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HYPERFINE STRUCTURE OF ATOMIC COPPER

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This is to certify that the

thesis entitled
Hyperfine Structure of Atomic Copper
presented by

Malik M. Quraishee

has been accepted towards fulfillment
of the requirements for

__M.._§.__degree inmflinfl.

aaam

Major professor

 

 

 

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- 0 4.;

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/98 cJClRC/DateDue.p65-p.14

HYPERFINE STRUCTURE OF ATOMIC COPPER

By
MALIK MOHAMMED QURAISHEE

A THESIS

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

\ \
Department of Physics \\
i\ \

L~

1953 L;

ACKNOWLEDGMENTS

I wish to express my gratitude and appreciation to Dr. C.
Duane Hause for the suggestion of this problem and for his very

willing and helpful guidance throughout the course of this work.

(1 3
O
f ’H
Vb

‘1
L53
he

TABLE OF CONTENTS

Introduction ..................................
General Theory of Hyperfine Structure ...............
63
Hyperfine Structure of Cu ......................
General Experimental Procedure ...................
. 63
Procedure With Enriched Cu .....................
Results .....................................
Conclusions ..................................

References ..................................

11

15

20

23

27

28

INTRODUCTION

Since the development of high resolution interferometers of
various types by Michelson, Fabry and Perot, and Lummer and Gehrcke
it has been found by these original investigators and others that many
spectral lines are not single but are made up of a number of com-
ponents.

It is now known that this hyperfine structure arises either
to the presence of isotopes or from elements whose nuclei possess
a nuclear spin. Thus investigation of this structure yields valuable
information about the nuclei giving rise to the effects.

In this report a brief review of the theory necessary to ac-
count for the hyperfine structure of radiation from elements whose
nuclei possess spin and quadropole moments will be given. This
will be applied specially to copper. Using copper in a hollow—cathode
discharge tube in conjunction with a Fabry-Perot interferometer and
a constant deviation spectroscope the hyperfine structure of the copper
triplet 2D—ZP has been photographed. The data so obtained will be
compared with that of previous investigators.

In addition a technique suitable to allow the use of enriched

’ 3
Cu0 in the hollow cathode will be described. The hyperfine structure

63
patterns of Cu have been observed visually but not photo-

graphed.

GENERAL THEORY OF HYPERFINE STRUCTURE

The hyperfine structure observed when atomic radiation from
an appropriate source is examined with high resolution equipment is
known to arise from one of two causes: (1) small shifts in the term
values due to the presence of isotopes; or (2) splitting of the terms
due to the presence of a nuclear spin and moment which interact
with the extra nuclear electrons. The first effect is largely due to
the mass difference of the isotopes in light elements. In heavier
elements nuclear volume effects seem necessary to explain the large

. —1 , ’2'
shifts observed. Shifts of the order of 0.08 cm. are (Ref.) observed
. . . 6 65
in the radiation from Cu and Cu

The second effect is of primary concern here. In general
hyperfine structure may be due to four types of interaction.

a. Interaction of electron orbit and nuclear spin (orbit spin

inte raction) .

M¢zaf--f

(1)

where a is a constant, L and I are orbit and nuclear quantum num—

‘-""'""'—'7
bers, with the magnitude of JL(L+I)% and /I(I+i)7_.L'
‘ an

L takes zero and integral numbers, but I may be integral or half integral.

In order to derive (1) one can consider a field H at the nu-
cleus, produced by the motion of the orbital electron, about which the

nuclear magnetic moment precess.

”a.

e
E - 2. (2)

“"1

 

(4)

1'"

where L is the electric field and r is the distance of electron from
nucleus.

F rom Bohr's relationship

I.” (5)

thus

where m and e are the mass and charge of the valence electron.

a

If one represent the magnetic moment of the nucleus by/') the ratio

of the magnetic to the mechanical moment will be

/%
jln.
Ln

 

- e
— Z. R (

:3

where Z, is the nuclear g factor, and M is the proton mass.

From (7) .
eh f
yaw/WC (8)

 

fl");

The potential energy of this nuclear magnetic moment, in the mag-

netic field which is produced by the electron orbital motion is

\/a4 =g‘f;

\4. =J.(S-~--".MC)L(.-,'i-_i1_._ ) . [j 1"

' 9” finmm :7 ' um

According to the definition of nuclear and Bohr magnetons,

 

‘_ sin . 9L
fl” *1/er I /B =‘yfl’vhc

b. Electron spin-nuclear spin interaction.

-9 --+ (12)

V04“: 0[;~——:~«-—— -I.S

This term arises because both the electron and the nucleus are like

little magnets.

The interaction between two dipoles of magnetic moment /(_7

. “H
and /“s is"
—9

f, '7 1 ~
.— 3 (I ‘ z '5 ‘ —’ -¢
v/ —--i .- ._-_ -/«, w]

 

(13)

The magnetic moment in terms of‘nuclear and Bohr magnetons are

4.4-, 4

n =1; M

.un.

[is =_——:./',3 S

Then (12) becomes

V .t /"~/'.,[3T.f§’.f 4—9]
— j} 1‘ ““"' L «I S
”L

m? .4 "" 4’ .
31.2 3.1 «a «I»

or \{AX—s a -—~———_1.}--__ .-_. - 1 i S] (14)

KJ

These interactions (a) and.(b) may be combined and written in the

following simplified form:
__, 4
\/ ‘=' “II‘ I '

where .I is a good quantum number.

This equation can be obtained as follows: It is known that
the quantum mechanical average of a vector L in the direction of
another vector suppose J is just the component of L along J if L

precesses about J.

From the diagram, the magnetude of the component of L along I is

 

”*9 --9 —- ——4
i L .
L3" ~---~-~—3; and since the unit vector along J is T-then
iTi iii“!
“E 3’ “' 7- -
(L >-=-.......l....-u.3 where .I has been replaced by j( 32H) ; 1.8.,
°’" INT“)

This reduced to:

QLI= [3"(I-H/ +L(LH) —-S($-HUI I

LTITM) (15)

Bethe (Ref.) shows that (12) reduces to the form:

=(LL.+3)(.LL-i)3’( T:f)"[11{3’13'+l)- UL“) - S! 5+0}

 

\ééx

{I(T+l/+L(L¢I)—S(S+’)}‘L(L+i/{I(J*'I+5(5t') —L(L+I{}]Iff
(15)

 

and hence the total interaction, V , is
total
-9 ‘9
Vi?! = “II.I (17)
where
a” [ ( ) L / a
a = c T aw i (Lu — 5(5 I]~-----——~-~----=~ -
I 1.3(3'oi) 15/ {1.1.4. 32,){ -;i_)I(T+I)

[3- {Iw’ui « LIL“) —Sis+i)J?§I(r+i)+L(L.i/-sun/j-LiLu)

{II 3-H} uHui—ULH/E]

c. There is another term in the interaction potential which
was discovered by Abrahm (Ref.) and Carr independently. It is of

the form

‘“ .‘s"
\4=0L31.

It is of importance if the state concerned is an S state or contains

an appreciable admixture of an S state. Following the previous

method:
.. s a? -
5a.»: __.--.r - _ I
- Tint)
-~ -+
9‘3 =1‘ 5

=7.:rr7q—[I<T+'/+5(S“/ “1””ij (18)

d. In addition to the above interaction some nuclei possess
an electric quadripole moment which gives rise to an unsymmetrical

shift of term values. The equation for this effect is (Ref. 7):

ill/:,¢2' 3 ('Jfi-l [-3- h'( HH)‘-I-I(T+IHT+1)j

k —___...__, , ,

- 1
£8 1((114) (LI i) (9)

where if : F(F*'/ -I(IH/‘ 373's!) ; = quadripole moment.

TABLE I

10

 

32-17.};—

1.1?
L133

3034-4

 

c4
4
\

 

Now if one calculate '3 CV34 —-.( for

“-27.". '

37.34, -i

There is no quadripole moment interaction term in

interaction might exist in some other case.

case of AD;-
I

 

2. ‘9
L__..__.i___- - _ _ a -.
\\

E“
~‘——— . \‘
- b-“
‘

~c... -_

MM— -- ~.__...._-.~_ —.A.‘.-_.. ._ _

"Da ,/

LP; whe re

aha-IL

/-.-.

J.

O

, This
3

Suppose it does exist in

c... I No quad. M. I.

L No S-state mixing

3 Quad. ye s

0 S-state yes

63
HYPERFINE STRUCTURE OF Cu

As an example of the above interactions the term values and
z 2 . . . 63 .
resultant Hgg patterns for the P— D tran51tion in Cu Will be cal-
culated.
63 . . 3 .
Cu 15 known to have a spinIrz and a quadripole moment.
The possibility of configuration mixing will ,be considered later. That

is interaction (c) will be omitted.

The term values may be obtained from the equation

7;:TI+:—lf+iait(it+i)

 

~—-——__

where b is the quadripole term E = - 2. i _ 3 (“‘66 “I Z”
8 29 1(46I-i) 311.124)

Hf gFiFH)- I(I+i/— In”)

. .Z.
The quadripole term is .zero for the E term and negligible for
L

Alia: The term values are listed in Table II.
In hyperfine structure I takes only one value. It is either
half or whole integral. F takes values differing by unity from each
other. If I} 3" the variation of F is between I - J- to I *3-

and if I 21 the variation will be from T-I to I + I . Selection

rule for the transition is

AF=2IJO

forbidden.

The relative intensities of the hyperfine structure multiples
obtained from White (Ref.). The energy levels, transitions,
sultant patterns for copper 63 are shown in Figure 1. The
2 ~ . .

D levels are drawn to different scales. The line patterns

tained by using data for the "a's" and "b" taken from the

Schule r and Schmitt.

12

may be

and re—

2

P and

were ob—

wo rk of

l3

 

 

 

 

 

 

TABLE n
Terms K K(K + l) (a/Z)K + bK(I{ + 1)
3/2 15/4 3a /4 + 15b /4
1 1
2P”z
-5/2 15/4 -5a1/4 + 15b1/4
9/2 99/4 9&2/4 + 99b2/4
-3/2 3/4 -3a /4 + 3b /4
2 z
2P3/2 .
—l/Z 99/4 -11a2/4 + 99bZ/4
-15/2 195/4 -15a2/4 + 195b2/4
9/2 99/4 9a3/4 + 99b3/4
-3/2 3/4 -3a /4 + 3b /4
3 3
ZD3/2
—11/2 99/4 -lla3/4 + 99b3/4
-15/2 195/4 -15a3/4 + 195b3/4
15/2 255/4 15a4/4 + 255b4/4
-1/2 —1/4 -la4/4 - 1b4/4
ZDS/Z
—13/2 143/4 -l3a4/4 + 143b4/4
-21/2 399/4 -21a4/4 + 399b4/4

 

 

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GENERAL EXPERIMENTAL PROCEDURE
The Source

In order to excite the copper radiation a hollow cathode dis-
charge tube was used. This system was designed and built by Mc-
Bryde (Ref.) and with some variations is similar to that used by
Arroe and Mack (Ref.). A picture of the discharge tube and asso-
ciated optical equipment appears in Figure 2.

Since drastic cooling is employed, liquid nitrogen is.used for
best operation, the main body of the tube is of monel metal. Within
this body is a glass tube closed at the upper and by a quartz ob-
servation window. Within the glass tube is suspended an aluminum
anode. A hollow cathode of the desired metal is placed in the re-
movable base. The base is sealed to the monel tube'with a com-
pressed fuse wire ring. The hollow cathode is so designed that its
interior is continuously bathed with argon which flows slowly through
the system the pressure being maintained at about 2 mm of Hg.

The argon flow is controlled by adjustable leak valves placed both
ahead and beyond the discharge tube. Additional control is obtained
with a large glass flask for ballast beyond the second leak valve and

immediately preceding the vacuum pump.

16

The necessary power for operation was supplied by a 2300
volts 1.2 KW filtered full wave rectifier. A ballast resistance of
2700 ohms was placed in series with the discharge tube. No diffi—
culty in operation was experienced when the system was free of
leaks and the hollow cathode properly sealed in its base. With
copper cathodes brilliant hollow cathode discharges were obtained

with tube currents as low as 100 ma.
Optical Equipment

For high resolution a quartz Fabry-Perot interferometer was
crossed with a higher constant deviation glass spectroscope. The
interferometer plates and separators were quartz. The plates were
aluminized to give a high reflecting power and resultant resolution.
Separators of l5 and 30 mm were available.

Before use, the interferometer was carefully adjusted for
parallelism with a low pressure mercury arc filtered to give the
mercury green line (5461 A). This may be done visually with high
precision by scanning the field from a distance of 1 to 2 meters.

With the source in operation the fringe patterns were first

focused carefully visually with the spectroscope and then photographed

with a plate camera, the camera lens being placed adjacent to the

spectrometer eyepiece. Focusing was completed by viewing the
fringes and the illuminated pointer. in the spectrometer on the cam-
era ground glass plate with an eyepiece. For the final pictures
Kodak film was used. With this film, and tube currents of 150 ma
the intensities were such that suitable exposures of the 5105 copper
line could be obtained with 5 minute exposures. The 5782, and 5700
lines required 15 minutes.

The interferometer plates were slightly inclined to the axis
of the spectrometer such that the center of the interference pattern
appeared at the top of the field. The photographs were anaIyzed
by .measuring the fringe separations with a comparator (least count
(0.001 mm.i. Using these measured separations the components were
calculated, using the method discussed in Tolawsky (Ref.) for off-
center Fabry-Perot fringes.

With the 15 mm separator (actually 15.037 mm), the spectral

-1
range (wave number separation of successive orders) was 0.333 cm.

 

on

 

ohsmah

 

 

 

 

 

 

Figure 2b

f3
PROCEDURE WITH ENRICHED of

In order to obtain the radiation of an element in the hollow
cathode either the cathode is made of that element or is coated with
it. Thus with proper design quite small amounts of materials can
be investigated.

Copper is a mixture of two isotopes 63 and 65.. Each isotope
has a similar spin of 3/2 and shows similar hyperfine structure pat-
terns with a slight relative shift. It seemed worthwhile therefore
to obtain a sample of enriched Cu63 and attempt to obtain the struc-
ture of the single isotope.

A small amount. (100 mg) of Cu()3 (98.2% pure) was loaned
by the Stable Isotopes Branch of the Atomic Energy Commission for
exPerimental purposes. This was in the form of CuO and a special
procedure was necessary to use it.

Since excitation in the hollow cathode depends upon the sput-
tering action of the rare gas and aluminum is difficult to sputter a
hollow cathode of aluminum was constructed and then coated with
copper.

To do this the CuO was first reduced to Cu by heating the

oxide in an atmosphere of hydrogen. A molybdenum boat with the

21
CuO was sealed in a glass tube and evacuated. Hydrogen was intro-
duced to about half an atmosphere of pressure and the boat heated
electrically until reduction was complete. The arrangement is shown
in Figure 3a.

After reduction the resultant copper was placed on a molyb—
denum ribbon in an evaporator and evaporated under high vacuum
into the aluminum hollow cathode.

In order to conserve the copper a special form of molybdenum
ribbon and cathode holder was constructed. These are shown in
Figure 3b. This method insured that at least 90 per cent of the

copper will enter directly into the hollow cathode.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figures 3a and 3b

 

22

RESULTS

Using ordinary copper as the hollow cathode the three copper
lines have been photographed with tap water, dry ice and acetone,
and liquid nitrogen as coolants, respectively. Prints of the negatives
appear in Figure 4. The patterns taken with liquid nitrogen as cool-
ant have been carefully measured and reduced.

A comparison of these results with those of previous inves—
tigators is shown in Figure 5. The agreement with the work of
Schuler and Schmidt seems to be as good as can be expected. How-
ever, in the case of the 5105 line the variation from the results of
Ritschl is larger than can be accounted for by experimental error.

There seems to be little doubt of the reality of this variation.
All the patterns were taken with the same interferometer, one after
the other with short exposures. It would seem, therefore, that ad-
justment errors giving rise to variations would be 'present in all
three patterns. Yet the agreement is good for the 5700 and 5782
lines.

If we accept these results the isotope shift is more nearly

-1 ‘
0.080 cm in 5105 than 0.085 as given by Ritschl. In addition the

2 -1
interaction constant I'a" for D5/2 becomes 0.024 cm rather than

24
-1 ‘. . . .
0.022 cm as given by Ritschl (due to neglect of a splitting factor
2 , , -1
in the P3/2 state this is in error and should be 0.025 cm).
This change in the constant removes a discrepancy which
. . 2
has been present in the ratio of the constants for the D3/2 and
D5/2 states and essentially rules out any measurable shift due to
admixture of an 8 state.
_ . 63
Hyperfine structure patterns With enriched Cu have been
observed visually. With the small amounts available the lines were
very weak and could not be photographed with the present system.

It was therefore decided that this should be abandoned until a faster

spectrograph was available .

25

 

 

Figure 4
5700 A
Coolants 5100 A and
5782 A

 

 

 

= Z

Wat -

e 1‘ I -

I -
. -
I I

Dry Ice

and

Acetone

Liquid

Nitrogen

 

 

 

26

m 9.56.“.
cm? lemme.” «nu. 00h» 3.3.00.0

.. L L LL 1.1.3 LLL

553...... 8.2. 8.2.. .38..
mzofi<>¢mmmo Eummca

 

 

 

 

 

 

 

 

 

:L LLL L a L: LL. L L L
8.55m ecu 5.95m 32380 28sz
14.34315 1. 13% 1L. iljfi. L1.

 

 

 

 

 

 

:85! 565m nee 855m 233m
09.4.5340 5.103 magma

CONCLUSIONS

1. The theory of hyperfine structure has been discussed
briefly.

2. Using the Fabry and Perot interferometer with a 15 mm
separator, three components of the 5100.5 A. line are resolved. In
5782 A and 5700 A four components are sufficiently well resolved
to allow measurements.

3. Comparison of this work with results of Ritschl and
Schuler and Schmidt indicates a variation in the 5105 line and gives
a different value for the isotope shift and the interaction constant.

4. The procedure for using the small sample in the hollow
cathode is satisfactory. Using Cu63 the hyperfine structure for

Z 2
P- D lines has been observed but not photographed.

REFERENCES
White, H. Introduction to Atomic Spectra (McGraw—Hill, 1934),.
p. 353, 418.

R. C. McBride. Thesis. High Resolution and Hyperfine Struc-
ture (1951).

_Tolansky, S. High Resolution Spectroscopy (Pitman, 1947), p.
133.

Weatherburn, C. E. Advanced Vector Analysis (Bell, 1944), p.
161.

H. Kopfermann, Kernmoment (19405, p. 63, 67.
Arroe, M.,,and Mack, J. J. O. S. A. 30, 387 (1950).

Schuler and Schmidt. Zeitschrift for Physik 100, 1936, 530. 5
Z 48.

Pauling and Goudsmit. Structure of Line Spectrum. p. 202.

Candler. Atomic Spectrum. Vol. II, p. 166.

mngunygngulnjmg "((111le "1111171155

 

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