Determination of the Magnetic Moment of Sul33

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Determination of the Magnetic Moment of Sul33

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m f m s m n m of the mghetic m m m

or s33

w \s>

H ’Brace Hiillips

4 thesis submitted in partial fulfillment of the requirements

for the degree of Doctor of Philosophy, in the Department of Physics, in the Graduate College of the State University of Iowa June, 195)0

ProQuest Number: 10992020

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.

uest ProQuest 10992020 Published by ProQuest LLC(2018). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346

r / 3so PS59 O o jp 'ct‘

Ih© author is indebted to Dr. Arthur Roberts for suggesting this research problem, and for his con­ stant guidance, advice, and encouragement throughout the period of research. Grateful acknowledgement is also made to Mr. J. G. Sentinella, who constructed mar^r components of the Microwave spectrometer, and to other members of the Basics Dep&idmtent Staff who mad© m m valuable suggestions for solving problems which

arose.

O >

O-

11

Chapter I

I

n

t

r

o

d

u

c

t

Chapter II

Magnetic Interactions in G

C

i S

o

n

*

1

-

^

*

3

Chapter III Apparatus and Procedure Chapter IV

Results and Conclusions

Appendix I

Method of Determining

Bibliography

13 .... for OGS ......... •*.»*»•««•* -**••**

iii

23 37

Page 1 * ^lyperfine structure pattern for the J = X-^2 6

transition of CX2S^\**, 33

2« 1aargj levels of OCS in a magnetic field .*....

11

3* Zeeman splitting of the J a 1-^2, F = 3/2-*“1/2 transition in Q

Q

S

^

*

*

*

*

*««••• 12

iu Schematic diagram of the aELerawave spectrometer, 1k 16

5>* Zeeman magnet 6 . Eecordinga of OGS*^ F m 3/2-»-l/2 transition with

and without a Zeeman field •

iv

21

%ahle

Page

33 X. Frequencies of OSS Zeeman Oomponen&Bs EKperimental ....* . U m GaXeulations of %

... ....**,.*. ****•.*...

for u « 0,07 and Curve C*

Tig. 3 XXX.

2k

.... .....

26

Calculations of gn for u =■ 0.07 and Curve B, Fig* 3 ******......... *----

27

17. Calculations of gn for u » 0*07 and Curve A9

ng. 5

-..-- ............... 28

7, Calculations of g„ il for u = 0 and Carve C. Fig* 3

29

71. Calculations of gR for u = 0 and Curve B, Fig* 3 VII*

30

Calculations of gn for u «*■ 0 and Curve A, Fig* 3

¥111,

31

Calculations of gn for u = -0*07 and Curve B? Fig* 3

....

32

IX. Calculations of gn for u « -0.07 and Curve A, Fig* 3

.**•*.

v

33

1

Chapter I Tm m m TKM

Recently several scsal-erapirical theories of nuclear shell structure have been proposed by Feenborg and !£a&iaack,^by !3ordheim,^ and by Mayer.^ Uh© purpose of those shell models is to eaplain the so-called Mmagto-»umberw nuclei, containing 2 , 8 , 20 , So, 82, or 126 neutrons or protons# which are particularly stable; & good the­

ory should also predict spins, magnetic moments, and other nuclear properties as well.

Consequently, it is of interest to have as

much data as possible concerning the spins, quadrupole moments, and magnetic moments of nuclei in order to test the validity of these theories, and possibly to form bases for improved theories.

It is

the purpose of this investigation to detuiwdne the previously un­ known magnetic moment of S^» Unclear properties may often be determined by their effects upon the rotational spectrum of a molecule which contains the nucleus in question. The method used in this work was to ex­ amine the rotational spectrum of the molecule GGS containing the isotope $33* this molecule has an absorption spectrum in tlie neigh­ borhood of 2h ,000 megacycles per second, and, accordingly, a micro­ wave spectrometer m s constructed with provisions for applying a magnetic field to the OCS gas. From the Zoeuian effect upon the rotational lines, the nuclear magnetic moment of s3-Vas then cal­ culated.

The following pages contain the theory of the geernan

effect in GCS33, and the method of using it in the determination the magnetic moment of S33 *

3

Chapter II

w m m m wmu&Ticm w oos33 The linear molecule OGS exhibits a rotational spectrum in the region of 2lt,G0Q megacycles per second due to the transik

tion J =•

Since this molecule is a limiting case for symmetric-

tops (the moment of inertia about the figure-axis is equal to zero), its rotational spectrum jus of simple structure* Of particular interest here is the spectrum of the isotopic species OCS^«

It was first showh by Townes and GeocJmind^

that the line near 2h»Q20 megacycles has a hyperfine structure which can be explained by attributing a nuclear electric qu&drupole moment to S33, and by giving S^3 a nuclear spin of 3/2* The appear­ ance of hyperfine structure makes it possible in principle to split the hyperfine components by the application of a magnetic field, and, accordingly* the behavior of the resultant Zeeman pattern is of interest. A* ilyperfins Spectrum of 003^3 The Ilamiltoaian of a molecule having nuclear quadrupole moments can be represented by: H = Hr -I- Hq where

lip = rotational energy of the free molecule

Hq =? interaction energy between the nuclear quadrupole moments and the molecular electric field. The eigenvalues of I*Ir for a linear molecule are known to he^t

(1 )

J s quantum master for the angular momentum

where

= the effective moment of inertia of the molecule* With the selection rule J J

+1

for absorption spectra# the ro­

tational transitions give the frequencies %-*J+l =

277X0

O)



The effect of the tern Ilj upon the rotational spectrum in the absence of external fields was derived by Fan Fleck, 7 by Coles and Good,^ and by Jauch,^ who adapted the results of Oasimir^ to symmetric—top molecules having one nuclear quadrupole« Hq takes the form: 11q =: A [3(J-I) 2 + 3/2(J*I) - I2!2]

(a)

where A=

.-eqQ 2i(H3T^3-53W+5*)

for linear tops

e - electronic charge q = gauss*

Fhe deep valley

labeled A is the bigh«.freqaency Stark component of the F ~ 3/2 3/2 transition, while the one marked B is the Stark component of the F - 3/2 1/2 transition*

It will be noticed that the frequency

markers are non-uniform, several of them being either doubled or smeared$ this defect was caused by jerkinoss in the klystron tun­ ing mechanism, by mechanical vibrations of the tuning motor, and by a small amount of 60-cycle frequency modulation* Since the Stark components are modulated 180-degrees out of phase with respect to

the undisplaced lines, the phase-sensitive detector gives opposite polarities to the Stark and unsplit lines*

23

Chapter I? EB5ULTS AMD O Cm W Sim S A series of recordings of the OCS-^ F » 3/2^l/2 absorp­

tion line 'Mas made, using different magnetic field strengths#

Of the

eighty-seven recordings made, nineteen were selected for analysis, the remainder being rejected became of poor definition of the Zeeman components, erratic frequency markers, o r off-scale records* For each record made, there are three independent m y s to calculate

* The separations of the high- and the low-fre­

quency' components from the aero-field position, and the separation between the two Zeeman components each afford a means of calculation according to Fig* 3 * fable I contains the data to be analysed! in this table the magnetic field is given, together with the fre­ quencies of the two Zeeman components*

Hie blank spaces in Table I

indicate that some frequencies could not be measured, either because of poor frequency markers, or because of lack of definition in the Zeeman pattern* The data of Table X were transferred to an enlarged drawing of Fig* 3 * and values of

calculated*

This was done

using the three, sets of curves for u «■ 0 , u =• 0*07 , and for u * -0*07, with the hope of obtaining a more consistent set of calculated gylts for one value of u than for the other values* Table IX contains the calculated values for gn using u » 0*07 and curve C of Fig* 3 ! Table XII contains similar calculations

2h

I Frequencies of CCS^ F * 3/2-*l/2 Zeeman Components* Esqjerimental Record Bo*

H(kilogauss)

floyf(me.)

f ^ gh(me»)

2M32.62

2USG33.65

1

2.225

2

2.875

3

2.8?5

k

2.875

32.28

— —

5

2.875

— —

33*79

6

hJXLQ

32.15

3U.U3

7

2.225

— —

33.56

8

3.09Q

32.39

33.90

9

3.305

32.1*6

33.98

10

2.725

32.h2

33.7U

n

U.lao

— —

3iu5i

12

2.225

32.61

33*62

13

UJtlO

32.30

31**63

lli

2.010



33.66

15

3.090

— —

33*99

16

2.225

-*— *■

33.68

17

2.225

32.51*

33*70

18

It.lao

32.37

3W50

X9

2.225

32.62

33.56

32*)4X

33*60 33.-96

v.

25 using n ~ 0*07 and curve Bj and. Table 17 contains calculated values of ^

using u «. 0*07 and curve A.

In all of these calculations

the value eqQ * -^29*13 mo*, which best fits our measurements of r .

the hyperfino frequencies, has been used. Values for gn based on u — 0 and u =■ -0.07 have also been calculated.

Tables V, 71, and 711 have been constructed from the

data, using u = 0, and curves C, B, and A* respectively.

Similarly,

Tables VIII and IX contain calculations based on u = -0.07 and curves B and A, respectively* Frobably the most striking feature of the results listed in Tables I — IX is the strong disagreement between the values of based on the low-frequency Zeeman components, and the values based on the high-frequency lines and the Zeeman component separations! the low-xrequoncy line calculations consistently give much loser values for en than do the other two methods. The reason for this is believe to be as follows s semination of Pig. 6 reveals a Stark component just slightly lower in frequency than the transi­ tion under study; to what transition this Stark component belongs is not known at this time. As the F — 3/2-*-l/2 line is split in a magnetic field, the ior-frequency Zeeman component moves rapidly towards the Stark component just mentioned, and, due to the phaseopposition of the Stark component, is cut off on the low-frequency side.

Mis tends to shift the apex of the low-frequency line to

a bigger frequency, thereby giving too low a value for gn * Since the Zeeman field also splits the Stark component, the situation is

26

liable II GalouX&tloas of Record No*

b)

for u » 0*0? and Curve C? Fig, 3 2

un

.0n 060

.103

67.28

.0162

*213

9*00

—— — ■

----------



.0 23 2

.309

133. 76

------------

« -------

----------

.0 3 2 1

.278

8 6 .8 9

1

2*223'

f/-eqQ -*0083

2

2*073

-.0 1 1 ?

3

2*873

---- --------

it

2*873

-.0 1 6 1

3

2.873

6

8 .8 1 0

7

2.223

8

3.090

-.0 1 2 8

9

3*303

10

2.723

11

8.810

12

2.223

~*oo83

,0063

*111

38.76

13

8 .61Q

-.0138

.0220

.191

.36

lit

2.010



13

3.090



*—

16

2.223

m m

17

-.0 2 0 6

x 10



---



.0 1 7 2

*213

7*88

-.0 1 0 0

.0133

.136

8.81

-.0 1 1 3

.0133

.218

10.89

--------- -

------- -

-



-------- -

_

------- --

>





-





*—■ —



mn.i*>ii|t

------------



2.223

-.0072

.0097

.167

3.28

18

8*810

-.0130

.0180

.136

8.81

19

2.223

-.0083

.0060

.103 .163“

probable error -- 0.083



67.28 39.60

27

liable III Calculations of gn for u « 0*07 and Curve B» Fig* 3 sort! Ho*

H(kHogauss)

n

f/-eqQ

^ 2xtO^

1

2*225

.0309

.0319

.51*8

2

2*875

*0292

.03014.

.1*08

125.1*0

3

2*875

.oU5

.010-3

.569

10.89

k

2,875

5

2*875

.0357

.0363

.1*82

11*56

6

It*1.0-0

*0577

.051*1*

.1*71

20.25

7

2.225

*0270

.0291

*5oo

2.60

8

3*090

*0395

*0397

.1*91

6.25

9

3*305

.0622

.OltlB

•H83

10.89

10

2.725

*03lt0

*031*8

.532

2.56

11

It* lo o

*060lt

.0565

.1*90

6.76

12

2.225

.0299

.0310

.532

2.56

13

lt.io .0

.061*5

.0597

.517

1.00

Xb

2*010

*032lt

.0333

.633

136.89

IS

3.090

.0^26

.01*22

.522

.36

16

2.225

.0319

.0329

.565

2i|.01

17

2*225

.0326

.0335

.575

36.81

18

k .ItlG

.0601

.0563

*!t88

7.31*

19

2.225

.0278

.0291

.500 .516

2.6 23.19

probable error



0*032

-

>»!*

10. 21*

-------

28

Table 1? Calculations of gn for u ~ 0.0? and Curve A, Fig. 3

1

2.225

.0354

n .0218

2

2*875

.0409

.0253

*336

3

2.8?S

-----



... am

2*875

— —

Eocord So.

H(kilogausB)

f/«eqQ

*374

< ?.2xlG^ we 2.56 29.20

---

----

-----

-- -

.049?

*431

----

----

.0513

*0323

*4oo

1.00

3.305

♦0522

.0324

*375

2.25

10

2.725

*0453

.0232

.395

.25

11

4.410

*-- -

■ ---

----

12

2.225

.0347

.0214

.367

5*30

13

4.4io

.0800

.0508

.440

25*00

Hi

2*010

— —



IS

3.090

-— ■

— —•

16

2*225

1?

2.225

.0393

*0247

.425

12.30

18

4*410

.0731

.0462

.4oo

1.00

19

2.225

.0323

.0199

.342 .390

23.00 10*80

5,

2*8?5

6

4.41Q

7

2.225

8

3*090

9

.0783

16.80

--- -

probable error — — 0*023

29

Table V Calculations of Record Slo*

H(kilogauss)

for u - 0 and. Curve 0, Fig* 3 f/-eqQ

n

1

2 .2 2 $

-.ool*5

.0063

.109

73.96

a

2*875

-.0117

.0170

.226

9.61

3

2.875

---- -



--- -

k

2.875

—.0161

.021*5

.326

5

2.675

— — •

— —

-- «

6

U.iO0

.0337

.292

9U.1Q

7

2.225



,

8

3.090

-.0121*

.0181

.221*

3.1*1

9

3.305

-.0100

.011*3

.166

8.1*1

10

2.725

-.0113

.0161*

.230

12.25

XI

kmkxo

——

— —

xa

2.225

—.001*8

.0068

.117

60.81*

13

k.Uio

-.0i5h

.0233

*202

.1*9

Hj

2.010

15

3.090

— —

16

2.225



17

2.225

-.0072

.0100

*172

5.29

18

li.ilX0

-.0130

.0190

•li>5

9.00

19

2.225

-.00^5

.0063

.109 .195

73.96 1*3.99

-.0206

probable error —— 0.01*5

-

171.60

— ~~

30

HablB TL

Calculations of Eeeord Ho.

H(lcLlogaxtss)

for u » q and Curve B, Fig, 3

f/-eqQ

n

%

1

2*225

.0309

.0293

.50)4

13*69

2

2*875

.0292

.0278

.370

9i*.09

3

2*875

•oioS

.0375

J498

9.61

k

2.875

_

-— .*



5

2.875

.0357

.0330

.1*39

7.81*

6

U.ljio

.0577

.01*92

.1*26

16.81

7

2.225

.0270

.0267

.1*59

.61*

8

3*090

.0395

,0360

.y*5

14.81*

9

3.3QS

.01*22

.0380

.1*39

7.81*

10

2*725

.031*0

.0317

AM

5.29

«G60l*

.0511

.1*1*3

5.76

11



12

2.225

.0299

.0281*

.1*88

1*,1*1

13

UO0

.061*5

.0539

.1*6?

0*00

11*

2.0X0

.0321*

.0305

.580

127.69

IS

3*090

.01*26

.0382

.1*73

.36

lo

2.225

.0319

.0300

.515

23.03*

17

2.225

.0326

.0306

.525

33.61*

18

IwUlO

.0601

.0508

.MiQ

7*29

19

2.225

.0278

.0267

.1*59 .1*67

,61* 21.6

probable error

0.031

31

Tab le T O

Calculations of Record $o»

H(kHogauss)

for u = 0 and Curve k 9 Fig* 3 f/-eqQ

n

In

(Id)

Using (13)? and applying the condition (Id) to equation (12), some algebraic manipulation gives the result: a

where

**

[?fn w^

Iw i V

+•/F

- 1/2 (w^ + £-) I*

(16)

w = the imlf-widbh of the unresolved doublet. The data used in calculating gTO consisted of six re-

'T5

cordings of the OCS*^ line, three at aero magnetic field, and tliroe for II ■* £,900 gauss.

Both (16) and (16) vrore used.

39 I

o

~ 60 m i

^aax w

l(* » ,65 M3.

s-an

H =- 5-1900 gauss

w w l«l me,

From (lU): a =■ 0,127 rac. From ( 1 6 ) : a = 0.230

B.

I0 = &7 HBI

Xm x * ^ riM

.53 me.

II * 5,900

w =■ .70 me,

From (lli): a = 0.12a From (16) i

a = 0.135 C.

I = 69.3 mn, o

^ = .52 MC:.

^

- 52 >” w = .77 me.

H ■» 5,900

From (la): a - 0.151 From (16): a — 0.152 Tuo average of tee six values of a given above is: a ~ 0.157 me. © 5,900 gauss, Using this value for a , the result for g is: “ 0«l57(me») x 1.312$(kilogauss/iy._) 5.9 (kilogauss)

- — 0.035 nuclear units. lo This result compares very well with that of Coles u, who obtained the value 0.036, and not quite so well with the result of 15 Jen , who obtained 0.026.

ko

BIBUOGRAPHT X.

Eugene Feenberg and Kenyon 0* Hammck, Phye. Rev. 7$, 1877(49)

2.

L. W. lk>ixlheim, Phys. Rev, 73, 1694 (49)

3* Stela Gooppert Mayer, Fhym, Key# 73, 16 (90) Phys. Rev. 78, 1969 (2$) 4. T. W* Bakin, W. E. Good, and D. K. Doles, Phys. lev. 70,360(46) A* Roberts, Fhy3 . Rev* 73, 1403 (1*8) 3*

G. H. Tovmes and S. Geechwind, Bays* Rev. 74, 626 (ho)

6m

Z. I. Slawsky and B. M. Etennison, J* Ch©su Phys. 7, 309 (39)

7.

J. H. Van Vleck, Phys. Rev. 71, 468 (4?)

8.

D. &* Doles and W* E* Good, Phys* Rev. 70, 979 (46)

9.

J. M. Jauch, Phys. Rev. 72, 713 (47)

10.

H. B. G. Oasindr, B