Paul Manti
a, for all he
has done for me on this long trek known as graduate s
hool. Paul, your wisdom
amazes me and I would not be in this position without your guidan
e. Thank you
for always keeping the big pi
ture in mind and reminding me to do the same. Thank
you for making me a better s
ienti(cid:28)
writer and speaker. Thanks for giving me the
opportunity to travel all over the world. Thank you for the group bonding time
over lun
hes, dinners, parties at your house, and pi
ni
s at your
ottage (thanks to
Sta
y for those as well!). I will never forget some of your favorite phrases in
luding:
(cid:16)Graduate s
hool is a stepping stone, not a
areer,(cid:17) and (cid:16)You have to love what you
do,(cid:17) (in response to my persistent question on how to be su

essful).
Another person that deserves re
ognition is physi
ist Kei Minamisono. Kei knows
β
justabouteverythingthereistoknowabout -NMRandwasalwayswillingtoanswer
questions, lend a hand in the lab, and dis
uss my work. Thank you, Kei! I would like
to thank the rest of the beta group members that overlapped with me: Andrew, Josh,
and Heather. Andrew, we did not overlap for long, but I will never forget your kind
and helpful emails before I even arrived at MSU, and your en
ouraging words during
my (cid:28)rst year as a graduate student. Josh, for all four of my years here I looked up to
you for help on everything from my (cid:28)rst
ommittee meeting to my se
ond year oral
exam to writing this dissertation. Thanks for doing everything (cid:28)rst and then being
willing to tell me what to do and what not to do! Heather, thanks for being a great
friend, travel buddy, and someone that I
ould always boun
e an idea o(cid:27). You always
helped me look to the positive side of things!
I would like to thank my
ommittee members in
luding David Morrissey, Mi
hael
Thoennessen, and Rem
o Zegers. Thank you for your guidan
e and for making me
55
a better s
ientist. Thanks to
ollaborator Warren Rogers who proposed the Ni
v
experiment the (cid:28)rst time around and for his help during the experiment. Thank you
AlexBrownandIanTownerforyourhelpfultheorydis
ussionsafterthemeasurement
was
omplete.ThankstoAndrewStu
hberyforinsightonthepolarizationsimulation,
espe
ially the gamma-ray deorientation
al
ulations. I would also like to a
knowledge
Mi
higan State University, the Department of Chemistry, NSCL, and the National
S
ien
e Foundation Graduate Resear
h Fellowship program for (cid:28)nan
ial support.
There are many people at NSCL that made my thesis experiment a su

ess. I
have greatly appre
iated the friendly attitude of all the sta(cid:27). Everyone is more than
willing to talk with you, answer questions, and help in any way they
an. Al Zeller
was always willing to answer my magnet questions. Thanks to John Yurkon for his
dis
ussions on magneti
shielding and for letting me borrow all kinds of mu metal.
Thanks to Craig Snow for helping me with the me
hani
al design of my equipment.
Thanks to Jim Wagner for making sure I had everything I needed in the S2 vault,
in
luding the new platform! Brad Powell, thanks for putting in the water lines for
our dipole magnet, in both the South High Bay and then the S2 vault. A lot of
redit
goes to the operations department for making sure my experiment ran smoothly.
Spe
ial thanks to the A1900 group, in
luding Tom Ginter, Thomas Baumann, and
Mar
Hausmann. I know that my experiment required A LOT of settings and I thank
you for your patien
e and hard work! Thanks to those spe
ial operators who gave me
great beam and ordered Big Ten Burrito during the midnight shifts: Carl Cormany
and Dave S
haub. Daniel Bazin deserves many thanks for his willingness to tune the
Radiofrequen
y Fragment Separator anytime day or night, and the great job that he
did! Thanks to Geo(cid:27) Grinyer for helping with the experiment and for the helpful
dis
ussions afterward.
I have grown
lose to a number of people here that I will dearly miss. Thanks for
the great times on DALMAC, guys and gal (Jon Babbage, Thomas Baumann, Jon
Bono(cid:28)glio, Renan Fontus, Cindy Fontus, Doug Miller, Dave Miller, Dave Sanderson,
Mathias Steiner, Chisom Wilson, John Yurkon, Andrew Ratkiewi
z, and Phil Voss).
vi
What a great ride with a great group of people! Jon Bono(cid:28)glio, thanks for getting up
at 5:30 AM for spinning
lass two days a week and for swimming on Fridays! Thanks
to my other spinning friends who I have grown
lose to during the wee hours of the
morning: Tom Mit
hell (the greatest spinning instru
tor ever), Sarah A
Moody, and
Robin Usborne. Phil Voss, I must thank you for organizing Happy Hour every Friday,
and for being a great softball
oa
h! Thanks to Rhiannon Mehar
hand, Krista Cruse,
Mi
helle Mosby, and Heather Crawford for the girly outings and for throwing me my
only wedding shower!
Spe
ial thanks to my family, in
luding ALL the Pinters and Berrymans. My mom
and dad have always been the most supportive parents a girl
ould have. Without
you, I would not have been able to do a lot of things. Dad, thanks for making me work
hard my whole life at the greenhouse. Hard work
omes naturally now be
ause of you.
Thanks for tea
hing me I
ould do anything the boys
ould do (and more), in
luding
(cid:28)x heaters, put in sprinkler systems, drive tra
tors and dump tru
ks, pour
ement,
and haul (cid:29)ats. Mom, thanks for instilling the importan
e of edu
ation into all your
kids. I will never forget how you made us do those math workbooks in the summer
whi
h I hated, but now I guess I thank you for it. Thanks for never restri
ting and
always en
ouraging my reading list, no matter how strange the topi
of the book. The
overwhelming support that you have both always given means more than you know.
Four years ago if someone had told me that I would get married during graduate
s
hool, I would have thought they were nuts. Marriage was not in the plans during
graduate s
hool or ever! Now, I
annot imagine life without him. Eri
, I never
ould
have gotten through these four years without your
onstant love and support. I never
thought I would (cid:28)nd someone that
ompletes me the way you do. As I write this we
have been together for 3.75 years, married for eight months, and I am giddy over the
fa
t that we get to spend the rest of our lives together. I love you more and more
everyday.
vii
Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introdu
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Ele
tromagneti
Intera
tion . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Ele
tri
multipole expansion . . . . . . . . . . . . . . . . . . . 2
1.1.2 Magneti
multipole expansion . . . . . . . . . . . . . . . . . . 7
1.2 Magnitude of the nu
lear magneti
moment . . . . . . . . . . . . . . 10
1.2.1 Single-parti
le model . . . . . . . . . . . . . . . . . . . . . . . 14
g
1.2.2 E(cid:27)e
tive nu
leon fa
tors: mi
ros
opi
treatment . . . . . . . 16
g
1.2.3 E(cid:27)e
tive nu
leon fa
tors: empiri
al (cid:28)t to data . . . . . . . . 17
1.3 Analysis of mirror moments . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.1 Isos
alar spin expe
tation value . . . . . . . . . . . . . . . . . 18
1.3.2 Bu
k-Perez mirror analysis . . . . . . . . . . . . . . . . . . . . 19
1.4 Nu
lear moments and nu
lear stru
ture . . . . . . . . . . . . . . . . . 22
1.4.1 Magneti
mo5m6 ents near
losed shells . . . . . . . . . . . . . . 22
1.4.2 Eviden
e of Ni as a doubl5y6-magi
nu
leus . . . . . . . . . . 23
1.4.3 Magneti
mµo5m5 ents around Ni . . . . . . . . . . . . . . . . . 24
1.4.4 Proposed ( Ni) measurement . . . . . . . . . . . . . . . . . 26
1.5 Organization of Dissertation . . . . . . . . . . . . . . . . . . . . . . . 28
2 Te
hnique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Nu
lear spin polarization . . . . . . . . . . . . . . . . . . . . . . . . . 30
β
2.2 De
ay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Ele
tron intera
tions . . . . . . . . . . . . . . . . . . . . . . . 40
β
2.2.2 -de
ay angular distribution . . . . . . . . . . . . . . . . . . . 41
2.3 Measuring spin polarization . . . . . . . . . . . . . . . . . . . . . . . 42
β
2.4 Nu
lear magneti
resonan
e of -emitting nu
lei . . . . . . . . . . . . 44
2.4.1 Spin-latti
e relaxation . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Line broadening . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1 Nu
lide Produ
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
β
3.2 -NMR Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.2 Radiofrequen
y system . . . . . . . . . . . . . . . . . . . . . . 59
viii
3.2.3 Ele
troni
s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.4 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.1 Fragment Produ
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Parti
le Identi(cid:28)
ation . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
β
4.3 energy spe
tra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4 Spin polarization measurement . . . . . . . . . . . . . . . . . . . . . 91
4.5 NMR measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5 Dis
ussion . . . .55. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1 Polarization of Ni
ompared to simulation . . . . . . . . . . . . . . 97
5.1.1 Momentum distribution reprodu
tion . . . . . . . . . . . . . . 97
5.1.2 Opti
al Potential . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.1.3 Results of simulation . . . . . . . . . . . . . . . . . . . . . . . 102
5.1.4 Extension to n5u5
leon pi
kup56rea
tions . . . . . . . . . . . . . . 103
5.2 Magneti
Moment of Ni and the Ni
losed shell . . . . . . . . . . 107
g
5.2.1 Single-parti
le wavefun
tion and e(cid:27)e
tive fa
tors . . . . . . . 108
g
5.2.2 Shell model in full fp shell and gfree . . . . . . . . . . . . . . . 108
5.2.3 Shell model in full fp shell and e(cid:27) T.=. 1./2. .A. =. .55. . . . . . . 110
5.2.4 Isos
alar spin expe
tation value at , . . . . . . 111
5.2.5 Bu
k-Perez analysis . . . . . . . . . . . . . . . . . . . . . . . . 114
6 Con
lusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . 115
Appendi
es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
β
A -de
ay Asymmetry Parameter Cal
ulation . . . . . . . . . . . . . 118
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
ix
List of Tables
55
1.1 Theoreti
al expe
tations for the magneti
moments of Ni. . . . . . 28
ρ 55
3.1 A1900 B values for Ni fragments. . . . . . . . . . . . . . . . . . . 54
3.2 Plasti
s
intillator energy
alibration data . . . . . . . . . . . . . . . 74
4.1 Fra
tion of
omponents of the se
ondary beam . . . . . . . . . . . . . 83
5.1 Input parameters for Monte Carlo simulation. . . . . . . . . . . . . . 103
5.2 Towner
orre
tions to the
al
ulated e(cid:27)e
tive magneti
moment operator109
55 55 σ A = 55
z
5.3 Magneti
moments of Ni, Co and h i for . . . . . . . . 110
Pσ
A.1 Experimentally determined values of h i. . . . . . . . . . . . . . . . . 119
x