The Nuclear Spin and Quadrupole Moment of C136

46 Pages·1.92 MB·English

by  Gilbert, Donald A

THE MTCLEAR SPIN AHD QWAPHTJPOUB MOHKHT OP Cl36
by
Donald Allan Oilbert
A dissertation submitted in partial fulfillment of the requirement*
for the degree of Doctor of Philosophy, In the Department
of Physios in the Graduate College of the
State University of Icma
August 1951
ProQuest Number: 10991978
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The author is indebted to Br# Arthur Eobert* for
9
suggesting this research problem* wad for his valuable advice
and encouragement at the outset of the problem# Grateful
acknowledgement is made to Dr* E» B» Eels on for many consultations
during the period of research* and for his advice in the
preparation of this manuscript# The author also wishes to express
appreciation to Mr. J* G# Sentinella, who constructed many
components of the microwave spectrometer* and to other members
of the Physios Department Staff who made many valuable suggestions
for solving problems which arose#
ii
TABLE OF OOBTBm
Pag,*
Chapter 1 Introduction* ..... I
Chapter 11 Theoretic**! Baale for the Spin MeasurementU
Chapter 111 Apparatus and Proeeedure******»**«*»••«*♦#*♦*15
Chapter IV Beftulta«****«*»»t*****«
Chapter V C o n c l u s i o n s # J 7
Appendix 1 •••«•••»•«*•»•%»*•«••»«*»•*.................*38
Bibliography*« « « * • « • * • • * • * « • » « • • • * * . * 1 + 0
iii
ILLUSTRATIONS
Fleur* Fab*
U The CH?CX MoleouXe*..........***««*»*.*,»*. 5
2» Microwave Spectrometer. «•«*«»••*«•••»*«•«••• Xli
5* Spectral T r e e i n g 23
U« Corapari®on of Theoretical and Observed
Hyperflne Pattern®»•*•♦••»••«»«««*##•••»•••• 27
5* Into modi ate Stark Speotrm for I as 2* •*<*** * JO
6* Systematic B r r o r JU
iv
TABLES
Table Page
X* Frequency Separation P ** 0 for Several
Stark Voltages*•««***••»•*«•**»••*«••••••*• 36
XX* Observed Frequency Separations in the
O^jOl36 Triplet ................ 32
XXI* Comparison of the Experimental Results
with Theory* *«* *••«»»••**«••«••*»•*««•»••»* 35
v
1
Chapter I
WBOBICTICM
In reoMb ymr® much emphasis 3ms bom placed on saspsri**
monts designed to obtain data on properties of atomic nuclei
such as spins* nagnotio moment®, and electric qu&drupol© momenta#
tho general purpose of these ©xporlments is to provide a sot of
reliable data In order to cheek the existing theories of nuclear
structure and provide a basis for n m improved theories# The
analysis of spectra in the microwave region has proved a valuable
tool for determining thee® nuclear properties* In particular,
the critical esmmimtian of the hyperf An© structure of molecular
rotational spectra has lead to marablguow results for the nuclear
spin In those case© here I & 1*
An attempt to measure the spin of the radionuclide 01^
'Was made by Townes and Aamodt^# Their method me to esmai.no the
hyperfino structure of the Z rotational line In the
micromv© spectrum of 01^0^!^* The presence of the small
electric quadrupol© moment of M & in addition to the desired
01^ quadrupole mostent* makes the hyporfin© pattern of
very complex and difficult to analyse* Townee and Aamodt war®
not able to completely resolve all of the hyper fine components,
and gave a spin value I » 2 ae their interpretation of the over­
all shape of the pattern*
tftt and h&m measured and ©mlyssed the beta
ipwrtm of Ol^ «md found the ©hap© b© be wet ©oneietenfe with a
©pin ©hang© A t tt % fM® result was particularly difficult to
reconcile with the spin of I « 2 ©imoe the final nucleus
in the f **d©©ay of 0i^ is which is a stable oireaa^ovon
nwolld© and presumably has spin aero* Homo there was a need for
36
an unambiguous experimental determination of th© 01' ©pin* The
36
purpose of the present investigation is to detwmine the QV
Spin wider ©mh experimental conditions that the interpretation
1© clear#
12!
tfa* a H?ai .xhihlts a rotational absorption opootrun,
in the ground ©leetronio and vibrational ©tat©, In the neigjhbor**
hood of 26,000 megacycles* this apcctrtm Is due- to the transition
<1 m 0 •> 1, where # is the qtmnbum nvmbet of the rotatioml angular
tmmwfcm* Ho nucleus in this molecule, other them the chlorine
isotope©, hm an ©leetrio qm&rupol© moment* Further, aa will bo
seen in the following chapter, the J *» 0 level is never split
by a quadripole lnteraotien# end the J sr 1 level will split into
three level© only*, regardless of the value of th© ©pin* The
ratio of th© two frequency separations in tide triplet will then
detemln© the nuclear ©pin I* The ratio© predicted by the theory
are 0*53 for spin 2 and 0*35 for spin 5* Thus th© measurement
need not be charaotorl^od by extreme precision* as accuracy on th©
or dor of & 10 percent would be sufficient#
5
a&mplee of OHjOl were prepared from HOI which contained
a email percentage of 01^ (ace Appendix X)# The HOI me
obtained from Oak Eidga national laboratory# A Merom?®
©peotromoter employ tog a 2855 klyatron eecillabor, ttmble tn
th&e frequency range* me mod to eeareh for md examine the
hyperfine ©tnactnre of bhi© icoboplo line# fhe following eoetion©
contain the theory of the qmdrupole interaction in OHjOlr
and the method of ueing it in the determination of the nwle&r
©pin and qoadrupoX© moment of Ql^»
h
Chapter IX
THEORETICAL BASIS FOB THE SPI* W U & V m m t
If two of the thro© principal momenta of Inertia of ft
molecule ar® equal the molecule 1® said to be a symmetric top*
Symmetric top molecules are divided into two groups* (1)
Molecule# with two equal moment® of Inertia due to a symmetrical
arrangement of identical nuclei with respect to an axis la the
molecule* (2) degenerate case of an asymmetric top* Methyl
chloride Is a symmetric top of group (l)* The chlorine and carbon
nuclei are on the symmetry axis* this axis is perpendicular to the
plane defined by the three protons* The protons are arranged
symmetrically with respect to this axis and are located below the
carbon nucleus (see Fig* 1)« This chapter deals with rotational
transitions which take place in the ground electronic and ground
vibrational state of such a molecule*
For the purposee of this investigation the relevant
terms in the Hamiltonian are
H S J ^ + H q+ B ^ (1)
whore
H0 = * th. free molecule
Hq a# interaction energy of the nuclear electric
quadrupol© moments and the Inhomogeneou® * molecular
electric field